PART I:

A GLOBAL VIEW ON COMETARY SCIENCE

 Festou et al.: A Brief History of Cometary Science 3

A Brief Conceptual History of Cometary Science

M. C. Festou
Observatoire Midi-Pyrénées

H. U. Keller
Max-Planck Institute für Aeronomie

H. A. Weaver
Applied Physics Laboratory of The Johns Hopkins University

The history of cometary astronomy can be naturally divided into five major periods, with
each transition marked by an important new insight. Before 1600, comets were usually viewed
as heavenly omens, or possibly meteorological phenomena in the terrestrial atmosphere, and
were not yet clearly established as astronomical bodies. Then followed two centuries of mostly
positional measurements triggered by the stunning discovery of the universal law of gravita-
tional attraction. Two highlights from this period, which lasted until the early nineteenth cen-
tury, were the successful prediction of the March 1759 return of 1P/Halley’s comet and the
discovery of the nongravitational motion of Comet 2P/Encke. The era of cometary physics began
with the passage of 1P/Halley in 1835, when spatial structures in a comet were described in
detail for the first time. The year 1950 marked the emergence of the modern picture of comets
as an ensemble of solar system objects composed of primordial ice and dust, generally on long-
period orbits and shaped by their interactions with the solar radiation field and the solar wind.
Finally, the space missions to Comet 21P/Giacobini-Zinner in 1985, and especially to 1P/Halley
in 1986, provided the first in situ measurements and the first images of a cometary nucleus. While
these in situ observations significantly improved our understanding of cometary phenomena,
they also posed many new questions for which we are still seeking answers. In this introductory
chapter, we only briefly discuss the pre-modern observations of cometary phenomena, which are
already well described in the monograph by Yeomans (1991), and focus instead on the advances
in cometary science during the past 65 years or so, especially on the developments since the
publication of the Comets book in 1982.

1. PRE-MODERN ERA: BEFORE 1950 men, like most of their contemporaries, strongly believed
that comets were evil omens.
The word “comet” comes from the Greek “kometes,” Toscanelli observed 1P/Halley in 1456 and several other
which literally means “long-haired,” but the earliest extant comets between 1433 and 1472 with improved accuracy,
records of cometary observations date from around 1000 BC inaugurating the renaissance of European observational
in China (Ho, 1962) and probably from about the same time astronomy after the long post-Aristotle scientific freeze.
in Chaldea. Ideas about the true nature of comets are avail- Brahe’s (1578) exceptionally accurate observations initiated
able from the time of the rise of Hellenistic natural philoso- a new era for observational astronomy, as he beautifully
phy around 550 BC, when the Pythagoreans considered demonstrated that the horizontal parallax of the bright
comets to be wandering planets that were infrequently seen, Comet C/1577 V1 was certainly smaller than 15 arcminutes,
mostly near the horizon in the morning or evening skies. corresponding to a distance in excess of 230 Earth radii,
In his Meteorology (ca. ~330 BC), Aristotle relegated com- consequently farther away than the Moon. This result raised
ets to the lowest, sublunary sphere in his system of spheri- the question of how comets move, and the suggestion that
cal shells and described them as “dry and warm exhala- they orbit in highly elongated ellipses was made in 1610 by
tions” in the atmosphere. There is no mention of comets in the amateur astronomer Lower (Rigaud, 1833). At about the
Ptolemy’s Almagest, presumably because he did not con- same time, Hooke and Borelli suggested that cometary or-
sider them to be of celestial origin, but he described them bits could be parabolic. Dörffel was the first to state spe-
in astrological terms in his Tetrabiblos. The Aristotelian cifically that the two bright comets seen in 1680 and 1681
ideas about planets and comets were upheld for an entire (C/1680 V1) were one and the same, before and after its
millennium during which there was little scientific advance- perihelion passage, and that it moved along a parabola with
ment in the field of astronomy. The first doubts about the the Sun as its focus, thus providing an explanation for the
Aristotelian view seem to have been expressed by Aquinas fact that many comets were seen in pairs, one in the morn-
and by Bacon in his Opus Tertium from 1267, although both ing and the other in the evening. Newton, in his Principia

3
4 Comets II

(Newton, 1687), developed the brilliant tool that could link to be polarized, hence it was “reflected” sunlight. He could
all these observations together. He applied his new theory not relate this observation to the presence of solid particles
of gravitation to show that the comet of 1680 (C/1680 V1) or gases because their respective effects on solar light were
moved in an elliptical, albeit almost parabolic, orbit and that then unknown. The observation by Bond in 1862 of Comet
it passed only about 0.00154 AU above the surface of the Donati (C/1858 L1) revealed that the plane of polarization
Sun. Halley (1705) computed the orbits of a dozen well- of the light was the Sun-Earth-comet plane, thus definitively
observed comets and demonstrated the periodic nature of the demonstrating the solar origin of the scattered light. Around
bright comet of 1682 (1P/1682 Q1). “Halley’s comet” was the same time, observations of Comet Tebbutt of 1861 (C/
telescopically recovered by Palitzsch in December 1758, 1861 J1, the great comet) by Secchi showed that the center
which conclusively proved the validity of Newton’s law of of coma light was not polarized while the outer coma was.
gravity out to the distance of the aphelion at 36 AU, more Other observations indicated different results, which we
than three times the distance of Saturn, the outermost planet interpret today as due to the varying gas-to-dust ratio in the
known at that time. coma. As publications during this period demonstrate, these
Cometary astronomy in the eighteenth century witnessed observations were ahead of their time and could not be
the gradual improvement in techniques for orbital compu- properly interpreted. In particular, it is striking to observe
tations (e.g., Brandt, 1985; Yeomans, 1991), and by the be- that even though in 1940 the polarization mechanisms were
ginning of the nineteenth century this had become a rather all understood [“reflection” or “scattering” by particles, a
straightforward task, albeit a somewhat arduous one when surface, or gases (see Öhman, 1939, 1941)], no mention of
planetary perturbations had to be taken into account. Some “solid particles” as constituents of cometary comae was
basic features of the orbital distribution of comets were made. In his review of 1942, Bobrovnikoff (1942) mentions
established, e.g., the extremely broad range of orbital peri- “meteoric dust” as a possible participant in producing comet
ods. While some comets were found to have orbits virtu- spectra, since the nucleus must be made of meteoritic ma-
ally indistinguishable from parabolas, others were clearly terial, but he also said that “the continuous spectrum is still
confined to the inner solar system inside Jupiter’s orbit. As a mystery.”
time passed, a concentration of comets moving in similar The link between comets and meteors was made by
orbits with fairly low inclinations and with aphelia close to Schiaparelli (1866, 1867), who observed that the Perseid
Jupiter’s orbit became more and more obvious, giving rise to and Leonid meteor streams coincided with the orbits of
the concept of the Jupiter family of comets. Two ideas were Comets 109P/Swift-Tuttle (1862 III) and 55P/Tempel-Tuttle
proposed to explain the existence of this family: Either (1866 I) respectively. This was the proof that comets were
there was a continual ejection of comets from Jupiter (La- indeed losing solid particles. Bredikhin (quoted by Jaeger-
grange, 1814), or there was a mechanism of dynamical evo- mann, 1903) further developed the comet tail theory based
lution, called “capture,” whereby the comets would become on an ad hoc repulsive force from the Sun that varied with
concentrated into such orbits (Laplace, 1816). It was soon the square of the heliocentric distance. This became known
recognized that comets in general, and members of the Ju- as the Bessel-Bredikhin mechanical model and was widely
piter family in particular, suffer by far their largest orbital used. Finson and Probstein (1968a,b) published a gas dy-
perturbations due to the action by Jupiter. The restricted namic model describing the gas-dust interaction and the
Sun-Jupiter-comet three-body problem consequently offered solar light-dust interaction that is still in widespread use
an interesting approximation for the study of their dynami- today. Eddington (1910) introduced the fountain model of
cal behavior. particle ejection, in which parabolas represent the outer en-
In 1835, 1P/Halley became the first comet for which velopes of particle trajectories emitted from the sunlit hemi-
spatially detailed structures were extensively observed. In sphere of the nucleus. The repulsive force acting on the par-
particular, Herschel, Bessel, and Struve described the pres- ticles was identified by Arrhenius (1900) as the pressure
ence of jets, cones, and streamers [cf. reproductions appear- exerted by sunlight. The corresponding theory was further
ing in Donn et al. (1986)]. This led Bessel (1836b), follow- developed by Schwarzschild (1901) and extended to mol-
ing Olbers (1812), to postulate the ejection of solid particles ecules by Debye (1909). (At this point, it is worth mention-
in the direction of the Sun, and that these particles were ing that neither observations nor ejection models suggested
somehow forced back into a “tail” by an unknown repul- that comets were losing material from the nightside.)
sive force acting in the anti-sunward direction. The connec- After Halley, Encke (1820) was the second to success-
tion between the Sun and comet tails had been suspected fully predict the return of a comet (in 1822). Comet 2P/
for a long time but never expressed so clearly before. Com- Encke has the shortest period of all known comets, 3.3 years,
ets were now identified as physical entities, and not solely which provides similar Sun-Earth-comet configurations
masses circulating around the Sun (described later as “vis- every 10 years. The comet was subsequently found to ar-
ible nothings” by Struve because of their inability to leave rive systematically at perihelion about 0.1 days earlier than
any sign of their existence — e.g., against the solar disk or predicted, even when taking planetary perturbations into
in front of stars — except for their response to the Sun’s account. Inspired by his observations of an asymmetric
gravitational pull). Arago directed his polarimeter toward distribution of luminous matter in the head of Comet Halley
the tail of Comet Tralles (C/1819 N1) and found the light in 1835, Bessel (1836a) interpreted this as a Sun-oriented
 Festou et al.: A Brief History of Cometary Science 5

asymmetric outflow and suggested that a nongravitational tinuous and discrete (dubbed “emission lines”) components
effect might arise due to the rocket-type impulse imparted of the spectrum. These differences were not understood,
by such an outflow, possibly explaining perihelion shifts since neither the emission mechanism of the light nor coma
such as those observed for Comet 2P/Encke. It would take abundances were known. Schwarzschild and Kron (1911)
over a century for this superb idea to be fully accepted by the studied the intensity distribution in P/Halley’s straight tail
scientific community because the existence of a solid body during the 1910 passage and suggested that the emission
at the center of the coma was far from being unanimously could be explained by the effect of absorption of solar light,
accepted. In fact, the theory that comets were a swarm of followed by its reemission, i.e., fluorescence. This naturally
solid particles was the most favored by scientists at that time. led to the key result obtained by Polydore Swings (Swings,
The first spectroscopic observations of the gas compo- 1941), who solved the long-standing problem of why the
nent of comets were made by Donati (1864) and Huggins violet CN bands (3875 Å) in cometary spectra did not re-
(1868), who visually compared the spectra of Comets Tem- semble CN laboratory spectra. Because of the presence of
pel (C/1864 N1) and Tempel-Tuttle (55P/1865 Y1), respec- absorption lines in the solar spectrum, the intensity at the
tively, with flame spectra. They found that the bands seen exciting wavelength depends on the Doppler shift caused
in the comet and in the flame were similar. Huggins also by the comet’s motion relative to the Sun, which thus de-
visually noted the presence of a broad continuum, which he termines the strength of the emission lines in the comet’s
identified with reflected sunlight. Sunlight was known since spectrum; this phenomenon is known today as the “Swings
the work of Fraunhofer to be characterized by the presence effect.” Many papers written during this time describe the
of numerous absorption lines, in particular the strong H and spectral properties of specific features in comets, such as
K lines in the UV region and the Na D lines in the yellow- the “central point” or “jets,” but are of little value today
orange region. Huggins was not a professional astronomer. because of the poor spatial resolution of the observations.
Nor was Usherwood, who in 1858 took the first photograph
of a comet, C/1858 L1 Donati. The bands recorded by Hug- 2. MODERN ERA: AFTER 1950
gins, known as the “carbon” or “Swan” bands, were found
in all subsequent observations of comets. The Swan bands A major evolution in cometary science took place in
so strongly dominated cometary spectra that carbon was im- 1950–1951 with the formulation of three very important
mediately believed to be an important constituent of com- ideas within a short timespan. The icy-conglomerate (“dirty
ets. While Draper was taking the second-ever image of a snowball”) model of the cometary nucleus was proposed
comet, C/Tebbutt (1881 K1, the great comet), Huggins was by Whipple (1950). Then, from dynamical studies of the
recording the first photographic spectrum of a comet when distribution of semimajor axes of comets, came the identi-
observing the same object through a slit spectrograph de- fication by Oort (1950) of a distant population of comets
signed to record stellar spectra. Photography and spectros- now known as the Oort cloud. Finally, Biermann (1951)
copy soon became the standard way of studying comets. gave the correct explanation for the motions of features in
In 1882, the Na D doublet was identified in the (bright) cometary plasma tails caused by their interactions with a
comets of that year that passed close to the Sun. A few other flow of charged particles emanating from the Sun’s surface
emissions were seen, but those would not be identified for (i.e., the solar wind). None of these ideas resulted directly
a few more decades. In particular, spectra of the tail were from new observational evidence, and important parts of
taken at the beginning of the twentieth century in Comets them had been proposed earlier by other scientists, but this
Daniel (C/1907 L2) and Morehouse (C/1908 R1). The N2+ was the first time that the known facts were effectively com-
emission was found near 3914 Å in the tail spectrum of the bined, leading to a comprehensive description. A new picture
latter comet, but it was likely an atmospheric feature as, in of comets, and the existence of a family of celestial bodies,
the light of modern observations, a careful subtraction of were suddenly revealed at the same time.
the telluric lines is required to allow any firm identification
of these faint emissions. In addition, such identification 2.1. The Icy-Conglomerate Model of the Nucleus
work is extremely difficult when working with photographic
prism objective spectra. In a series of enlightening papers published between
Baldet (1926) published a comprehensive catalog of the 1932 and 1939, Wurm suggested that since the radicals and
spectra of 40 comets obtained since 1864, together with a ions observed in cometary comae were not chemically sta-
complete bibliography of all comets observed until that time ble, these species must be created by photochemistry of
by spectroscopy. This work, and that of Nicholas Bobrov- more stable molecules residing inside the nucleus [see, e.g.,
nikoff on the 1910 apparition of Comet 1P/Halley, which the reviews by Wurm (1943) and Swings (1943) and refer-
appeared five years later (Bobrovnikoff, 1931), are the first ences therein]. It is Wurm who first proposed the concept
two comprehensive papers of cometary physics published of “parent” compounds/molecules in the nucleus, while
in the twentieth century. Because only very bright comets “daughter” species would be created in the coma by photo-
were studied at that time, all observed comets appeared to chemistry. Spectroscopic studies revealed the nature of the
have very similar spectra, although differences were quali- daughter species but not the parents. In the 1940s, Swings
tatively noted, in particular the relative strength of the con- developed his ideas based on Wurm’s reasoning, and the
6 Comets II

key role of these two scientists appears to have been over- approaches the Sun and the surface temperature of the nu-
looked in the later literature. The presence of CO or CO2, cleus rises. Meteoritic dust is also released from the nucleus
C2N2, CH4, N2, and NH3 in the comet was invoked on the when these ices evaporate, hence the famous expression
basis that CO+, CN, CH, CO2+, N+2 , and NH emissions were “icy conglomerate.” The relative proportions of the various
found in cometary spectra. H2O was also considered as a ices were discussed only qualitatively; not only was the
potential parent molecule, following the discovery of the nature of all the parent species needed to explain the un-
OH 3090 Å UV emission in 1941. Additional molecules known coma composition, but Whipple’s main concern was
(e.g., C2) were required since all known coma species could to explain the non-Keplerian motion of Comet 2P/Encke.
not be explained from the above molecules. In 1948, Swings Nevertheless, Whipple’s model was hugely influential be-
came very close to proposing an icy model for the nucleus cause of its ability to successfully explain within a single
by suggesting that the above-mentioned molecules could conceptual framework many observed cometary phenomena,
exist in the solid state in the nucleus (Swings, 1943, 1948). such as (1) the large gas production rates [200 kg/s of C2
(We note here that quantitative arguments were largely for 1P/Halley in 1910 derived by Wurm (1943)], for which
missing from the discussion because of the lack of appro- the desorption model was totally inadequate; (2) the ob-
priate observational material and laboratory measurements served jet-like structures in the coma and the erratic activ-
on the parent molecule properties. The situation signifi- ity, impossible to produce if the source of gas and dust was
cantly improved in that regard about 30 years later.) a cloud of particles; (3) the observed nongravitational forces
A key question was how molecules were stored in the by means of the momentum transfer by the outflow of gas
cometary material. Since the middle of the nineteenth cen- from the nucleus, the sign of the net effect on the orbital
tury, a great deal of research had concentrated on under- motion being dependent on the orientation of the nucleu
standing the nature of the central source of gas and dust in spin vector; (4) the fact that most comets that pass extremely
comets, and the alternate theory to Lyttleton’s sandbank close to the Sun, e.g., the Kreutz Sun-grazing comet group,
model (Lyttleton, 1948) was that an invisible solid nucleus apparently survive such approaches; and (5) the fact that
was the source of all observed cometary material. Swings comets are the sources of meteor streams. Items (2)–(4) gave
(1942) suggested that molecules similar to those found in particularly strong arguments for a solid nucleus rather than
meteorites could possibly be stored in the nucleus by oc- a sandbank structure, a model that had other difficulties in
clusion. Independently (probably) of Swings, Levin (1943) addition to failing to explain the above-mentioned points.
developed his desorption theory from the surface of mete- Although Whipple’s model quickly won general accep-
oritic material to demonstrate that his sandbank model for tance, there were some shortcomings. The main one was
the nucleus had a solid basis. An average desorption heat described by Whipple himself, namely, the large differences
of 6000 cal/mole was deduced from the interpretation of the among the latent heats of vaporization of the various ices he
brightness law followed by comets as the heliocentric dis- thought might be present in the nucleus. He also remarked
tance changes, which was in agreement with laboratory data that the low vapor pressure of water was a serious problem
for the above-mentioned cometary molecules (in the 2,000– when explaining the observed presence of the OH emission
10,000 cal/mole range). However, the amount of material far from the Sun. As a result, the highly volatile material
that could be desorbed from a swarm of particles with an should be removed from the surface layer of the nucleus
expected cometary mass could not explain the persistence long before perihelion, in contradiction with the observa-
of comae over several months during single passages, and tion of radicals and ions such as CH and CH+ near the Sun.
consequently the survival of comets such as 1P/Halley or This objection was tentatively removed when Delsemme and
2P/Encke for centuries and millennia. Seeing-limited ob- Swings (1952) noticed that almost all parent molecules (ex-
servations of comets passing near Earth showed a central, cept NH3) required to explain the observed radicals and ions
unresolved light source of dimensional upper limits in the in comets could coexist in the nucleus in the form of solid
10–100-km range (cf. review by Richter, 1963). Upper lim- clathrate hydrates of H2O, where the volatile “guest mol-
its to cometary masses had also been estimated from the ecule” occupies a cage in the H2O crystal lattice. From the
absence of evidence for mutual gravitational attraction of stoichiometry of hexagonal ice, the mean value of the occu-
the components of Comet P/Biela in 1846, or of any influ- pation number is somewhat smaller than 6. In this way, the
ence on the Earth’s orbit for very close passages, like those highly volatile material does not disappear too rapidly, and
of Comet P/Lexell (D/1770 L1). Masses in the 1012–1017 kg is also freed together with less-volatile molecules, which
range were surmised (Whipple, 1961). explains why the spectrum remains more or less similar
In an attempt to synthesize all known facts about the throughout a comet’s apparition. Delsemme and Swings’
cometary nucleus, and with particular attention to the long- ideas also implied that comets contain mostly water mol-
standing problem of explaining the nongravitational perihe- ecules, something that was not proven at that time, nor even
lion passage delays, Whipple (1950, 1951) laid the founda- discussed in any detail.
tions for the modern model of a solid nucleus. Building on
the ideas of Laplace (1813) and Bessel (1836a) (cf. Levin, 2.2. The Oort Cloud
1985), Whipple (1950, 1951) described the nucleus as a
mixture of ices from which the gases in the coma are pro- As a consequence of the nineteenth century work on
duced by sublimation in increasing quantities as the comet cometary orbits and the discovery of nongravitational
 Festou et al.: A Brief History of Cometary Science 7

forces, dynamical studies of individual comets were carried (1978), and the catalogs of cometary orbits regularly pub-
out during the first decades of the twentieth century, with lished by the Central Bureau for Astronomical Telegrams].
particular attention paid to the influence of planetary per- Our ideas regarding the long-term dynamics of the Oort
turbations. The earlier results on the non-existence of inter- cloud have evolved considerably over the years. While pas-
planetary ether were confirmed and statistical considerations sages of individual stars dominated the discussion in early
about the distribution and dynamical origin of comets natu- investigations, the tidal effects of the galaxy as a whole have
rally followed, including the question of whether or not become recognized in the last two decades as the prime
some comets have “original” hyperbolic orbits (reciprocal mechanism providing new comets to the inner solar sys-
semimajor axis 1/a orig < 0), which would mean that they tem from the outer part of the cloud. The dramatic effects
were not members of the solar system. The work by Ström- that might follow upon close encounters with massive per-
gren (1914, 1947) and colleagues demonstrated that there turbers, such as giant molecular clouds (Biermann and Lüst,
were no original hyperbolic orbits among the observed 1977), also received a great deal of attention.
comets; all apparently hyperbolic orbits were actually per- Although Oort explored the possibility of having an in-
turbed into those states by planetary effects, mainly the ner cloud extending inside of 20,000 AU, his preferred
influence of Jupiter. Comets were not coming from inter- model was a thick shell of comets near the outskirts of the
stellar space. Sinding (1937) produced a list of values of 1/ solar system. The idea of an inner Oort cloud was proposed
a orig for 21 long-period comets, which, together with the later by Hills (1981) for two reasons: (1) to explain the
work by van Woerkom (1948), formed the basis for Oort’s replenishment of the Oort cloud inevitably depopulated by
famous paper (Oort, 1950) on the existence of a cometary the above-mentioned perturbations, and (2) to provide an-
population residing in the outer reaches of the solar sys- other source region for Oort cloud comets besides scatter-
tem. The idea of a cloud of distant hypothetical comets, ing by the giant planets, which is a very inefficient process.
stable against stellar perturbations, necessary to explain the These ideas are currently being completely revisited to in-
fact that many comets had a orig >10,000 AU, had been ex- corporate the existence and role of the recently discovered
pressed earlier by Öpik (1932). Oort (1950) deduced the transneptunian belt and the various subpopulations of trans-
existence of such a cloud by studying the actual distribu- neptunian objects.
tion of the semimajor axes of 19 observed comets. He dis- In most theories, Oort cloud comets formed in the Jupiter-
cussed the important excess of long-period comets with 1/ Neptune region. The mass of the solar nebula and the time
a orig < 10–4 AU–1, i.e., with aphelia beyond 20,000 AU, and of formation of the planets are key ingredients of Monte
concluded that while comets can remain in stable orbits out Carlo simulations that investigate the transfer of comets
to distances of about 200,000 AU, some of them could from from the region of the outer planets to the Oort cloud. The
time to time be diverted inward by the perturbations of pass- number of comets currently residing in the Oort cloud re-
ing stars. These stellar perturbations should have random- quired to explain the discovery rate of new comets is on the
ized the orbital inclinations of the comet orbits over the age order of 1–2 × 1012 (Heisler, 1990; Weissman, 1996). Re-
of the solar system. Oort estimated that the cloud should cent simulations indicate that comets that were formed in
contain about 2 × 1011 comets to explain the discovery rate the Saturn-Uranus region currently make up the bulk of the
of new comets each year. With a mean cometary mass of surviving Oort cloud comets, whereas few comets formed
1013 kg, the total mass of the Oort cloud would be ~2 × near Jupiter are left [see Dones et al. (2004) for a current
1024 kg, or ~0.3 M . perspective on the complex formation and evolution of the
Based on van Woerkom’s (1948) theory of the orbital Oort cloud].
diffusion caused by planetary perturbations, Oort found that
the number of comets with 1/aorig ≤ 10 –4 AU–1 is much 2.3. Ion Tails and the Solar Wind
larger than what would be expected from the population of
long-period elliptical orbits, which suggested that many of Because the tails of comets can be so impressive, both
the comets become unobservable after their first passage to the layman and to the professional astronomer, they have
through the inner solar system. This observational fact still been the subject of many investigations. Astronomers of all
does not have a universally accepted explanation. In a sub- eras have been struck by the fact that the tail appearances
sequent study, Oort and Schmidt (1951) distinguished be- may vary dramatically from one comet to another. In the
tween “new comets” (those making their first visit near the early twentieth century, it was deduced from the study of the
Sun’s neighborhood and the planets) and “old comets” motion of kinks and knots in the tail that the antisolar force
(those returning on much less elongated elliptic orbits). The acting on straight tails was enormous, up to 1000 times the
former appeared to be dustier and to brighten more slowly solar gravity. As early as 1859, Carrington (1859) suspected
than the latter. These kinds of analyses were revisited later a physical connection between a major solar flare and en-
to include the role of interstellar clouds and the galactic tide hanced magnetic activity on Earth some hours later. Ideas
in delivering new comets to the planetary region. However, about the possible existence of a stream of particles from
the basic concept of the Oort cloud as an outer halo of the the Sun, perhaps electrically charged, emerged toward the
solar system has been substantiated by later studies, based end of the nineteenth century, in particular to explain the
on continuously improved cometary orbits by Marsden and excitation of molecules and ions observed in cometary co-
co-workers [Marsden and Sekanina (1973), Marsden et al. mae. It was also found that cometary ion tails (formerly
8 Comets II

called Type I tails) develop closer to the Sun than dust tails contains detailed information about the data obtained within
(formerly called Type II tails; the comet tail type is directly the various IHW networks. The observations were made by
related to the strength of the repulsive force that obviously both professionals and amateurs in all wavebands from the
varies smoothly, hence the difficulty of any categorization ultraviolet (UV) at 120 nm to the radio at 18 cm. It was par-
scheme). However, it was only 50 years later that Hoff- ticularly fruitful to combine space- and Earth-based obser-
meister (1943) provided the crucial observations of a gas vations for calibration and long-term monitoring purposes.
tail aberration of 6°, i.e., the angle between the observed tail The earlier cometary models could be tested and refined
and the antisolar direction. This was correctly interpreted with the aid of the in situ measurements, leading to many
by Biermann (1951) in terms of an interaction between the new insights.
cometary ions in the tail and the solar wind (hereafter SW), The nucleus was observed at close range for the first
a continuous stream of electrically charged particles from time; it was found to be larger (equivalent radius 5.5 km)
the Sun with velocities of several hundred kilometers per and darker (albedo ~4%) than expected. In the Giotto im-
second. His derived plasma densities were unrealistically ages, surface features (craters, ridges, mountains, etc.) and
high, since electrons were thought to accelerate the com- source regions were observed (Keller et al., 1988). There
etary ions. Alfvén (1957) removed this discrepancy by intro- were no signs of nightside outgassing. The coma was found
ducing the role of a “frozen” interplanetary magnetic field, to be highly structured on all scales (jets, shells, ion stream-
which is carried along with the SW particles. Until space ers, etc.) and the gaseous component was analyzed in situ
probes could study the SW in situ, cometary ion tails were by mass spectroscopy. Signals at atomic masses of 1 and
the only well-distributed SW probes in interplanetary space from 12 to ~55 amu were detected. H2O was confirmed to
and they largely remain so for regions outside the ecliptic represent 85% by weight of the gas phase (see further dis-
plane. The existence of sector boundaries in the SW ex- cussion below), and the likely presence of large organic
plains the separation of ion tails from the head of comets; polymeric molecules was indicated. The dust was analyzed
this is one of many phenomena that indicate that the SW by size and composition and there was an unexpectedly high
properties may change on very short timescales, as de- fraction of very small grains, down to the sensitivity limit of
scribed in numerous papers published beginning in 1968 by ~10–19 kg. Particles rich in metals and silicates were found
Brandt and collaborators. as expected, but particles rich in H, O, C, and N (“CHONs”)
were seen for the first time and were thought to be related
3. SPACE MISSIONS TO COMETS to the smallest grains mentioned above (Kissel et al., 1986).
The integrated mass loss experienced by the nucleus at this
Following the increased interest in comets that arose in passage, on the order of 4 × 1011 kg (but very uncertain)
the late 1970s, due in large part to the predicted return of was ~0.5% of the total mass of the nucleus, estimated at
1P/Halley, another giant leap in our understanding of comet 1–3 × 1014 kg. Nucleus images taken in situ and ground-
phenomena occurred in March 1986 when six spacecraft based observations were not sufficient to unambiguously
(henceforth “S/C”) made in situ observations of this comet. determine the complex (excited) rotational state of the nu-
There are undoubtedly “pre-Halley” and “post-Halley” eras cleus. A cavity devoid of magnetic field was detected within
(much as historians describe the transition from the Dark 5000 km of the nucleus. The various predicted plasma ef-
Ages to the Renaissance period); for the first time, the nu- fects were confirmed, including the existence of a bow
cleus of a comet was seen. However, the first cometary en- shock, and the adjacent interplanetary medium was found
counter took place six months earlier — on September 11, to be kinematically and magnetically extremely turbulent.
1985 — when the International Cometary Explorer (ICE) Some of the species invoked to explain the mass spectra
passed through the tail of Comet 21P/Giacobini-Zinner, were produced by gas phase reactions in the coma, as an-
~8000 km from the nucleus. The main results were the con- ticipated a decade earlier by Oppenheimer (1975).
firmation of the plasma tail model, indications about the ion The fast flybys of Comets 19P/Borrelly in September
composition, and the detection of a neutral current sheet at 2001 (NASA’s Deep Space 1 mission) and 81P/Wild 2 in
the center of the tail. ICE continued on to register the effects January 2004 (NASA’s Stardust mission) have produced
of 1P/Halley on the interplanetary medium from a distance two new images of cometary nuclei. In some respects, these
of 28 × 106 km sunward. two nuclei are very similar to that of 1P/Halley, i.e., all are
Five spacecraft encountered 1P/Halley in early 1986: very dark objects with complex surface structures. There
Vega 1 (March 6, closest approach distance of 8890 km), appear to be some significant differences among the three
Suisei (March 8, 150,000 km), Vega 2 (March 9, 8030 km), nuclei (e.g., the more spherical shape and possibly “younger”
Sakigake (March 11, 7 × 106 km), and Giotto (March 14, surface of 81P/Wild 2), but the different spatial resolutions
600 km). Concurrently, an unparalleled, long-term Earth- of the three investigations may account for some of the ap-
based observational effort was coordinated by the Interna- parent diversity. 81P/Wild 2 is covered by what will prob-
tional Halley Watch (IHW) (Newburn and Rahe, 1990). The ably soon be called “erosion craters,” but we must await
IHW archive, with more than 25 GB of data, was released the full publication of the results, and probably in situ in-
in December 1992 (International Halley Watch, 1992), and vestigations of other nuclei in the future, to understand how
the associated summary volume (Sekanina and Fry, 1991) these craters are activated and how long they survive. De-
 Festou et al.: A Brief History of Cometary Science 9

spite the advances enabled by the spacecraft encounters, our suggestion was not explored in detail until 1964 (Biermann
knowledge of the composition of the non-icy component and Trefftz, 1964). Their work led to the prediction that
will have to await new in situ measurements or, better yet, photodissociation of parent molecules is the main produc-
the return to Earth of a coma dust sample, very likely in tion mechanism of the excited O atoms. The resulting pro-
2007 from the Stardust experiment. duction rates of the parent molecules were estimated to log
Q(s–1) ~ 30–31 in case of a bright comet, much larger than
4. THE INVENTORY OF COMETARY those of the parents of CO+, CN, or C2. However, it is worth
VOLATILES AND COMPARATIVE noting that in the mid 1960s, the evaluation by Arpigny
COMETOLOGY (1965) that the total content of the coma in OH radicals was
similar to that of CN or C2 was not used to discuss the pos-
Although number density estimates for cometary comae sible abundance of water in comets. This figure was actu-
had been derived since the time of Wurm’s investigations ally considered as being on the low side by Biermann (1967,
in the 1930s, the figures obtained were rather uncertain and 1968), who concluded that cometary nuclei must consist of
their reliability limited by the lack of quantitative informa- molecules of H bound to C, O, and N atoms with the con-
tion on the excitation mechanisms for the observed emis- sequence that a huge cloud of H atoms must surround com-
sions. Thus, it is not too surprising that, continuing the ear- ets. What is striking in the literature of those times is that
lier investigations by Swings and McKellar, most spectro- OH and O are treated as two independent species. The most
scopic studies between 1950 and 1970 were devoted to a often-quoted parent molecules were — as in 1950 — H2O,
never-ending attempt to discover and identify new emission CO, CO2, CH4, and NH3, and unsuccessful attempts were
lines and bands, as well as unraveling the structure of the made in the mid 1970s to find the two latter molecules in
ro-vibrational bands of the comet radicals and ions. In that spectra of Comet Kohoutek (C/1973 E1). In this context,
regard, special reference must here be made to the numer- the discovery in 1970 by the Orbiting Astronomical Obser-
ous and important contributions from the “Liège school,” vatory (OAO-2) and the Orbiting Geophysical Observatory
reviews of which are given by Swings (1956) and Arpigny (OGO-5) of huge Ly-α haloes of neutral H (>1.5 × 107 km)
(1965). During this epoch, rather complete and fairly ac- around Comets Tago-Sato-Kosaka (C/1969 T1) and Bennett
curate models of the fluorescence of the CN, CH, OH, and (C/1969 Y1) (see Code and Savage, 1972) did not come
C2 radicals were built. The advent of high-resolution spec- as a complete surprise. However, linking these H atoms to
troscopy in the late 1950s allowed the identification of many water only came later, when the relative abundances of H
unknown lines, most of which were due to C2 and NH2. and OH were investigated in the same comets (see below).
Despite these efforts, it is worth noting that thousands of An unknown ion was observed in Comet C/1973 E1(Ko-
lines in the optical spectra of comets remain unidentified houtek) by Herbig (1973) and Benvenuti and Wurm (1974).
even today; the most likely candidate molecules responsible Herzberg and Lew (1974) had just obtained the first labo-
for these emissions are S2, CO+, CO+2 , and C3 in the near- ratory spectra of the H2O+ ion and tentatively identified this
UV, C2 and NH2 in the optical, and NH2 and H2O+ in the ion as the source of the new cometary emission. The same
optical infrared (IR). Many new lines have been recently emission was later found in cometary spectra recorded as
discovered in the near-IR and radio regions (the submilli- early as 1942 [e.g., data given in Swings et al. (1943)]. Al-
meter region is also becoming increasingly accessible), and though the water ions are profusely injected in comet tails,
these domains eagerly await a new generation of cometary their presence there is not conspicuous, which is a clear
spectroscopists. indication that the ion is rapidly lost, unlike the other tail
ions, especially CO+. The main loss mechanism is a charge
5. WATER AS THE MAIN exchange reaction with water molecules leading to the for-
CONSTITUENT OF COMETS mation of the H3O+ ion (Aikin, 1974), which itself is likely
destroyed in electron recombination reactions. H3O+ was
In 1958, high-resolution spectroscopy allowed the sepa- indeed found to be one of the main ions in the comae of
ration of the terrestrial oxygen lines from the cometary ones 21P/Giacobini-Zinner and 1P/Halley during the later in situ
and also led to the definitive confirmation of the presence investigations. Although the presence of the H2O+ ion pro-
of the isotopic lines of 13C, long suspected to be present in vided strong evidence for the presence of H2O in the nu-
comets. The detection of the [O I] red lines in Comet Mrkos cleus, observations of this ion have not generally been used
(1957 V) (Swings and Greenstein, 1958) created a com- to derive H2O production rates in comets because of the
pletely new problem: It was demonstrated by Wurm (1963) many difficulties in producing accurate models for the ion
that if fluorescence was responsible for this emission, then distributions in cometary comae.
very large amounts of O must be present in the coma, dwarf- Although the OH emission band at 3090 Å was first
ing the amount of C (e.g., C2). Thus, Wurm proposed a dif- identified in Comet C/1941 I (Cunningham) by Swings
ferent mechanism, photodestruction of an O-bearing species, (1941), the first reliable OH production rate measurements
to produce atomic oxygen in an excited state. The idea that only date from the early 1970s (Code et al., 1972; Blamont
some coma species may be produced directly into an ex- and Festou, 1974; Keller and Lillie, 1974). The analysis of
cited state can be traced back to McKellar (1943), but this the Ly-α isophotes of Comet C/1969 Y1 (Bennett) by Ber-
10 Comets II

taux et al. (1973) showed that the velocity of the H atoms (1984). The detailed mechanism by which comets emit OH
was about 8 km s–1. Following an investigation of the pho- photons at radio wavelengths was investigated by Despois
tolysis of water molecules by sunlight, these authors sug- et al. (1981).
gested the possibility that the majority of the observed H The radio observations of OH have become the main
atoms were the result of the dissociation of OH radicals. source of water production rates since 1996. Including both
Keller and co-workers reached similar conclusions in a series the radio and UV OH observations, water production rates
of independent papers: Keller (1971) discussed the possi- have been derived for about 100 comets. Comets were often
bility that the observed H atoms in Comet C/1969 Y1 (Ben- followed during a significant fraction of their orbits. The
nett) might arise from the direct dissociation of water, ideas radio and UV determinations of the water production rates
that he further developed later (Keller, 1973a,b). However, do not always agree, as has been discussed by Schloerb
these investigations, as well as that of Bertaux et al. (1973), (1988, 1989), but these large databases are still extremely
were limited by the fact that the parameters governing the useful.
water photolysis were not well known at that time. Blamont H2O itself was not definitively detected until its strong IR
and Festou (1974) measured both the unknown scale length ro-vibrational emissions were measured by Mumma et al.
of OH and the production rate of that radical in Comet C/ (1986) in the coma of 1P/Halley during observations from
1973 E1 (Kohoutek). Keller and Lillie (1974) also measured the Kuiper Airborne Observatory, and later from the Vega
the scale length of OH (in Comet Bennett) and found a flyby spacecraft (Combes et al., 1986). The water molecule
value in complete agreement with that found for Comet was also directly detected in 1P/Halley using the neutral
Kohoutek. An important clue that H2O was the main source mass spectrometer on the Giotto spacecraft (Krankowsky et
of both the H atoms and the OH radicals came when the al., 1986). Non-resonance fluorescence emissions of water
velocity of the H atoms was measured directly from Coper- at IR wavelengths can now be used rather routinely to
nicus observations (Drake et al., 1976) and, indirectly, from monitor water production rates in comets (cf. Dello Russo
the analysis of the velocity of H atoms from Ly-α obser- et al., 2000), but the number of comets observed in this way
vations (cf. review by Keller, 1976), and was found to be is still rather small, at least compared to the number whose
fully consistent with the water photolysis scheme. For the OH emission has been monitored at radio wavelengths.
first time, based on an experimental study of the photoly- There are multiple production pathways for H atoms.
sis of water molecules and simultaneous measurements of Their excitation by the solar Ly-α line; their interaction with
the H and O production rates, it was demonstrated that water the SW, molecules, and ions; and their kinematics are hard
was the likely parent of most of the H atoms and the OH to model. Water production rates can nevertheless be de-
radicals. rived from the observation of H lines, as demonstrated in
Subsequent systematic observations of OH, H, and O the insightful investigation of the H I UV emission in comets
emissions in more comets using the International Ultravio- of Richter et al. (2000), which summarizes the most recent
let Explorer (IUE) (Weaver et al., 1981a,b) further strength- work on this topic. One often overlooked conclusion that
ened the case for H2O as the dominant cometary volatile. can be drawn from the many observations of the H comae
Beginning with Comet C/1979 Y1 (Bradfield), a long series of comets is that, even with the modeling errors and calibra-
of high-quality observations of the UV spectra of comets tion uncertainties, the production of non-water H-bearing
was obtained with the IUE in programs led by A’Hearn, species probably can be no larger than ~20–30% of the H2O
Feldman, and Festou, from which a self-consistent set of production rate for most comets observed within 1 AU of
OH production rates was derived (e.g., Festou and Feldman, the Sun, which leaves CO, CO2, and a few hydrocarbon
1987). About 50 comets were observed during the period molecules, as we shall see below, as the main candidates to
from 1978 through 1995, and OH production rates were supply, after H2O, the bulk of the remaining volatile portion
systematically derived for all of them. A comprehensive of the cometary nucleus.
theory of OH fluorescence, which has been used to inter-
pret the UV observations, was developed by Schleicher and 6. OTHER COMETARY
A’Hearn (1982, 1988). PARENT MOLECULES
Following the discovery of the 18-cm maser emission
of OH (Biraud et al., 1974; Turner, 1974), radio OH emis- In 1970, the known optical emissions were from daugh-
sion has been monitored by the Nançay observatory in over ter or granddaughter species (e.g., C2, C3, CN, CH, O, NH,
50 comets by Crovisier and collaborators (Crovisier et al., NH2) with uncertain and not very abundant progenitors in
2002), with observations continuing to the present day with the nucleus. Only the O atom was thought to be possibly
improved sensitivity. These OH monitoring programs estab- as abundant as the newly discovered dominant H and OH.
lished without a doubt the ubiquity of water as the domi- For compositional research to develop, technological ad-
nant volatile constituent in comets; no comet was found to vances that broadened the wavelength range of the observa-
be deficient in water. In addition, many parameters of the tions were required. The UV window was the first to be ex-
OH radical are derived from 18-cm observations, and in- plored, followed a few years later by the IR region, and
formation on the kinematics in the coma as well as the deter- slightly later by the radio region.
mination of the OH production rates are obtained on a regu- Feldman and his collaborators recorded high-quality and
lar basis. The methodology for determining OH velocity high-sensitivity UV spectra of comets during sounding rocket
profiles was worked out by Bockelée-Morvan and Gérard observations of C/1973 E1 (Kohoutek) (Feldman et al.,
 Festou et al.: A Brief History of Cometary Science 11

1974) and C/1975 V1-A (West) (Feldman and Brune, 1976). gives a detailed account of the era that began after the pas-
The latter observations provided the first detection of CO sage of Comet 1P/Halley when groundbased IR spectrom-
in a comet and demonstrated that this molecule was one of eters and radio telescopes were systematically used to inves-
the most abundant in comets, although we now know that tigate cometary composition.
the amount of CO varies greatly from comet to comet. The
CO UV emission has been observed in nearly every bright 7. COMETARY ORBITS
comet since then, first by the IUE and subsequently by the
Hubble Space Telescope (HST) and the Far Ultraviolet From the perspective of cometary dynamics, the mod-
Spectroscopic Explorer (FUSE). The UV observations also ern era is defined by the advent of efficient and powerful
provide access to two other potential parent molecules: the computers. For the first time, numerical simulations of the
short-lived S2, which was discovered during IUE observa- orbital evolution of comets over the age of the solar sys-
tions of C/1983 H1 (IRAS-Araki-Alcock) (A’Hearn et al., tem, including the gravitational influences of close encoun-
1982), and CO2, which can be indirectly probed via emis- ters with Jupiter and other planets, stars, and interstellar
sion in the forbidden CO Cameron band emission (Weaver clouds, have been performed. Computers also revolution-
et al., 1994). ized the work on orbit determination and allowed the link-
The 1970s witnessed the development of systematic, age of past and recent apparitions of observed comets, as
quantitative observations of optical cometary emissions by well as the preparation of ephemerides for upcoming ap-
means of photoelectric narrow-band filter photometry (by paritions, even for long-lost comets. Whereas Oort had been
A’Hearn, Schleicher, Millis, and their collaborators) and working on a small sample of comets to build his theory,
CCD spectroscopy (by several groups led by Cochran, Marsden et al. (1978) improved the earlier statistics by
Newburn, and Fink). A review of the early observations and using 200 well-determined long-period orbits. They found
the observing techniques is given by A’Hearn (1983). In a concentration of inverse semimajor axes corresponding
the early 1980s spectrophotometry developed rapidly when to an average aphelion distance <60,000 AU for q > 2 AU,
fast detectors became available. This method provides both only about half as remote as Oort’s original distance. Be-
a good separation of band or line emissions and spatial in- sides the apparently abnormal fading of new comets (re-
formation on the distribution of coma species. In parallel, quired because Oort’s peak is too high), a major problem
numerous theoretical studies, aimed at calculating the fluo- remained: the apparent overabundance of Jupiter-family
rescence efficiencies of the coma radicals and ions, resulted comets. Everhart (1972) found a possible route of direct
in the establishment of reliable conversions of observed transfer from the Oort cloud via jovian perturbations at
surface brightnesses into column densities of the different repeated encounters with the planet, but the efficiency of
species. The last step in the data analysis process is then this transfer was too low to account for the observed num-
the derivation of gas production rates. A systematic survey ber of Jupiter-family comets. An alternative scenario came
of the principal optical emissions from 85 comets produced from orbital integrations of the observed comets by Kazi-
the first evidence for the existence of compositional fami- mirchak-Polonskaya (1972): The comets might not be cap-
lies among the comets (A’Hearn et al., 1995). tured by Jupiter alone, but rather by a stepwise process
A real breakthrough in the detection of parent species involving all the giant planets. The modern solution is that
occurred in the mid 1980s with the development of new a disk-like source of comets in the outer reaches of the solar
instrumentation and techniques at IR and radio wavelengths, system is required to explain the properties of the Jupiter
which could be used to detect ro-vibrational and pure rota- family of comets (now called “ecliptic comets,” adopting
tional emissions from molecules. Thus, parent species can Levison’s 1996 taxonomy of comet orbits). Kazimirchak-
now be observed directly, leading to more direct information Polonskaya’s process naturally explains the existence of the
than that obtained from their destruction products. The ap- Centaur’s family.
parition of two exceptionally bright comets in the mid 1990s, A major step forward during this period dealt with the
C/1996 B2 (Hyakutake) and C/1995 O1 (Hale-Bopp), to- modeling of nongravitational effects in cometary motions.
gether with improvements in instrumentation and the use Marsden (1969) introduced a nongravitational force into the
of the Infrared Space Observatory (ISO), permitted the dis- Newtonian equations of motion with simple expressions for
covery of more than two dozen parent molecules (Brooke the radial and transverse components in the orbital plane.
et al., 1996; Mumma et al., 1996; Crovisier et al., 1997; These involved a function of the heliocentric distance r ex-
Bockelée-Morvan et al., 2000), among which is the fairly pressing a standard “force law,” multiplied by a coefficient
abundant CO2 molecule, first detected in 1P/Halley both whose value was determined along with the osculating or-
spectroscopically at IR wavelengths (Combes et al., 1986) bital elements by minimizing the residuals of the fit to posi-
and with a neutral mass spectrometer (Krankowsky et al., tional observations. The radial coefficient was called A1 and
1986) and suspected to be present in comets for decades the transverse A2. It was recognized that the model might not
because of the well-known CO2+ bands. Subsequent obser- be physically realistic and that more meaningful parameters
vations of other comets are leading to interesting composi- might be derived from a more general formalism, but at-
tional intercomparisons (Mumma et al., 2003; Biver et al., tempts in this direction were unsuccessful (Marsden, 1970).
2002), although caution regarding the interpretation of com- The final update of the model was made in 1973 (Marsden
positional trends is advised because of the small number et al., 1973), stimulated by calculations of the H2O subli-
statistics for most species. Bockelée-Morvan et al. (2004) mation rate as a function of r (Delsemme and Miller, 1971).
12 Comets II

This was taken as the model force law, expressed as an and new analysis techniques are employed. Thus, we should
algebraic function g(r) whose parameters were chosen to fit not be surprised to find in five years that the ideas presented
Delsemme and Miller’s results. Eventually, more realistic in Comets II on the origin and evolution of the Kuiper belt
models were constructed for the jet force resulting from and Oort cloud have changed significantly.
asymmetric H2O outgassing, including the heat flow in the
surface layers of the nucleus (Rickman and Froeschlé, 1983). 9. FINAL REMARKS
As a result it was found that the true force law might be
very different from the g(r) formula. These efforts led Rick- During the last few decades, theories based on the origi-
man (1989) and Sagdeev et al. (1988) to the first evalua- nal ideas of Kant and Laplace have obtained the status of
tion of the density of a comet that, not too surprisingly, was the “standard” theory for the formation of the solar system.
quite low and implied a high porosity for the nucleus. The Numerical calculations and a wealth of new information on
new image of a comet nucleus after the in situ exploration the structure and composition of planetary bodies, as well
of 1P/Halley, and the intensive efforts of Crifo and collabo- as data gathered from astrophysical studies of circumstel-
rators to model the near-nucleus environment, has opened lar disks and extra-solar-system planets, seem to leave little
the door to improved models, as described in Yeomans et al. room for alternate theories.
(2004). These efforts will never be completely successful Data from comets have strengthened our understanding
until we finally understand what the expression “activity of of the formation and evolution of the solar nebula and have
comets” really means. helped us to see the intimate connections between our so-
lar system, the interstellar medium, and extra-solar-system
8. THE TRANSNEPTUNIAN BELT planets. However, these connections are not always clear
AS A COMET RESERVOIR and easy to recognize and many mysteries still remain. In
particular, our knowledge of the composition and physical
Around 1950, the Kant-Laplace nebular hypothesis for structure of cometary nuclei remain rather primitive in many
the origin of the solar system was reconsidered in the light respects, and we can expect surprising discoveries with
of the chemical compositions of the planets and their var- ever-increasingly sophisticated observations. The imminent
iation with heliocentric distance. Edgeworth (1949) and return of a sample of cometary matter from 81P/Wild 2 is
Kuiper (1949, 1951) argued that it is unlikely for the solar especially anticipated, as those results will almost certainly
nebula to have ended abruptly at the position of Neptune’s guide our future exploration of comets. On the other hand,
orbit, and thus a large population of planet precursors with the Stardust results will likely leave many questions about
a generally icy composition had to exist outside the region the icy composition of cometary nuclei, which should be
of the giant planets. Kuiper (1951) claimed that such bod- better addressed by the Rosetta mission, due to rendezvous
ies could be identified with Whipple’s cometary nuclei and with Comet 61P/Churyumov-Gerasimenko in 2015.
suggested that Pluto’s gravitational action (its mass was then Nevertheless, we offer Comets II as the best compendium
thought to be in the 0.11 Ms range) might have scattered of cometary knowledge for the next decade. With the help
the objects into Neptune’s zone of influence, whereupon of our colleagues in the cometary community, we have at-
ejection into the Oort cloud would ensue. Both Kuiper and tempted to put together a volume that presents a logical and
Edgeworth suggested that the original comet belt just be- comprehensive treatment of cometary science. The structure
yond Neptune might still be intact. Fernández (1980) was of the book was laid out with the clear objective of covering
the first to predict the existence of such a belt in a quanti- most areas of cometary science through a set of contigu-
tative way, and he demonstrated that this belt is probably ous, non-overlapping chapters. In a sense, it is a book writ-
the principal source of the ecliptic comets. This latter idea ten by a team of about 100 collaborative authors. We have
was later expanded by Duncan and collaborators; Duncan included at the beginning of this volume a series of chapters
et al. (2004) provides the current perspective on this subject. that describe what may happen to interstellar materials that
The discovery of the transneptunian object 1992 QB1 by are used to make up a planetary system. Obviously, the path
Jewitt and Luu in 1992 provided dramatic observational between interstellar molecules/grains and comets is quite
evidence that the basic hypothesis of Kuiper and Edgeworth long and complicated. It is this long journey and what hap-
might be correct. The number of observed “Kuiper belt pens along the way that is described in this book. Enjoy!
objects” (KBOs) is now approaching 1000, and the total
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 A’Hearn: Cometary Science: The Present and Future 17

Cometary Science: The Present and Future

Michael F. A’Hearn
University of Maryland

1. INTRODUCTION fact, binning the data in uniform size ranges rather than
using each individual object implies a steeper slope (–2.5)
The subsequent chapters in this book provide a compre- for the cumulative size distribution than is generally ac-
hensive study of our present knowledge of comets, from cepted (–1.5 to –2.0), suggesting that our sample size is
the interstellar medium, through formation of the solar sys- limiting our precision. What we do not know yet is whether
tem and the present day, to the death of comets. This chapter the flattening of the cumulative distribution at sizes below
will make no attempt to summarize these chapters. Rather, 2 km is due mostly to selection effects or mostly to a real
based on the material in the following chapters, this chap- dearth of small comets. Physical arguments suggest that
ter will ask about the high-level state of our knowledge in most small “comets” (much less than a kilometer) must be
major areas. Is our knowledge mostly speculation based on either dormant or extinct and thus not recognizable as com-
fragmentary data? Is our knowledge mature in terms of data ets, and this means that we should expect a turnover at some
but immature in interpretation? Is the entire area mature point not too far from where it is observed. Provided suffi-
with a full understanding of the implications for the larger cient telescope time can be made available, this is an area
fields of science? A natural outgrowth of this approach is in which we can expect a final answer within the decade,
to ask where we might be a decade into the future. What although statistics may still not be good enough to deter-
would we like to know? What are we likely to know? Where mine the differences in size distribution for certain dynami-
might the big surprises lie? cal classes even though differences are expected, e.g.,
No references (except one noncometary reference) are between comets from the Oort cloud and comets from the
given in this chapter because the topics are all covered in Kuiper belt.
more detail elsewhere in this book and those chapters con- Separating the size from the albedo is still a major chal-
tain a far more appropriate set of primary references than lenge with fewer than two dozen comets having both pa-
could be provided here. Some of the areas, notably dynam- rameters well known. The availability of the Spitzer Space
ics, are also surveyed at a higher level later in this book. Telescope (SST, née SIRTF) can lead to a large sample of
Other scientists will likely disagree with some of the con- comets for which the size and albedo are independently
clusions and speculations presented here, but the main pur- determined. The only question is whether enough observ-
pose of the chapter is not to be definitive but to stimulate ing time will be made available in the 5- to 7-year expected
the reader to think about future directions. As such, it is lifetime of the SST. Rotational lightcurves, if done in suf-
more important to be provocative than to be definitive. ficient detail and from different aspects, can provide the
convex hull of the body and the rotational state. However,
2. BASIC PHYSICAL PROPERTIES the necessity to carry out these observations either at very
high spatial resolution or when the comets are far from the
One of the fundamental anomalies of cometary studies Sun and thus possibly inactive makes it likely that, unlike
is how far we have come without knowing basic physical the case for asteroids, it will not be practical to get com-
parameters like the sizes of the nuclei. The true shapes, plete rotational lightcurves for more comets than the ones
sizes, and albedos of nuclei come only from in situ imaging of special interest, such as spacecraft targets.
and this is necessarily limited to a small number of comets. The amazing aspect of the basic properties of comets,
Because of the small size and infrequent close approaches and surprisingly little realized outside the community of
to Earth, the radar studies that have contributed so much to cometary specialists, is that we still do not have a single,
asteroid sizes and shapes have been comparatively ineffec- measured mass for a cometary nucleus, and thus not a
tive in elucidating the same parameters for comets. Fortu- single, measured density. Clever use of the nongravitational
nately, we are now beginning to get reasonable estimates of acceleration of comets has led to a series of estimates that
the size distribution, albeit mostly from optical data, which appear to be converging on densities around 0.5 g cm–3, but
require an assumed albedo to yield a size. Many of the data, this is still an extremely model-dependent result and thus
furthermore, consist of only single observations rather than uncertain by as much as half an order of magnitude. We will
complete rotational lightcurves, which adds scatter to the not have a directly measured mass for a typical cometary
distribution. Because of the limited size of the dataset avail- nucleus until there is a rendezvous mission, although one
able now, the slope of the distribution is not accurately could in principle measure a mass for an unusually large
known but we are beginning to get reasonable estimates. In comet, such as Chiron or even Hale-Bopp, with a slow flyby

17
18 Comets II

provided drag by the coma can be separated out. The first coverage of all species up to a given mass, but with insuf-
rendezvous mission currently underway is Rosetta, which ficient mass resolution to uniquely separate, e.g., N2 from
will not measure the mass of P/Churyumov-Gerasimenko CO. On the other hand, remote sensing at the highest spec-
until 2014. There is some hope that one or another of the tral resolution can easily separate all species but suffers from
smaller missions being proposed might be selected and incompleteness of coverage, depending on dipole moments
arrive at its target earlier. of the molecules, on lifetimes, and on excitation conditions.
Determining interior structure, which would be invalu- There are roughly 80 species firmly identified in comets,
able for our understanding of formation and evolution, will but this is almost certainly a very incomplete list. All but
be limited to what can be learned from the Deep Impact one of these (S2) are also seen in the interstellar medium,
mission until there is a rendezvous mission and/or a soft but the converse is not true and the abundance ratios, in
lander, again something that is not currently scheduled to general, are not similar. The in situ measurements with mass
occur for another decade. Deep Impact will excavate a large spectrometers show a continuum of all masses at higher
crater with an artificial meteorite impact in order to study masses and these have generally not been deconvolved to
the outermost tens of meters. Suggestions of chemical het- individual species. Although the majority of new species
erogeneity come from remote sensing. We know from D/ recently have been found at infrared and millimeter wave-
Shoemaker-Levy 9 (SL9) that, at least for scales comparable lengths, new species continue to be found at shorter wave-
to a kilometer, the strength is <103 dyn/cm2 and rubble-pile lengths as well.
models with similarly low strength at smaller scales suc- Unfortunately, many of the identified species have had
cessfully describe various phenomena, but we do not have abundances measured only in one or a few comets, so that
any model-independent, direct constraints on the strength one has no sense of whether or not there is wide variation
other than SL9. from comet to comet that might be correlated with origin
Although our knowledge of basic physical properties is or evolution. At optical wavelengths there does appear to
sparse now, we expect to have a mature understanding of be a correlation of abundances of C2 and C3 (relative to
the properties not related to the mass well within the next H2O) with place of origin but these are the only species,
decade. Our knowledge of mass and density will still be other than CN and possibly NH and NH2, for which there
immature, although we should have good numbers for one are data on a sufficiently large number of comets to study
or two bodies. such correlations reliably. Even where we have a correla-
tion, the mechanism for producing the correlation is not
3. CHEMICAL COMPOSITION understood beyond speculation. While the field of gaseous
abundances is mature in many ways, there are still many
Although the separation between volatiles and refracto- discoveries and measurements to be made, particularly in
ries is not rigid, it is convenient to think of the composi- expanding the infrared and millimeter-wave measurements
tion in these terms, the volatiles being those species seen to a large ensemble of comets but also in identifying new
in the gas phase and the refractories being those seen in the species since the list of unidentified lines seen in comets is
solid phase, for which mineralogy and crystal structure are extremely long.
also important. Clearly some species can be considered in Interpretation of the chemistry of the coma is further
both ways and, in the future, we can expect that many more limited by the fact that most of the species observed, in-
species will be studied both as solids and as gases. Our cluding virtually all the easily observed species at optical
knowledge of composition is limited almost entirely to the and ultraviolet wavelengths, are clearly fragments of larger
coma, the spectra of nuclei being almost featureless, a no- molecules that existed in the nucleus. Extensive chemical
table exception being two very weak features seen in the models of the coma, including many hundreds of reactions,
Deep Space 1 spectra of P/Borrelly. Other than that, the sur- have been constructed by several authors. To the extent that
faces of comets are known only to be very dark, presumably processes other than photodissociation and photoionization
from a combination of particle shadowing due to porosity matter, these models are sensitive to the physical conditions
and the inclusion of very dark, carbonaceous material as in the coma, primarily the density and kinetic temperature
one of the abundant components at the surface. We are thus as a function of distance from the surface. Furthermore,
faced with the problem of deciding the extent to which the processes such as photodissociation are sources of heating
composition in the coma is representative of the composi- in the coma and even the shape of the nucleus may play a
tion in the nucleus. major role in the spatial profile of density and temperature.
The feedback between photochemistry and physical con-
3.1. Volatiles ditions has been calculated only for water, but other spe-
cies could also affect the physical conditions. Furthermore,
Our knowledge of the composition of the gaseous coma there is some likelihood that reactions involving excited
is quite extensive, coming from remote sensing at wave- states (electronically excited molecules and/or molecules
lengths from the X-ray to the radio and from in situ mea- with excess kinetic energy) may be important in produc-
surements with a mass spectrometer primarily at P/Halley ing some species and these reactions have generally not
and to a minor extent in the tail of P/Giacobini-Zinner. In been included in the calculations with large chemical net-
the data available to date, the in situ measurements provide works. The net result is that in only a very few cases have
 A’Hearn: Cometary Science: The Present and Future 19

the chemical pathways been reliably traced from observed micrometeorites, but the evidence that they are cometary is
species to parent molecules. Several species thought on mostly circumstantial, including, e.g., stratospheric particles
chemical grounds to be parent molecules directly from the collected during the Leonid meteor storm. At least in part
nucleus have even been shown to have spatial profiles, because of difficulty in associating micrometeorites with
implying that they are produced from other species, prob- specific comets, the micrometeorites have not yet led to any
ably by thermal or photodesorption from grains, at some significant constraints on comets. Rather, the particles have
distance from the nucleus. Furthermore, as was made es- been associated with comets at least in part because they
pecially clear with the advent of C/Hale-Bopp, the relative resemble what we think ought to come from comets.
abundances of species vary dramatically with heliocentric On the other hand, in January 2006 the Stardust mission
distance even in a single comet. Again, a few cases of varia- will return a large number of refractory particles that are
tion can be explained in terms of processes in the coma, unambiguously from P/Wild 2, as well as others that are
but most are not explained at all and in virtually no case is almost certainly interstellar. This should enable us to de-
there consensus that we can correct for the variation with termine which of the micrometeorites are truly from com-
heliocentric distance adequately to say something defini- ets and it should give us the first true measurements of the
tive about nuclear abundances. actual distribution of particle composition, size, and min-
In the area of evolution of nuclear ices, the theoreticians eralogy. There may be some selection effects in which par-
have far outstripped the observers and there are extensive ticles can be lifted from the surface to be collected by the
models of the depletion and migration of nuclear ices due Stardust spacecraft, e.g., due to chemical differences cor-
to successive perihelion passages. These models have been related with size and/or with stickiness, but these selection
used to explain the asymmetries in visual lightcurves, but effects are small compared to the advance that will be
there are insufficient observational data on the predominant achieved from analyzing these particles in the laboratory.
ices to properly test any of the models. The predictions of Particles on the surface of a nucleus will be analyzed in situ
the models cover a wide range so detailed measurements of by Rosetta a decade hence, while contextual information
ice with depth in a cometary nucleus would easily discrimi- is simultaneously gathered and this will provide even greater
nate among the models. advances. In particular, we can hope to understand what
In the next decade we can anticipate numerous discov- fraction of the solid grains were brought directly from the
eries of previously unknown species. A few will come with interstellar medium and perhaps the conditions under which
traditional telescopes and instruments when there is a suit- other grains condensed in the protoplanetary disk.
ably bright comet. More will come from new facilities like Our knowledge of the refractory composition is far more
the Atacama Large Millimeter Array (ALMA) and SST. primitive than our knowledge of the volatiles, but already
Observations with the spectrometer on the Deep Impact we are unable to explain the variation from comet to comet
flyby spacecraft may provide new species seen only very of crystalline olivine vs. disordered silicates.
close to the nucleus, but the limited sensitivity is not ex-
pected to show new molecules with typical spatial profiles. 4. EVOLUTIONARY EFFECTS
Our knowledge of volatile abundances in the coma is
reasonably mature, but, despite considerable important 4.1. Dynamical
work, our interpretation of these abundances in terms of the
nuclear abundances is primitive. Our understanding of the orbital evolution of comets
seems clear at some high level — formation from Jupiter
3.2. Refractories outward, followed by ejection to the Oort cloud or capture
into the giant planets for comets formed inside Neptune or
The refractory species are much less well known. Re- by successive gravitational captures leading ultimately to
mote sensing has brought us primarily the silicate feature, Jupiter’s family of comets for comets formed beyond Nep-
including identification of crystalline olivine, and specifi- tune, possibly involving some time in the scattered disk
cally Mg-rich crystalline olivine in addition to amorphous population. The details, however, are not well understood.
olivine and pyroxene. In situ measurements of grains at P/ For example, the relative proportions of Oort cloud comets
Halley brought us CHON particles, but the specific chemi- formed at different distances from the Sun, while calculable
cal composition of the particles can not readily be inferred with current models of planetary evolution, are sensitive to
from those measurements. The presence of CHON particles the models for the formation of the solar system as a whole
filled a major gap in our understanding of the overall abun- and these are not well constrained. The injection of comets
dances, since combining these particles with the volatiles from the Oort cloud to the inner solar system is also under-
leads to more or less solar abundances for all but the light- stood in general but not in quantitative detail.
est elements and the most volatile species, such as N2 and Our simulations of the orbits for comets with small
the noble gases. Remote sensing has also brought us the (<3 AU) perihelia are quite good and we have detailed, but
CH-stretch feature in the near-infrared. Much of this is from model-dependent, simulations of the nongravitational forces
formaldehyde and methanol, but there may be a more re- acting on comets that appear quite reliable. The results of
fractory component as well. We probably have a large num- the nongravitational forces are also reasonably well under-
ber of refractory cometary particles in our collection of stood. The models of the nongravitational forces for com-
20 Comets II

ets seem somewhat ad hoc in the cases of comets for which servational data in the evolution of the nucleus. The cohe-
the nongravitational parameters change significantly from siveness of the refractory material, the porosity at various
one apparition to the next. While this can probably be traced stages of the evolution, the effective thermal conductivity,
to changes in the angular momentum vector induced by the the choice of the initial abundances of the ices, and even the
torques of the jets themselves, the simulations do not ap- tortuosity of the pores are all critical parameters in under-
pear to provide unique solutions to the problem. standing the evolution. Relatively little work has been done
Closely related to the precession-induced changes in on the evolution of the refractory components, other than
nongravitational accelerations is the effect of torques on calculations of the parameters that affect the amount of dust
total angular momentum. Rotational periods are generally lifted off the surface. There should be, for example, differ-
longer than for comparably sized asteroids and this may be ences between the surface refractory solids and those in the
due to the influence of outgassing torques. However, there interior due to different densities and the consequent differ-
is only one well-determined case of excited state rotation, ence in the effect of drag forces. Similarly, there should be
namely P/Halley, although torques from outgassing jets differences in composition due to different types of cohe-
should be quite capable of producing excited-state rotation siveness or ability to stick together in larger aggregates.
in many cases. Is the lack of other comets in excited-state However, we have no data on such selection effects and will
rotation due to the fact that the phenomenon is rare or due not have it until we have measurements on the surface of a
to the limited nature of the data on rotational state for most nucleus.
comets? This author thinks that it is mostly the latter — the Perhaps the most dramatic form of physical evolution
data needed to show excited state rotation are very exten- is the breakup of comets. Breakups range from releasing
sive unless the data include in situ images that show the one or more discrete fragments, which usually disappear on
rotational orientation accurately over many rotations. timescales of an orbital period or even much less, through
repeated release of small fragments (C/Hyakutake 1996
4.2. Physical B2), to complete dispersal of the entire comet (C/LINEAR
1999 S4). Statistically there appears to be a few percent
The physical evolution of comets is not well understood chance of any given comet breaking up on its passage
at all, even though everyone agrees that some comets, such through the inner solar system. The statistics of observed
as P/Encke, are very evolved. There is surprisingly little breakups are not yet good enough to know whether there
systematic, observable difference between comets that ap- are differences among dynamical groups of comets or to
pear to have had very different evolutionary histories. The verify the suggestion above that very many dynamically
chemistry is similar, there is a wide range of gas/dust ratios new comets might break up on their first approach to the
for various evolutionary states, and there are insufficient planetary region. Except in a few cases where the disrup-
data on the nuclei of any but Jupiter-family comets to make tion can be reliably explained by tidal forces, e.g., D/Shoe-
any sensible comparison. maker-Levy 9, the mechanism for breakups is not at all
Statistical arguments show that short-period comets must understood, several alternative scenarios having been pro-
somehow become inactive on a timescale comparable to or posed.
less than their dynamical lifetime. Similar statistical argu- The fundamental dichotomy in our work with comets is
ments suggest that a large fraction of dynamically new com- that we claim to use them to study the conditions in the
ets from the Oort cloud must break up or disperse by other early solar system but we do not know how to separate out
means on their first approach to the Sun. Direct photomet- the evolutionary effects to reveal the primordial conditions.
ric evidence shows that the surviving dynamically new com-
ets from the Oort cloud behave differently on approach to 5. ORIGIN AND THE EARLY
the Sun than do any other comets, including these very same SOLAR SYSTEM
comets on their first departure from the inner solar system.
This last effect is generally understood to be due to the loss The key questions in this area are (1) whether interstel-
of the outer layer of the comet, which had been so irradiated lar ices survived the accretion shock and were incorporated
by cosmic rays over 4.5 G.y. that it was chemically unstable, directly into comets, (2) whether any chemical reactions
by explosive release at some large heliocentric distance as (either in the gas phase or on grain surfaces) were important
the comet first enters the planetary region. Is this photomet- in that part of the accretion disk in which comets formed,
ric difference related to the inferred breakup of dynamically and therefore, (3) whether or not the details of the abun-
new comets? All other aspects of evolution are even less dances of ices in comets are good constraints on the condi-
well understood. tions in the early solar system. Laboratory experiments have
There are many models for the evolution of the outer shown, for example, that if condensation is the only impor-
layers of cometary nuclei, but they consider different pro- tant process, the relative abundances of common ices (H2O,
cesses and lead to a wide variety of possible scenarios for CO2, CO) are very sensitive to the temperature. But this
the evolution, depending not only on the orbital properties assumes that the material is initially in the gas phase, a
and the initial mix of ices and dust but also on the actual condition that is not satisfied if any interstellar ices survive
processes assumed to dominate in the models. As noted until they are incorporated in comets. This condition, of
above, the theoretical modelers have far outstripped the ob- course, may vary with distance from the Sun. In particular,
 A’Hearn: Cometary Science: The Present and Future 21

comets formed in the vicinity of Jupiter are much more bedos of many cometary nuclei and also of many TNOs and
likely to have formed from locally condensed ices, particu- thus to dramatically improve our knowledge of the size
larly if they form in the outer parts of the protojovian disk. distribution of both types of objects. There may be surprises
Models of the early solar system predict varying amounts in the values of the albedos, just as many people were sur-
of radial mixing of material. This probably implies mixing prised when Comets P/Arend-Rigaux, P/Neujmin 1, and
at a macroscopic scale of cometesimals that accreted at P/Halley all turned out to be very dark, but this kind of surprise
different locations in the protoplanetary disk. Studying the can be anticipated and used to argue for observing time.
heterogeneity of cometary nuclei at scales of tens to hun- The conceptually utterly simple experiment of Deep
dreds of meters can thus provide key information on the Impact will dramatically narrow the uncertainty in our un-
degree of radial mixing in the early solar system. The data derstanding of the structure of cometary nuclei. This is a
from remote sensing are only suggestive of heterogeneity case in which we can scope the range of plausible outcomes
and insufficient thus far to provide useful constraints. and eliminate all but one or two immediately after the ex-
periment, thus constraining the properties of the nucleus.
6. COMETS AND TERRESTRIAL PLANETS The Rosetta mission, unless beaten by a shorter-lifetime
mission selected in the near future, will provide us with the
The role of comets at the terrestrial planets is still un- first direct measurement of the mass (and low-order mo-
clear, both in the early solar system and today. Did comets ments) of a cometary nucleus and thus of its density. Rosetta
deliver most of Earth’s water and organics? The difference will also provide breakthrough tomographic measurements
in D/H ratios between comets and terrestrial ocean water of a nucleus to understand for the first time the large-scale
(SMOW) strongly argues at first glance against comets heterogeneity. It will also provide unprecedented informa-
being the primary source. There are ways around this since tion on “how a comet works.” We can anticipate that there
comets that formed near Jupiter and were scattered into the will likely be one or more small cometary missions selected
inner solar system at a very early stage might well have had for flight in the next half decade so that there would be
different D/H ratios than do today’s Oort cloud comets (the major results well within the next decade and a half.
only ones for which D/H has been measured). Other au- Proposals have already been solicited for a mission to
thors have argued that the water could have been delivered return a cold sample from the surface layers of a cometary
by asteroids containing hydrated minerals. This appears to nucleus. Such a mission would provide even more tremen-
be a question that is wide open today, although a cometary dous advances than those from Stardust. Being able to
origin for both water and organics appears more likely to measure the details of icy grains, the intimacy of mixing
this author. between ices and refractories, and the relative abundances
The role of comets today is also unclear. It has been of different volatiles will be a tremendous advance. Such a
argued that the Chicxulub crater was formed by a comet, mission will be a great complement to Rosetta. The next
although others have argued that it was formed by a car- logical step after return of a surface sample is to return a
bonaceous chondrite. This specific example aside, there is cold sample from deep (tens of meters) inside a nucleus that
no doubt that comets impact Earth and the other terrestrial preserves the chemical and crystalline form of the ices
planets today. Recent estimates suggest that they are a rela- sampled, thus providing details on what will be hinted at
tively small contributor to the flux of impactors, and it ap- by Deep Impact. Such a mission would provide crucial in-
pears to this author that future estimates will continue to formation on the scale at which different ices are mixed in
show them as a rather small fraction of the impact flux, whatever layers can be probed, from the evolved layers near
except insofar as the near-Earth-object (NEO) population the surface where we can understand the transport of vola-
includes a large subpopulation of dormant or extinct comets. tiles as the comet evolves to the more nearly primordial
layers below the thermal wave where we might understand
7. BREAKTHROUGH GOALS the condensation process. All these space missions will be
invaluable in helping us interpret the remote sensing data
In the next one or two decades, we can anticipate nu- from far more comets than we can ever visit with spacecraft.
merous breakthroughs in cometary science. It is instructive, We can also expect major advances from a large-aperture,
however, to divide these breakthroughs into two different dedicated, survey telescope, whether it be an expanded ver-
types: the predictable, paradigm-settling measurements and sion of the Pan Stars array of telescopes being built by the
the serendipitous, paradigm-changing measurements. In the University of Hawai‘i or the Large Synoptic Survey Tele-
former category we can put the definitive questions that we scope (LSST) being designed by the U.S. National Optical
ask when proposing a major investigation, while in the latter Astronomy Observatory and several partners. Depending on
we can only speculate. how the survey is implemented, particularly depending on
Among the predictable breakthroughs, we can expect how strongly the search strategy emphasizes NEOs, we
Stardust to enable us to relate cometary dust to the dust could expect major advances in our understanding of the size
captured in the stratosphere and to the zodiacal dust. We distribution and the orbital distribution of comets and in the
can realistically expect that it will even tell us a lot about size distribution of transneptunian objects (TNOs). If some
the formation of comets and the preservation of interstellar survey goes faint enough, we might even be able to pro-
refractory grains. We can expect SST to pin down the al- vide a good estimate of what fraction of Jupiter-family com-
22 Comets II

ets are primordial bodies from the Kuiper belt as opposed these new domains have been either previously unobserved
to being fragments of larger bodies in the Kuiper belt. spectral ranges or order-of-magnitude improvements in sen-
We will certainly have many discoveries of newly iden- sitivity or in spectral or spatial resolution. Astronomy as a
tified chemical species from ALMA, because of both its whole has the entire universe to study so there is more scope
superb sensitivity and its superb spatial resolution. Similar for serendipitous discovery than in the relatively narrow
discoveries should come from the tremendously increased domain of cometary science, but the principle is still the
sensitivity and reduced beam dilution of the Large Milli- same and still important.
meter Telescope being built in Mexico by the University Cometary science has gained from serendipitous discov-
of Massachusetts and the Mexican Instituto Nacional de eries in the past. The use of new wavelength domains led,
Astrofísica, Optica, y Electrónica. at the shortest wavelengths, to the discovery of high fluxes
Even dramatic increases in computational power and/or of X-rays from comets and thus to new emission mecha-
algorithm design could lead to breakthroughs. One such nisms and, at the longest wavelengths, to the discovery of
advance might be the ability to integrate a very large num- the ultraviolet-pumped maser of OH at 21 cm in comets.
ber of orbits in order to assess with proper statistics, based The application of radar led to the discovery of clouds of
on the uncertainty in the observed orbit, the probability that large particles (more than a centimeter) in surprising dy-
any given Jupiter-family comet had, at an earlier time in namical situations in more than one comet. None of these
its orbital evolution, been for some time in an orbit with would be considered paradigm-altering, i.e., none of these
smaller perihelion distance. Such a calculation has been changed our picture of the role of comets in the solar sys-
done, for example, for Chiron but with only a small set of tem, but they were surprising, serendipitous results. There
possible, current orbital elements, and the recent discovery are more new domains of measurement to be applied to
of “keyholes” in the uncertainty space of the orbits of NEOs comets than there are for most of astronomy and this com-
suggests that our understanding of cometary orbital evolu- pensates in part for the fact that we are considering a much
tion will require far more computation than has been done smaller piece of the universe. In addition to the new domains
for any comet thus far. In another computational arena, one of measurement available to traditional astronomy, the new
can certainly expect major advances in our ability to com- domains of measurement for cometary science certainly in-
bine many physical processes into a single simulation in clude all the new types of experiments and measurements,
order to better understand the origin of the comets and the both microscopic and macroscopic, that can be carried out
outer planets. Calculations that incorporate, simultaneously in situ, as well as new domains of computational space.
and with all feedback loops, the complete gravitational field, Thus we can expect serendipitous discoveries, whether
the network of gas phase, and surficial chemistry includ- new populations of comets, new physical processes, or a
ing kinetic inhibition, radiative processes, and magnetohy- new picture of how comets work, as long as we continue
drodynamics are tremendously difficult. Carrying out such to apply dramatically new techniques to studying comets.
calculations would be a major step forward in understand- There is no way to predict the areas in which area the most
ing the formation of comets and the solar system. exciting such discoveries will occur.
While some cometary scientists might think it heresy, it
seems likely that we might learn more about comets from REFERENCES
certain missions to other bodies than from many types of
missions to comets. In particular, detailed, in situ studies Harwit M. (1984) Cosmic Discovery: The Search, Scope, and
of or return of samples from a jovian Trojan might tell us Heritage of Astronomy. Massachusetts Institute of Technology,
directly about the primordial comets that formed near Cambridge. 334 pp.
Jupiter’s orbit. A similar mission to a classical Kuiper belt
object might tell us about the primordial state (except for
collisions) of cometary material now in Jupiter-family com-
ets. This is not to say that they would be more revealing
than any mission to a comet, since missions that explore
new parameter space at a comet will be extremely valuable.

8. SERENDIPITY

Turning to the truly serendipitous, paradigm-altering dis-

coveries, Harwit (1984) has written eloquently about the
nature of dramatic new discoveries in astronomy and shown
very well that nearly all the dramatic, new discoveries have
come from making measurements in new domains. These
are entirely different from the breakthroughs described
immediately above in that there is no way to predict the
area in which these surprises might occur. In astronomy
 PART II:
FROM THE INTERSTELLAR MEDIUM TO THE SOLAR
NEBULA
 Irvine and Lunine: From Clouds to Comets 25

The Cycle of Matter in Our Galaxy:

From Clouds to Comets
William M. Irvine
University of Massachusetts

Jonathan I. Lunine
University of Arizona

The processing of grains from original interstellar material to that contained in comets oc-
curred under a complex range of conditions extending from the diverse environments within
molecular clouds to the protoplanetary disk itself. Grain surface chemistry at very low tem-
peratures gives way to grain growth, heating and partial sublimation, recondensation, and then
agglomeration into cometary-sized bodies and larger. While the overall direction of the evolu-
tion can be sketched, little in the way of direct observations is available once collapse occurs,
so that it remains difficult to describe specifically the temperature-pressure-composition histories
of grains that will eventually find their way into comets.

1. INTRODUCTION (Dutrey et al., 2004), models of the formation and evolu-

tion of solids from the grains to cometesimals (Weidenschil-
All cometary matter was once, of course, interstellar. But ling, 2004), and the coupled physics and chemistry within
unresolved is whether comets still contain demonstrable and the disk (Lunine and Gautier, 2004). This progression rep-
significant signatures of the interstellar material from which resents a temporal sequence, but it also represents a dra-
they formed, either in terms of preserved or partially altered matic reduction in the spatial scales of the evolution — and
molecular constituents or in the isotopic ratios found in consequently a steep increase in the difficulty of the con-
cometary molecules. This fundamental issue has been dis- straining observations. We know a lot about the broad na-
cussed, e.g., by Ehrenfreund et al. (2002, 2004), Charnley ture of chemistry and physical processes in the vast sweep
et al. (2002), Irvine and Bergin (2000), Irvine et al. (2000), of the interstellar clouds; we know much less in a direct
Bockelée-Morvan et al. (2000), Crovisier and Encrenaz sense about the details of the chemical and physical pro-
(2000), and Fegley (1999). One can imagine two extreme cesses affecting grains on spatial scales of astronomical
scenarios in this regard: first, that comets are conglomer- units in planet-forming disks. But the chemical and isoto-
ates of essentially unprocessed interstellar grains, as pro- pic evidence from small bodies in our solar system, includ-
posed by Greenberg (1982, 1998); second, that the forma- ing comets, provides a detailed local perspective provided
tion of the solar nebula was a sufficiently energetic process, we can correctly interpret it. In briefly recapitulating this
even in its outer portions, that presolar molecules were com- cycle of matter from molecular clouds to comets, we will
pletely destroyed and that the infalling material was homog- emphasize some of the major outstanding gaps in our cur-
enized (Lewis, 1972). In the latter case the chemical com- rent knowledge.
position of dense interstellar clouds is not directly relevant to
the chemistry of comets; in the former situation, exactly the 2. THE INTERSTELLAR MEDIUM,
opposite is true. As is usually the case in science, the truth INCLUDING MOLECULAR CLOUDS
probably lies somewhere between these two extreme views.
To understand the extent to which cometary material has Cometary dust begins with the nucleosynthetic produc-
been reprocessed from its initial interstellar state requires tion of heavy elements in stars, both during their main se-
that we understand the coupled physical and chemical pro- quence and the sometimes-explosive terminal phases of
cesses at work in the various environments leading from the evolution. Novae, supernovae, and the winds of asymptotic
interstellar medium to the modern Kuiper belt and Oort giant branch (AGB) stars (the state arrived at by stars less
cloud — the main dynamical reservoirs of comets today. than 10 M when all the H and He is exhausted in the stel-
The chapters in this section of the book consider each of lar core) enrich the interstellar medium in new elements.
these environments in turn, from molecular clouds (Wooden Because the interstellar medium is mixed, and matter is
et al., 2004), to the formation and evolution of planet-form- cycled through multiple generations of stars, the elements
ing circumstellar disks (Boss, 2004), the observational prop- and the stable isotopes are a mixture of the products of stars
erties of disks and their interactions with the central star of a variety of masses and stellar generations (the latter de-

25
26 Comets II

termined by the heavy element abundance at the time of group represent the third most abundant molecule after
the star’s formation). molecular H and CO (Wooden et al., 2004). They are the
Grains may form in a variety of environments, but the most plausible candidate species for producing the diffuse
circumstellar envelopes of AGB stars are particularly im- interstellar bands, whose origin has long been a mystery
portant for forming both silicate and carbonaceous grains (e.g., Herbig, 1995). However, no single PAH has defini-
as the C/O ratio varies over time in the star’s envelope. Once tively been identified in the interstellar medium, and the
formed, grains do not simply persist until their incorpora- precise mix of species and the (presumably environment-
tion in comets; rather, they are cycled many times from gase- dependent) ratio of neutral to ionized molecules remain
ous to condensed phases. Grains formed in the diffuse inter- unknown. Polycyclic aromatic hydrocarbons crop up in a
stellar medium may be modified or evaporated by ultraviolet multitude of environments, from barbeque grills to martian
photolysis powered by the intense radiation from newly meteorites to the interstellar medium; they should be present
formed stars. Shocks generated by supernova explosions — as well in cometary matter. Because of their ubiquity and
the end product of massive star formation — may destroy ease of formation, they are rather ambiguous signposts to
grains at large distances from the original site of the explo- the details of C chemistry, and in the diffuse interstellar
sion, with grains reforming both in the wakes of the shocks medium are only the most abundant of a menagerie of C
and in the much denser environments of molecular clouds. forms such as chains, fullerenes, and (rarely) diamonds.
A detailed characterization of the chemical nature and The cold, dense (n > 200 cm–3) clouds of the interstel-
physical structure of grains has not been achieved. The na- lar medium are sites of star formation, most likely of low
ture of the circumstellar and interstellar silicates, including mass stars, and are characterized by extremely low tempera-
their composition and crystal structure, is complex and is tures around 10–20 K. External ultraviolet radiation is ex-
relevant to the origin of cometary silicates (see Wooden et cluded, but penetrating cosmic rays provide a population
al., 2004). For the more volatile elements, it seems unavoid- of ions and electrons that provide what little heating there
able that the grains are the primary reservoir for C and a is. Under such conditions, very tiny (0.1-µm radius) grains
major reservoir for O, and very likely that there is a continu- and hence extensive surface chemistry dominate, and it is
ous size range from large carbonaceous molecules (PAHs; here that some of the very-low-temperature features of com-
see below) to particulate grains (cf. Whittet, 2003; van Di- etary matter, such as the para-ortho ratio in water, may be
shoeck and Blake, 1998). Given the difficulty of characteriz- locked in (Mumma, 1997). The dominant C form in the gas
ing terrestrial kerogen, the lack of consensus on the nature is CO, and observations of nearby clouds such as TMC-1
of the organic component of interstellar grains is perhaps and the perhaps more typical L134N indicate a rich suite
not surprising. of hydrocarbons, nitriles, and acids — foreshadowing a com-
Mixing processes in the galaxy must be fairly efficient, plexity of C-based cometary chemistry that has yet to be
for the vast majority of material in interplanetary dust par- fully explored (Wooden et al., 2004). Unlike the major res-
ticles (IDPs) — perhaps the best samples of the non-ice ervoir for C in the grains, the bulk of the N in these clouds is
phases of comets available — is isotopically of so-called probably in the gas phase as N2, although direct observa-
“solar” composition. Although isotopic anomalies are dra- tional confirmation is limited.
matic and informative of the details of solar system forma- Water is present in the dense clouds, but is frozen out on
tion (Cameron, 2002), the material exhibiting these typically grains where it is the dominant ice component. This water
represent only 1% of the material present (see Wooden et ice may be the principal O reservoir in these regions, al-
al., 2004). though quantitative assessment is difficult (cf. Bergin et al.,
Chemistry in the interstellar medium is complex because 2000). Water ice forms predominately on more refractory
of the enormous range of environments contained therein. grains through H-atom additions to O atoms, rather than
In the diffuse interstellar medium (H density 1–100 cm–3, direct condensation in what is still an extremely tenuous
temperature ~100 K), gas phase chemistry is dominated by medium. Mechanisms for returning molecules to the gas
the abundant ultraviolet radiation pumped out by massive from cold (10 K) grains are highly uncertain, although a
O and B stars and largely unimpeded over stellar distances. variety of means have been proposed. Thermal and cosmic-
The size of the molecules formed is generally limited be- ray-powered sublimation and chemical cycling of water
cause of the instability of long chains and other complex likely occur in portions of the cloud. Thermal processing
structures against UV dissociation. There is a relatively high of the water aided by exothermic chemical reactions could
abundance of atomic (ionized or neutral) C, N, S, H, etc. sublimate the ice, which then would reattach to grains by
However, the molecular phase in the diffuse clouds is domi- adsorption. In any case the ice would be expected to be
nated by polycyclic aromatic hydrocarbons (PAHs), which amorphous. What other types of chemistry might occur, and
are relatively stable against UV dissociation and may be a the isotopic fractionation achievable (for example, in H, C,
very important, if not dominant, agent in determining the N), depend on the details of very-low-temperature chemi-
thermal balance of the interstellar medium. Astoundingly, cal processes on grains that are extremely challenging to
they may contain up to 10% of the C in the galaxy (although replicate under normal laboratory conditions. Wooden et al.
some estimates are an order of magnitude lower), and as a (2004) claim that clathrate formation has been inferred to
 Irvine and Lunine: From Clouds to Comets 27

occur in dense clouds, although the crystalline form — what The survival of interstellar grains during the infall is
is normally called a clathrate — is likely kinetically inhib- assured only for those that fall into the outermost parts of
ited at 20 K in favor of direct adsorption. The abundance the disk, where the shock is weak and infall velocities low.
of ammonia (NH3) in these ice mantles is also somewhat Grain material that is sublimated may readsorb or condense
uncertain. on the grain residues in the relatively cool and high-den-
Low-mass and high-mass star formation lead to warmer sity gas of the disk midplane, but the resulting distribution
clouds and “hot cores” respectively. The hot cores provide a of various molecular species in the recondensation may
wealth of information on condensed species in colder en- differ from that of the original grain. Inward, progressively
vironments because such species are sublimated at the high more refractory species are sublimated during infall; in the
hot-core temperatures, while still protected against the free- inner regions of the disk it is likely that all but the most
radical chemistry abundant in high-ultraviolet environments. refractory material is returned to the gas phase.
In the Orion hot core, for example, H2O, H3N, H2S, CH3OH, Given that interstellar (as opposed to circumstellar) sili-
and HCN are all more abundant than in cold clouds. To- cates appear to be amorphous, the nature of cometary sili-
gether with CO and HCHO, this mix of species is “familiar” cates, which include both crystalline and amorphous ma-
to us from the cometary point of view — the hot-core sub- terial, presents a challenge. The prevailing view is that the
limated mix contains the species seen in cometary comae, amorphous component probably represents surviving inter-
if not quite in the same relative abundances. Regardless of stellar material, presumably similar to the GEMS (glass
whatever other processing occurs in the protoplanetary disk, imbedded with metal and sulfides) found in IDPs, while the
the existence of some familiar species emphasizes the link crystalline silicates are probably produced or at least an-
between cometary and interstellar (molecular cloud) grains nealed in the solar nebula. The issue is discussed in detail
(cf. Irvine and Bergin, 2000; Tielens, 2001). This link is in Ehrenfreund et al. (2004).
even more evident in the large isotopic fractionation mea- As the protostar grows, ignites fusion reactions, and
sured for H in cometary H2O and HCN, which reflects that develops a strong bipolar outflow roughly perpendicular to
seen in molecular species in interstellar clouds, although not the disk, other chemistry begins to affect the grains. Ultra-
always to the same extent (see Ehrenfreund et al., 2004; violet irradiation again becomes an issue for gas and grains
Irvine et al., 2000). While the environments of low-mass that end up at large distances from the disk center, where
star formation typically do not exhibit the same relative they may be wafted upward periodically to the surface of
abundances, this is surely because temperatures are not high the flared disk and hence be exposed to the protostellar
enough to sublimate the material except in the observa- emission by virtue of their altitude above the midplane. The
tionally inaccessible, optically thick, inner portions of the bipolar flow encounters the surrounding molecular cloud
collapsing clumps. Some recent high-spatial-resolution ob- in the form of a wind-cloud shock (Wooden et al., 2004),
servations do reveal hot-core-type molecules in the hot gas where additional heating and energetic chemistry may occur.
close to the low-mass protostar IRAS 16293-2422 (Cazaux There are, however, major uncertainties concerning the
et al., 2003). physical nature of the disk. As Boss (2004) points out, the
detailed thermal, density, and turbulent structure cannot yet
3. FROM COLLAPSING CORES TO DISKS be predicted, and there is a serious lack of observational
data (Dutrey et al., 2004), reflecting the need for higher-
The loss of magnetic support as cloud clumps become angular-resolution studies that will only become possible
denser and the neutral molecules “slip through” the much- with future facilities such as the Atacama Large Millimeter
smaller ion population is thought to initiate the collapse Array (ALMA) telescope and the James Webb Space Tele-
toward formation of a low-mass protostar and, depending scope (JWST). There is, for example, no agreement on the
on the clump’s angular momentum, a protoplanetary disk mechanisms for transfer of mass and angular momentum
[outflows from massive stars may also trigger clump col- in the disk, a problem related to uncertainties in the char-
lapse; see Boss (2004) for a comparison of the two pro- acter of the “viscosity” that is assumed to exist and is mod-
cesses]. Once initiated, the collapse leads to elevated tem- eled through the parameter α (hence, the so-called α-disk
peratures in the center eventually sufficient to trigger ther- models). Moreover, the process of giant planet formation
monuclear fusion, and the protostar feeds on the gaseous is still controversial. All this is relevant to comets, since it
and solid material falling inward over a period on the or- describes the environment in which volatile species con-
der of 1 million years. If a disk forms (Boss, 2004), then dense/sublimate, material is transferred radially, etc.
the interaction of the disk with the surrounding collapsing Furthermore, an even greater uncertainty exists as to
cloud is complex. Infalling grains, subjected to increasing whether low-mass stars like the Sun might in fact form in
density, grow in size well past that of the tiny interstellar clusters where massive stars form, such as the Orion mo-
material. However, heating of the grains by direct exposure lecular cloud, which would be suffused with ultraviolet
to accretion shocks and drag (Lunine et al., 1991; Chick and radiation from surrounding young protostars, shocks, and
Cassen, 1997) occurs, and can modify the grain composi- infusion of material from supernovae (Boss, 2004), lead-
tion or destroy it entirely by sublimation. ing to a much more active chemistry than in the more tra-
28 Comets II

ditional picture of relatively isolated star formation. Even trapped volatiles for comets: water ice that survived infall
if they formed in a less-energetic environment that might into the disk and water ice formed in the disk by conden-
characterize more isolated low-mass star formation, Dutrey sation. The mechanism of volatile trapping and the total
et al. (2004) point out that many T Tauri stars are mem- volatile content are likely to be very different for the two
bers of binary or multiple systems, complicating the tradi- sources, but both may be relevant since the source region
tional approach to the physics of the disks. Although the for some of the Oort cloud comets could be the Jupiter-
physics of some of these processes has been modeled, little Saturn feeding zone, which was not far from the snowline.
attention has been paid to the connection to the resulting The Galileo probe measurements of supersolar abun-
grain chemistry and isotopic reequilibration at various dis- dances in the jovian atmosphere do not rule out a prima-
tances from the protostar. Furthermore, direct observation rily solar nebula condensed (“native”) vs. interstellar (Owen
of the material in the collapsing core is exceedingly difficult et al., 1999) origin for the water ice that carried these
as spatial scales shrink from parsecs to tens or hundreds of volatiles into growing Jupiter, because we do not yet know
astronomical units and densities rise by many orders of the O (hence H2O) abundance of the bulk planet (Gautier
magnitude relative to the average (103–105 cm–3) in the mo- et al., 2001). It is highly likely that these two kinds of water
lecular cloud itself. ice both existed in the protoplanetary disk, because it is hard
to avoid sublimation and recondensation of some of the
4. EVOLUTION OF GRAINS WITHIN THE water, but equally difficult to argue that all the infalling
PROTOPLANETARY DISK grains were heated sufficiently to completely sublimate the
water ice phases. Cometary tests of just how much native
Assuming that the protoplanetary disk is not destroyed vs. interstellar water ice is present must rely on the isoto-
on very short timescales by the external molecular cloud pic composition of the water ice and trapped volatiles, and
environment, gas phase processes drive chemistry in the perhaps the ortho-para ratio of the H in the water. Unfor-
disk over timescales on the order of 1 million years or more, tunately, definitive predictions of these properties tied to
based on astronomical observation of gas in disks (Dutrey the disk evolution are difficult to make.
et al., 2004). Gravitational and magnetic torques presum- Within protoplanetary disks, the chemistry and proper-
ably launch waves in the gas and dust, compressing and ties of grains will be altered in the immediate environment
heating material and perhaps in some disks forming giant of formation of giant planets. Depending upon the details
gaseous planets that may or may not be analogs of Jupiter of such planet formation, the balance of oxidized vs. re-
and Saturn. These torques could be strong enough to melt duced C and N species will be altered in the gas very close
solids in certain parts of the disk, one explanation offered to the giant planets (Mousis et al., 2002; Irvine et al., 2000).
for the chondrules seen in meteorites; strong gas dynamical More reduced species may find their way into solids form-
heating of material falling into the inner portion of the disk ing near the planets, these solids then are transported out-
could also lead to such melting. Turbulent viscosity within ward through the main disk, or grains may be destroyed
the disk heats the midplane even in the absence of stellar entirely by catastrophically rapid giant planet formation
radiation blocked by the optically thick conditions. Excur- (Mayer et al., 2002). In our own solar system, the latter
sions in the accretion rate may lead to cooling and then seems unlikely, because abundant solid material remained to
sudden heating events akin to the observed “FU Orionis” populate the Kuiper belt and the Oort cloud. Nonetheless,
phenomenon. The star itself, in blowing a bipolar flow ver- the gaps that giant planets open during their formation re-
tically, also clears out the innermost part of the disk, sub- duce the gas density and perturb the orbits of larger solid
jecting adjacent material to extreme heating. bodies, while inward and outward of the gap higher densi-
The strong radial temperature gradient imposed on the ties might have perturbed the volatile content of the icy
protoplanetary disk by turbulent dissipation ensures a ra- planetesimals.
dial gradation in the condensation and stabilization in grains The growth of comet-sized planetesimals, their dynami-
of species of differing volatility. Hence the most refractory cal histories as they were ejected from the region of giant
silicates (e.g., corundum) condense closest to the protostar, planet formation and portions of the Kuiper belt, and the
followed by the less-refractory Mg silicates and Fe, then a resulting compositional distinctions between comets resid-
complex series of S compounds, followed by water ice at ing in different dynamical reservoirs were rather complex
several astronomical units or beyond. The condensation (Weidenschilling, 2004). This evolution occurred as the disk
front of water ice — sometimes called the snowline — is transitioned from gas-rich to gas-poor, a process that was
crucial because it represents a steep outward increase in the complex and may differ in terms of timescale from one
surface density of solids in the disk, with potential impli- protoplanetary disk to another. The growth from centime-
cation for the formation timescale of giant planets if these ter- to kilometer-sized bodies is particularly poorly under-
were seeded by initial formation of solid cores. But from stood, as it is unclear theoretically in which circumstances
the point of view of cometary grains and their composition, collisions among the objects will lead to a net gain in the
the condensation of water ice adds complexity to the his- mass of the larger partner (Weidenschilling, 2004). The
tory. We are forced to consider two sources of water ice and vertical as well as the radial structure of the disk may be
 Irvine and Lunine: From Clouds to Comets 29

important in particle growth, but no three-dimensional simu- this time, comets existed much as they exist today — in
lations have yet been carried out. different dynamical reservoirs, some perturbed inward to-
During the gas-rich phase, interactions of comet-sized ward the Sun to sublimate, possibly break up, and generate
small bodies with each other and with the giant planets was wonder in the skies of Earth for humans who would arise
strongly affected by the presence of the gas, both from a 4.55 billion years after the solar system’s formation.
dynamical point of view and with respect to the incorpora-
tion of additional volatiles in the water ice of the small bodies 6. EXPULSION OF COMETARY MATTER
(Lunine and Gautier, 2004). As the gas dissipated, additional AT THE END OF THE SUN’S
volatile incorporation ceased and the dynamical interactions MAIN-SEQUENCE EVOLUTION
of the cometary bodies and the planets simplified.
The Sun is approximately halfway through its main-se-
5. COMETS IN THE REMNANT DISK quence life, and at the end of this time will expand to be-
come a red giant, with an outer envelope at the orbit of the
The disk remaining after much of the gas is removed — Earth. The initiation and then termination of He fusion in
a process that might take 107 yr or more, although the mas- the red giant’s core will trigger a second collapse and expan-
sive gas phase is likely to be a factor of 10 shorter — con- sion, this time to a red supergiant with an outer envelope
sists of solids ranging from dust to giant planets. Planet at the orbit of Mars. A subsequent series of “flashes” and
formation is not complete, however, because the formation thermal pulses will eject half the mass of the Sun to space,
of the terrestrial planets in our system evidently took sev- leaving behind a white dwarf and stripping the atmosphere
eral tens of millions of years, based on isotopic evidence of Saturn’s moon Titan (Lorenz et al., 1997). The luminos-
(Yin et al., 2002; Kleine et al., 2002) and dynamical simula- ity excursions during this time will sublimate the ices from
tions (Chambers and Wetherill, 1998). The process during Kuiper belt comets, and the loss of half the Sun will free
this time was the pumping up of the eccentricities of an much of the Oort cloud from the gravitational bonds of the
initially quiescent disk, inward of Jupiter, dominated in mass solar system — an echo of the postformation ejection of
by bodies from Mercury- to Mars-sized. As the orbits of cometary bodies from the region of the giant planets. Com-
these perturbed “planets” crossed, collisions and net growth etary material, in the gaseous and solid phases, will travel
occurred. Meanwhile the giant planets were perturbing the freely through the interstellar medium, and the cycling of
orbits of more distant icy bodies — the massive host of what matter that 10 billion years before became the Sun and solar
we would today call comets — leading both to outward system will have been closed.
ejection and movement inward on eccentric orbits (Morbi-
delli et al., 2000). 7. FUTURE OBSERVATIONS
Many of these comets struck the growing terrestrial plan-
ets over millions of years, supplying organic compounds It is neither unkind nor disrespectful to refer to the above
and water, but comets were not the dominant supplier of as a kind of fairy tale grounded in a spotty tapestry of ob-
water to Earth if the isotopic evidence is taken at face value. servations glued together by dynamical and chemical mod-
The D-to-H ratio of measured long-period comets is twice eling. Seminal spacecraft observations, such as the ESA
that of the Earth’s oceans (Meier et al., 1998). Furthermore, Giotto compositional studies, have been supplemented by
the dynamical simulations themselves suggest that large increasingly powerful groundbased studies. Nonetheless, it
bodies in an asteroid belt much more heavily populated than is exceedingly difficult to penetrate collapsing cores or to
today were the principal contributors to the ocean of the tease apart the details of planet-forming disks on scales of
Earth (Morbidelli et al., 2000), although the same conclu- astronomical units. Remnant disks are easier, but spatial
sion need not hold for the waters of Mars. Nonetheless, the resolution is still a problem. Future cometary measurements
accretion of cometary material by the Earth was a direct re- from, most spectacularly, Rosetta, are discussed elsewhere
sult of the process by which the giant planets gravitationally in this book, but upcoming ground- and space-based facili-
cleared much of the outer solar system of small icy bodies, ties for examining astronomical structures involved in planet
relegating these to the Oort cloud. formation are equally exciting (Dutrey et al., 2004). ALMA
At the same time, modest migration of the giant plan- will see details in planet-forming disks on scales of a few
ets — particularly Neptune — sculpted the orbits of comets astronomical units, and will be able to sensitively probe the
remaining beyond 30 AU into what are now the classical and gas composition and grain properties. The Space Infrared
resonant disks of the Kuiper belt, and also ejected comets in- Telescope Facility (SIRTF) will track the colder dust in rem-
ward into the so-called scattered Kuiper belt disk (Luu and nant and planet-forming disks with sufficient sensitivity to
Jewitt, 2002). These gravitational interactions with the giant perhaps indicate the effect of massive planets on the dust
planets — and for the Oort cloud comets, with the surround- populations, while the JWST will apply more powerful an-
ing environment of young stars formed in the same epoch gular resolution and midinfrared sensitivity to probe the
as the Sun — represent another set of perturbations on the compositional gradations in the grains of remnant disks.
thermal and radiation environment of the comets. Beyond These and other facilities will severely test our ideas about
30 Comets II

the process of planet formation, and how interstellar grains Gautier D., Hersant F., Mousis O., and Lunine J. I. (2001) Enrich-
become — through many different evolutionary path- ments in volatiles in Jupiter: A new interpretation of the Gali-
ways — the stuff of cometary nuclei. leo measurements. Astrophys. J. Lett., 550, L227–L230
(erratum 559, L183).
Acknowledgments. J.L. and W.I. acknowledge the support of Greenberg J. M. (1982) What are comets made of? A model based
the NASA Origins of Solar Systems, Astrobiology, and Planetary on interstellar dust. In Comets (L. L. Wilkening, ed.), pp. 131–
Astronomy Programs in the preparation of this chapter. We are 163. Univ. of Arizona, Tucson.
grateful for the helpful comments from two anonymous reviewers. Greenberg J. M. (1998) Making a comet nucleus. Astron. Astro-
phys., 330, 375–380.
Herbig G. H. (1995) The diffuse interstellar bands. Annu. Rev.
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32 Comets II
 Wooden et al.: Composition and Evolution of Interstellar Clouds 33

Composition and Evolution of Interstellar Clouds

D. H. Wooden
NASA Ames Research Center

S. B. Charnley
NASA Ames Research Center

P. Ehrenfreund
Leiden Observatory

In this chapter we describe how elements have been and are still being formed in the galaxy
and how they are transformed into the reservoir of materials present in protostellar environments.
We discuss the global cycle of matter from stars, where nucleosynthesis produces heavy elements
that are ejected through explosions and winds into the interstellar medium (ISM), through the
formation and evolution of interstellar cloud material. In diffuse clouds, low-energy cosmic rays
impact silicate grains, amorphizing crystals, and UV photons easily penetrate, sponsoring a
simple photochemistry. In dense cold molecular clouds, cosmic rays penetrate, driving a chem-
istry where neutral-neutral reactions and ion-molecule reactions increase the complexity of mole-
cules in icy grain mantles. In the coldest, densest prestellar cores within molecular clouds, all
available heavy elements are depleted onto grains. Dense cores collapse to form protostars and
the protostars heat the surrounding infalling matter and release molecules previously frozen in
ices into the gas phase, sponsoring a rich gas-phase chemistry. Some material from the cold
regions and from hot or warm cores within molecular clouds probably survives to be incorpor-
ated into the protoplanetary disks as interstellar matter. For diffuse clouds, for molecular clouds,
and for dense hot cores and dense warm cores, the physiochemical processes that occur within
the gas and solid state materials are discussed in detail.

1. GALACTIC INTERSTELLAR MEDIUM volumes such as in shocks and in small intermittent regions
of velocity shear where viscous dissipation occurs (Vázquez-
1.1. Overview: Cycle of Matter from Stars through Semandeni et al., 2000). In the ISM, gas is processed rapidly
the Interstellar Medium to the Solar System through a wide range of temperatures, densities, and ioniza-
tion stages, as given in Table 1, under the influence of turbu-
As with our Sun, new stars form in the dense cores of lent and thermal processes, pressure gradients, and magnetic
quiescent cold molecular clouds (Boss, 2004) from interstel- and gravitational forces. Interstellar clouds comprise defin-
lar materials. To a minor extent, pre-main-sequence stars re- able structures in the ISM, but only represent two of five
plenish the interstellar medium (ISM) with material through ISM components (section 1.2). Stars enrich the ISM (sec-
their bipolar outflows and jets. The ISM primarily becomes tion 2) with the gas and dust that eventually contributes to
enriched with nucleosynthesized “metals”, i.e., elements the formation of new star systems after cooling and passing
heavier than H and He, through supernovae (SNe) explo- through interstellar cloud phases. Processes that contribute
sions of high-mass stars (SNe type II) and of primary stars in to increasing the complexity of solid-state and molecular
a low-mass binary systems (SNe type I). Other sources of materials are introduced by Irvine and Lunine (2004) and
enrichment include the massive winds of low-mass asymp- discussed here in detail; these processes primarily occur in
totic giant branch (AGB) stars and novae (e.g., Jones, 2001; interstellar clouds, i.e., in diffuse clouds (section 3) and mo-
Chiappini et al., 2003; Wheeler et al., 1989). Supernovae lecular clouds (section 4), at low temperatures (≤100 K). In
explosions (McKee and Ostriker, 1977), the UV photons interstellar clouds, molecules and solid-state materials are
from massive O and B stars (Wolfire et al., 2003), and, to a more protected from the destruction mechanisms — UV irra-
lesser extent, AGB stellar winds inject energy into the ISM. diation, cosmic rays, fast electrons — prevalent in the highly
This energy is deposited in shocks and generates turbulence energetic intercloud environment of the ISM of the galaxy.
that acts on many different length scales to bring together, In the dense, hot high-mass and warm low-mass protostel-
compress, and even shear apart enhancements in the inter- lar cores (section 5) that only comprise tiny fractions of the
stellar gas density. Turbulent energy is degraded efficiently mass of molecular clouds, a rich gas-phase chemistry occurs
into thermal energy when turbulence is concentrated in small that increases the complexity of the materials infalling onto

33
34 Comets II

Fig. 1. Representative fractional abundances of ions, atoms, and molecules in different regions of the interstellar medium. The frac-
tional abundances for ζ Oph that sample a line of sight through diffuse clouds are relative to the total abundance of H. Fractional
abundances listed for the other objects are relative to H2. The species included are for comparative purposes and are not a complete
inventory of these sources.

the protostellar disks. The increase in the complexity of mol- spiral arms but also occur in interarm regions and in the
ecules from diffuse clouds, through molecular clouds to star- galactic halo above and below the galactic plane.
forming cores, is demonstrated from left to right in Fig. 1. Physical conditions in the ISM lead to the description of
A fraction of these ISM materials survive to be incorporated ISM as the coexistence and interaction of five components
into comets (Ehrenfreund et al., 2004). (included in Table 1): (1) the hot ionized medium (HIM),
also called the coronal gas; (2) the warm ionized medium
1.2. Components of the Interstellar Medium (WIM) containing ionized atomic hydrogen atoms (H+), re-
ferred to in other works as the diffuse ionized gas (DIG);
Of the total mass and volume of the galaxy, the ISM (3) the warm neutral medium (WNM), containing neutral
constitutes only ~10–15% of the mass but most of the vol- atomic hydrogen atoms (H0 or H); (4) the atomic cold neu-
ume. The mass of the ISM is concentrated within a thin disk tral medium (CNM), hereafter referred to as diffuse clouds,
that extends to ~25–30 kpc and has a vertical scale height dominated by H but containing some molecular hydrogen
of ~400–600 pc [cf. Ferrière (2001) for an extensive review (H2); and (5) the molecular CNM, dominated by H2, here-
on the galactic ISM]. About half the mass of the ISM is in after referred to as molecular clouds or dark clouds.
discrete interstellar clouds that occupy ~1–2% of the inter- The components of the ISM (Spitzer, 1985) character-
stellar volume. Interstellar clouds are concentrated along the ized by significantly different temperatures — hot, warm,
 Wooden et al.: Composition and Evolution of Interstellar Clouds 35

TABLE 1. Interstellar medium components and their physical properties.

Common Density* State of Typical

ISM Component Designations T (K) (cm–3) Hydrogen xe † Diagnostics
Hot ionized medium (HIM) Coronal gas 10 6 0.003 H+ 1 X-ray emission,
UV absorption
Warm ionized medium (WIM) Diffuse ionized gas 10 4 >10 H+ 1 Optical, UV, IR,
(DIG) Hα, H II regions
Warm neutral medium (WNM) Intercloud H I 8 × 103–10 4 0.1 H0 0.1 21-cm emission
Atomic cold neutral Diffuse clouds 100 10–100 H0 + H2 ~10 –3 21-cm absorption,
medium (CNM) 3.4-µm absorption,
UV absorption
Molecular cold neutral Molecular clouds 0–50 103–105 H2 10 –7–10 –8 Extinction, far-IR,
medium (CNM) Dense clouds 1 radio: CO, CS,
Dark clouds NH3, H2CO, HCO+
Molecular hot cores Protostellar cores 100–300 >10 6 H2 ≤10 –8 Rovibrational
emission CH3CN,
CH3OH, NH3,
HCN, SO2
*Density of H2 in molecular clouds and cores (nH2), otherwise density of H (nH).
† Ionization fraction (x ).
e

and cold — result from the balance between energy injected interactions increase the complexity of molecular materials
(primarily) by supernova shock waves and radiative losses that are of interest to understanding the formation of com-
(Spitzer, 1990; Ferrière, 2001; Wolfire et al., 2003). The gas etary materials. Therefore, we will concentrate on the pro-
atoms and ions are excited by collisions with electrons and cesses in the interstellar clouds in the following discussion,
other atoms and ions and by absorption of UV photons. The as well as in other sections of this chapter.
gas is cooled by electronic transitions of highly ionized Diffuse clouds have sheet-like or filamentary structures
heavy elements in the hot component, by electronic transi- (Heiles, 1967), and are often seen as cocoons around cold,
tions of singly ionized and neutral atoms in the warm ion- giant molecular clouds and smaller molecular (dark) clouds
ized and warm neutral components, and by vibrational and (dense molecular CNM with nH > 100 cm–3, 10 K ≤ Tg ≤
rotational modes of molecules in the cold atomic and cold 20 K, AV ≥ 5 mag). Heating of molecular clouds is primarily
molecular components of the ISM. by cosmic rays, and at molecular cloud surfaces by grain
Ionized hydrogen (H II) gas constitutes the WIM, where photoelectric heating and collisions with excited H2 mole-
gas temperatures of 104 K and higher pervade, and Lyα and cules. Cooling is primarily by CO molecular line emission.
Hα photons arise from the H+ recombination cascade. Neu- Gas temperatures in molecular clouds also are affected by
tral atomic hydrogen (H I) gas and neutral (e.g., C, N, S) collisions with dust grains that either cool or warm the gas,
and singly ionized atoms (e.g., C+, S+) constitute the WNM, depending on the density (Burke and Hollenbach, 1983) and
i.e., the low-density intercloud medium (nH ≈ 0.2–0.5 cm–3, on the freezing out of molecules (coolants) from the gas
6000 K ≤ Tg ≤ 10,000 K, AV ≤ 0.5 mag). H I gas exists in phase (Goldsmith, 2001).
diffuse clouds of rarefied atomic CNM (nH ≈ 20–50 cm–3, Translucent clouds are intermediaries (1 < AV < 5 mag)
50 K ≤ Tg ≤ 100 K, 0.5 ≤ AV ≤ 1 mag). The dominant heat- between the cold atomic diffuse clouds and cold molecu-
ing process of both the WNM and the diffuse CNM is by lar clouds, and are most easily distinguished in the galac-
collisions with photoelectrons ejected by polycyclic aromatic tic halo at high galactic latitudes (Hartmann et al., 1998)
hydrocarbon (PAH) macromolecules (Bakes and Tielens, and by H2, CH, CN, CO (Rachford et al., 2002), and H2CO
1994, 1998). The WNM is cooled by far-IR forbidden line molecules (Magnani and Onello, 1995). We do not discuss
emission of the [C II] 158-µm and [O I] 63-µm lines, by re- these translucent clouds in detail; see Turner (2000) for a
combination of electrons onto grains, and by Lyα emission discussion of their properties and Ingalls et al. (2002) for
from recombining H+ atoms. The CNM is primarily cooled recent modeling of heating and cooling processes. Figure 1
through the [C II] 158-µm line emission (Wolfire et al., summarizes the fractional abundances of gas-phase ions,
2003). The atomic CNM and molecular CNM are distinct atoms, and molecules in four different components of the
structures in the ISM, constituting the diffuse clouds and ISM. Note the increased complexity of molecules present
molecular clouds respectively, where gas-grain and gas-gas in hot and warm dense molecular cloud cores.
36 Comets II

1.3. Interstellar Medium Structures HIM and WIM, i.e., the shocks and pressures from ionized
gas, can sweep up and compress WNM or shear apart CNM
A large fraction of the volume of the Milky Way is filled diffuse clouds. Hence, primarily supernovae, and to a lesser
with the HIM, i.e., a tenuous, ionized coronal gas (McKee extent stellar winds, are responsible for the turbulent nature
and Ostriker, 1977). Supernovae explosions generate the of the ISM, the multiple components of the ISM, and the
coronal gas (Spitzer, 1990) when their ejecta collide with structures of the interstellar clouds.
and shock the surrounding medium. Expanding supernova Diffuse clouds are thought to form when streams of
ejecta sweep up ambient ISM material, compressing it into WNM H I collide (e.g., Ballesteros-Paredes et al., 1999b).
rapidly expanding shells that cool quickly due to their high Widespread warm H I gas (WNM at 6,000–10,000 K) exists
densities, possibly becoming molecular gas after ~10 6 yr in the space between cold H I diffuse clouds (CNM at 50–
(McCray and Kafatos, 1987). Upon collision with a massive 100 K), as observed by H I 21-cm emission and absorption
interstellar cloud the supernova remnant slows and breaks lines, respectively (cf. Ferrière, 2001). The density ratio be-
up into fragments, mixing with the interstellar clouds. Ions, tween the WNM and diffuse clouds is approximately the
primarily from H (87%), He (10%), ~1% metals (C, N, O), inverse of the temperature ratio, supporting the view that
and ~2% electrons, are accelerated in supernova shocks and the atomic WNM and CNM are in rough thermal pressure
are the major source of relativistic particles in the ISM com- equilibrium (Boulares and Cox, 1990; Wolfire et al., 2003).
monly referred to as cosmic rays. The cosmic-ray spectrum However, recent arguments have been made that diffuse
(1–1000 MeV) is the main energy source for ionizing the clouds are not pressure confined by the WNM but rather
molecular gas (Cravens and Dalgarno, 1978; Cesarsky and result from turbulent density fluctuations in colliding gas
Völk, 1978). The low-energy cosmic-ray spectrum is not streams (Ballesteros-Paredes et al., 1999b). Such nonther-
measured, because the solar wind with its magnetic field mal pressures due to turbulent motions, magnetic fields, and
deflects these particles, but is instead inferred from the cos- cosmic rays are required to produce the observed vertical
mic-ray ionization rate deduced from diffuse cloud chemical scale height of the WNM component (Wolfire et al., 2003)
models (section 3.6). There is a high probability that 1-MeV and maintain sufficient pressures such that the neutral com-
cosmic rays will be absorbed close to their place of origin ponent of the ISM occurs in the galaxy as two phases —
[within ~2 pc (Spitzer and Jenkins, 1975)]. In fact, the cos- WNM and CNM. The balance between heating and cooling
mic rays (E ≤ 100 MeV) that ionize the WNM and CNM processes in the neutral medium, either through turbulent
do not travel far from their supernova sources (Kulsrad and dynamics (Ballesteros-Paredes et al., 1999b) or in equilib-
Cesarsky, 1971). EUV (13.6 eV ≤ hν ≤ 100 eV) and X-ray rium conditions (Wolfire et al., 2003), generates a relation-
radiation dominate the ionization of the intercloud WNM. ship between pressure and neutral hydrogen density that is
The gas in the WNM dominates the EUV and X-ray opacity. double-valued for a range of pressures: The neutral two-
FUV (6 eV ≤ hν < 13.6 eV) radiation dominates the heat- phase ISM consists of either warm and rarefied (WNM) or
ing of the WNM and the photoelectric heating of the CNM cold and dense (CNM) material (Goldsmith et al., 1969).
diffuse clouds and molecular cloud boundaries. The dust in The two phases are in thermal equilibrium but not hydro-
the CNM clouds dominates the FUV opacity. static equilibrium. The kinematics of atomic gas and molec-
Massive stars often form in clusters, and their explosions ular gas are similar (Grabelsky et al., 1987), and the mor-
supply enough of a continuum of energy to form supershells phological distinction between WNM and CNM is often not
or superbubbles. The HIM that fills ~20% of the galactic clear: Warm H I gas is seen as an intercloud medium and
ISM local to the Sun is mostly seen as superbubbles (Fer- diffuse clouds are seen to have H I halos. Massive stars form
rière, 1998). The expansion of superbubbles may extend in molecular clouds that have diffuse cloud cocoons that are
beyond the local scale height of the galaxy and form chim- embedded within the intercloud WNM, so much of the mass
neys, expelling HIM material into the galactic halo. As the of the CNM and the WNM is in photodissociation (PDR)
expelled material gains height, the gas cools and forms high- regions illuminated by UV photons from massive stars (Hol-
and intermediate-velocity diffuse clouds in the halo (e.g., lenbach and Tielens, 1999).
Richter et al., 2003). These diffuse clouds then fall back Most of the mass of H I is in the CNM as diffuse clouds
down onto the galactic disk and contribute even more en- even though most of the volume of the ISM containing H I
ergy to turbulent excitation of the ISM than supernovae; this is in the rarefied intercloud WNM (Dickey and Lockman,
convective cycle is called the galactic fountain (Shapiro and 1990). Furthermore, most of the mass of CNM clouds is in
Field, 1976). Through Hα emission line studies, the WIM is molecular clouds. Specifically, most of the mass of gas in
observed to persist not only in the galactic plane in patches, the ISM is in giant molecular clouds (GMCs) that each span
filaments, and loops, but also in the galactic halo. The es- tens to hundreds of parsecs and contain 105–106 M of gas.
cape of UV photons from massive stars through super- GMCs with masses greater than ~10 4 M are gravitation-
bubbles and chimneys accounts for the energy required to ally bound [e.g., for the outer galaxy (Heyer et al., 2001)].
maintain the WIM in the halo (Dove et al., 2000). From By number, most molecular clouds are less massive than
the temperatures and densities determined for the ionized 10 4 M and have internal turbulent motions in excess of
and neutral components, the thermal pressures of the HIM their gravitational binding energies (cf. Heyer et al., 2001).
and the WIM exceed the WNM by factors of ~3–15 and The formation and existence of these gravitationally un-
~2, respectively. The turbulence and thermal forces in the bound molecular clouds is thought to be a result of a highly
 Wooden et al.: Composition and Evolution of Interstellar Clouds 37

energetic turbulent ISM in which diffuse cloud material is to live longer than the star-forming molecular clouds. That
compressed through supernova shocks, colliding H I streams, is, the rarefied CNM that takes the form of diffuse clouds
spiral density waves, and gravity. All molecular clouds in- could stay diffuse for a long time between its successive
cluding GMCs fill only 1–2% of the volume of the ISM. incorporations into dense CNM as GMCs or smaller mo-
lecular clouds. Each individual diffuse cloud is probably
1.4. Interstellar Cloud Lifetimes buffeted by turbulence and changed from diffuse cloud to
molecular clouds in only a short time. Molecular clouds
The lifetimes of diffuse clouds and molecular clouds is become diffuse clouds when dispersed by star formation or
a rapidly evolving subject. A couple of decades ago, con- turbulent forces. Thus, much of the volume of the H I gas
cepts of molecular cloud formation were motivated to ex- is retained in diffuse clouds.
plain the formation of GMCs because that is where most of The rapid formation of molecular clouds within diffuse
the molecular gas resides. The formation of molecular clouds clouds is thought to occur on the order of a few million
by ballistic aggregation of smaller clouds on timescales of years (Ballesteros-Paredes et al., 1999a,b; Hartmann et al.,
4 × 107 yr was considered (Field and Hutchins, 1968). This 2001). Most numerical simulations of diffuse cloud forma-
view was superseded by the concept that large-scale mag- tion, however, are not followed to high enough densities
netic Parker instabilities formed molecular clouds and pro- (100 cm–3) to confirm that a large fraction of the H I gas is
duced lifetimes of ~2 × 107 yr (Blitz and Shu, 1980). Based turned to H2 on timescales of ~10 6 yr (Ballesteros-Paredes
on the supposition that the entire GMC could form stars, the et al., 1999b; Ostriker et al., 2001). The formation of H2
long lifetimes of GMCs were consistent with the observed (section 3) occurs when a sufficient column of H I shields the
slow rate at which molecular gas turns into stars. Mecha- H2 against UV dissociation [AV(min) ≈ 0.5–1 (van Dishoeck
nisms were evoked to delay the onset of star formation in and Blake, 1998)] and when there is a sufficient concentra-
GMCs, including ambipolar diffusion of magnetic flux (Shu tion of dust on whose surfaces H2 forms (cf. Richter et al.,
et al., 1987) and turbulent cloud support (e.g., Nakano, 2003). Molecular hydrogen formation can occur in diffuse
1998). We now know that only a small fraction of a GMC, or clouds in the galactic halo with volume densities of only
of any molecular cloud, has sufficient density to be proto- nH ≈ 30 cm–3 because the UV field is not as intense as in the
stellar cores (Boss, 2004; Elmegreen, 2000). Therefore the galactic plane (Richter et al., 2003). In the galactic plane,
observed low star formation rate is a result of the small vol- H2 can form under equilibrium conditions in ~106 yr when
ume fraction of molecular clouds that are dense enough to both the densities are sufficient (nH ≈ 100 cm–3) and the sur-
be protostellar cores (Elmegreen, 2000). rounding H I intercloud medium has sufficient H I column
Modern models of diffuse cloud formation involve gravi- depth. These conditions occur for diffuse clouds that encom-
tational instabilities and turbulence (e.g., Vázquez-Seman- pass ~104 M of gas and are gravitationally bound (Hart-
deni et al., 2000). The structure of the ISM is very fragmen- mann et al., 2001). Many gravitationally unbound smaller mo-
tary: Even on the largest scales, GMCs are seen as fragments lecular clouds exist, however, at densities of nH ≈ 100 cm–3;
inside H I clouds (Grabelsky et al., 1987). Structures inside these clouds contain H2 and CO but are without massive H I
GMCs are created by turbulence and are of similar fractal cocoons. The conundrum is that timescales for H2 formation
dimension to larger structures (Falgarone et al., 1991). It appear to be faster than the timescales constrained by equilib-
takes about a volume of WNM 1 kpc in diameter to make rium processes (Cazaux and Tielens, 2002) at the densities
a CNM GMC. If this material is brought together within observed for molecular clouds. Pavlovski et al. (2002) find
several tens of parsecs, the density of the gas is higher than that H2 formation occurs in shock-induced transient higher-
average (103 cm–3), but most of it is WNM. Gravity might density enhancements more rapidly than expected from the
pull this material together in a dynamical time (Gρ –1/2) of average density of the gas. Three-dimensional computations
~107 yr (Elmegreen, 2000). However, turbulent processes of decaying supersonic turbulence in molecular gas show
stimulated by gravity, supernovae shocks, collisions with the complete destruction and the rapid reformation of H2
supernova remnant shells, spiral density waves (e.g., Elme- in filaments and clumps within a diffuse cloud structure.
green, 1979), or collisions with other clouds can speed up These regions of turbulent compression then relax and the
this process. In this view, molecular clouds are an interme- H2 becomes relatively evenly distributed throughout the
diate-scale manifestation of the turbulent cascade of energy cloud. Therefore, molecular clouds may form out of diffuse
from its injection into the HIM and WIM to small dissipa- cloud material several times faster in a turbulent ISM (Pav-
tive scales (Vázquez-Semandeni, 2004). lovski et al., 2002), hence making the rapid formation and
The lifetimes of diffuse clouds are not known. There is existence of gravitationally unbound molecular clouds of
less mass in diffuse clouds than in molecular clouds, so ~103 M , such as the Chameleon I–III and ρ Ophiuchi
under equilibrium conditions, the lifetimes of diffuse clouds molecular clouds, theoretically realizable.
would be shorter. In the local cloud containing the solar
neighborhood, the fraction of ISM in molecular clouds is 1.5. Rapid Star Formation
less than half. The self-gravitating or star-forming fraction
of molecular clouds is significantly less than half. In the The rapid formation of molecular clouds, of stars within
turbulent scenario, the diffuse clouds that are not dense molecular clouds, and of molecular cloud dispersal, is a
enough or massive enough to be self-gravitating would have controversial issue. For detailed discussions on the subject,
38 Comets II

see recent excellent reviews by Boss (2004), Mac Low and birth sites of stellar clusters containing high-, intermediate-,
Klessen (2003), and Larson (2003). After a molecular cloud and low-mass stars. By number, most of the low-mass stars
forms, star formation appears to proceed quickly in about a form in regions of high-mass star formation. Low-mass stars
cloud crossing time, and the crossing time depends on the tur- also form in lower mass molecular clouds in the galactic
bulent velocities in the cloud (Elmegreen, 2000; Hartmann plane, such as the ~104-M Taurus molecular cloud complex
et al., 2001; Vázquez-Semandeni, 2004). The duration of star that spans ~30 pc. The formation of our proto-Sun and the
formation corresponds to the size of the region: Spreads of solar system is often thought to have formed in a Taurus-
less than ~4 × 106 yr in age are deduced for star clusters, the like cloud because T Tauri stars are proto-Sun analogs, al-
Orion region has a spread of ages of 107 yr, and the Gould’s though the high levels of radioactive isotopes in primitive
Belt a spread of 3 × 107 yr (Elmegreen, 2000). Careful ap- bodies suggests the solar system formed in a region of high-
plication of pre-main-sequence theoretical stellar evolution mass star formation (Boss, 2004; Vanhala and Boss, 2000).
tracks to stellar associations in Taurus shows that there is a Complex gas phase chemistry occurs in protostellar cores
107-yr spread in the ages of the association members, but the because the reservoir of infalling material is rapidly made
majority of stars are ≤4 × 106 yr and the fewer older stars more complex: Gases trapped in the solid phase in icy grain
tend to lie on the cloud boundaries (Palla and Stahler, 2002). mantles are warmed by the protostar and released into the
Many stellar associations do not show evidence for inter- gas phase. High-mass protostars are more luminous than
mittent stellar formation activity in their derived stellar ages low-mass protostars and therefore heat the surrounding in-
but do show over the past ~107 yr an acceleration in the rate falling core material to a greater extent, producing hot cores,
of stellar births during the most recent ~4 × 106 yr (Palla while low-mass protostars produce warm cores. In so far that
and Stahler, 2000). This is as expected because the rate of this infalling core material has not yet passed through the
star formation accelerates as the cloud contracts (B. G. Elme- protostellar disk, the rich gas-phase chemistry that occurs in
green, personal communication, 2003). Thus the rapid-star- hot and warm cores is considered part of the reservoir of
formation scenario is invoked to explain the absence of mo- interstellar cloud materials that contributes to the proto-
lecular gas from clusters more than ~4 × 10 6 yr in age, and planetary disk and the formation of cometary materials.
the — still controversial (Palla and Stahler, 2002) — lack of
an age dispersion in T Tauri stars of more than ~4 × 10 6 yr 1.6. Cycling of the Elements through
(Hartmann et al., 2001). Given the concept that small regions Diffuse Clouds and Molecular Clouds
collapse to form stars and star clusters in ~1–3 × 106 yr dur-
ing the lifetime of the larger complex, then rapid molecular Stars that form in quiescent dense cold molecular clouds
cloud formation (~106 yr) is followed by rapid dissolution of heat and energize the ISM by ejecting matter. The ISM is
molecular gas back to diffuse cloud material by the energy continually enriched in newly nucleosynthesized heavy ele-
injected by young, newly formed stars or by turbulent mo- ments primarily through supernovae and AGB star winds
tions. Shorter lifetimes of molecular clouds (~1– 4 × 106 yr) (section 2.1). Much of the matter that is shed into the ISM
also help to resolve the many problems for interstellar chem- occurs through the circumstellar envelopes (CSE) of late-
istry posed by longer lifetimes (~107 yr) (section 4.3). type stars where the physical conditions are conducive to the
Molecular clouds are very inhomogeneous in density, con- condensation of dust grains (section 2.2–2.5). Dust grains
taining density-enhanced “clumps” (approximately a few par- are also thought to condense in supernovae and novae (e.g.,
secs, 103 H2 cm–3), and within these clumps contain smaller, Jones, 2000). Most of the heavy elements are therefore in-
particularly dense, self-gravitating “cores” (~0.1 pc, ≥105 H2 jected into the ISM as dust grains.
cm–3) (Larson, 2003). Clumps are thought to be the pre- The dust grains in interstellar clouds, however, are not
cursors of star clusters and small groups of stars, although necessarily those produced by AGB stars and supernovae.
most clumps are not as a whole self-gravitating (Gammie Interstellar medium processes contribute to the rapid de-
et al., 2003). In the view of rapid cloud formation, proto- struction of dust grains, including shocks produced by su-
stellar core masses result from a rapid sampling of existing pernovae and turbulence, the same turbulence that can act
cloud structures (clumps and cores) (Elmegreen, 2000). Evi- to form interstellar clouds (section 1.4). Grain destruction
dence for this lies in the fact that the distribution of masses processes are most efficient in the warm neutral component
of newly formed stars, i.e., the initial mass function, is simi- (WNM) of the ISM where gas densities are moderate (nH ≈
lar to the distribution of masses of protostellar cores in mo- 0.25 cm–3) and temperatures are high (8 × 103–104 K) (Jones
lecular clouds (Motte et al., 1998; Testi and Sargent, 1998; et al., 1996; McKee et al., 1987). In shocks, collisions occur
Luhman and Rieke, 1999). Protostellar cores formed by tur- between grains and gas atoms and ions, and between the
bulent processes are supercritical, i.e., their gravitational dust grains themselves. Gas-grain collisions result in erosion
energies available for collapse are greater than their inter- and sputtering of grains. Grain-grain collisions result in
nal thermal and magnetic energies (Mac Low and Klessen, fragmentation and, for the larger-velocity collisions, vapori-
2003). This concept is supported by the fact that the exist- zation. From the passage through supernovae shocks, grain
ence of a subcritical core has yet to be convincingly dem- lifetimes are predicted to be shortened to 6 × 108 and 4 ×
onstrated (Nakano, 1998). 108 yr for carbonaceous and silicate grains respectively
Most of the molecular mass is in GMCs; GMCs contain a (Jones et al., 1996), about 50 times too short compared to
wide range of core masses (Nakano et al., 1995) and are the a nominal grain lifetime of 2 × 1010 yr required to maintain
 Wooden et al.: Composition and Evolution of Interstellar Clouds 39

>90% of the silicates ejected by stars as particles in the ISM. were produced via nucleosynthesis in the interiors of stars
Fragmentation is about 10 times faster than grain destruction or in the explosive nucleosynthesis of novae and superno-
by sputtering and vaporization (Jones et al., 1994, 1996; vae. Nuclear burning sequences are subjects of detailed
Jones, 2000), rapidly removing grains larger than ~0.05 µm study (Clayton, 1983; Wheeler et al., 1989) and differ con-
from the ISM grain size distribution. However, grains as siderably for low- to intermediate-mass stars (Renzini and
large as 1 µm are observed in the ISM. Thus, most ISM dust Voli, 1981) and high-mass stars (Woosley and Weaver, 1995;
grains are not stardust but grains that formed in the ISM Thielemann et al., 1996).
(section 3.2) (Jones et al., 1994, 1996, 1997; Tielens, 1998; In brief, during a star’s life on the main sequence, H fuses
Jones, 2000, 2001; Draine, 2003). The timescales for the into He primarily through three temperature-dependent proc-
cycling of the elements through the diffuse clouds and mo- esses: two proton-proton reactions and the CNO bi-cycle.
lecular clouds can therefore be quantified by studying the In the CNO cycle, He is a primary product and N is a secon-
evolution of the ISM dust-grain population. dary product formed at the expense of C and O already pres-
In the diffuse clouds, the compositions of the dust grains ent in the stellar interior. After time on the main sequence,
are studied by deducing from observed absorption lines the H is exhausted in the core and a He core is formed. This He
fraction of each element that appears depleted from the gas core will begin nuclear burning into C through the triple-
phase (see Sembach and Savage, 1996). The timescales for α-particle reaction when the core has sufficiently contracted
the cycling of the elements through diffuse clouds appears and heated to temperatures of ~108 K. During the time that
to be rapid because of the uniformity of depletion patterns in H is burning only in a shell around the preignited He core,
diffuse clouds of similar physical conditions (Jones, 2000). the stellar envelope expands and the star transits from the
For example, no galactic vertical gradients in the elemen- main sequence to the red giant branch of the luminosity-
tal depletion patterns are seen, so the galactic fountain (sec- temperature or Hertzprung-Russell (HR) diagram (Willson,
tion 1.2) effectively mixes supernovae-enriched material in 2000; Iben, 1974). The He core ignites and is later exhausted;
the disk with the halo on timescales of 107 –108 yr (Jenkins the star expands again due to He shell burning and outer H
and Wallerstein, 1996). Also, the observed extreme deple- shell burning as an asymptotic giant branch (AGB) star.
tions of supernovae elements (Ca, Ti, Fe) only can occur if During this AGB phase of low- to intermediate-mass stars
>99.9% of all interstellar gas is cycled at least once through when the expanded envelopes have low surface gravity, stars
the dust-forming circumstellar envelope of a cool star (Jen- shed material through their winds and eject significant
kins, 1987). amounts of 4He, 12C, 13C, and 14N into the ISM. An AGB
The cycle of matter between the different components star is observed to undergo substantial mass loss in the form
of the ISM is rapid. The resident times spent in different com- of a stellar wind. In cooler outer regions of the stellar atmos-
ponents are set by various processes such as supernovae- phere, elements form molecules, and these gas phase mol-
driven and turbulence-driven shock dissipation in the HIM, ecules condense into solid particles at temperatures lower
WIM, and WNM, and turbulent compression, velocity shear- than about 2000 K. The ratio of C to O (C/O) in the gas de-
ing, and H2 formation in the CNM. Supernovae shocks that termines the mineralogy of the dust that forms (Tsuji, 1973),
sweep up ambient interstellar matter may form molecular as will be discussed below (sections 2.2–2.4). Stellar radia-
clouds in times as short as 106 yr (McCray and Kafatos, tion pressure on these dust grains drives them outward and
1987). Since most of the molecular mass is in giant molecu- gas-grain collisions drag the gas along with the dust. This
lar clouds that form massive stars, the timescales for mas- leads to the existence of a massive circumstellar envelope
sive star formation and dissipation (~4 × 106 yr; section 1.5) (CSE) and a slow AGB stellar wind that enriches the sur-
drive the cycling times for the WNM and CNM components rounding ISM with molecules and dust.
of the ISM. If molecular clouds form in times as short as The evolution of the stellar structure is critical to the
~1–3 × 106 yr (section 1.4), then diffuse cloud material prob- yields of C and N (Busso et al., 1999; Chiappini et al.,
ably passes rapidly into and out of the colder, denser mo- 2003). Carbon and N are primary products during the third
lecular cloud structures. Theoretical models now predict that dredge-up stage on the AGB if nuclear burning (“hot bottom
diffuse cloud material that was previously molecular cloud burning”) at the base of the convective envelope is sufficient.
material will have an enriched gas-phase chemistry com- During thermal pulses in 13C-rich pockets, slow neutron cap-
pared to diffuse cloud material that formed from WNM ture through the “s-process” leads to elements such as 14N,
(Bettens and Herbst, 1996; Price et al., 2003). The chem- 22Ne, 25Mg, and rare-earth elements including Sr, Y, Zr, Ba,

istry of diffuse clouds may help to trace their history. La, Ce, Nd, Pr, Sm, Eu, and in the presence of Fe seed nu-
clei slow neutron capture uniquely creates very heavy nu-
2. FORMATION OF THE ELEMENTS clei such as 134Ba, 152Ga, and 164Er. For a description of the
AND DUST GRAINS IN STARS dependence of nucleosynthesis in AGB stars on stellar struc-
ture and metallicity, see the review by Busso et al. (1999).
2.1. Nucleosynthesis Iron is produced when long-lived white dwarf low-mass
stars in binary star systems eventually explode as type Ia
Beyond the large amounts of H, some He, and small supernovae. Oxygen is produced when short-lived massive
amounts of Li created during the Big Bang, other elements stars explode as type II supernovae (SNe II). In a SNe II all
that constitute cometary bodies, the planets, and our Sun the burning shells (the star’s “onion skin structure”) are
40 Comets II

expelled back into the ISM. The massive star’s elemental most primitive interplanetary dust grains, of probable com-
abundances from outside to inside echo the burning cycles: etary origin, is that the material that came into the solar
H, He, C, O, Ne, Mg, S, and Si. Silicon burns to Fe, and as nebula primarily was of approximate solar composition.
Fe is the most stable of all the elements, it therefore cannot
be fused into another form. Once an Fe core forms, the star 2.2. Asymptotic Giant Branch Star
no longer produces enough photons to support itself against Circumstellar Envelopes
gravity, and the core collapses. The collapsing core reaches
such high densities and temperatures that nuclear statisti- The circumstellar envelope (CSE) of an AGB star pro-
cal equilibrium occurs: All elements break down into nucle- vides the ideal environment for complex silicates and car-
ons and build back up to Fe (Woosley, 1986). At even higher bonaceous material to grow and polymerize (see Draine,
densities and temperatures, all matter turns into neutrons, 2003, for a review). The chemistry of the dust that con-
and the implosion is halted at the neutron star core. Then denses depends on the C/O ratio. The molecule CO is very
the star that is collapsing onto the neutron core “bounces” tightly bound and consumes all available C or O, whichever
and the massive star explodes. If the neutron core is larger is less abundant. If there is C left over after the formation of
than the Chandrasekhar mass limit of 1.2 M , a black hole CO, then a C-based dust chemistry occurs. Conversely, if
forms. In the inner Si- and O-rich layers of the star that are there is leftover O, O-rich silicate dust forms. Early in the
expanding at 2500–5000 km s–1, explosive nucleosynthesis AGB phase, when C/O ratios are less than unity, silicate
occurs, where the capture of neutrons by nuclei occurs in dust forms, as is widely observed in the dust shells around
the rapid “r-process” to build up the Fe-peak elements and these stars (Molster et al., 2002a,b,c). The chemistry of the
the interesting radioactive nuclear chronometers 232Th, 235U, O-rich dust follows condensation pathways for silicates,
238U, and 244Pu. Explosive O burning leads to Si, S, Ar, and aluminum oxides, and alumino-silicates. Later in the AGB
Ca. Explosive Si burning also leads to Si, S, Ar, Ca, as well phase, sufficient newly synthesized C is dredged up from
as stable Fe and Ni, and radioactive Co that decays to radio- the stellar interior to increase the atmospheric C/O ratio
active Ni that then decays to stable Fe (Woosley, 1988). Mas- above unity. In this case, carbonaceous dust is formed. The
sive stars contribute most of the O, and significant amounts chemistry of C-dust formation is believed to be similar to
of He and C to the galaxy (Chiappini et al., 2003), although that which produces soot in terrestrial combustion, and im-
there are significantly fewer massive stars than low-mass portant chemical intermediates are the PAH molecules
stars. (Frenklach and Feigelson, 1989; Tielens and Charnley,
The reservoir of elements out of which the solar system 1997). Distinctive IR emission bands from hydrocarbon
formed is the result of the mixing of nucleosynthetic prod- grains are detected in C-rich AGB stars, but the aromatic
ucts from many generations of stars of different masses. infrared bands (AIBs) from PAHs are not detected prob-
Galactic chemical evolution (GCE) is modeled by folding
together the history of star formation in the Milky Way; the
initial mass function that describes the relative number of
stars of a given initial stellar mass; the increase of stellar
metallicity with time; the spatial distribution of stars in the
galaxy; and the nucleosynthetic yields as functions of stel-
lar mass, structure, and metallicity (Matteucci, 2001; Chiap-
pini et al., 2003). In the Milky Way 4.5 × 109 yr ago, GCE
had created the reservoir of elements of “solar composition.”
Even though GCE reveals that most of the O and Si origi-
nates from SNe II, the isotopically anomalous dust grains
from SNe II are very few in number in meteorites (Yin et
al., 2002; Nittler et al., 1996). In fact, in interplanetary dust
particles (IDPs), O-isotopic anomalies are now being found
that are attributable to AGB stars (Messenger, 2000; Mes-
senger et al., 2002, 2003). This isotopically anomalous O
found in silicate grains within IDPs has a high (1%) abun-
dance by mass. Within the measurement errors, the other
99% of the IDPs are composed of approximately solar com-
position materials. Therefore, even the more primitive dust Fig. 2. PAH emission (arrows) in different lines of sight through
the ISM. (a) Mon R2 IRS2 depicts a line of sight toward a mas-
grains in our solar system indicate that most of the heavy
sive protostar, exhibiting dust grains with ice mantles (H2O, CO2),
elements locked in dust grains lost the isotopic signatures
and a UV-illuminated region where the gas is photodissociated and
of their birth sites prior to entering the solar nebula. It has PAH emission is evident. (b) Orion Bar, which is a photodisso-
been hypothesized that dust grains are evaporated and re- ciation region; the chemistry is dominated by UV and the PAH
condensed in supernova shocks in the galaxy (Jones et al., emission dominates the IR spectra. (c) PAH emission is also seen
1996). Furthermore, dust grains probably reform in molecu- in the environs of the reflection nebula NGC 2023. Figure cour-
lar clouds (Dominik and Tielens, 1997). The evidence in the tesy of J. Keane and E. Peeters.
 Wooden et al.: Composition and Evolution of Interstellar Clouds 41

ably because AGB stars are too cool to produce the UV pho- phous silicate bands (with central wavelengths at ~9.7 µm
tons that excite the PAHs. In the global cycle of matter in and spanning ~8–12.5 µm) are the most common bands seen
the galaxy, PAHs are small enough to survive supernovae in O-rich AGB stars, with the 13-µm feature being second.
shocks (Papoular, 2003) and UV exposure in the WIM com- Postulated carriers for the 13-µm feature include corundum
ponent of the ISM, thereby enabling them to be the carriers (e.g., Onaka et al., 1989), silica (Speck et al., 2000), and
of the AIB features (see Fig. 2; section 3.4) in protostellar spinel (Posch et al., 1999; Fabian et al., 2001b). Spinel
regions (e.g., Mon R2 IRS2), photodissociation regions (MgAl2O4) can account for the rather common 13-µm fea-
around massive stars (e.g., the Orion Bar), and reflection ture, as well as the 16.8-µm and 32-µm features in the ISO
nebulae (e.g., NGC 2023). Thus, stellar mass loss during SWS spectra (Cami, 2002). Alumina (Al2O3), in the case of
the AGB phase is an important source of silicate and C-rich G Her, matches the profile of 11-µm feature. Magnesiowüst-
dust for the ISM (Willson, 2000). ite (Mg0.1Fe0.9O) is identified as the carrier of the 19.5-µm
feature (Posch et al., 2002; Cami, 2002).
2.3. Oxygen-rich Asymptotic Giant Branch The silicates and the Al oxides follow two distinct con-
Silicate and Oxide Dust densation pathways because Si is much more abundant than
Al. These thermodynamic condensation sequences were de-
Oxygen-rich dust grains in the ISM are recognized to veloped for the solar nebula (Grossman, 1972). In an AGB
be primarily Fe-bearing amorphous, i.e., disordered, silicate outflow that originates at the stellar photosphere and ex-
dust grains (Li and Greenberg, 1997). Oxygen-rich AGB pands and cools, the first grains to condense are those with
stars are recognized through their IR spectra to be the main the highest condensation temperature: corundum (Al2O3)
producers of these amorphous silicates. Silicates largely fall at 1760 K. After corundum condenses, aluminosilicates con-
into two mineral families: olivine (Mg,Fe)2SiO4 and pyrox- dense, including Ca-bearing gehlenite (Ca2Al2SiO7). Geh-
ene (Mg,Fe)SiO3 (cf. Hanner and Bradley, 2004). The Mg- lenite then reacts with the Mg in the gas at about 1550 K
pure end members of the olivine group and pyroxene group to form spinel (MgAl2O4) (Speck et al., 2000). Isotopically
are forsterite and enstatite respectively. The “ISM” 9.7-µm anomalous presolar spinel grains from AGB stars are found
silicate absorption band is attributed to Fe-bearing amor- in meteorites (Nittler et al., 1997).
phous olivine (Li and Greenberg, 1997) or to Fe-bearing In the same parcel of gas, the silicates condense: Mag-
olivines and pyroxenes in a ratio of ~5 : 1 (Kemper et al., nesium-rich olivine condenses first as forsterite at about
2004). In the past five years, analysis of IR spectra of O-rich 1440 K. By reactions with SiO molecules in the gas phase,
AGB stars obtained with the short wavelength spectrometer cooling of the forsterite leads to the formation of enstatite.
(SWS) onboard the Infrared Space Observatory (ISO) re- At high temperatures the incorporation of Fe into crystalline
veals other amorphous forms and crystalline forms of sili- silicate minerals is inhibited thermodynamically (Grossman,
cates and oxides. In particular, O-rich AGB stars also pro- 1972). When the gas temperatures drop below the crystal-
duce Mg-rich crystalline olivine and Mg-rich crystalline lization temperature of ~1000 K, conditions prevail where
pyroxene grains in varying abundance ratios (Molster et al., Fe can be incorporated into the minerals and amorphous
2002a,b,c). The high Mg-content of the crystalline silicates forms of silicates can grow. This is the mechanism sug-
is confirmed by the wavelengths of the resonant peaks (Fa- gested for the formation of Fe-bearing amorphous silicates
bian et al., 2001a). In O-rich AGB stars characterized by in AGB stars (Tielens et al., 1997). Iron is present in the gas
high mass loss rates of ~10 –4 M yr –1, i.e., the OH/IR stars, phase and condenses as pure Fe grains at temperatures of
at most a few percent of the total mass of dust ejected can about 900 K (Gail and Sedlmayr, 1999), significantly cooler
be crystalline silicates, while the preponderance is amor- than the Mg-rich silicates. Pure Fe grains, even though spec-
phous silicates (Kemper et al., 2001). In O-rich AGB stars trally featureless, have been invoked to explain the hot near-
with low mass-loss rates of ~10–6 M yr –1 and CSEs that IR continuum in AGB stars (Kemper et al., 2002).
are less optically thick in their IR continuum than the OH/ Not all minerals appear to follow a thermodynamic se-
IR stars, i.e., the Mira variable stars, the ISO SWS detec- quence. Magnesiowüstite (MgFeO) is not expected to form,
tion limits constrain the crystalline silicates to be ~40% or yet it is seen in spectra of O-rich AGB stars (Cami, 2002).
less of the total mass ejected (Kemper et al., 2001). More Similarly, the preponderant amorphous silicates in the CSE
stringent limits will be determined for Miras by Spitzer of AGB stars are not a consequence of a thermodynamic con-
Space Telescope observations. The crystalline silicates are densation sequence. A quantitative explanation of their for-
not seen, however, in the diffuse ISM: Constraints of <5% mation will probably require the application of a kinetic con-
and <0.5% are determined from the ISM 9.7-µm feature and densation theory that includes surface exchange processes
the 9.7-µm feature toward the galactic center by Li and (Gail and Sedlmayr, 1999).
Draine (2002) and Kemper et al. (2004) respectively. Silicate
crystals are efficiently transformed to amorphous silicate 2.4. Asymptotic Giant Branch Carbon-rich Dust
structures in the ISM, probably through cosmic-ray impacts
during their residence in diffuse clouds (section 3.3). The extended convective envelopes of AGB stars evolve
Oxygen-rich AGB stars with more rarefied CSEs than from O-rich to C-rich during the third dredge-up phase when
Miras show emission features of either amorphous silicates, C is nucleosynthesized at the base of the CSE and brought
or oxides, or both (Cami, 2002). The spectrally broad amor- to the stellar surface. In the CSE of C-rich AGB stars, a com-
42 Comets II

plex carbon chemistry occurs that is analogous to carbon that contributes to the interstellar extinction curve (Whittet
soot formation in a candle flame or in industrial smoke et al., 1990). All solid grains larger than a few micrometers
stacks. An active acetylene (C2H2) chemistry appears to be lack spectroscopic signatures, so large SiC grains may be
the starting point for the development of hexagonal aromatic present in the ISM but are not spectroscopically detected.
rings of C atoms, the structure of which mimics the cross- Presolar SiC grains constitute all the β-SiC structure (Daul-
section of a honeycomb. These aromatic rings probably ton et al., 2002), have isotopic anomalies indicative of AGB
react further to form large aromatic networks such as soot. CSEs, and are typically larger than 1 µm in size (Amari et
The kinetic theory for PAH and soot formation is a subject al., 2001). Perhaps only the largest SiC grains survive their
of current astrophysics research (Cherchneff et al., 1991; journey through the ISM to be incorporated into meteorites.
Cadwell et al., 1994; Hudgins et al., 2001). These soot par-
ticles also contain aliphatic bonds, i.e., nonaromatic C–C, 3. PHYSIOCHEMICAL PROCESSES
C=C, C≡C, and C–H bonds. IN DIFFUSE CLOUDS
At intermediate radii in the AGB CSE a transient photo-
chemistry occurs (Glassgold, 1996), but by the time the CSE 3.1. Overview
edge is reached, all small volatile molecules that formed in
this region, as well as at the photosphere (e.g., HC3N, SO2, In this section we summarize the composition of and the
H2CO, CO, H2, C2H2, SiO), are completely destroyed and important chemical processes operating in diffuse clouds of
hence play no part in interstellar cloud chemistry. The solid gas and dust. (Note that the lines of sight to background stars
particles from AGB CSE, upon entering the warm ionized frequently sample many diffuse clouds, so diffuse cloud mat-
and warm neutral components of the ISM, can be structur- ter often is called the diffuse interstellar medium, or DISM.)
ally altered by large fluxes of UV photons (Mennella et al., Cosmic dust forms in the atmospheres of evolved stars (sec-
2001) and fast H atoms (Mennella et al., 1999) present there tions 2.2–2.4). Subsequent complex evolution of dust and
(Chiar et al., 1998; Pendleton and Allamandola, 2002). gas is driven by interactions with gas and by processes such
After many thermal pulses the AGB star has shed much of as heating, UV radiation, shocks, and cosmic-ray (energetic
its extended envelope and transitions to the protoplanetary ion) bombardment. However, during this journey only the
nebula phase. The white dwarf central star begins to be re- most refractory compounds survive, while most of the sim-
vealed, its strong UV radiation field dissipating and reveal- ple species are destroyed. Supernova remnants are a source
ing a carbon chemistry that is dominated by aliphatic carbon of galactic cosmic rays, and these play an important chemi-
materials (Chiar et al., 1998). The aliphatic bonds emit cal role throughout all phases of the ISM, including diffuse
through the 3.4-µm feature (e.g., Chiar et al., 1998; Goto clouds. Diffuse interstellar clouds are subject to dynamical
et al., 2003). The 6.9-µm band is also observed, which is phenomena such as supernovae-driven shocks and cloud-
characteristic of aliphatic-aromatic hybrid compounds con- cloud collisions. As the interstellar plasma is highly com-
taining methylene (–CH2) substructures (Hrivnak et al., pressible, sound waves and magnetohydrodynamic waves
2000). As the CSE is becoming rarefied and excited by the readily steepen into shock waves; the energy available from
wind and the UV photons of the hot white dwarf stellar these shocks opens up many pathways in a high-tempera-
core, UV photons destroy the aliphatic bonds (Menella et ture chemistry (Flower and Pineau des Forêts, 1998). The
al., 2001). Some of this aliphatic material formed in AGB dissipation of interstellar turbulence has also been consid-
CSE may survive the intense galactic UV field and inter- ered as potentially important fo driving chemical reactions
stellar shocks to be incorporated into the diffuse clouds, as that cannot take place at the low average kinetic temperature
evidenced by the strong similarities between the shapes and of the diffuse medium (Falgarone et al., 1995; Joulain et
substructures in the 3.4-µm features in the protoplanetary al., 1998).
nebula CRL 618 and in the line of sight to the galactic cen- Diffuse clouds have temperatures of around 70–100 K that
ter (Chiar et al., 1998, 2000). In the mere few thousand are the result of the thermal balance between heating and
years during which a planetary nebulae emerges, however, radiative cooling. Diffuse cloud gas is heated through photo-
the hydrocarbon dust becomes dehydrogenated and the ali- electron emission (section 1.2) from dust grains, PAHs (sec-
phatic bonds are transformed to aromatic bonds. The greatest tion 2.1), and C atoms. Cooling is predominately through
evolution of the PAH features occurs in the rapid post-AGB radiation from fine-structure transitions of C+ and O; these
protoplanetary nebula phase (cf. Mennella et al., 2003). are excited by collisions with H atoms and with the elec-
Ultraviolet light from AGB stars is insufficient to excite the trons produced from the photoionization of C atoms.
PAHs, and so the PAHs are not directly observable at their A diffuse cloud is characterized by a density of ~1–100
birth sites in the AGB CSE. H atoms cm–3, a gas temperature of ~100 K, and an active
In addition to soot (hydrocarbon grains containing aro- photochemistry that forms, destroys, and shapes interstellar
matic and aliphatic bonds), silicon carbide (SiC) forms in the matter. As they have optical depths less than unity, diffuse
C-rich AGB CSE. Silicon carbide grains have two primary clouds are almost unshielded from the UV radiation pro-
crystallographic forms: α-SiC and β-SiC. Only β-SiC is duced by massive O and B stars. These UV photons can
spectroscopically detected in C-rich AGB stars (Speck et al., easily penetrate almost the entire extent of a diffuse cloud
1999). Silicon carbide grains are only a minor component of and lead to a gas phase composition that is dominated by
the ISM, constituting less than 5% of the submicrometer dust photochemical reactions, and this, in turn, only permits the
 Wooden et al.: Composition and Evolution of Interstellar Clouds 43

formation of fairly simple molecules. Spectroscopy from the elements, over 70% are contained in the dust. The patterns
UV to radio wavelengths reveals a diversity of solid-state of elemental depletions for different diffuse cloud lines of
species and gas molecules that exist in the diffuse clouds. sight also show that the more depleted the element, the
Several diatomic molecules such as CO, CH, CN, CH+, and higher the condensation temperature of the dust species that
H2 have been identified in diffuse clouds (Lucas and Liszt, the element constitutes. There are two chemically distinct
2000). Simple polyatomic species such as hydrogen cyanide grain populations. Some investigators refer to these dust
(HCN), formylium (HCO+), H2CO, and cyclopropenylidene populations as “core” and “mantle” (Savage and Sembach,
(C3H2) are observed in diffuse clouds and in translucent 1996), or “more-refractory” and “less-refractory” dust com-
clouds (section 1.2) (Turner, 2000), which are interstellar ponents (Jones, 2000). Only the more-refractory dust grains
clouds of a slightly higher extinction and density than diffuse survive in the harsher environments of high-velocity clouds
clouds. In contrast, dense molecular clouds whose interiors in the galactic halo. These more-refractory grains are pri-
are shielded from the ISM UV radiation field are the sites marily composed of O, Mg, Fe, and Si with smaller amounts
where more complex molecules form (see Fig. 1; section 4). of Ni, Cr, and Mn. The deduced mineralogic composition of
the grains depends on the relative abundances of the ele-
3.2. Depletion of Heavy Elements into ments, which in turn depends on the abundances taken as
Dust Grains in Diffuse Clouds solar or cosmic. Currently, there are three different refer-
ences for cosmic abundance: (1) meteorites (Anders and
Dust grains form in the cool CSE of AGB stars, in novae, Grevesse, 1989; Grevesse and Noels, 1993), (2) B stars in
and in supernovae ejecta (e.g., Draine, 2003; Jones, 2001) the solar neighborhood (Snow and Witt, 1996, and refer-
(sections 2.2–2.4). Fragmentation and sputtering of dust ences therein), and (3) that deduced for the ISM (Snow and
grains in low- and high-velocity shocks in the HIM and Witt, 1996). Depending on the three different cosmic abun-
WIM release heavy elements into the gas phase and selec- dance references, Jones (2000) deduces the more-refractory
tively enhance the abundances of very small grains (e.g., dust component in the diffuse medium to be either (1) an
Zagury et al., 1998). In diffuse clouds, however, the heavy Fe-rich olivine-type silicate, (2) a mixed silicate and oxide,
elements (except N and S) primarily reside in dust grains as or (3) an Fe oxide. Savage and Sembach (1996) deduce the
deduced from the observed depletion of the heavy-element more-refractory dust component to be a combination of
abundances from the gas phase relative to cosmic abun- olivine-type silicate (Mgy,Fe1 – y)2SiO4, oxides (MgO, Fe2O3,
dances (for a review, see Savage and Sembach, 1996). Thus Fe3O4), and pure Fe grains. Both more- and less-refractory
dust destruction in the hot and warm components of the grains appear to exist in the diffuse clouds in the galactic
ISM is followed by reformation and aggregation in diffuse disk. By subtracting the abundances of the more-refractory
clouds (Jones, 2001), and the grains quickly become chemi- component from the total, the less-refractory grain compo-
cally and isotopically homogenized (Jones, 2000). Interstel- nent is deduced to consist of Mg-rich olivine-type grains
lar medium grain size distribution ranges from 0.001- to (Jones, 2000; Savage and Sembach, 1996).
0.05-µm grains (PAHs, HACs, amorphous carbons) up to Moreover, not all Si appears to be bound in silicates and
1-µm grains (amorphous silicate). To account for the larger oxides (Jones, 2000). This can be interpreted to mean that
grains in the ISM grain size distribution, grain growth and Mg and Fe exists in forms independent of Si (Sofia et al.,
aggregation is inferred to occur in diffuse clouds, molecular 1994; Savage and Sembach, 1996). On the other hand, a
clouds, and dense cores. Grains aggregated in diffuse clouds continuous evolution of the chemistry of the grains may
are likely to be highly porous and fractal in structure be- occur by the preferential erosion of Si with respect to Mg,
cause coagulation processes do not make highly compact and the further erosion of both Si and Mg with respect to
grains (Weidenschilling and Ruzmaikina, 1994). Evidence for Fe (Jones, 2000). The erosion of Mg with respect to Fe is
coagulation into fluffy aggregates in a translucent (AV ≈ 4) expected for sputtering (Jones et al., 1994, 1996; Jones,
filamentary cloud in the Taurus region is shown through 2000). The enhanced erosion of Si with respect to Mg may
analysis of multiwavelength emission data (Stepnik et al., occur with low-energy (~4 KeV) cosmic-ray bombardment
2001). Grains may coagulate into larger grains at the bound- (Carrez et al., 2002) in diffuse clouds (section 3.3).
aries of diffuse and molecular clouds (Miville-Deschênes For a given level of depletion in different diffuse clouds,
et al., 2002) and within dense molecular clouds (Bianchi et the elemental variations are small. Perhaps the relative ele-
al., 2003). mental abundances are established early in the life of the
Dust grain compositions are measured through the deple- dust grain and are not significantly altered. The maintenance
tion studies of diffuse clouds, and grain mineralogical types of grain composition over the lifetime of a grain is surpris-
are then deduced from the relative ratios of the depleted ing because theoretical models predict that shocks of only
elements. Depletion measurements indicate four groups of ~100 km s–1 are required to release enough material from
dust-forming elements in the following order, where each grains to explain the abundances derived for the halo clouds
group represents about a factor of 10 drop in abundance (Sembach and Savage, 1996), and this in turn suggests sig-
(Jones, 2000): (1) C and O; (2) Mg, Si, and Fe; (3) Na, Al, nificant reprocessing. Dust grain recondensation following
Ca, and Ni; and (4) K, Ti, Cr, Mn, and Co. Oxygen is not the passage of supernova shocks (Jones et al., 1994, 1996)
measured along the lines of sight of the halo clouds, but and formation of grains in molecular clouds (Dominik and
it is assumed that O resides in the dust. Of the rare earth Tielens, 1997) are suggested mechanisms to account for the
44 Comets II

long lifetime of interstellar dust grains. If significant frac- (2004)], and is insufficient to account for the fraction of crys-
tions of ISM dust are destroyed and reaccreted, it is diffi- talline silicates deduced for comets (Hanner and Bradley,
cult to see how pure silicates, uncontaminated by C, could 2004; Ehrenfreund et al., 2004). Therefore silicate crystals
form (Jones, 2000). In diffuse clouds, grains may form in are efficiently amorphized in the ISM. Laboratory experi-
non-thermal-equilibrium conditions because temperatures ments demonstrate the bombardment of crystalline silicates
and pressures are low compared to AGB CSEs. In higher- by energetic ions amorphizes the silicates, which simulates
density regions, accretion onto preexisting grains is faster cosmic-ray impacts in ISM shocks (Demyk et al., 2001).
than in lower-density regions, and grain mantles can form When cosmic rays impact grains, significant processing
under conditions far from thermodynamic equilibrium. occurs. Most cosmic rays are H+ and He+ ions. Recent labo-
Grain formation may occur through kinetic processes (e.g., ratory measurements show that the following changes occur
Gail and Sedlmayr, 1999). Low-temperature grain-formation to Fe-bearing olivine crystals when bombarded by 4-KeV
processes also have been suggested (Sembach and Savage, He+ ions (Carrez et al., 2002): (1) The crystalline structure
1996), but the details of these processes are as yet unknown. changes to a disordered, amorphous structure; (2) the poros-
Only the most refractory materials, i.e., minerals that ity is increased; (3) Fe is reduced from its original stoichio-
have high condensation and vaporization temperatures, ap- metric inclusion in the mineral lattice to embedded nano-
pear to have survived intact through the hot and warm com- phase Fe; and (4) Si is ejected, changing the chemistry from
ponents of the ISM to the CNM. These presolar grains are olivine to pyroxene. When higher-energy He+ ions of 50 KeV
identified by their anomalous isotopic ratios and are found are used, similar changes occur to the structure of the min-
in meteorites and in IDPs (Hanner and Bradley, 2004; Sykes eral as occurred with the 4-KeV He+ ions, but the chemistry
et al., 2004). Dust grains that have isotopically anomalous [i.e., (4) in the above list] is unaltered (Jäger et al., 2003).
presolar signatures of their birth sites include diamonds Through depletion studies of diffuse clouds we know that
(Lewis et al., 1987) and TiC grains (Nittler et al., 1996) that less Si (more Mg and Fe) in the grains exists than is con-
condensed in the ejecta of SNe II, SiC grains that primarily sistent with silicate mineral stoichiometry. Cosmic-ray bom-
formed in AGB CSE (Lewis et al., 1994), graphite grains that bardment of silicate grains by ~4-KeV He+ ions is a feasible
formed in the CSEs of massive stars (Hoppe et al., 1992), explanation for the observed preferential ejection of Si from
oxide grains that formed in the O-rich CSE of red giant stars the grains (section 3.2). Cosmic-ray bombardment of Fe-
and AGB stars (Nittler et al., 1997), and silicates from AGB bearing silicate minerals also serves to reduce the Fe from its
stars (Messenger, 2000; Messenger et al., 2003). Presolar incorporation in the mineral lattice to nanophase Fe grains
silicate grains currently are not found in meteorites, and are embedded within a Mg-rich silicate (Carrez et al., 2002).
<1% by mass of IDPs. Out of more than 1000 subgrains This reduction mechanism explains the presence of nano-
measured in 9 IDPs, 6 subgrains have extreme isotopic 17O/ phase Fe in GEMS in IDPs (section 3.2) (Bradley, 1994;
16O and 18O/16O ratios: Three are of unknown origin, two Brownlee et al., 2000). Thus cosmic-ray bombardment of
are amorphous silicates [glass with embedded metal and silicates in diffuse clouds may be a viable process for ex-
sulfides, or GEMS (Bradley, 1994; Hanner and Bradley, plaining the lack of crystalline silicates in the ISM, the ob-
2004)], and one is a Mg-rich crystalline olivine (forsterite) served properties of the more- and less-refractory grains in
(Messenger et al., 2003). The dust grains mentioned above diffuse clouds (section 3.2), and the amorphous silicate
that are known to be presolar by their isotopic signatures component of cometary IDPs (Hanner and Bradley, 2004;
do not represent the typical grains in the ISM that are com- Ehrenfreund et al., 2004; Wooden, 2002).
posed primarily of silicates, metal oxides (from depletion The cosmic-ray energies that are utilized in the laboratory
studies), amorphous C, and aromatic hydrocarbons. At this to change the properties of silicates only penetrate the diffuse
time, the only link that exists between presolar grains and clouds. It is the higher-energy cosmic rays (1–100 MeV, sec-
the silicates deduced from diffuse clouds depletion studies tion 1.3) that penetrate the dense molecular clouds and ion-
are the GEMS (Bradley, 1994). Recall that of the nine IDPs ize the gas, contributing to the coupling between the gas and
measured by Messenger et al. (2003), 99% of the mass falls the magnetic field and to ion-molecule chemistry (Gold-
in an error ellipse centered on solar composition, albeit the smith and Langer, 1978). Thus it is the lower energy (1–
measurement errors on these submicrometer samples are 100 keV) cosmic rays that penetrate diffuse clouds that can
still large, and this supports the suggestion by Jones (2000) amorphize silicates, and therefore change the composition
that grain materials are rapidly homogenized through de- of the silicates in a manner necessary to explain the deple-
struction-formation processes in the ISM. tion studies of the diffuse clouds (Jones, 2000).

3.3. Cosmic-Ray (Ion) Bombardment of 3.4. Carbonaceous Dust and Macromolecules

Silicate Dust in Diffuse Clouds in the Diffuse Clouds

Oxygen-rich AGB stars produce a fraction of their sili- By observing the “extinction” of starlight toward stars
cate dust in crystalline forms (~4–40%) (sections 2.2–2.3). we can trace the nature of interstellar dust particles. The
In the ISM the fraction of crystalline silicates is very low, so-called interstellar extinction curve samples the spectro-
however [<5%; Li and Draine (2002); <0.5%, Kemper et al. scopic absorption and emission features of interstellar dust
 Wooden et al.: Composition and Evolution of Interstellar Clouds 45

from the UV to IR wavelengths. Two of the most relevant The AIBs are ubiquitous in the diffuse ISM in locations
signatures of interstellar dust are observed at 217.5 nm where UV photons can excite them. Polycyclic aromatic
[called the “ultraviolet extinction bump” (e.g., Fitzpatrick hydrocarbon emission arises from photodissociation regions
and Massa, 1990)] and 3.4 µm (Pendleton et al., 1994). The (PDRs) where UV light ionizes and excites the gas and dust
217.5-nm feature is well modeled by UV-irradiated nano- (e.g., the Great Nebula in Orion) and in reflection nebulae
sized amorphous carbon (AC) or hydrogenated amorphous (e.g., NGC 2023), and where massive stars are illuminat-
carbon (HAC) (Mennella et al., 1998) or by a bimodal dis- ing the edges of molecular clouds, as shown in Fig. 2. The
tribution of hydrocarbon particles with a range of hydro- AIB bands also are found in external galaxies. Only PAHs
genation and a dehydrogenated macromolecule coronene (a in the gas phase provide the necessary properties for inter-
compact PAH C24H12) (Duley and Seahra, 1999). Other ma- nal energy conversion after absorbing a photon, in order to
terials such as carbon black of different composition, fuller- emit at this wavelength range. Though little is known about
enes, and PAHs do not show a good match with the UV the exact PAH species present in those environments, their
extinction bump (Cataldo, 2002). Due to constraints on the abundance and size distribution can be estimated (Boulan-
abundance of elemental C in the ISM (Sofia et al., 1997; ger et al., 1998). Laboratory experiments and theoretical
Gnacinski, 2000), C atoms in sp2 bonds and C atoms in C–H calculations of PAHs have revealed important details about
bonds in the same hydrocarbon grains may be responsible for their charge state and structural properties (Allamandola et al.,
the 217.5-nm and 3.4-µm features respectively. The 3.4-µm 1999; Van Kerckhoven et al., 2000; Bakes et al., 2001a,b).
stretching band and the 6.85- and 7.25-µm bending modes A long-standing spectroscopic mystery in the diffuse
[e.g., toward the galactic center (Chiar et al., 2000)] are at- medium is the diffuse interstellar bands (DIBs). More than
tributed to the C–H bonds in hydrocarbon grains that occur 300 DIBs, narrow and broad bands, and many of them of
in –CH2 (methylene) and –CH3 (methyl) aliphatic groups. weak intensity, can be observed toward hot stars through-
Carriers of the interstellar 3.4-µm absorption feature exist out the diffuse interstellar medium. Substructures detected
in material ejected from some C-rich evolved stars, i.e., the in some of the narrow, strong DIBs strongly suggest a gas-
protoplanetary nebula CRL 618 (Chiar et al., 1998). The phase origin of the carrier molecules. Consequently, good
intense galactic UV field (Mennella et al., 2001) and cosmic candidates are abundant and stable C-bearing macromole-
rays (Mennella et al., 2003), however, rapidly destroy ali- cules that reside ubiquitously in the diffuse cloud gas (Ehren-
phatic bonds. The aliphatic bonds in hydrocarbon grains are freund and Charnley, 2000). Polycyclic aromatic hydrocar-
probably formed primarily in diffuse clouds (section 3.5). bons are therefore among the most promising carrier candi-
Carbonaceous dust in the diffuse medium appears to be dates (Salama et al., 1996). The same unidentified absorp-
highly aromatic in nature, consisting of aromatic hydrocar- tion bands are also observed in extragalactic targets (Ehren-
bon moieties bonded by weak van der Waals forces and ali- freund et al., 2002).
phatic hydrocarbon bridges (cf. Pendleton and Allamandola, The harsh conditions in the diffuse component of the
2002). Among the most abundant C-based species in diffuse ISM, e.g., a UV radiation field of 108 photons cm–2 s–1, de-
clouds are PAHs (see Puget and Léger, 1989). Polycyclic termines the chemistry in such a way that large stable spe-
aromatic hydrocarbons contain 1–10% of the total C in the cies may either stay intact, change their charge state, become
Milky Way, and are the next most abundant molecules after dehydrogenated, or get partially destroyed. Small unstable
H2 and CO. They play a vital role in the heating and cooling species are rapidly destroyed. Small amounts of cosmic C
of the WNM, diffuse clouds, and surfaces of molecular clouds probably are incorporated into species such as carbon chains,
(Salama et al., 1996; Wolfire et al., 1995, 2003). Ultraviolet diamonds, and fullerenes (Ehrenfreund and Charnley, 2000).
photons more energetic than 13.6 eV ionize H and produce The presence of such small species in the diffuse clouds,
energetic electrons that, in turn, heat and ionize the gas in including short carbon chains, thus indicates an efficient for-
photodissociation regions. Ultraviolet photons less energetic mation mechanism. Grain fragmentation by shocks and sub-
than 13.6 eV would pass practically unattenuated through sequent release of subunits into the gas phase can also pro-
space if it were not for the PAHs. When PAHs absorb UV vide a source of relatively large and stable gas-phase spe-
photons, both energetic electrons are ejected that collision- cies (e.g., Papoular, 2003). Among those, fullerenes have
ally heat the gas (Bakes and Tielens, 1994), and energy re- not been unambiguously identified. Recently it has been
tained by the molecules is transferred to vibration modes that shown that UV radiation and γ-radiation cause the oligo-
then radiate through strong thermal-IR emission bands. These merization or polymerization of fullerenes in the solid state.
aromatic infrared bands (AIBs) result from C–H stretching Continuous ion irradiation causes the complete degradation
and bending modes and C–C ring-stretching modes (Tielens of the fullerene molecules into carbonaceous matter that
et al., 1999) and have characteristic wavelengths (see Fig. 2): resembles diamond-like carbon (Cataldo et al., 2002). This
3.3 µm, 11.3 µm, and 12.5 µm for the C–H bonds on the raises doubts as to whether fullerenes can ever be observed
periphery of the PAH, and 6.2 µm, 7.7 µm, and 8.6 µm for as an interstellar dust component. In contrast, PAHs have
the PAH skeletal C–C bonds. The relative band strengths large UV cross-sections and can survive in harsh UV en-
depend on the size of the PAH macromolecule and on its vironments. Due to their high photostability, PAHs are
negatively charged, neutral, or positively charged ionization among the only free-flying gas-phase molecules that can
state (Bakes et al., 2001a,b). survive passage through the harsh UV environment of the
46 Comets II

WIM and WNM components of the ISM to the diffuse tion for the observed presence of the 3.4-µm feature in the
clouds. diffuse medium and its absence from the dense medium
(Mennella et al., 2003). Between the two destruction mecha-
3.5. Ultraviolet and Cosmic-Ray Processing of nisms, UV photons dominate over cosmic rays in diffuse
Hydrocarbon Dust in the Diffuse Clouds clouds while cosmic rays dominate over UV photons in
dense molecular clouds. In molecular clouds, the same cos-
The 3.4-µm absorption bands are seen along many lines mic rays (1–100 MeV) that ionize the gas also break C–H
of sight through the diffuse medium (Pendleton et al., 1994; bonds. C–H bonds are destroyed and not readily formed:
Rawlings et al., 2003). The 3.4-µm feature was well meas- C–H bond formation is stifled by the absence of H atoms
ured in emission in the protoplanetary nebulae CRL 618 in the gas (hydrogen is in H2 molecules) and by ice mantles
(Chiar et al., 1998) and shown to match the 3.4-µm absorp- on grains that inhibit C–H bond formation. The C–H bond
tion feature toward the galactic center, suggesting that at destruction rates in molecular clouds are estimated from the
least some of the hydrocarbons in diffuse clouds originate cosmic-ray ionization rates deduced from molecular cloud
as stardust (Chiar et al., 1998, 2000). Some AGB hydro- chemical models (section 4).
carbon dust grains are likely to survive ISM shocks and the
transition to diffuse clouds (Jones et al., 1996; Papoular, 3.6. Gas-Phase Chemical Reactions
2003), where, if they maintain or regain their degree of in the Diffuse Clouds
hydrogenation, they will contribute to the 3.4-µm aliphatic
feature. Grain destruction is so efficient in the ISM (sec- Here the key reaction processes occurring in interstellar
tion 1.6), however, that most AGB carbonaceous grains chemistry are summarized in the context of diffuse clouds
probably readily lose the memory of their birth sites and a (e.g., van Dishoeck and Black, 1988). Many of the basic
new equilibrium for the formation of aliphatic hydrocarbon chemical processes that operate in diffuse clouds also op-
bonds is set up in diffuse clouds (Mennella et al., 2002). erate, to a greater or lesser extent, in other regions of the
A long history of laboratory studies exists on the forma- ISM and in protostellar environments. Additional processes
tion of organic residues from the UV photolysis of ices de- are described below where appropriate. Diffuse cloud chem-
posited at low temperatures. These organic residues have istry predominantly forms simple molecules as a direct con-
aliphatic bonds and so the carriers of the 3.4-µm feature in sequence of the high UV flux, as shown in Fig. 1. In diffuse
the diffuse clouds were thought to be the products of ener- clouds most of the nitrogen is present as N0 and N+; in dense
getic processing of icy grain mantles within dense molecular molecular clouds nitrogen is mostly in the form of N2. Re-
clouds (e.g., Greenberg et al., 1995). Several lines of evi- cent observations indicate the presence of several polyatomic
dence show that the carriers of the 3.4-µm feature are more species in diffuse clouds, the origin of which is uncertain at
consistent with plasma-processed pure hydrocarbons than present (Lucas and Liszt, 2000).
with energetically processed organic residues: (1) The 3.4-µm Molecular hydrogen plays a key role in the gas-phase
feature toward the galactic center is unpolarized (Adamson chemistry but cannot be produced from it since the low den-
et al., 1999), while the 9.7-µm silicate feature is polarized, so sities and temperatures of the diffuse clouds mean that three-
the 3.4-µm feature is not a mantle on silicate cores; (2) the body reaction pathways to H2 are excluded. Such reactions
3.4-µm feature is not observed in dense clouds, requiring can form H2 in dense, high-energy environments such as
that at least 55% of the C–H bonds seen in diffuse clouds the early universe or in the winds of novae and supernovae
be absent from dense molecular clouds (Muñoz Caro et al., (Rawlings et al., 1993). Instead, in diffuse clouds interstellar
2001), the presumed sites of their formation; and (3) by com- H2 is produced when H atoms collide, stick, migrate, and
parison with laboratory analogs, carriers of the 3.4-µm fea- react on the surfaces of dust grains (Hollenbach and Sal-
ture have little O and N, which is uncharacteristic of organic peter, 1971). This catalytic process releases about 4.6 eV of
residues. energy, so the H2 formed is ejected into the gas and also
The carrier of 3.4-µm aliphatic bonds in diffuse clouds contributes to heating the gas. Experimental studies of H2
plausibly is a consequence of the equilibrium between de- formation on surfaces analogous to those believed to be
struction of C–H bonds via UV photons and cosmic rays present in the diffuse clouds indicate that H+ recombina-
and the rapid formation of C–H bonds by the collisions with tion appears to be slower (Pirronello et al., 1997, 1999) than
abundant atomic H atoms. The C–H bond destruction rates predicted by theory (Hollenbach and Salpeter, 1971). This
for diffuse clouds environments are deduced from experi- may raise difficulties for producing H2 in diffuse clouds.
ments of UV irradiation and 30-KeV He+ ion bombardment Nevertheless, the H/H2 ratio that is obtained in diffuse clouds
of hydrocarbon grains. Competition between the formation is a balance between H2 formation on dust and UV photo-
and destruction results in saturation of C–H bonds in ~104 yr, destruction; the latter is controlled nonlinearly by H2 self-
i.e., short times compared to the lifetime of material in dif- shielding. Although NH formation by grain-surface chem-
fuse clouds (Mennella et al., 2002, 2003). istry has been suggested (Crawford and Williams, 1997),
Assessment of formation and destruction rates of C–H the role of surface catalysis for other interstellar molecules
bonds in different CNM environments provides an explana- is highly uncertain at present.
 Wooden et al.: Composition and Evolution of Interstellar Clouds 47

The forms in which the major heavy elements are present lar cations are lost primarily through mutual neutralization
are based largely on their ionization potentials and the en- with PAH anions (Lepp and Dalgarno, 1988).
ergy spectrum of the interstellar UV field. Atoms with ion- Radiative association can initiate a limited hydrocarbon
ization potentials less than 13.6 eV are readily photoionized, chemistry starting from
i.e.,
C+ + H2 → CH+2 + ν
C+ν→ C+ +e
and leading to CH and C2. Neutral-neutral exchange reac-
Thus, whereas C, S, and various refractory metals (e.g., tions can also be important for producing simple molecules
Fe, Mg, Na) are almost completely ionized, there are in-
sufficient photons energetic enough to ionize O and N. Cos- C + OH → CO + H
mic-ray particles can ionize H and H2, and He atoms, to H+,
H+2, and He+. The H+2 ions can subsequently react rapidly N + CH → CN + H
with H2 molecules to produce H+3 and this ion readily trans-
fers a proton to other atomic and molecular species with The in situ production of complex molecules within dif-
greater proton affinities than H2. The electrons produced in fuse clouds is inhibited by the efficient photodestruction of
these ionizations are lost through radiative recombination diatomic and triatomic molecules, e.g.,
reactions such as
OH + ν → O + H
C+ + e → C + ν
Of course, other chemical reactions have to occur, and
or in dissociative recombination reactions such as we now discuss these in the context of the so-called “CH+
problem” (Williams, 1992; Gredel, 1999). Chemical models
H+3 + e → H2 + H, or 3H of the diffuse interstellar medium can reproduce the ob-
served column densities of many species (van Dishoeck and
The charge transfer process Black, 1988). However, to date no model has been able to
reproduce the observed abundance of CH+ while obeying
H+ + O → O+ + H all the other observational constraints. The obvious forma-
tion reaction is highly endoergic by 4640 K
followed by
C+ + H2 → CH+ + H (1)
O+ + H2 → OH+ +H
and will not proceed at normal diffuse clouds temperatures.
initiates a sequence of exchange reactions with H2 that ends When diffuse interstellar gas is heated and compressed by
with the dissociative recombination of H3O+ producing OH shock waves, many chemical reactions that are endothermic,
and H2O. Ion-molecule reactions also partially contribute to or possess activation energy barriers, can occur in the post-
CO production in diffuse clouds through shock gas (e.g., Mitchell and Deveau, 1983). For example,
the reaction above (equation (1)) and
C+ + OH → CO+ + H
O + H2 → OH + H
CO+ + H2 → HCO+ + H
C + H2 → CH + H
HCO+ + e → CO + H
However, hydrodynamic shocks have not been shown to be
The precise value of the appropriate rate coefficient for able to resolve the CH+ issue without violating the con-
H+3 recombination is at present controversial (McCall et al., straints on, e.g., the observed OH abundance and the rota-
2002). Exothermic ion-molecule processes typically pro- tional populations of H2 (e.g., Williams, 1992).
ceed at the Langevin (collisional) rate. It should be noted, As interstellar clouds are magnetized and only partially
however, that a large population of PAH molecules can ionized, slow shock waves can exhibit more complex struc-
qualitatively alter the chemistry of interstellar clouds. In tures than simple shock discontinuities (e.g., Roberge and
diffuse clouds, where a substantial abundance of PAHs is Draine, 1990). The fact that some magnetohydrodynamic
required to heat the gas through the photoelectric effect waves can travel faster than the sound speed in these plas-
(e.g., Bakes and Tielens, 1994, 1998), positive atomic ions mas means that there is a substantial difference in the veloc-
are destroyed more efficiently by PAHs than by electrons ities of the ions and neutrals. This effect gives rise to C-
(Lepp et al., 1988; Liszt, 2003). If a substantial PAH popu- shocks in which all variables are continuous across the shock
lation exists in molecular clouds, then atomic and molecu- structure (see Draine, 1980). C-shocks also have been pro-
48 Comets II

TABLE 2. Ice composition* toward interstellar sources†.

W33A High-Mass NGC7538 IRS9 Elias 29 Elias 16

Molecule Protostar High-Mass Protostar Low-Mass Protostar Field Star
H2O 100 100 100 100
CO 9 16 5.6 25
CO2 14 20 22 15
CH4 2 2 <1.6 —
CH3OH 22 5 <4 <3.4
H2CO 1.7–7‡ 5 — —
OCS 0.3 0.05 <0.08 —
NH3 15 13 <9.2 <6
C2H6 — <0.4 — —
HCOOH 0.4–2‡ 3 — —
OCN– 3 1 <0.24 <0.4
HCN <3 — — —
*Abundances by number relative to water ice.
† Adapted from Ehrenfreund and Charnley (2000).
‡ Abundances with large uncertainties are shown as a range of values.

posed to produce CH+ (Pineau des Forêts et al., 1986; Draine duce H+3 , He+, and electrons that heat the gas. This results in
and Katz, 1986) but with mixed success when compared a rich gas phase chemistry (van Dishoeck et al., 1993). Dust
to observation (Gredel et al., 1993; Flower and Pineau des grains shield the inner regions of the cloud from external
Forêts, 1998; Gredel et al., 2002). UV radiation and most of the photons capable of dissociat-
Finally, while dissipation of interstellar turbulence oc- ing H2 (and other molecules) are absorbed at cloud surfaces.
curs in shocks, it also occurs intermittently in small regions Hence, grain catalysis can convert almost all the available
of high-velocity shear (Falgarone et al., 1995), and the asso- H to H2 (section 3.6). As most of the gas phase C is present
ciated heating has been suggested as important for driving as CO, these clouds cool principally by molecular rotational
the reaction shown in equation (1) (Joulain et al., 1998). emission from CO molecules excited by collisions with H2
In both cases, the high heating efficiency occurs because the and He. The gas and dust temperatures are tightly restricted
energy available from dissipation of turbulence is degraded to lie in a range around 10 K (Goldsmith and Langer, 1978).
to thermal energy within a small volume. At present, the CH+ At lower densities, the gas and dust are not thermally well
problem remains unsolved, but it is clear that solving the coupled and depletion of coolant species may increase the
origin of CH+ will significantly impact the study of the phys- gas temperature (Goldsmith, 2001). Although external UV
ics and chemistry of diffuse clouds. photons do not significantly penetrate these clouds, there
probably exists a weak UV flux throughout molecular cloud
4. PHYSIOCHEMICAL PROCESSES IN interiors. This flux derives from excitation of H2 by ener-
COLD DENSE MOLECULAR CLOUDS getic electrons produced in primary cosmic-ray impacts. The

4.1. Overview

In this section we describe the gaseous and solid-state

composition of dark, dense molecular clouds, the regions
where high- and low-mass stars form. Considering an evo-
lutionary chemical sequence originating from AGB enve-
lopes and the diffuse ISM, molecular clouds are the point
where interstellar chemistry starts to have direct relevance
for cometary composition (e.g., Langer et al., 2000). Spe-
cifically, molecular ice mantles (see Table 2) can form on
siliceous and carbonaceous dust grains, and processing of
these ices opens up many more chemical pathways (see
Fig. 3).
Molecular clouds possess higher densities of gas and
dust than diffuse clouds, their presumed precursors. Cos- Fig. 3. Physiochemical processes experienced by ice and gas in
mic rays penetrate into the deepest cloud interiors and pro- dense clouds (Ehrenfreund and Charnley, 2000).
 Wooden et al.: Composition and Evolution of Interstellar Clouds 49

subsequent UV emission spectrum can photodissociate and fore regions where molecules exhibiting substantial frac-
photoionize interstellar molecules (Prasad and Tarafdar, tionation of isotopes of H, C, and N can form. Deuterium can
1983), and can significantly influence the abundances of become enhanced in H+3 since the reverse of the reaction
some species (e.g., atomic C) (Gredel et al., 1987).
H+3 + HD → H2D+ + H2
4.2. Gas-Phase Chemistry
is very slow at 10 K. Similar reactions also occur for some
Most of the chemical reactions described for diffuse hydrocarbon ions such as CH+3 and CH+5 . The H2D+ ions
clouds (section 3.6) also play a role in molecular cloud formed can initiate the distribution of D atoms throughout
chemistry. Cosmic-ray ionizations drive a chemistry where the molecular chemistry (e.g., Millar et al., 1989, 2000).
ion-molecule and neutral-neutral reactions convert an ap- Isotopic exchange involving 13C+ and 12CO leads to enhance-
preciable fraction of the heavy elements to molecular forms. ments of 13C in CO (Langer et al., 1984) and a general de-
Thus, one finds that most C exists as CO, although a signi- crease of 13C/12C in other molecules. Chemical fractionation
ficant fraction of atomic C is present (C/CO ≈ 0.1). The of 15N also occurs in ion-neutral reactions (Terzieva and
dominant form of O is not well determined in these sources Herbst, 2000) but the highest 15N/14N ratios theoretically
but is understood to be atomic, from chemical models and possible in interstellar molecules may require special con-
the observed lack of O2 (Goldsmith et al., 2000, 2002). ditions apart from very low temperatures [such as CO de-
Based on observed N2H+ abundances, almost all the avail- pleted but N2 not depleted in the gas phase (Charnley and
able nitrogen is in N2. Sulfur constitutes a puzzle, as its ele- Rodgers, 2002)]. The extreme sensitivity of these fractiona-
mental depletion with respect to the diffuse ISM, and its tion reactions to the gas temperature is further strong evi-
major form, are unknown (e.g., Charnley et al., 2001a; dence of the importance of cold cloud chemistry for under-
Scappini et al., 2003). Many S-bearing molecules are de- standing the origin of the enhanced isotopic fractionation
tected and this suggests that atomic S is probably the major found in primitive solar system material such as comets and
repository of this element. Molecules containing refractory meteorites.
metals (e.g., Fe, Mg, Na) are not present and metals are un-
derstood to be completely depleted on/in dust grains. 4.3. Gas-Grain Interactions
Proton transfer reactions produce many molecular ions
and observations of these (HCO+, DCO+) can be used to esti- Siliceous and carbonaceous micrometer- and submicro-
mate the electron density or the abundances of undetect- meter-sized dust particles that are produced in the outflows
able molecules (e.g., N2H+ to trace N2). It appears that many of late-type AGB stars provide a catalytic surface for a vari-
neutral-neutral reactions have significant rate coefficients ety of reactions to occur when they are dispersed through-
at low temperatures (Chastaing et al., 2001). Reactions in- out molecular clouds. Atoms and molecules strike and stick
volving various hydrocarbons (e.g., C2H2 acetylene) with to the surfaces of these cold dust grains and this process
C atoms and with the CN radical are particularly important leads to the formation of an amorphous, mixed, molecular
in producing many of the long carbon-chain compounds ice mantle covering the siliceous/carbonaceous grains. Table 2
(Cherchneff and Glassgold, 1993), e.g., cyanoacetylene shows the observed composition of interstellar ices. The form-
ing ice mantles consist of molecules directly accreted from
CN + C2H2 → HC3N + H the gas (e.g., CO) and molecules formed through chemical
reactions at about 10 K. These ices are susceptible to various
These reactions can generate many of the higher cyano- kinds of energetic processing: cosmic-ray impacts, heating
polyenes [i.e., HC5N, HC7N (Dickens et al., 2001), HC9N, near protostars, and perhaps UV photolysis.
and HC11N], as well as various hydrocarbon chains (e.g., At typical molecular cloud densities, particles are ac-
C4H, C6H, C8H), that are detected in molecular clouds, such creted from the gas at the rate of about one per day. The
as TMC-1 in Taurus (Pratap et al., 1997; Markwick et al., sticking coefficients for most of these species at 10 K are
2000) (Fig. 1). Several important species are known in star- calculated to be close to unity (e.g., Leitch-Devlin and Wil-
forming clouds but are not shown in Fig. 1 (e.g., atomic O liams, 1985). On the surface, heavy particles such as CO
and CO2). Some species, undoubtedly present in molecu- are relatively immobile. Atoms can diffuse and react with the
lar clouds, are difficult or impossible to detect directly in immobile species, as well as among themselves. Hydrogen
sources like TMC-1 (e.g., S, O, N2, CO2 and C2H2). It is atoms can rapidly explore the surface by quantum-mechani-
worth noting that significant compositional differences are cal tunnelling. Experiments show that, once a monolayer has
found among molecular clouds. For example, L134N does formed, quantum diffusion by H atoms is very rapid (Manico
not contain large abundances of carbon-chain molecules et al., 2001). An H atom can therefore scan the entire sur-
(Pagani et al., 2003; Dickens et al., 2000) and may be more face to find any available co-reactants. Heavy atoms (e.g.,
typical than TMC-1 (Dickens et al., 2001). C and O) can diffuse by thermal hopping (e.g., Tielens and
The extremely cold temperatures in these dense clouds Allamandola, 1987). Slowly, the accreted atoms react chemi-
mean that molecular zero-point energies can be an important cally, are converted to various molecules, and as a result,
factor in the gas-phase kinetics. Molecular clouds are there- ice mantles are formed.
50 Comets II

Unabated accretion, i.e., in the absence of an efficient heavy atoms have been incorporated into molecular ices.
means of returning molecules to the gas, would completely Short cloud lifetimes (section 1.4), and the inference that
remove the heavy element component from the molecular molecular clouds are indeed chemically young, could also
gas on an accretion timescale of 3 × 109 nH–1 yr, i.e., about provide a natural explanation for other astrochemical prob-
105 yr at a density of nH ≈ 104 cm–3 (e.g., Brown and Charn- lems, such as the high C 0/O2 ratio that is observed to be wide-
ley, 1990). Hence, if molecular clouds are dynamically much spread in galactic clouds (Goldsmith et al., 2000). However,
older than this, there must be some desorption from the the existence of small-scale (~0.01 pc) molecular differentia-
grain surfaces to prevent this “accretion catastrophe.” How- tion in dense clouds still presents a major challenge for chem-
ever, the precise nature of the putative desorption mecha- ical models (Dickens et al., 2001; Takakuwa et al., 2000).
nism (or mechanisms) is not yet unambiguously identified. Observations of dense cores within molecular clouds show
Several candidate mechanisms have been proposed, includ- strong evidence for substantial depletions (Bergin et al.,
ing evaporation following grain heating by cosmic rays, 2002); this suggests whatever desorption mechanism oper-
mantle explosions, and ejection upon molecule formation ates at lower densities is overwhelmed in dense cold cores.
(see Willacy and Millar, 1998). As molecular clouds are also
regions of star formation, dynamical events also have been 4.4. Observations of Astronomical Ices
proposed for removing and reforming the molecular ices
within the accretion timescale; these include sputtering in The protostars that form in molecular clouds are natural
low-velocity shock waves (Bergin et al., 1998; Charnley IR background sources, which can be utilized to perform
et al., 2001a) and grain-grain collisions induced by clump solid-state spectroscopy on the column of gas along the line-
collisions or wave motions (Markwick et al., 2000; Dickens of-sight. Groundbased observations performed since the
et al., 2001). 1970s demonstrated the presence of abundant water ice as
The “accretion catastrophe” is most evident in a dynamical well as CO ice (e.g., Whittet, 1993) (see Fig. 2a). The absorp-
scenario where molecular clouds are long-lived (~107 yr), tion features of water ice and silicates observed at 3 µm and
and where low-mass star formation is controlled quasistati- 10 µm, respectively, dominate the spectrum toward stars in
cally by ambipolar diffusion, the relative drift between ions dense molecular clouds. Those bands are broad and often satu-
and neutrals in partially ionized plasma. Ambipolar diffusion rated and are the reason why the inventory of ices will never
leads to interstellar cloud material losing magnetic support be complete. Many species, in particular NH3 and CH3OH
against gravity on characteristic timescales of ~5 × 10 6 yr as well as species with a C=O group, are either blended or
that are determined by the electron density. The electron masked by those dominant spectral bands. This strongly
density is set by the ionization rate that is, in turn, deter- biases abundance determinations.
mined from the chemistry of molecular cloud material (e.g., Other species remained undetected until sophisticated IR
Shu et al., 1987, 1993). An enormous effort has been made satellites provided the full range of spectral data from 1 to
over the past two decades to reconcile observed molecular 200 µm. The ISO provided us with very exciting spectra that
abundances and the results of chemical models with such allowed us to compile an inventory of interstellar ice spe-
long cloud lifetimes, i.e., to reconcile the apparent “chemi- cies and measure their abundances in various interstellar en-
cal youth” of objects many millions of years old. However, vironments [for reviews on ISO data, see Ehrenfreund and
when viewed in the context of the more recent dynamical Schutte (2000) and Gibb et al. (2000)]. ISO identified two
scenario (section 1.4) where molecular cloud formation and distinct ice layer compositions: hydrogen-rich ices (“polar”
star formation are controlled by supernovae-driven super- H2O-dominated with traces of CO, CO2, CH4, NH3, CH3OH,
sonic turbulence (e.g., Mac Low and Klessen, 2003; Larson, HCOOH, and H2CO) and the more volatile “apolar” CO-
2003), and the shorter cloud lifetimes (~1–3 × 106 yr) in- dominated ices (with small admixtures of O2 and N2). The
ferred from observations (Elmegreen, 2000; Hartmann et build up of apolar ice layers occurs at successively lower
al., 2001), the accretion catastrophe problem may be resolv- temperatures than polar ice layers on grain mantles. Abun-
able. In this picture, most interstellar cloud materials are dances and inventories of ice species toward low- and high-
in a low-density, primarily atomic phase as diffuse clouds mass protostars can be found in Table 2.
and hence can have accretion timescales longer than the mo- The solid CO band at 4.67 µm can be well studied by
lecular cloud lifetimes. The long lifetimes of diffuse cloud groundbased observations. Laboratory studies reveal that
material will not greatly affect the molecular composition of the CO band profile is strongly influenced by neighboring
molecular clouds. species in the ice and acts therefore as a good tracer of the
Dense prestellar cores evolve roughly on free-fall time- overall grain-mantle composition (Ehrenfreund et al., 1996).
scales and have shorter lifetimes than the molecular clouds Recent high-resolution measurements of CO using 8-m class
in which they lie. The fact that substantial selective deple- telescopes reveal a multicomponent structure. Boogert et al.
tions (e.g., CO relative to N2) are observed in these regions (2002a) observed the M-band spectrum of the class I proto-
(Bergin et al., 2002) indicates that a viable surface desorp- star L1489 IRS in the Taurus molecular cloud. The CO band
tion mechanism is still needed. However, this mechanism profile showed a third component apart from CO in “po-
eventually should be overwhelmed in the most dense, cold- lar” ices (CO mixed with H2O) and CO in “apolar” ices (see
est regions. It is very likely that the central regions of pre- above). The high-spectral-resolution observations show that
stellar cores pass through a phase where all the available the apolar component has two distinct components, likely
 Wooden et al.: Composition and Evolution of Interstellar Clouds 51

due to pure CO and CO mixed with CO2, O2, and/or N2. such as CO (and 13CO), NH3, and CH3OH (Thi et al., 2002;
Pontoppidan et al. (2003a) conclude from recent ground- Boogert et al., 2002b; Dartois et al., 2002; Pontoppidan
based observations of more than 40 targets that the CO band et al., 2003a,b; Taban et al., 2003). The CH3OH abundance
profile can be fitted with a three-component model that in- relative to water ice measured in star-forming regions lies
cludes pure CO, CO embedded in water ice, and a third between 0% and 30%. Two high-mass protostars have been
component that is attributed to the longitudinal component identified with very large CH3OH abundances, namely up
of the vibrational transition in pure crystalline CO ice (ap- to 25% relative to water ice (Dartois et al., 1999). New VLT
pearing when the background source is linearly polarized). data of the 3.52-µm band (C-H stretching mode of CH3OH)
This three-component model applied in varying ratios pro- also show abundances up to 20% toward low-mass stars in
vides an excellent fit to all bands observed, and indicates a the Serpens cloud (Pontopiddan et al., 2003b).
rather simple universal chemistry in star-forming regions
with 60–90 % of the CO in a nearly pure form (Pontoppidan 4.5. Solid-State Chemical Reactions on Dust
et al., 2003a). The freezeout of CO in a circumstellar disk
around the edge-on class I object CRBR 2422.8-3423 has Astrochemical theories suggest that only a few classes of
been recently observed with the ISAAC instrument on the reactions appear to be necessary to form most of the mole-
Very Large Telescope (VLT) by Thi et al. (2002) with the cules observed in ices (Herbst, 2000). Several exothermic
highest abundance observed so far. H atom additions to C, O, N, and S produce methane (CH4),
In high-spectral-resolution spectra, Boogert et al. (2002a) water, ammonia (NH3), and hydrogen sulphide (H2S). Atom
detected toward the massive protostar NGC 7538 IRS 9 a additions to closed-shell molecules such as CO possess
narrow absorption feature at 4.779 µm (2092.3 cm–1) attrib- substantial activation-energy barriers. However, due to their
uted to the vibrational stretching mode of the 13CO isotope small mass, H and D atoms could saturate these molecules
in pure CO icy grain mantles. This is the first detection of by tunnelling through this barrier (Tielens and Hagen, 1982;
13 CO in icy grain mantles in the ISM. A ratio of 12 CO/ Tielens, 1983). Hydrogenation of CO has been suggested
13CO = 71 ± 15 (3σ) was deduced, in good agreement with to be the source of the large abundances of solid methanol
gas-phase CO studies (12CO/13CO ≈ 77) and the solid 12CO2/ (CH3OH) seen in many lines of sight toward protostars (e.g.,
13CO ratio of 80 ± 11 found in the same line of sight (Boo- Tielens and Charnley, 1997; Charnley et al., 1997; Caselli et
2
gert et al., 2002b). The ratio is confirmed by the ratio ob- al., 2002), and the enormous D/H ratios observed in both for-
served in the low-mass star IRS 51, namely a 12CO2/13CO2 maldehyde (H2CO) and methanol in protostellar cores where
ratio of 68 ± 10 (Pontoppidan et al., 2003a). CO ices have been sublimated to the gas phase (Loinard
The abundance of NH3 in interstellar grain mantles has et al., 2000; Parise et al., 2002). Additionally, CO2 could
been a hotly debated subject for a long time (e.g., Gibb et form by O atom addition to CO at 10 K (Tielens and Hagen,
al., 2001). The reported abundances for NH3 relative to H2O 1982). Based on these mechanisms many large organic mol-
range from 5–15%. The most recent VLT data confirm ecules may form on grains (e.g., Charnley, 1997b).
abundances on the lower end of this scale. Dartois et al. Thermal processing close to the protostar leads to mo-
(2002) report ~7% for the NH3/H2O ratio toward the evolved lecular diffusion, structural changes within the ice matrix,
massive protostars GL 989 and GL 2136, derived from a and subsequently to sublimation. Ice segregation, and pos-
band at 3.47 µm attributed to ammonia hydrate. Taban et al. sibly even clathrate formation, has been observed in dense
(2003) observe the 2.21-µm band of solid NH3 and provide clouds (Ehrenfreund et al., 1998). Simple thermal process-
only an upper limit toward W33A; their limit is ~5% for the ing of ice mixtures can itself produce new molecules. In
NH3/H2O ratio. the laboratory, it has been shown that the heating of ice mix-
The lines of sight toward star-forming regions consist tures containing formaldehyde [H2CO, also called metha-
of regions with strongly varying conditions. Temperatures nal) and ammonia (NH3) results in polymerization of the
are low in molecular cloud clumps but can be very high in formaldehyde into polyoxymethylene (POM, (-CH2-O-)n]
hot core regions close to the star, where ices are completely (Schutte et al., 1993). Extensive and detailed laboratory
sublimated. The spectra that sample the different regions studies have been undertaken to study the chemistry of in-
in the line of sight toward star forming regions need to be terstellar ice analogs (Cottin et al., 1999). For many years
deconvolved using additional information about the gas these studies were restricted to either UV photolysis (e.g.,
phase composition and geometry of the region. For ex- Allamandola et al., 1997) or proton irradiation (e.g., Moore
ample, Fig. 2a shows spectra of material in the line of sight and Hudson, 1998) of bulk ices; in both cases the effects of
to a massive protostar that intercepts both cold cloud ices warming the ices are usually considered (“thermal chemis-
and UV-illuminated PAHs. In the past few years, ground- try,” Fig. 3). The strongly attenuated UV flux in such dense
based telescopes of the 8–10-m class have allowed us to ob- environments strongly limits photolysis processes. In con-
serve some ice species with unprecedented spectral resolu- trast, cosmic rays can penetrate dense molecular clouds and
tion. The spectral resolution also enables us to study lines of effect the structure and composition of the ices, including
sight toward low-mass protostars, which usually were too sputtering of icy grain mantles (Cottin et al., 2001).
faint to be observed with the ISO satellite. VLT and KECK II, Atom addition reactions on grain surfaces are necessary
equipped with the ISAAC and NIRSPEC spectrographs, re- to initially form water ice mantles, as gas phase ion-molecule
spectively, have delivered exciting new data on ice species reactions cannot produce large quantities of water. How-
52 Comets II

ever, it is only recently that atom reactions on analog sur- One interstellar molecule that certainly originates in
faces have come to be studied in detail (e.g., Hiraoka et al., energetically processed ices is the carrier of the so-called
1998; Pironello et al., 1999; Watanabe and Kouchi, 2002). “XCN” 4.62-µm absorption feature, observed in the diffuse
From the existing laboratory data it is possible to make com- clouds (Pendleton et al., 1999), toward protostars (e.g., Teg-
parisons of the relative efficiency of each chemical proc- ler et al., 1995), and, most recently, in the nearby dusty star-
ess (photolysis, radiolysis, and atom additions) in producing burst AGN galaxy NGC 4945 (Spoon et al., 2003). Labora-
the major observed mantle molecules from CO. Both radi- tory experiments indicate that “XCN” is produced both by
olysis (i.e., proton irradiation) and photolysis easily produce photolysis (Lacy et al., 1984; Bernstein et al., 2000) and by
CO2. Recent experiments show that, although oxidation of radiolysis (Hudson and Moore, 2000; Palumbo et al., 2000).
CO by O atoms has a small activation energy barrier, this At present, the best candidate for the identity of this carrier
reaction can form CO2 (Roser et al., 2001). However, in these appears to be the OCN– ion, formed in a solid-state acid-
experiments CO2 is only produced efficiently when the react- base reaction between NH3 and isocyanic acid (HNCO) (see
ing CO and O atoms are covered by a layer of H2O mole- Novozamsky et al., 2001, and references therein).
cules and warmed. This appears to increase the migration
rates in the ice and suggests that the longer migration times 4.6. Theoretical Modeling of Solid-State Reactions
available on grain surfaces in dense clouds, times much
longer than can reasonably be studied in the laboratory, may There have been many attempts to model low-tempera-
make this reaction the source of the observed CO2. Also, ture grain-surface chemical reactions (e.g., Allen and Robin-
cold H additions in ices containing acetylene (C2H2) have son, 1977; Tielens and Charnley, 1997; Herbst, 2000).
been proposed as the origin of the ethane (C2H6) found in Heterogeneous catalytic chemistry on grain surfaces occurs
comets (Mumma et al., 1996) and experiments support this primarily through the Langmuir-Hinshelwood mechanism.
idea (Hiraoka et al., 2000). As yet, ethane is not detected in Here reactive species arrive from the gas, stick to the sur-
the ISM but these experiments suggest it has an interstellar face, and then migrate until they encounter another species
origin (see Ehrenfreund et al., 2004). with which they can react (section 4.3); the product mol-
Ultraviolet photolysis of ice mantles produces radicals ecule may either remain on the surface or be desorbed. In
that may migrate and react (see Fig. 3). However, experi- deterministic theoretical models it is relatively straightfor-
ments show that UV processing of H2O/CH4 mixtures is ward to quantitatively treat the accretion and desorption of
very inefficient at producing methanol (CH3OH) (d’Hende- surface species (e.g., Charnley, 1997c). However, to cor-
court et al., 1986). In fact, experiments show that metha- rectly model surface diffusion and reaction, a fully stochas-
nol is readily decomposed to formaldehyde under photolysis tic treatment involving solution of the associated master
(Allamandola et al., 1988). By contrast, radiolysis of dirty equation for the surface populations is necessary (Charnley,
ice mixtures can produce methanol in astronomically inter- 1998). A number of recent papers have modeled surface
esting amounts (Hudson and Moore, 1999). Initial reports chemistry in this way, although the adopted methods of so-
that cold H atom additions to CO could produce methanol lution have differed considerably (Charnley, 2001; Biham
at low temperatures were positive (Hiraoka et al., 1994, et al., 2001; Green et al., 2001; Stantcheva et al., 2002;
1998) but were not supported by more recent experiments Caselli et al., 2002). However, in marked contrast to the
by the same group (Hiraoka et al., 2002). However, recent amount of effort expended in trying to model surface reac-
laboratory experiments (Watanabe and Kouchi, 2002; tions, there has been almost no theoretical modeling of the
Watanabe et al., 2003) strongly argue for CH3OH produc- kinetics associated with the photolysis or radiolysis of the
tion via this mechanism. bulk ice mantle (however, see Ruffle and Herbst, 2001;
Experiments involving H+ irradiation (radiolysis) are de- Woon, 2002).
signed to simulate cosmic-ray bombardment (see Fig. 3).
Radiolysis proceeds by ionization of H2O to H2O+, from 5. PHYSIOCHEMICAL PROCESSES IN
which a proton then transfers to water to form protonated DENSE STAR-FORMING CORES
water, H3O+. Subsequent dissociative electron recombina-
tion of protonated water produces a population of energetic, 5.1. Overview
reactive H atoms and hydroxyl (OH) molecules in the ice
(Moore and Hudson, 1998). Experiments show that radioly- Understanding the physics and chemistry of low-mass
sis of H2O/CO ice mixtures can produce high abundances star formation is most relevant for solar system studies.
of H2CO and CH3OH (Hudson and Moore, 1999), although Modeling well-studied sources at various evolutionary
formic acid (HCOOH, also called methanoic acid) is over- stages enables us to understand how much processing in-
produced relative to the HCOOH/CH3OH ratio observed in terstellar material experienced as it became incorporated
interstellar ices. Radiolysis of ice mixtures containing CO into the nascent protosolar nebula (van Dishoeck and Blake,
and C2H2 also produces ethane, as well as several other 1998; Ehrenfreund and Charnley, 2000).
putative mantle molecules such as CH3CHO and C2H5OH Star formation occurs rapidly in molecular clouds, prob-
(Hudson and Moore, 1997; Moore and Hudson, 1998). ably within a million years (section 1.4). The mass scale and
 Wooden et al.: Composition and Evolution of Interstellar Clouds 53

the occurrence of isolated stars, binaries, stellar clusters, and in much colder conditions (section 4). Similar chemical proc-
associations are determined by the local and global com- esses also can be expected to play a key role in low-mass
petition between self-gravity and the turbulent velocity field star-formation environments, and so here a brief overview
in interstellar clouds. Massive stars may form from a single of chemistry in massive star formation is given.
isolated core (Stahler et al., 2000), or may grow in stellar The basic chemistry of massive star formation can be
clusters through coalescence of two or more low-mass and best described by distinguishing between processes that
intermediate-mass stars (Clark et al., 2000; Bonnell and occur in a cold prestellar phase and those that occur in a
Bate, 2002). Formation of single and binary low-mass stars hot phase after a protostar has formed (Brown et al., 1988).
can proceed from collapse and fragmentation of less-mas- The cold phase includes the quasistatic chemical evolution
sive regions of lower density (Mac Low and Klessen, 2003). in molecular clouds (section 4) and eventually an isother-
The chemistry of its surroundings is dramatically influ- mal gravitational collapse to a small, cold (10 K), dense
enced by the protostar. A central aspect in understanding core. Rapid protostellar heating of the core to hot core tem-
the chemical evolution prior to and following star forma- peratures (100–300 K) induces thermal evaporation (subli-
tion appears to be the prestellar accretion of molecules onto mation) of icy grain mantles and hot core chemistry.
grains and their subsequent removal, which occurs in a hot During the isothermal collapse, gas-grain collision times
(or warm) dense core of the molecular cloud surrounding the become so short that most of the heavy atoms and mole-
accreting protostar. Due to the higher intrinsic line fluxes, cules in the center of the cloud core are in the solid state
and stronger IR emission, most previous studies of proto- (section 4). There is recent observational evidence for the
stellar gas and solid-phase compositions have focused on disappearance of CO and N2 molecules in the central region
high-mass star-forming hot cores, such as Orion A and Sag- of dense cores (e.g., Bergin et al., 2002; Bacmann et al.,
ittarius B2 (Johansson et al., 1984; Cummins et al., 1986; 2002; Caselli et al., 2003). Subsequent protostellar heating
Blake et al., 1987; Turner, 1991; Smith et al., 1989). How- returns the volatile ices to the gas phase. Radioastronomy
ever, it is now becoming clear that low-mass protostars also permits the ice composition to be studied in more detail when
pass through a warm core phase (e.g., Schoier et al., 2002; in the gas phase than is possible by direct IR absorption
Cazaux et al., 2003). In this section we present an overview studies of the solid phase using field stars behind molecular
of the chemistry, and associated molecular morphology that clouds, or toward embedded protostars (e.g., Charnley et al.,
develops around an accreting protostar. 2001b). For example, the recently discovered gas-phase or-
ganics, including vinyl alcohol (Turner and Apponi, 2001),
5.2. Hot Cores Around Massive Protostars glycolaldehyde (Hollis et al., 2000), and ethylene glycol
(Hollis et al., 2002), are inferred to be present in the solid-
Hot molecular cores are most commonly identified with phase on grains only in trace amounts.
the earliest phases of massive star formation (Churchwell, In the collapse phase, the warming and subsequent re-
2002). Hot cores contain a young protostar embedded within lease of the grain material can be used to constrain the na-
its dense cocoon of gas and dust and the most sophisticated ture of grain-surface reactions. Identifying the origin of
chemical models have been developed to account for the specific molecules (and classes of molecules) can provide
observations of these massive hot cores (Doty et al., 2002; important information on the composition of the prestellar
Rodgers and Charnley, 2003). The elevated temperatures core and on the nature of grain-surface chemistry. There
and densities in these small regions (<0.1 pc, see Table 1) are three ways in which the molecules observed in hot cores
produce a chemical composition markedly distinct from can originate: First, molecules produced in the cold prestel-
other regions of the ISM as shown in Fig. 1. Note that in lar phase (e.g., CO) that accreted on grains and formed ices
Fig. 1 the abundances listed for IRAS 16293 are for the can simply be returned to a hot environment. Second, other
warm inner component as determined by Schoier et al. atoms and radicals can stick to grains and take part in grain-
(2002) except for CO, HCO+, CN, HCN, C2H, C3H2, and surface reactions to form mixed molecular ices (section 4).
CS. The C2H5CN entry and the remarkably high abun- However, not all the complex molecules observed in hot
dances of HCOOCH3, CH3OCH3, and HCOOH are taken cores are products of grain-surface chemistry. It transpires
from Cazaux et al. (2003). Many large organic molecules that a highly transient chemistry can also occur in the gas
are also detected in hot molecular cores but have been during the hot core phase, and therefore the third forma-
omitted from Fig. 1; these include ethanol, glycolaldehyde, tion pathway for hot core molecules is in situ molecule for-
ethylene glycol, acetone, acetic acid, and glycine (Ohishi mation (Charnley et al., 1992; Caselli et al., 1993). For
et al., 1995; Hollis et al., 2000, 2002; Snyder et al., 2002; example, alkyl cation transfer reactions involving surface-
Remijan et al., 2003; Kuan et al., 2003). It is now under- formed alcohols can produce many larger organic mol-
stood that hot core chemistry is mainly the result of the ecules, such as ethers (e.g., Charnley et al., 1995; Charnley,
volatile contents of the ice mantles being deposited into the 1997b). Hot core chemistry is more accurately described
gas via desorption. Evidence for this are the high abundances than that of warm cores because the initial conditions (i.e.,
of saturated molecules (water, ammonia, methane) and en- the grain mantle composition) are constrained better, and
hanced D/H ratios, both of which could only have been set because the evolution lasts less than ~105 yr or so.
54 Comets II

Between individual cores, a strong chemical differentia-

tion is observed between O-bearing and N-bearing mole-
cules. This chemical differentiation is modeled and attrib-
uted to differences in temperature and evolutionary state of
the core: Hotter cores tend to have higher abundances of
N-bearing molecules (Rodgers and Charnley, 2001). Mod-
els of the hot-phase chemistry have been constructed for
the chemistries of second-row elements (P, Si, S), which
are particularly sensitive to the temperature in the hot gas
(Charnley and Millar, 1994; Mackay, 1995; Charnley,
1997a). Observations of S-bearing molecules may be par-
ticularly useful as molecular clocks for star-formation time-
scales (Hatchell et al., 1998; Buckle and Fuller, 2003; Wake-
lam et al., 2003). Ice mantles also can be sputtered in shock
waves, and postshock chemistry could play a role in either
initiating, or contributing to, hot core chemical evolution
(Charnley and Kaufman, 2000; Viti et al., 2001). ISO SWS
observations of solid and gaseous CO2 toward many proto-
stars indicate that shock processing may be common (Boon-
man et al., 2003). Finally, hot cores surrounding massive
protostars eventually evolve into ultracompact HII regions
(Churchwell, 2002) and photodissociation regions where the Fig. 4. Chemistry around a low-mass protostar. In the environ-
strong UV field and X-rays rapidly destroy molecules (Tie- ment of a low-mass protostar, physical processes determine the
lens and Hollenbach, 1985; Maloney et al., 1996). chemistry of distinct regions in the protostellar core. Distinct
physical regions are characterized by different molecular tracers
5.3. Warm Cores Around Low-Mass Protostars and include Region I — cold cloud, HCO+ and N2H+; Region II —
infall, N2H+; Region III — sphere of thermal influence, (CH3)2O;
At the heart of a low-mass star-forming core lie the pro- Region IV — bipolar outflow (CO); Region V — wind-cloud bow
tostar and its surrounding disk, from which comets, aster- shock, H2S, SO, SO2, SiO, CH3OH, D2CO; and Region VI —
oids, and planets eventually form. Observations show that accretion shock at the disk surface, CS. Details of the chemical
processes active in each region are discussed in the text (section 5).
many of the chemical characteristics seen in hot cores —
Artwork by J. Woebcke.
small-scale differentiation, shock tracers, high D/H ratios,
and the presence of putative mantle organic molecules —
are also present toward low-mass sources (Fig. 1) (van
Dishoeck et al., 1993; McMullin et al., 1994; Langer et al., with the Atacama Large Millimetre Array (ALMA) (Woot-
2000; Loinard et al., 2001; Schoier et al., 2002; Cazaux ten, 2001). Below we discuss the physiochemical proper-
et al., 2003). Many of the chemical processes described ties of each of the six regions identified in Fig. 4 around a
above (section 5.2) should come into play in determining low-mass protostar.
the overall chemical morphology and evolutionary state of Region I: Cold cloud. The chemistry in this region is
these regions. Hence, elucidating the major physiochemical essentially that which is outlined for cold, dense molecu-
processes that occur around massive protostars may allow lar clouds (section 4). Molecular tracers of the cold cloud
us to determine the likely chemical structure of the low- include HCO+ and N2H+.
mass protostellar core in which the Sun formed. Figure 4 Region II: Infall. The initial density structure and the
shows schematically the main physical regions in the envi- precise details of the subsequent collapse are the subject of
ronment of a low-mass accreting protostar (see Mumma et current debate (Larson, 2003; Mac Low and Klessen, 2003).
al., 1993; Lunine et al., 2000). Several regions exist where It is clear, however, that when gravity dominates over sup-
the local physical conditions will drive a specific chemical port by thermal, turbulent, and magnetic pressures, a dy-
evolution. Interstellar materials from the ~0.1-pc dense core, namic core collapse will occur and cold material from the
and in particular from the innermost core heated by the infalling envelope will become incorporated into the pro-
protostar, may become incorporated into the protoplanetary tostar and its accretion disk. These infall motions can be
disk after passing through the accretion shock at the bound- detected spectroscopically from molecular line observations
ary between the disk and the infalling core. However, the (Evans, 1999; Myers et al., 2000). Chemical models utilizing
innermost core regions including accretion shock, which are various collapse scenarios (Shu, 1977; Larson, 1969; Pens-
most important for understanding the processing/connec- ton, 1969) have been constructed (Rawlings et al., 1992;
tion of interstellar and cometary materials, have not yet been Aikawa et al., 2001, 2003; Rodgers and Charnley, 2003).
observed directly in great detail; this will become possible A common molecular tracer of infall is N2H+.
 Wooden et al.: Composition and Evolution of Interstellar Clouds 55

Region III: The “sphere of thermal influence.” As ma- such as L1157, are observed to exhibit a particularly rich
terial approaches the protostellar disk, the accretion lumi- chemical composition — a mixture of sputtered solid ma-
nosity of the disk heats the infalling dust and gas. The dust terial and the products of high-temperature reactions in the
and gas temperatures at any radii are controlled by the mass postshock gas (Bachiller et al., 2001). Molecular tracers of
accretion physics (Adams and Shu, 1985; Ceccarelli et al., the wind-cloud bow shock include H2S, SO, SO2, CH3OH,
1996) and this should therefore be reflected in the chemical D2CO, and, as mentioned above, SiO.
evolution of the core. The chemistry is strongly radially de- Region VI: Disk accretion shock. Gravitational col-
pendent in the protostellar cocoon since the molecular de- lapse of a rotating core will generally lead to the formation
sorption rate depends exponentially on the local dust tem- of an accretion disk (Cassen and Moosman, 1981; Terebey
perature, as well as on the abundances and binding energies et al., 1984; Boss, 2004). Infalling material is decelerated
of molecules present in the grain mantles (see Ehrenfreund in an accretion shock at the disk surface where interstellar
et al., 1998; Rodgers and Charnley, 2003). As interstellar chemistry effectively ends. Shock chemistry and other pro-
gas and dust falls down toward the protostar, initially only cesses associated with disk accretion begin to dominate the
the most volatile molecules are efficiently desorbed (CO, chemistry of the material first entering the nebula (Lunine
N2, O2, CH4) and the chemistry is similar to that of molecu- et al., 1991; Chick and Cassen, 1997). Neufeld and Hollen-
lar clouds (Brown and Charnley, 1991). Eventually, those bach (1994) have modeled the disk accretion shock as a
remaining molecules with binding energies less than water dissociative “J-shock” and determined the regions of the
and ammonia (e.g., CH3OH, H2CO, C2H2) are desorbed. In disk where various interstellar materials (refractory metals,
the inner regions, all the volatile mantle molecules have been refractory and volatile organics, and ice) would be vapor-
removed and water, methanol, and ammonia are present in ized. The smallest accretion shock speeds and preshock
the gas at high abundances (see van der Tak et al., 2000). In densities favor the survival of the most volatile materials;
these innermost regions the chemical evolution should most this occurs in the outermost region of the disk. Apart from
strongly resemble that of massive hot cores (section 5.2). a few CS observations (Blake et al., 1992; Walker et al.,
A molecular tracer of the sphere of thermal influence is 1994; Velusamy et al., 2002), thus far there have been no
(CH3)2O. detailed observational studies of this critical region, and so
Region IV: Bipolar outflow. Accretion of infalling in- the chemical composition of the (interstellar) material in this
terstellar material onto the protostellar disk appears to be phase is relatively uncharacterized.
intimately connected with the presence of atomic jets and
bipolar molecular (i.e., CO) outflows (Konigl and Pudritz, 6. SUMMARY
2000). Low-velocity bipolar flows (less than about 25 km s–1)
are believed to be molecular gas entrained from the ambient The ISM is turbulent and interstellar cloud structures are
cloud by the higher velocity jets (typically 150–400 km s–1). very filamentary and fragmentary. Stars that form in rela-
The jets themselves are probably driven through magneto- tively quiescent cold dense molecular cloud cores then inject
hydrodynamic processes in the accretion disk (e.g., Konigl energy into the ISM at the ends of their lives via explosions
and Pudritz, 2000; Shu et al., 2000). Although hydrogen or winds. Supernovae-driven shocks accelerate cosmic rays
in the jets is primarily atomic, some molecule formation can and generate turbulence. Gas is rapidly processed from very
proceed within jets (Glassgold et al., 1991) and this, for high temperatures (106 K) and rarefied densities (≤1 cm–3)
example, could be the origin of some of the high-velocity to low temperatures (≤102 K) and moderately high densities
CO in the outflows. Alternatively, as ambient cloud mate- (nH > 10–102 cm–3) as turbulence concentrates matter into
rial is entrained, atomic material from the jet can turbulently shocks and small intermittent regions of high-velocity shear
mix with surrounding molecular gas and an active chemis- where viscous dissipation and heating and cooling processes
try can occur along the jet edge (Taylor and Raga, 1995). occur. Turbulent compression of H I in the WNM, driven
Region V: Wind-cloud bow shock. Bipolar outflows by supernova shocks, colliding H I streams, spiral density
drive strong shock waves into the surrounding natal cloud waves, or gravity, leads to the rapid formation of cold H I
material. The associated high temperatures and compres- diffuse clouds. Turbulence may also speed up the formation
sion permit many endothermic chemical reactions to occur. of H2 on grain surfaces in intermittent shock-induced den-
Nonthermal sputtering of icy grain mantles by neutral atoms sity enhancements (nH >> 103 cm–3), enabling the formation
of He and H and H2 removes icy grain mantles and erodes of molecular clouds on short timescales (~106 yr). Most of
refractory grain cores (Draine et al., 1983; Flower and the galaxy’s molecular gas is in giant molecular clouds that
Pineau des Forêts, 1994). Silicon-bearing molecules are fill only 1–2% of the volume of the ISM. Rapidly, stars form
observed to be highly depleted in cold molecular clouds out of molecular cloud cores that encompass only a small
(Herbst et al., 1989) so common chemical signposts of fraction of the volume of a molecular cloud. Massive stars
shock activity in star-forming regions are the greatly en- only live a few million years, so molecular cloud material
hanced abundances of gaseous SiO, produced by the sput- is dispersed in ~4 × 10 6 yr from the energy injected by the
tering of silicate grains (Schilke et al., 1997; Garay et al., winds and jets of young stars or by turbulence. Diffuse cloud
2002). The shocked outflow lobes of low-mass protostars, material is converted to molecular clouds and back to diffuse
56 Comets II

clouds on relatively short timescales. Physiochemical pro- of sight through molecular clouds to protostars: CO-rich
cesses in diffuse clouds and molecular clouds increase the ice mantles with O2 and N2 and H2O-rich ice mantles with
complexity of solid-state and molecular materials, a frac- traces of CO, CO2, methane (CH4), ammonia (NH3), metha-
tion of which survives the protostellar collapse to be incor- nol (CH3OH), formic acid or methanoic acid (HCOOH), and
porated into comets. formaldehyde or methanal (H2CO). A few classes of reac-
Stars enrich the ISM with nucleosynthesized elements: tions are needed to form most of the molecules observed
SNe II contribute O, SNe Ia contribute Fe, and AGB stars in ices. Reactions beginning with simple hydrocarbons such
contribute C and N. Supernovae also provide the energy for as acetylene (C2H2) form long C-chain molecules. Further-
the turbulence in the ISM. Most of the heavy elements are more, many large organic molecules can form on grain sur-
deposited into the ISM as dust grains. In particular, O-rich faces. Low kinetic temperatures favor the fractionation of
AGB circumstellar envelopes (CSE) produce silicates, ox- isotopes of H, C, and N. In order to maintain molecules in
ides, and alumino-silicates, and C-rich AGB CSEs produce the gas phase, desorption from grain surfaces must occur,
amorphous carbon, hydrocarbons with aromatic moieties possibly due to grain heating by cosmic rays, mantle ex-
(i.e., PAHs) and aliphatic bonds, and silicon carbide. How- plosions, sputtering in low-velocity shocks, or grain-grain
ever, dust grains are rapidly destroyed in the ISM by super- collisions.
novae shocks and recondense in postshock gas or form in Ice mantles consisting of molecules accreted from the
diffuse clouds by processes that as yet are unknown. Fur- gas are made more complex by energetic processing by
thermore, most aliphatic bonds in hydrocarbon dust from cosmic rays, heating in protostellar cores, and perhaps UV
AGB stars are destroyed by interstellar UV photons or by photolysis. Although UV photons cannot penetrate deep
UV photons from hot white dwarf stellar cores when AGB into molecular clouds, UV photons are created in molecular
stars become planetary nebulae over the course of a few clouds by H2 excited by energetic electrons produced by
thousand years. Aliphatic bonds probably are reformed in primary cosmic-ray interactions. In particular, the carrier of
diffuse clouds when H atoms impinge on carbonaceous dust the “XCN” band is produced by photolysis and/or radiolysis
grains. Cosmic-ray bombardment of silicate grains in diffuse (proton irradiation). The complex molecules formed on cold
clouds selectively removes primarily Si and secondarily Mg grain surfaces are revealed in hot and warm protostellar
from the grains, and efficiently converts silicate crystals to cores when these molecules are returned to the gas phase
amorphous silicates. Only a minor fraction of the most re- via desorption.
fractory stardust grains survive their passage through the In a collapsing molecular cloud core the protostar dra-
ISM to be incorporated as presolar grains in meteorites and matically influences the chemistry of its surroundings. Hot
cometary IDPs. cores and warm cores surround high-mass and low-mass
Galactic UV photons also destroy all small volatile mole- protostars respectively. Molecules are evaporated from icy
cules formed in the AGB CSE and thus simple molecules grain mantles, react on grain surfaces to form mixed molec-
must be reformed in diffuse clouds. The only molecules to ular ices, and participate in a highly transient chemistry in
survive the passage through the WIM and WNM to diffuse which molecules form through gas-gas reactions. A strong
clouds are PAHs. Photoelectric heating of the diffuse clouds chemical differentiation occurs between O-bearing and N-
and molecular cloud boundaries occurs when UV photons bearing molecules with temperature and time: Hotter cores
are absorbed by PAHs. tend to have high abundances of N-bearing molecules. The
Diffuse clouds are unshielded from UV and photochem- chemical processes occurring in hot cores are discussed, and
istry only permits the formation of fairly simple molecules. many of the same processes apply to warm cores. The chem-
Many major heavy elements that are not depleted into istries that delineate six different regions around a low-mass
grains are singly ionized: C+, S+, Fe+, Mg+, and Na+; only protostar are described and shown in Fig. 4. The molecular
O and N are neutral. This means that many neutral-neutral cloud core collapses (N2H+) and heats the surrounding ma-
chemical reactions that occur in dense clouds are not viable terial as traced by (CH3)2O. Bipolar CO outflows and jets
in diffuse clouds, as exemplified by the “CH+ problem.” shock the ambient cloud core material as traced by H2S,
Neutral H2 reacts with C+ to form CH and C2. Cosmic rays SO, SO2, CH3OH, SiO, and D2CO. Interstellar material
ionize H and H2 that can then subsequently react rapidly falling onto the protoplanetary disk passes through an accre-
to produce other ions and species such as OH. Ion-molecule tion shock traced by CS emission. The physical conditions
reactions also contribute to the formation of CO in diffuse of the accretion shock region in the outer disk will become
clouds. better constrained by future high-spatial-resolution, high-
Cosmic rays penetrate dense molecular clouds where UV sensitivity observations using ALMA.
photons do not, ionizing and heating the gas, promoting ion- Interstellar chemistry, i.e., physiochemical processes in
molecule chemistry, and affecting the composition of icy diffuse clouds and molecular clouds, sets the chemical
mantles on dust grains. Ion-molecule and neutral-neutral boundary conditions on the composition of the material that
reactions convert an appreciable fraction of the available was initially available for incorporation into the protosolar
heavy elements into molecules. This process begins with the nebula, and thereafter into cometary matter. Understanding
freezing out of atoms from the gas onto silicate and car- the degree of modification of these pristine interstellar
bonaceous grain surfaces. Ices are observed along the lines molecules and solids as they passed through the accretion
 Wooden et al.: Composition and Evolution of Interstellar Clouds 57

shock in the outer disk, to subsequently take part in nebular cores. Astron. Astrophys., 389, L6–L10.
chemistry, will permit detailed comparison of the compo- Bakes E. L. O. and Tielens A. G. G. M. (1994) The photoelectric
sition of comets with ISM material, and hence an apprecia- heating mechanism for very small graphitic grains and poly-
tion of the chemical diversity among comets (Ehrenfreund cyclic aromatic hydrocarbons. Astrophys. J., 427, 822–838.
Bakes E. L. O. and Tielens A. G. G. M. (1998) The effects of poly-
et al., 2004).
cyclic aromatic hydrocarbons on the chemistry of photodisso-
ciation regions. Astrophys. J., 499, 258–266.
Acknowledgments. The authors collectively thank P. Gold-
Bakes E. L. O., Tielens A. G. G. M., and Bauschlicher C. W. Jr.
smith, W. Irvine, and an anonymous reviewer for their time and
(2001a) Theoretical modeling of infrared emission from neutral
comments on this chapter. Discussions with B. Elmegreen (D.H.W.)
and charged polycyclic aromatic hydrocarbons. I. Astrophys.
and L. Allamandola (S.B.C.) are gratefully appreciated. Studies
J., 556, 501–514.
at NASA Ames (D.H.W.) of dust in comets and pre-main-sequence
Bakes E. L. O., Tielens A. G. G. M., and Bauschlicher C. W. Jr.
stars are supported by NASA’s Planetary Astronomy and Origins
(2001b) Theoretical modeling of infrared emission from neutral
of Solar Systems Programs. Studies of theoretical astrochemistry
and charged polycyclic aromatic hydrocarbons. II. Astrophys.
at NASA Ames (S.B.C.) is supported by NASA’s Planetary Atmos-
J., 560, 261–271.
pheres and Origins of Solar Systems Programs through funds allo-
Ballesteros-Paredes J., Hartmann L., and Vázquez-Semandeni E.
cated by NASA Ames under Interchange No. NCC2-1412 and by
(1999a) Turbulent flow-driven molecular cloud formation: A
the NASA Astrobiology Institute. Laboratory astrochemistry and
solution to the post-T Tauri problem? Astrophys. J., 527, 285–
astrobiology (P.E.) is supported by NWO (VI), SRON, and ESA.
297.
We are grateful to S. Rodgers for preparation of Fig. 1. We thank
Ballesteros-Paredes J., Vázquez-Semandeni E., and Scalo J. (1999b)
E. Peeters and J. Keane for the ISO reduced data and preparation
Clouds as turbulent density fluctuations: Implications for pres-
of Fig. 2.
sure confinement and spectral line data interpretation. Astro-
phys. J., 515, 286–303.
Bergin E. A., Neufeld D. A., and Melnick G. J. (1998) The post-
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 Boss: From Molecular Clouds to Circumstellar Disks 67

From Molecular Clouds to Circumstellar Disks

Alan P. Boss
Carnegie Institution of Washington

We now have examples of nearly all the phases of evolution of a dense molecular cloud
core into a young star, and at least a provisional theoretical understanding of the star formation
process. However, our understanding of the processes by which the material leftover from the star
formation process is converted into planets and comets is much less secure, both observationally
and theoretically. Major questions remain unanswered, such as the processes by which proto-
planetary disks transport mass and angular momentum, and the formation mechanism of the
solar system’s gas and ice giant planets. Indeed, the latter question raises the issue of whether the
solar system formed in a relatively benign region of low-mass star formation, similar to Taurus,
or in a more violent region, similar to Orion. Evidently much remains to be learned before we
can claim to understand the origin of the solar system.

1. INTRODUCTION improbable formation mechanisms could be plausibly ar-

gued to have operated in the solar nebula, so long as only
By their very nature as primitive bodies that have never one such planetary system was known to exist. The discov-
experienced prolonged metamorphism or strong heating, ery of the first extrasolar planets (Mayor and Queloz, 1995;
comets are believed to preserve much of the record of the Marcy and Butler, 1996) has forever changed that view-
formational processes that led to the origin of our solar sys- point. While the planetary census of the solar neighborhood
tem. Presolar grains contained in comets undoubtedly carry is still underway, in the next few years we will have a good
much of the history of galactic nucleosynthesis in their iso- idea about the prevalence of planetary systems with long-
topic abundances, while fragile molecular species in com- period Jupiter-mass planets, systems that might be close
ets speak of the cold, dark clouds that form new generations analogs to our own. We already know that in some cases, the
of stars, and of processes in the circumstellar disk from planetary formation process produces planets with masses
which the solar system originated about 4.6 G.y. ago. Much considerably larger than that of Jupiter, moving on highly
of the motivation for observational and cosmochemical eccentric orbits in the very region of the planetary system
studies of meteorities and comets stems from the desire to where we find the terrestrial planets and asteroids in the
use the results to constrain or otherwise illuminate the phys- solar system.
ical and chemical conditions in the solar nebula, the Sun’s This shocking fact is a sobering lesson that the outcome
circumstellar disk, in the hope of learning more about the of the planet formation and evolution process need not re-
processes that led to the formation of our planetary system. semble our system. Understanding the reasons for such
In addition to studies of comets, there are important les- wide variations in outcome remains a central issue in planet
sons to be learned about the planet formation process from formation theory (Weidenschilling, 2004). Until we can
astrophysical observations of young stellar objects and their claim to have a general understanding of planet formation
accompanying protoplanetary disks (Dutrey et al., 2004), processes, our understanding of the origin of any single sys-
from the discovery of other planetary systems, and from tem, including the solar system, must be considered provi-
theoretical models. A key resource for learning more about sional. Given that the Oort cloud comets are thought to have
these subjects is the compendium volume Protostars and formed in the same general region of the nebula as the giant
Planets IV (Mannings et al., 2000). The present chapter is planets, the specific question of the formation mechanism
adapted and modified from a recent review article about the of the solar system’s giant planets is of critical interest for
solar nebula, focusing on issues of interest to cosmochem- cometary science.
ists (Boss, 2004). Here we address topics of more interest
for comets. 1.2. Theoretical Progress in Understanding
Basic Physics of the Solar Nebula
1.1. Implications from the Discovery of
Extrasolar Planetary Systems Theoreticians specializing in planet formation have been
energized by the discovery of extrasolar planetary systems,
Prior to 1995, the solar system was the only known ex- often to the detriment of further understanding of the ori-
ample of a planetary system in orbit around a Sun-like star, gin of the solar system. Nevertheless, the rejuvenation of the
and the question of the uniqueness of the solar system was field engendered by these discoveries will have a major
more of a philosophical than a scientific matter. Somewhat effect there as well, as new theories designed for extrasolar

67
68 Comets II

systems are applied to our own. For example, the disk in- ted at infrared wavelengths in the process of exiting the pla-
stability mechanism for gas-giant-planet formation (Boss, cental cloud core. Such cores have already succeeded in
1997) may be equally applicable to extrasolar protoplane- forming stars. Initial conditions for the collapse of the pre-
tary disks or to the solar nebula. The importance of under- solar cloud can be more profitably ascertained from obser-
standing the basic physics of the solar nebula has led to vations of dense cloud cores that do not appear to contain
innovative new approaches to old problems, such as the X- embedded infrared objects; i.e., precollapse cloud cores.
wind mechanism for processing of solids (Shu et al., 1996), Precollapse cloud cores are composed of cold molecu-
and the rediscovery of the magneto-rotational instability as lar gas with temperatures in the range of about 7 K to 15 K,
a mechanism for disk evolution (Balbus and Hawley, 1991). and with gas densities of about 1000 to 100,000 molecules
Coupled with ever-increasing computational power, which per cubic centimeter. Some clouds may be denser yet, but
permits brute-force numerical solutions of otherwise intrac- this is hard to determine because of the limited density
table problems, theoretical models of the varied processes ranges for which suitable molecular tracers are abundant
in the solar nebula have made considerable progress, al- (typically isotopes of CO and H3N). Masses of these clouds
though the need for guidance from observations and labo- range from roughly 1 M to thousands of solar masses, with
ratory studies cannot be overestimated. the distribution of clump masses fitting a power law such
that most of the clumps are of low mass, as is also true of
2. MOLECULAR CLOUD COLLAPSE stars in general. In fact, one recent estimate of the mass
distribution of precollapse clouds in Taurus is so similar to
The protosun and solar nebula were formed by the self- the initial mass function of stars, that it appears that the
gravitational collapse of a dense molecular cloud core, much stellar mass distribution may be determined primarily by
as we see new stars being formed today in regions of ac- processes occurring prior to the formation of precollapse
tive star formation. The formation of the solar nebula was clouds (Onishi et al., 2002). The cloud properties described
largely an initial value problem: i.e., given detailed knowl- below are used to constrain the initial conditions for hydro-
edge of the particular dense molecular cloud core that was dynamical models of the collapse of cloud cores.
the presolar cloud, one could in principle calculate the flow Large radio telescopes have enabled high-spatial-reso-
of gas and dust subject to the known laws of physics and lution mapping of precollapse clouds and the determination
thus predict the basic outcome. Specific details of the out- of their interior density structure. While such clouds un-
come cannot be predicted, however, as there appears to be doubtedly vary in all three space dimensions, the observa-
an inevitable amount of stochastic, chaotic evolution in- tions are typically averaged in angle to yield an equivalent,
volved, e.g., in the orbital motions of any ensemble of gravi- spherically symmetric density profile. These radial density
tationally interacting particles. Nevertheless, we expect that profiles have shown that precollapse clouds typically have
at least the gross features of the solar nebula should be flat density profiles near their centers, as is to be expected for
predictable from theoretical models of cloud collapse, con- a cloud that has not yet collapsed to form a star (Bacmann
strained by astronomical observations of young stellar ob- et al., 2000), surrounded by an envelope with a steeply de-
jects. For this reason, the physical structure of likely pre- clining profile that could be fit with a power law. The den-
collapse clouds is of interest with regard to inferring the sity profile thus resembles that of a Gaussian distribution,
formation mechanism of the protosun and the structure of or more precisely, the profile of the Bonnor-Ebert sphere,
the accompanying solar nebula. which is the equilibrium configuration for an isothermal gas
cloud (Alves et al., 2001).
2.1. Observations of Precollapse Clouds While precollapse clouds often have a complicated ap-
pearance, attempts have been made to approximate their
Astronomical observations at long wavelengths (e.g., shapes with simple geometries. Triaxial spheroids seem to
millimeter) are able to probe deep within interstellar clouds be required in general, although most lower-mass clouds
of gas and dust that are opaque at short wavelengths (e.g., appear to be more nearly oblate than prolate (Jones et al.,
visible wavelengths). These clouds are composed primarily 2001). On the larger scale, prolate shapes seem to give a
of H2 gas, He, and molecules such as CO, hence the term better fit than oblate spheroids. Another study found that the
molecular clouds. About 1% by mass of these clouds is in observations could be fit with a distribution of prolate sphe-
the form of submicrometer-sized dust grains, with about roids with axis ratios of 0.54 (Curry, 2002), and argued that
another 1% composed of gaseous molecules and atoms of the prolate shapes derived from the filamentary nature of
elements heavier than He. Regions of active star formation the parent clouds. We shall see that the precollapse cloud’s
are located within molecular clouds and complexes ranging shape is an important factor for the outcome of the proto-
in mass from a few solar masses to >1,000,000 M . This stellar collapse phase.
association of young stars with molecular clouds is the most Precollapse clouds have significant interior velocity
obvious manifestation of the fact that stars form from these fields that appear to be a mixture of turbulence derived from
clouds. Many of the densest regions of these clouds were fast stellar winds and outflows, and magnetohydrodynamic
found to contain embedded infrared objects, i.e., newly waves associated with the ambient magnetic field. In addi-
formed stars whose light is scattered, absorbed, and reemit- tion, there may be evidence for a systematic shift in veloci-
 Boss: From Molecular Clouds to Circumstellar Disks 69

ties across one axis of the cloud, which can be interpreted ing molecular clouds that are swept up and compressed by
as solid-body rotation around that axis. When estimated in the expanding supernova shock front (Preibisch and Zin-
this manner, typical rotation rates are found to be below the necker, 1999). Even strong protostellar outflows are capable
level needed for cloud support by centrifugal force, yet large of triggering the collapse of neighboring dense cloud cores
enough to result in considerable rotational flattening once (Foster and Boss, 1996). A supernova shock-triggered ori-
cloud collapse begins. Ratios of rotational to gravitational gin for the presolar cloud has been advanced as a likely
energy in dense cloud cores range from 0.002 to 1, with a source of the short-lived radioisotopes (e.g., 26Al) that ex-
typical value being 0.02 (Goodman et al., 1993). The pres- isted in the early solar nebula (Cameron and Truran, 1977).
ence of a net angular momentum for the cloud is essential Detailed models of shock-triggered collapse have shown
for the eventual formation of a centrifugally supported cir- that injection of shock-front material containing the 26Al
cumstellar disk. into the collapsing protostellar cloud can occur, provided
that the shock speed is on the order of 25 km/s (Boss, 1995),
2.2. Onset of Collapse Phase as is appropriate for a moderately distant supernova or for
the wind from an evolved red giant star.
Dense cloud cores are supported against their own self-
gravity by a combination of turbulent motions, magnetic 2.3. Outcome of Collapse Phase
fields, thermal (gas) pressure, and centrifugal force, in
roughly decreasing order of importance. Turbulent motions Once a cloud begins to collapse as a result of ambipolar
inevitably dissipate over timescales that are comparable to diffusion or triggering by a shock wave, supersonic inward
a cloud’s freefall time (the time over which an idealized, motions develop and soon result in the formation of an
pressureless sphere of gas of initially uniform density would optically thick first core, with a size on the order of 10 AU.
collapse to form a star), once the source of the turbulence This central core is supported primarily by the thermal pres-
is removed. For a dense cloud core, freefall times are on sure of the H2 gas, while the remainder of the cloud con-
the order of 0.1 m.y. However, dense clouds do not collapse tinues to fall onto the core. For a 1-M cloud, this core has
on this timescale, because once turbulence decays, magnetic a mass of about 0.01 M . Once the central temperature
fields provide support against self-gravity. reaches about 2000 K, thermal energy goes into dissociating
Magnetic field strengths in dense clouds are measured the H molecules, lowering the thermal pressure and lead-
by Zeeman splitting of molecular lines, and found to be ing to a second collapse phase, during which the first core
large enough (about 10–1000 µG) to be capable of support- disappears and a second, final core is formed at the center,
ing dense clouds, provided that both static magnetic fields with a radius a few times that of the Sun. This core then
and magnetohydrodynamic waves are present (Crutcher, accretes mass from the infalling cloud over a timescale of
1999). Field strengths are found to depend on the density to about 1 m.y. (Larson, 1969). In the presence of rotation or
roughly the 1/2 power, as is predicted to be the case if ambi- magnetic fields, however, the cloud becomes flattened into
polar diffusion controls the cloud’s dynamics (Mouschovias, a pancake, and may then fragment into two or more pro-
1991). Ambipolar diffusion is the process of slippage of the tostars. At this point, we cannot reliably predict what sort
primarily neutral gas molecules past the ions, to which the of dense cloud core will form in precisely what sort of star
magnetic field lines are effectively attached. This process or stellar system, much less what sorts of planetary systems
occurs over timescales of a few million years or more for will accompany them, but certain general trends are evident.
dense cloud cores, and inevitably leads to the loss of suffi- The standard model pertains only to formation of single
cient magnetic field support such that the slow inward con- stars, whereas most stars are known to be members of bi-
traction of the cloud turns into a rapid, dynamic collapse nary or multiple star systems. There is growing observa-
phase, when the magnetic field is no longer in control. This tional evidence that multiple star formation may be the rule,
is generally believed to be the process through which stars rather than the exception (Reipurth, 2000). If so, then it may
in regions of low-mass star formation begin their life, the be that single stars like the Sun are formed in multiple pro-
“standard model” of star formation (Shu et al., 1987). tostar systems, only to be ejected soon thereafter as a result
Recently this standard model has been challenged by of the decay of the multiple system into an orbitally stable
evidence for short cloud lifetimes and a highly dynamic star configuration (Bate et al., 2002). In that case, the solar
formation process driven by large-scale outflows (Hartmann nebula would have been subject to strong tidal forces dur-
et al., 2001). In regions of high-mass star formation, where ing the close encounters with other protostars prior to its
the great majority of stars are believed to form (Fig. 1), qui- ejection from the multiple system. This hypothesis has not
escent star formation of the type envisioned in the standard been investigated in detail (but see Kobrick and Kaula,
model occurs only until the phase when high-mass stars 1979). Detailed models of the collapse of magnetic cloud
begin to form and evolve. The process of high-mass star cores, starting from initial conditions defined by observa-
formation is not understood as well as that of low-mass tions of molecular clouds, show that while initially prolate
stars, but observations make it clear that events such as the cores tend to fragment into binary protostars, initially ob-
supernova explosions that terminate the life of massive stars late clouds form multiple protostar systems that are highly
can result in the triggering of star formation in neighbor- unstable and likely to eject single protostars and their disks
70 Comets II

Fig. 1. Hubble Space Telescope mosaic image of the Orion Nebula, showing a region about 1 pc across (left) centered on the four
massive stars of the Orion Trapezium. Also shown (right) are individual circumstellar disks orbiting around young stars in Orion,
with a typical size of about 1000 AU. Many of these disks are being photoevaporated by UV emission from the Trapezium stars.
[Photo credits: C. R. O’Dell and S. K. Wong (Rice University) and NASA. Hubble image STScI-PRC95-45a.]

(Boss, 2002a). Surprisingly, magnetic fields were found to In the case of nonmagnetic clouds, where thermal pres-
enhance the tendency for a collapsing cloud to fragment by sure and rotation dominate, single protostars can result from
helping to prevent the formation of a single central mass the collapse of dense cloud cores that are rotating slowly
concentration of the type assumed to form in the standard enough to avoid the formation of a large-scale protostellar
model of star formation. disk that could then fragment into a binary system (Boss
 Boss: From Molecular Clouds to Circumstellar Disks 71

and Myhill, 1995). Alternatively, the collapse of an initially infrared protostars with so much dust emission that the cir-
strongly centrally condensed (power-law), nonmagnetic cumstellar gas mass is on the order of 0.1 M or more.
cloud leads to the formation of a single central body (Yorke Class II objects have less dust emission, and a gas mass of
and Bodenheimer, 1999). However, considering that most about 0.01 M . Class II objects are usually optically visi-
cloud cores are believed to be supported to a significant ble, T Tauri stars, where most of the circumstellar gas re-
extent by magnetic fields, the applicability of these results sides in a disk rather than in the surrounding envelope.
is uncertain. In the case of shock-triggered collapse, calcu- Class III objects are weak-line T Tauri stars, with only trace
lations have shown that weakly magnetic clouds seem to amounts of circumstellar gas and dust. While these classes
form single protostars when triggering occurs after the core imply a progression in time from objects with more to less
has already contracted toward high central densities (Van- gas emission, the time for this to occur for any given ob-
hala and Cameron, 1998). ject is highly variable: Some Class III objects appear to be
In the case of the nonmagnetic collapse of a spherical only 0.1 m.y. old, while some Class II objects have ages of
cloud (Yorke and Bodenheimer, 1999), the protostar that several million years, based on theoretical models of the
forms is orbited by a protostellar disk with a similar mass. evolution of stellar luminosities and surface temperatures.
When angular momentum is transported outward by as- Evidence for dust disks has been found around even older
sumed gravitational torques, and therefore mass is trans- stars, such as Beta Pictoris, with an age of about 10 m.y.,
ported inward onto the protostar, the amount of mass re- although its disk mass is much smaller than that of even
maining in the disk is still so large that most of this matter Class III objects. Stars with such “debris disks” are often
must eventually be accreted by the protostar through other classified as Class III objects.
processes. Hence the disk at this phase must still be con- Multiple examples of all these phases of protostellar
sidered a protostellar disk, not a relatively late phase, proto- evolution have been found, with the exception of the short-
planetary disk where any objects that form have some hope lived Class I objects, which have not yet been detected. It
of survival in orbit. Thus even in the relatively simple case is noteworthy that observations of protostars and young stars
of nonmagnetic clouds, it is not yet possible to compute the find a higher frequency of binary and multiple systems than
expected detailed structure of a protoplanetary disk, starting is the case for mature stars, implying the orbital decay of
from the initial conditions of a dense cloud core. Calcula- many of these young systems (Reipurth, 2000; Smith et al.,
tions starting from less-idealized initial conditions, such as 2000).
a segment of an infinite sheet (Fig. 2), suffer from the same
limitations (Boss and Hartmann, 2001). 2.5. Interactions of Young Stars
Because of the complications of multiple protostar for- with Their Disks
mation, magnetic field support, possible shock-wave trig-
gering, and angular momentum transport in the disk during A remarkable aspect of young stellar objects is the pres-
the cloud infall phase, among others, a definitive theoreti- ence of strong molecular outflows for essentially all young
cal model for the collapse of the presolar cloud has not yet stellar objects, even the Class 0 objects. This means that at
emerged. the same time that matter is still accreting onto the protostar,
it is also losing mass through a vigorous wind directed in a
2.4. Observations of Star-forming Regions bipolar manner in both directions along the presumed ro-
tation axis of the protostar/disk system (Fig. 3). In fact, the
Observations of star-forming regions have advanced our energy needed to drive this wind appears to be derived from
understanding of the star formation process considerably in mass accretion by the protostar, as observed wind momenta
the last few decades. We now can study examples of nearly are correlated with protostellar luminosities and with the
all phases of the evolution of a dense molecular cloud core amount of mass in the infalling envelope (Andrè, 1997).
into a nearly fully formed star (i.e., the ~1-M T Tauri stars). There are two competing mechanisms for driving bipolar
As a result, the theory of star formation is relatively ma- outflows, both of which depend on magnetic fields to sling
ture, with future progress expected to center on defining the ionized gas outward and to remove angular momentum
role played by binary and multiple stars and on refining ob- from the star/disk system (see Shu et al., 2000; Königl and
servations of known phases of evolution. Pudritz, 2000). One mechanism is the X-wind model, where
Protostellar evolution can be conveniently subdivided coronal winds from the central star and from the inner edge
into six phases that form a sequence in time. The usual start- of the accretion disk join together to form the magnetized
ing point is the precollapse cloud, which collapses to form X-wind, launched from an orbital radius of a few stellar
the first protostellar core, which is then defined to be a radii. The other mechanism is a disk wind, launched from
Class I object. The first core collapses to form the final, the surface of the disk over a much larger range of distances,
second core, or Class 0 object, which has a core mass less from less than 1 AU to as far away as 100 AU or so. In both
than that of the infalling envelope. Class I, II, and III ob- mechanisms, centrifugal support of the disk gas makes it
jects (Lada and Shu, 1990) are defined in terms of their easier to launch this material outward, and bipolar flows
spectral energy distributions at midinfrared wavelengths, develop in the directions perpendicular to the disk, because
where the emission is diagnostic of the amount of cold, the disk forces the outflow into these preferred directions.
circumstellar dust. Class I objects are optically invisible, Because it derives from radii deeper within the star’s gravi-
72 Comets II

Fig. 2. Density contours and velocity vectors for a model of the collapse of an initially sheet-like molecular cloud to form a star and
circumstellar disk (Boss and Hartmann, 2001). Four times are shown: (a) t = 0.0 tff, ρmax = 2.1 × 10 –18 g cm–3, vmax = 6.6 × 10 –3 cm s –1;
(b) t = 1.4 tff, ρmax = 3.2 × 10 –17 g cm–3, vmax = 5.8 × 103 cm s –1; (c) t = 5.7 tff, ρmax = 1.3 × 10 –14 g cm–3, vmax = 1.7 × 103 cm s –1;
(d) t = 8.6 tff, ρmax = 2.0 × 10 –13 g cm–3, vmax = 2.1 × 10 4 cm s –1. Density contours correspond to changes by a factor of 2. Region
shown has a radius of 5700 AU ~ 0.03 pc. Only one quadrant of the two-dimensional calculation is shown, which has symmetry above
and below the midplane (bottom border) and around the cloud’s rotation and symmetry axis (left hand border). The initially flat sheet
contracts and then collapses vertically and radially to form a central protostar with a mass of about 0.1 M (unseen, at lower lefthand
corner of plot), orbited by a flattened circumstellar disk and an infalling envelope with modest infall velocities on the largest scale.

tational potential well, an X-wind is energetically favored of mass available for accretion onto the disks and the
over a disk wind. However, observations show that during amount of momentum in the outflow (Bontemps et al.,
FU Orionis-type outbursts in young stars, mass is added 1996), suggesting that disk mass accretion is directly re-
onto the central star so rapidly that the X-wind region is lated to outflow energetics. It is unclear at present what
probably crushed out of existence, implying that the strong effect an X-wind or a disk wind would have on the planet
outflows that still occur during these outbursts must be formation process, beyond being responsible for the loss
caused by an extended disk wind (Hartmann and Kenyon, of energy (and angular momentum in the latter case), as the
1996). winds are thought to be launched either very close to the
All T Tauri stars are believed to experience FU Orionis protostar in the former case, or from the disk’s surface in
outbursts, so disk winds may be the primary driver of bi- the latter case.
polar outflows, at least in the early FU Orionis phase of The simple picture of the solar nebula being removed
evolution. There is a strong correlation between the amount by a spherically symmetric T Tauri wind has long since
 Boss: From Molecular Clouds to Circumstellar Disks 73

Fig. 3. Hubble Space Telescope images of circumstellar disks in the Taurus star-forming region, taken with the NICMOS camera.
The images reveal the disks to be roughly hourglass-shaped configurations with openings threaded by molecular outflows (unseen),
extending about 500 AU across. The central stars are mostly hidden from view by the nearly edge-on disks (dark stripes), but their
light is reflected off the top and bottom surfaces of the disks and by the infalling envelopes of gas and dust. [Photo credits: D. Padgett
(IPAC/Caltech), W. Brandner (IPAC), K. Staplefeldt (JPL), and NASA. Hubble image STScI-PRC1999-05a.]

been supplanted by the realization that young stars have ever, these observations are unable to probe the innermost
directed, bipolar outflows that do not sweep over most of regions (i.e., within 50 AU or so), because of limited spa-
the disk. However, mature stars like the Sun do have ap- tial resolution, so the true amount of disk mass at early
proximately isotropic winds, so there must be some transi- phases remains uncertain. Nevertheless, the expectation is
tion phase where the bipolar star/disk wind evolves into a that protostellar disks must somehow transport most of their
more spherically symmetric stellar wind. Presumably this mass inward to be accreted by the protostar, eventually
enhanced stellar wind would eventually scour any remain- evolving into protoplanetary disks, where planetary bodies
ing gas and dust from the system. In addition, Poynting- should be able to form and survive their subsequent inter-
Robertson drag and radiation pressure are able to remove actions with the disk. This process occurs even as collapse
the smaller dust grains around older stars, such as Beta of the presolar cloud onto the growing disk continues, add-
Pictoris, the former by orbital decay inward onto the star, ing significant amounts of mass and angular momentum.
and the latter by being driven. The transition point from a protostellar disk to a protoplane-
tary disk is not clear, and the physical mechanisms respon-
3. EVOLUTION OF sible for disk evolution in either of these two phases remain
CIRCUMSTELLAR DISKS uncertain, although progress seems to have been made in
ruling out several proposed mechanisms.
On theoretical grounds, even an initially highly centrally
condensed (i.e., power-law-density profile) cloud core is 3.1. Angular Momentum Transport Mechanisms
likely to collapse to form a protostar surrounded by a fairly
massive protostellar disk and envelope. Currently available The basic theory of the evolution of an accretion disk
observations of disks around young stars (e.g., Dutrey et can be derived by assuming that there is some physical
al., 2004) imply that at early ages, disk masses are not al- mechanism operating that results in an effective viscosity
ways a significant fraction of the protostar’s mass. How- of the gas. Because the intrinsic molecular viscosity of H2
74 Comets II

gas is far too small to have an appreciable effect on disk It has also been suggested that finite-amplitude (nonlin-
evolution in a reasonable amount of time, theorists have ear) disturbances to Keplerian flow could result in a self-
sought other sources for an effective viscosity, such as tur- sustaining shear instability that would produce significant
bulence. In a fully turbulent flow, the effective viscosity can turbulence (Dubrulle, 1993). However, when three-dimen-
be equal to the molecular viscosity multiplied by a large sional hydrodynamical models were again used to investi-
factor: the ratio of the Reynolds number of the disk (about gate this possibility, it was found that the initially assumed
10 billion) to the critical Reynolds number for the onset of turbulent motions decayed rather than grew (Stone et al.,
turbulence (about 1000), or a factor of about 10 million. 2000). Evidently purely hydrodynamical turbulence can
Under very general conditions, it can be shown (Lynden- neither grow spontaneously nor be self-sustained upon be-
Bell and Pringle, 1974) that a viscous disk will evolve in ing excited by an external perturbation.
such a manner as to transport most of its mass inward, In spite of these discouraging results for hydrodynamical
thereby becoming more tightly gravitationally bound, and turbulence, another possibility remains and is under inves-
minimizing the total energy of the system. In order to con- tigation (Klahr and Bodenheimer, 2003), that of a global
serve angular momentum, this means that angular momen- baroclinic instability. In this mechanism, turbulence results
tum must be transported outward along with a small fraction in essence from steep temperature gradients in the radial
of the mass, so that the accretion disk expands outside some direction, which then battle centrifugal effects head-on.
radius. The loss of significant angular momentum by cen- Three-dimensional hydrodynamical models imply that this
trifugally launched winds somewhat relieves this need for mechanism can drive inward mass transport and outward
the accretion disk to expand; this additional angular mo- angular momentum transport, as desired. However, mod-
mentum sink was not recognized when the theory was first els by Klahr with a different numerical code have reached
developed (note, however, that in the case of an X-wind, different conclusions, so the situation regarding this mecha-
relatively little angular momentum can be lost by the X- nism is unclear.
wind). While the basic physics of a viscous accretion disk Rossby waves occur in planetary atmospheres as a re-
is fairly well developed, the physical mechanism(s) respon- sult of shearing motions and can produce large-scale vorti-
sible for disk evolution remain contentious. ces such as the Great Red Spot on Jupiter. Rossby waves
Given the high Reynolds number of a protoplanetary have been proposed to occur in the solar nebula as a result
disk, one might expect that a turbulent cascade of energy of Keplerian rotation coupled with a source of vortices.
would occur and result in an effective turbulent viscosity While prograde rotation (cyclonic) vortices are quickly dis-
that might be sufficient to drive disk evolution. However, sipated by the background Keplerian flow, retrograde (anti-
because of the strong differential rotation in a Keplerian cyclonic) vortices are able to survive for longer periods of
disk, a high Reynolds number is not a sufficient condition time (Godon and Livio, 1999). Rossby waves have been ad-
for fully developed turbulence. Instead, the Rayleigh crite- vanced as a significant source of angular momentum trans-
rion, which applies to rotating fluids but is not strictly ap- port in the disk (Li et al., 2001). Rossby vortices could serve
plicable to the solar nebula, suggests that Keplerian disks as sites for concentrating dust particles, but the difficulty
are stable with respect to turbulence. in forming the vortices in the first place, coupled with their
While differential rotation may inhibit convective mo- eventual decay, makes this otherwise attractive idea some-
tions in the radial direction in a disk, motions parallel to what dubious (Godon and Livio, 2000). In addition, the
the rotation axis are relatively unaffected by rotation. In a restriction of these numerical studies to thin, two-dimen-
disk where heat is being generated near the midplane, and sional disk models, where refraction of the waves away from
where dust grains are the dominant source of opacity, the the midplane is not possible, suggests that in a fully three-
disk is likely to be unstable to convective motions in the dimensional calculation, Rossby waves may be less vigor-
vertical direction, which carry the heat away from the disk’s ous than in the thin disk calculations (Stone et al., 2000).
midplane and deposit it close to the disk’s surface, where While a purely hydrodynamical source for turbulence
it can be radiated away. Convective instability was conjec- has not yet been demonstrated, the situation is much differ-
tured to lead to sufficiently robust turbulence for the result- ent when magnetohydrodynamical (MHD) effects are con-
ing turbulent viscosity to be large enough to drive disk sidered in a shearing, Keplerian disk. In this case, the Ray-
evolution (Lin and Papaloizou, 1980), a seemingly attrac- leigh criterion for stability can be shown to be irrelevant:
tive, self-consistent scenario that has motivated much of the Provided only that the angular velocity of the disk decreases
work on viscous evolution of the solar nebula. However, with radius, even an infinitesimal magnetic field will grow
three-dimensional hydrodynamical models of vertically con- at the expense of the shear motions, a fact that had been
vectively unstable disks have shown that the convective cells noted by S. Chandrasekhar in a 1960 paper but was largely
that result are sheared by differential rotation to such an ignored until it was rediscovered some 30 years later.
extent that the net transport of angular momentum is very Balbus and Hawley (1991) pointed out that in the pres-
small, and may even be in the wrong direction (see Stone ence of rotational shear, even a small magnetic field will
et al., 2000). As a result, convectively driven disk evolution grow on a very short timescale. The basic reason is that
does not seem to be a major driver. In addition, heating of magnetic field lines can act like rubber bands, linking two
the surface of the disk by radiation from the central proto- parcels of ionized gas. The parcel that is closer to the proto-
star will also act to suppress vertical convection. sun will orbit faster than the other, increasing its distance
 Boss: From Molecular Clouds to Circumstellar Disks 75

from the other parcel. This leads to stretching of the mag- 1 AU or so, where they are attenuated (Glassgold et al.,
netic field lines linking the parcel, and so to a retarding force 1997). As a result, the solar nebula is likely to be a layered
on the forward motion of the inner parcel. This force trans- accretion disk (Gammie, 1996), where MRI turbulence re-
fers angular momentum from the inner parcel to the outer sults in inward mass transport within thin, lightly ionized
parcel, which means that the inner parcel must fall farther surface layers, while the layers below the surface do not
inward toward the protosun, increasing its angular veloc- participate in MRI-driven transport. Thus the bulk of the
ity, and therefore leading to even more stretching of the field disk, from just below the surface to the midplane, is ex-
lines and increased magnetic forces. Because of this posi- pected to be a magnetically dead zone. Layered accretion
tive feedback, extremely rapid growth of an infinitesimal is thought to be capable of driving mass inflow at a rate of
seed field occurs. Consequently, the magnetic field soon about 1 M in 100 m.y., sufficient to account for observed
grows so large and tangled that its subsequent turbulent mass accretion rates in quiescent T Tauri stars.
evolution must be computed with a fully nonlinear, multi- The remaining possibility for large-scale mass transport
dimensional MHD code. in the solar nebula is gravitational torques. The likelihood
Three-dimensional MHD models of a small region in the that much of the solar nebula was a magnetically dead zone
solar nebula (Hawley et al., 1995) have shown that, as ex- where MRI transport was ineffective leads to the sugges-
pected, a tiny seed magnetic field soon grows and results tion that there might be regions where inward MRI mass
in a turbulent disk where the turbulence is maintained by the transport would cease, leading to a local pileup of mass,
magnetic instability. In addition, the magnetic turbulence which might then cause at least a local gravitational insta-
results in a net outward flow of angular momentum, as de- bility of the disk (Gammie, 1996). In addition, there is ob-
sired. The magnetic field grows to a certain value and then servational and theoretical evidence that protostellar disks
oscillates about that mean value, depending on the assumed tend to start their lives with sufficient mass to be gravita-
initial field geometry, which is large enough to result in rela- tionally unstable in their cooler regions, leading to the for-
tively vigorous angular momentum transport. While prom- mation of nonaxisymmetric structure and hence the action
ising, these studies of the magneto-rotational instability of gravitational torques, and that these torques may be the
(MRI) are presently restricted to small regions of the nebula, dominant transport mechanism in early phases of evolution
and the global response of the disk to this instability remains (Yorke and Bodenheimer, 1999).
to be determined. In order for gravitational torques to be effective, a proto-
Magneto-rotational instability is a powerful phenomenon, stellar disk or the solar nebula must be significantly nonaxi-
but is limited to affecting nebula regions where there is suf- symmetric, e.g., threaded by clumps of gas, or by spiral
ficient ionization for the magnetic field, which is coupled arms, much like a spiral galaxy. In that case, trailing spiral
only to the ions, to have an effect on the neutral atoms and structures, which inevitably form as a result of Keplerian
molecules. The MRI studies described above all assume shear, will result in the desired outward transport of angu-
ideal MHD, i.e., a fully ionized plasma, where the the mag- lar momentum. This is because in a Keplerian disk, an ini-
netic field is frozen into the fluid. At the midplane of the tial bar-shaped density perturbation will be sheared into a
solar nebula, however, the fractional ionization is expected trailing spiral arm configuration. The inner end of the bar
to be quite low in the planetary region. Both ambipolar rotates faster than the outer end and therefore moves ahead
diffusion and resistivity (ohmic dissipation) are effective at of the outer end. Because of the gravitational attraction
limiting magnetic field strengths and suppressing MRI- between the inner end and the outer end, the inner end will
driven turbulence, but a fractional ionization of only about have a component of this gravitational force in the back-
1 ion per 1000 billion atoms is sufficient for MRI to pro- ward direction, while the outer end will feel an equal and
ceed in spite of ambipolar diffusion and ohmic dissipation. opposite force in the forward direction. The inner end will
Close to the protosun, disk temperatures are certainly high thus lose orbital angular momentum, while the outer end
enough for thermal ionization to create an ionization frac- gains this angular momentum. As a result, the inner end falls
tion greater than this, and thus to maintain full-blown MRI closer to the protosun, while the outer end moves farther
turbulence. Given that a temperature of at least 1400 K is away, with a net outward transport of angular momentum.
necessary, MRI instability may be limited to the innermost Models of the growth of nonaxisymmetry during the
0.2 AU or so in quiescent phases, or as far out as about collapse and formation of protostellar disks show that large-
1 AU during rapid mass accretion phases (Boss, 1998; Stone scale bars and spirals can form with the potential to transfer
et al., 2000). most of the disk angular momentum outward on timescales
At greater distances, disk temperatures are too low for as short as 1000 yr to 0.1 m.y. (Boss, 1989), sufficiently fast
thermal ionization to be effective. Cosmic rays were thought to allow protostellar disks to transport most of their mass
to be able to ionize the outer regions of the nebula, but the inward onto the protostar and thereby evolve into proto-
fact that bipolar outflows are likely to be magnetically driven planetary disks.
means that cosmic rays may have a difficult time reaching Early numerical models of the evolution of a gravitation-
the disk midplane (Dolginov and Stepinski, 1994). How- ally unstable disk (e.g., Cassen et al., 1981) suggested that
ever, the coronae of young stars are known to be prolific a disk would have to be comparable in mass to the central
emitters of hard X-rays, which can penetrate the bipolar protostar in order to be unstable, i.e., gravitational instabil-
outflow and reach the disk surface at distances of about ity could occur in protostellar, but not in protoplanetary
76 Comets II

disks. Analytical work on the growth of spiral density waves model. The strength of an effective viscosity is usually
implied that for a 1-M star, gravitational instability could quantified by the α parameter. α is often defined in vari-
occur in a disk with a mass as low as 0.19 M (Shu et al., ous ways, but typically α is defined to the constant that
1990). Recent three-dimensional hydrodynamical models when multiplied by the sound speed and the vertical scale
have shown that vigorous gravitational instability can oc- height of the disk (two convenient measures of a typical
cur in a disk with a mass of 0.1 M or even less, in orbit velocity and length scale), yields the effective viscosity of
around a 1-M star (Boss, 2000), because of the expected the disk (Lynden-Bell and Pringle, 1974). Three-dimen-
low midplane temperatures (about 30 K) in the outer disk sional MHD models of the MRI imply a typical MRI α
implied by cometary compositions (Kawakita et al., 2001) of about 0.005 to 0.5 (Stone et al., 2000). Similarly, three-
and by observations of disks (D’Alessio et al., 2001). Simi- dimensional models of marginally gravitationally unstable
lar models with a complete thermodynamical treatment disks imply an α of about 0.03 (Laughlin and Bodenheimer,
(Boss, 2002b), including convective transport and radiative 1994). Steady mass accretion at the low rates found in
transfer, show that a marginally gravitationally unstable quiescent T Tauri stars requires an α of about 0.01 (Calvet
solar nebula develops a robust pattern of clumps and spiral et al., 2000), in rough agreement with these estimates. Once
arms, persisting for many disk rotation periods, and result- planets have formed and become massive enough to open
ing in episodic mass accretion rates onto the central proto- gaps in their surrounding disks, their orbital evolution be-
sun that vary between accreting 1 M in 10 m.y. to as short comes tied to that of the gas. As the gaseous disk is trans-
as 1000 yr. The latter rates appear to be high enough to ac- ported inward by viscous accretion, these planets must also
count for FU Orionis outbursts. migrate inward. The perils of orbital migration for planetary
Because angular momentum transport by a strongly formation and evolution are addressed in Ward and Hahn
gravitationally unstable disk is so rapid, it is unlikely that (2000) and Lin et al. (2000). Here we limit ourselves to
protostellar or protoplanetary disks are ever strongly gravi- considering the evolution of dust and gas prior to the for-
tationally unstable, because they can probably evolve away mation of planetary-sized bodies.
from such a strongly unstable state faster than they can be The generation of viscous accretion disk models was an
driven into it by, e.g., accretion of more mass from an in- active area of research during the period when convective
falling envelope or radiative cooling. As a result, it is much instability was believed to be an effective source of viscos-
more likely that a disk will approach gravitational instabil- ity. Ruden and Pollack (1991) constructed models where
ity from a marginally unstable state (Cassen et al., 1981). convective instability was assumed to control the evolution,
Accordingly, recent models of gravitationally unstable disks so that in regions where the disk became optically thin and
have focused almost exclusively on marginally gravitation- thus convectively stable, the effective viscosity vanished.
ally unstable disks (e.g., Boss, 2000), where primarily the Starting with an α of about 0.01, they found that disks
outer disk, beyond about 5 AU, participates in the instabil- evolved for about 1 m.y. before becoming optically thin,
ity. Inside about 5 AU, disk temperatures appear to be too often leaving behind a disk with a mass of about 0.1 M .
high for an instability to grow there, although these inner Midplane temperatures at 1 AU dropped precipitously from
regions may still be subject to shock fronts driven by clumps about 1500 K initially to about 20 K when convection
and spiral arms in the gravitationally unstable, outer region. ceased and the disk was optically thin at that radius. Simi-
One-armed spiral density waves can propagate right down larly dramatic temperature drops occur throughout the disk
to the stellar surface. Gravitational forces are intrinsically in these models, and the outer regions of the models even-
global in nature, and their effect on different regions of the tually became gravitationally unstable as a result.
nebula can be expected to be highly variable in both space Given that convective instability is no longer considered
and time. On the other hand, turbulent viscosity is a local to be a possible driver of disk evolution, the Ruden and
process that is usually assumed to operate more or less Pollack (1991) models are interesting, but not likely to be
equally efficiently throughout a disk. As a result, it is un- applicable to the solar nebula. Unfortunately, little effort has
clear if gravitational effects can be faithfully modeled as a gone into generating detailed viscous accretion models in
single, effective viscosity capable of driving disk evolution in the interim: The theoretical focus seems to have been more
the manner envisioned by Lynden-Bell and Pringle (1974). on the question of determining which mechanisms are con-
Nevertheless, efforts have been made to try to quantify the tenders for disk evolution than on the question of the re-
expected strength of gravitational torques in this manner sulting disk evolution. In particular, the realization that the
(Lin and Pringle, 1987). Three-dimensional models of mar- MRI mechanism is likely to have operated only in the mag-
ginally gravitationally unstable disks imply that such an netically active surface layers of the disk, and not in the
effective viscosity is indeed large and comparable to that magnetically dead bulk of the disk, presents a formidable
in MRI models (Laughlin and Bodenheimer, 1994). technical challenge for viscous accretion disk models, which
have usually been based on the assumption that the nebula
3.2. Evolution of the Solar Nebula can be represented by a thin, axisymmetric disk (e.g., Ruden
and Pollack, 1991), greatly simplifying the numerical so-
Given an effective source of viscosity, in principle the lution. The need for consideration of the vertical as well as
time evolution of the solar nebula can be calculated in great the radial structure of the disk, and possibly the azimuthal
detail, at least in the context of the viscous accretion disk (nonaxisymmetric) structure as well, points toward the re-
 Boss: From Molecular Clouds to Circumstellar Disks 77

quirement of a three-dimensional magnetohydrodynamical by the conventional means of core accretion. The standard
calculation of the entire disk. Such a calculation has not model for Jupiter formation by core accretion envisions a
been performed, and even the MRI calculations performed nebula that has a surface density high enough for a solid
to date on small regions of a disk can only be carried for- core to form within about 8 m.y. through runaway accre-
ward in time for a small fraction of the expected lifetime tion (Pollack et al., 1996). However, such a nebula is likely
of the disk. to be marginally gravitationally unstable, a situation that
Some progress has been made in two-dimensional hydro- could result in the rapid formation of gas giant planets in a
dynamical models of a thick disk evolving under the action few thousand years by the formation of self-gravitating
of a globally defined α viscosity, representing the effects clumps of gas and dust (Boss, 1997, 2000, 2002b).
of torques in a marginally gravitationally unstable disk In their pioneering study of a marginally unstable disk,
(Yorke and Bodenheimer, 1999), but in these models the Laughlin and Bodenheimer (1994) found strong spiral arm
evolution eventually slows down and leaves behind a fairly formation, but no clumps, presumably in large part as a re-
massive protostellar disk after 10 m.y., with a radius on the sult of the limited spatial resolution that was computa-
order of 100 AU. tionally possible at the time (up to 25,000 particles). Recent
One aspect of particular interest about viscous accretion work has shown (Boss, 2000) that when a million or more
disk models is the evolution of solid particles, both in terms grid points are included, three-dimensional hydrodynamic
of their thermal processing and in terms of their transport in models of marginally gravitationally unstable disks demon-
the nebula. Interstellar dust grains are small enough (sub- strate the persistant formation of self-gravitating clumps,
micrometer-sized) to remain well-coupled to the gas, so they although even these models do not appear to have sufficient
will move along with the gas. During this phase, the gas spatial resolution to follow the high-density clumps indefi-
and dust may undergo trajectories that are outward at first, nitely in time. Regardless of whether or not such disk in-
as the disk accretes matter from the infalling envelope and stability models can lead to gas-giant-planet formation, the
expands by outward angular momentum transport, followed likelihood that the solar nebula was at least episodically
by inward motion once accretion stops and the disk con- marginally gravitationally unstable has important implica-
tinues to accrete onto the protostar (Cassen, 1996). Once tions for cosmochemistry.
collisional coagulation gets underway and grain growth Perhaps the most well-known, unsolved problem in cos-
begins, solid particles begin to move with respect to the gas, mochemistry is the question of the mechanism whereby
suffering gas drag and additional radial migration as a re- dust grain aggregates were thermally processed to form
sult (Weidenschilling, 1988, 2004). chondrules and some rounded refractory inclusions. Chon-
The bulk compositions of the bodies in the inner solar drule compositions and textures require rapid heating and
system show a marked depletion of volatile elements com- somewhat slower cooling for their explanation; a globally
pared to the solar composition. Cassen (2001) has shown hot nebula is inconsistent with these requirements (Cassen,
that these volatile depletions can be explained as a result 2001). A wide variety of mechanisms has been proposed
of the condensation of hot gases and coagulation of the and generally discarded, but recent work seems to have
resulting refractory dust grains into solids that are decoupled largely solved the problem (Desch and Connolly, 2002). In
from the gas through the rapid growth of kilometer-sized a marginally gravitationally unstable nebula, clumps and
planetesimals. The volatile elements remain in gaseous form spiral arms at about 8 AU will drive one-armed spiral arms
at these temperatures, and so avoid being incorporated into into the inner nebula that at times result in shock fronts
the planetesimals that will eventually form the terrestrial orientated roughly perpendicular to the orbits of bodies in
planets and asteroids. In order for this process to work, sig- the asteroidal region. Because of the tendency toward co-
nificant regions of the nebula must have been hot enough at rotation in self-gravitating structures, this will lead to sol-
the midplane to keep volatiles in the gaseous form, a situ- ids encountering a shock front at speeds on the order of
ation that would characterize the nebula when mass accre- 10 km/s, sufficiently high to result in postshock tempera-
tion rates were on the order of 1 M in less than 10 m.y. tures of about 3000 K. Detailed one-dimensional models of
The volatile gases would then be removed from the terres- heating and cooling processes in such a shock front have
trial planet region by viscous accretion onto the protosun. shown that shock speeds around 7 km/s are optimal for
The postulated rapid growth from dust grains to kilometer- matching chondrule cooling rates and therefore textures
sized bodies required by this scenario appears to be pos- (Desch and Connolly, 2002).
sible (Woolum and Cassen, 1999). If disk evolution near the midplane is largely controlled
by gravitational torques rather than by a turbulent process
3.3. Marginally Gravitationally Unstable Disks such as MRI or convection, then mixing processes might
be profoundly different as a result. Gravitational torques
Given the apparent limitation of MRI-driven accretion could potentially result in matter flowing through the disk
to the surfaces of protoplanetary disks, it would appear that without being rapidly homogenized through mixing by tur-
gravitational torques may have to be responsible for the bulence. As a result, spatially heterogeneous regions of the
evolution in the bulk of the disk. In addition, there are strong disk might persist for some amount of time, if they were
theoretical reasons why gravitational torques may be effec- formed in the first place by processes such as the triggered
tive, including the difficulty in forming the gas giant planets injection of shock-wave material (Vanhala and Boss, 2000)
78 Comets II

or the spraying and size-sorting of solids processed by an mation, similar to Orion (Fig. 1), with a smaller fraction
X-wind onto the surface of the nebula (Shu et al., 1996). forming in smaller clusters of low-mass stars, like Taurus
However, because convective motions appear to play an (Fig. 3). The radiation environment differs considerably
important part in cooling the disk midplane in recent mod- between these two extremes, with Taurus being relatively
els of disk instability (Boss, 2002b), it is unclear if gravita- benign, and with Orion being flooded with ultraviolet (UV)
tional torques could act in isolation without interference radiation once massive stars begin to form (Hollenbach et
from convective motions or other sources of turbulence. At al., 2000). Even in Taurus, though, individual young stars
any rate, spatially heterogeneous regions might only last for emit UV and X-ray radiations at levels considerably greater
a short fraction of the nebular lifetime, requiring rapid co- than mature stars (Feigelson and Montmerle, 1999). Ultra-
agulation and growth of kilometer-sized bodies if evidence violet radiation from the protosun has been suggested as a
of this phase is to be preserved. means of removing the residual gas from the outermost
If an X-wind is responsible for driving bipolar outflows, solar nebula (i.e., beyond about 10 AU) through photoevap-
then there are possibly important implications for the ther- oration of H atoms (Shu et al., 1993), a process estimated
mal processing of solids and the production of short-lived to require about 10 m.y.
radioisotopes (Shu et al., 1996, 2001). The basic idea is that Ultraviolet radiation from a nearby massive star has been
some of the solids that spiral inward and approach the invoked as a means to photoevaporate more rapidly the gas
boundary layer between the solar nebula and the protosun in the outer solar nebula (beyond about 10 AU) and then
will be lifted upward by the same magnetically driven wind to form the ice giant planets by photoevaporating the gas-
that powers bipolar outflows. While close to the protosun, eous envelopes of the outermost gas giant protoplanets
these solids will be subject to heating by the solar radia- (Boss et al., 2002), as may be happening in the protoplane-
tion field and to spallation by particles from solar flares. tary disks seen in Hubble images of the Orion nebula clus-
Following this processing, the solids will be lofted onto ter (Fig. 1). The Orion proplyds imply a considerably differ-
size-sorted trajectories that return them to the surface of the ent evolution scenario in the outer disk than is the case for
solar nebula at several AU or beyond. Note, however, that isolated disks in regions like Taurus (Fig. 3), where the disks
if a disk wind operates along with or instead of an X-wind, appear to be classic cases of symmetric, circumstellar disks
then any solids lofted from the inner region may be unable with perpendicular outflows, similar to that envisioned in
to return directly to the asteroid region around 2.5 AU, as simple theoretical models (e.g., Fig. 2).
the disk wind being launched at those same distances may The full implications for cometary formation and dynam-
prevent their infall onto the disk. Lofting of solids to dis- ics in the Orion scenario remains to be elucidated, but
tances greater than 2.5 AU, e.g., to where the Oort cloud clearly the Orion environment would lead to much shorter
comets presumably formed, might also be prohibited by a disk lifetimes than in regions like Taurus, yet such disks
disk wind operating closer to the protosun. may still be able to yield planetary systems similar to our
The X-wind model has also been advanced as a means own. Considering the timescale for growth to kilometer-
for thermal processing of chondrules (Shu et al., 1996). sized bodies (Weidenschilling, 2004), this should not ad-
While it has not yet been possible to calculate the detailed versely impact the formation of comets. Shortening the
thermal history of chondrule precursors to see if the re- outer disk lifetime may lead to more rapid depletion of the
quired impulsive heating and slower cooling rates can be inner disk that it otherwise feeds, however, and so may help
matched, the fact that this mechanism implies size-sorting to prevent subsequent loss of the inner planets by inward
of the particles as they are lofted upward and return to the orbital migration driven by disk interactions. The process
nebula on ballistic trajectories means that small dust parti- of ejection of the solar nebula from a region of high-mass
cles and chondrule-sized particles that were thermally pro- star formation (prior to the eventual supernova explosion
cessed together in the X-wind region will eventually be sep- that accompanies high-mass star formation) might even help
arated upon their return to the nebula (Desch and Connolly, explain the high eccentricities and inclinations found for
2002). As a result, it is difficult to explain the fact that chon- Kuiper belt comets (Ida et al., 2000).
drules and the fine-grained matrix in which they reside are Comets subjected to the intense UV radiation of an
chemically complementary: Their combined, bulk compo- Orion-like environment will undergo photochemical pro-
sition is roughly solar, although individually they are not. cessing, leading to the production of a thick layer of or-
This seems to indicate that thermal processing in a more ganic compounds, containing, e.g., amino acids (Bernstein
closed system, such as occurs with shock-wave processing et al., 2002), which will act as an effective sunblock against
within the nebula, may be a better means to explain chon- subsequent radiation processing. Thus the Orion scenario
drule thermal processing. could offer a means of getting a head start on the prebiotic
chemistry that is necessary for the origin of life. If correct,
3.4. New Scenario for Solar System Formation this hypothesis could be used to argue that planetary sys-
tems similar to our own, even to the extent of supporting
While formation as a single star in an isolated, dense life, might well be common in the galaxy.
cloud core is usually imagined for the presolar cloud, in
reality there are very few examples of isolated star for- Acknowledgments. This work was partially supported by the
mation. Most stars form in regions of high-mass star for- NASA Planetary Geology and Geophysics Program under grant
 Boss: From Molecular Clouds to Circumstellar Disks 79

NAG 5-10201, and by the National Science Foundation under Icarus, 48, 377–392.
grant AST-99-83530. Cassen P. (1996) Models for the fractionation of moderately vola-
tile elements in the solar nebula. Meteoritics & Planet. Sci.,
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 Dutrey et al.: Gas and Dust Components of Circumstellar Disks 81

Observation of Circumstellar Disks: Dust and Gas Components

Anne Dutrey
Observatoire de Bordeaux

Alain Lecavelier des Etangs

Institut d’Astrophysique de Paris

Jean-Charles Augereau
Service D’Astrophysique du CEA-Saclay and Institut d’Astrophysique de Paris

Since the 1990s, protoplanetary disks and planetary disks have been intensively observed
from optical to the millimeter wavelengths, and numerous models have been developed to in-
vestigate their gas and dust properties and dynamics. These studies remain empirical and rely
on poor statistics, with only a few well-known objects. However, the late phases of the stellar
formation are among the most critical for the formation of planetary systems. Therefore, we
believe it is timely to tentatively summarize the observed properties of circumstellar disks around
young stars from the protoplanetary to the planetary phases. Our main goal is to present the
physical properties that are considered to be observationally robust and to show their main
physical differences associated with an evolutionary scheme. We also describe areas that are
still poorly understood, such as how protoplanetary disks disappear, leading to planetary disks
and eventually planets.

1. INTRODUCTION protoplanetary disks. During this phase, the dust emission

is optically thick in the near-IR (NIR) and the central young
Before the 1980s, the existence of protoplanetary disks of star still accretes from its disk. Such disks are also naturally
gas and dust around stars similar to the young Sun (4.5 b.y. called accretion disks.
ago) was inferred from the theory of stellar formation (e.g., On the other hand, images of β Pictoris by Smith and
Shakura and Suynaev, 1973), the knowledge of our own Terrile (1984) demonstrated that Vega-type stars or old PMS
planetary system, and dedicated models of the protosolar stars can also be surrounded by optically thin dusty disks.
nebula. The discovery of the first bipolar outflow in L1551 These disks were called debris disks or later planetary disks,
in 1980 drastically changed the view of the stellar forma- because planetesimals should be present and indirect evi-
tion. In the meantime, optical polarimetric observations by dence of planets was found in some of them (β Pictoris).
Elsasser and Staude (1978) revealed the existence of elon- In this chapter, we review the current observational
gated and flattened circumstellar dust material around some knowledge of circumstellar disks from the domain of the
pre-main-sequence (PMS) stars such as the low-mass T Tauri ultraviolet (UV) to the millimeter (mm). We discuss in sec-
stars. The T Tauri are understood to be similar to the Sun tions 2 and 3 the properties of protoplanetary disks found
when it was about 106 yr old. A few years later, observations around young low-mass (T Tauri) and intermediate-mass
from the InfraRed Astronomical Satellite (IRAS) found sig- (Herbig AeBe) stars. In section 4, we summarize the prop-
nificant infrared (IR) excesses around many T Tauri stars, erties of transition disks that still have some gas compo-
showing the existence of cold circumstellar dust (Rucinski, nent but also have almost optically thin dust emission in the
1985). More surprisingly, IRAS also showed the existence of NIR, objects that are thought to be in the phase of dissipat-
weak IR excess around main-sequence stars such as Vega, ing their primary gas and dust. We present the properties of
ε Eridani, or β Pictoris (Aumann et al., 1985). These excit- optically thin dust disks orbiting old PMS, zero-age-main-
ing discoveries motivated several groups to model the spec- sequence (ZAMS) or Vega-type stars, such as the β Pictoris
tral energy distribution (SED) of T Tauri stars (e.g., Adams debris disk in section 5. We conclude by reviewing future
et al., 1987) and Vega-like stars (Harper et al., 1984). instruments and their usefulness for studying such objects.
On one hand, for PMS stars, the emerging scenario was
the confirmation of the existence of circumstellar disks or- 2. PROTOPLANETARY DISKS:
biting the T Tauri stars, the gas and dust being residual from T TAURI STARS
the molecular cloud that formed the central star (Shu et al.,
1987). Since such disks contain enough gas (H2) to allow, Following the standard classification (see Boss, 2004),
in theory, formation of giant planets, they are often called T Tauri stars typically present the SEDs of Class II objects.

81
82 Comets II

Evidence for disk features around these young stars comes Small dust particles (of radius a) are efficient absorbers
principally from the following observational considerations: of wavelengths radiation with λ ≤ a. In equilibrium between
1. A flat and geometrically thin distribution accounts for heating and cooling, at longer wavelengths they reemit a
the SED (produced by the dust emission) from the optical to continuous spectrum that closely resembles a thermal spec-
the millimeter (including the IR excess) because the extinc- trum. At short wavelengths, the scattering of the stellar light
tion toward most T Tauri stars is very low. by dust grains can dominate the spectrum, with the limit
2. In the 1990s, adaptive optics (AO) systems on ground- between the scattering and the thermal regimes being
based telescopes and the Hubble Space Telescope (HST) around ~3–5 µm. Very close to the star (~0.1–5 AU), the
began to image these disks. Dust grains at the disk surface temperature is sufficiently high (~500–1000 K), and the
scatter the stellar light, revealing the disk geometry of cir- NIR/optical continuum can be dominated by the thermal
cumstellar material, as in the case of HH30 (see Plate 2). emission of very hot grains.
3. By mapping the CO J = 1–0 and J = 2–1 line emis- Spectral energy distributions can be reproduced by mod-
sion from the gas, large millimeter arrays such as OVRO els of disks (e.g., Pringle, 1981; Hartman, 1998) that as-
or the IRAM interferometers clearly demonstrate that the sume that (1) the disk is reprocessing the stellar light (pas-
circumstellar material has a flattened structure and is in sive disk) or (2) the disk is heated by viscous dissipation
Keplerian rotation. (active disk). In both models, since there is no vertical flow, the
Most T Tauri stars form in binary or multiple systems motions are circular and remain Keplerian [v(r) = GM*/r ,
(Mathieu et al., 2000), and many observational results show where M* is the stellar mass]. As a consequence the disk, in
that binarity strongly affects the dust and gas distribution hydrostatic equilibrium, is geometrically thin with H << r
as a result of tidal truncations. The material can be in a cir- where H is the disk scale height. For viscous disks, the vis-
cumbinary ring as in the GG Tau disk (Dutrey et al., 1994) cosity ν is usually expressed by the so-called α parameter
or confined in small, truncated, circumstellar disks. How- linked to ν by ν = αcsH where cs is the sound speed. The ac-
ever, for simplicity, we will focus here on properties of disks cretion remains subsonic with ν/r ~ αcsH/r << cs and α ~ 0.01.
encountered around stars known as single. Chiang and Goldreich (1997) have also developed a
model of the passive disk in which the optically thin upper
2.1. Mass Accretion Rates layer of the disk is superheated above the blackbody equi-
librium temperature by the stellar light impinging on the
T Tauri stars with IR excess usually present optical emis- disk, which produces a kind of disk atmosphere. Both vis-
sion lines (e.g., Edwards et al., 1994). Studies of these lines cous heating and superheated layers seem to be necessary to
reveal that the stars are still accreting/ejecting material from properly take the observations into account (D’Alessio et al.,
their disk even if the main ejection/accretion phase is over. 1998, 1999).
When they present strong Hα emission lines (equivalent Many observers interpret the SEDs assuming the disk
linewidth WHα ≥ 10 Å), they are called classical line T Tauri is geometrically thin with simple power law dependencies
stars (CTTs). vs. radius for the surface density [Σ(r) = Σo(r/ro)–p] and the
Observations show that the mass accretion rate (and the temperature [Tk(r) = To(r/ro)–q]. In this case, there is no
mass ejection rate) decreases from the protostars to the assumption about the origin of the heating mechanism, and
Class III phases by several orders of magnitude (Hartmann the results are compared to more sophisticated models simi-
et al., 1998; Boss, 2004). Despite the uncertainties result- lar to those described above.
ing from the various observational methods and tracers used Dust disks are usually optically thick up, to λ ~ 100–
for measuring both rates, there is a clear correlation between 200 µm, allowing us to trace the disk temperature. In ac-
mass loss and mass accretion. Typical values for the mass tive disks as in passive geometrically thin disks, the radial
accretion rate of a few 10–5 M /yr are found for Class 0 ob- dependence of the temperature follows T k (r) ∝ r –0.75.
jects, while T Tauri stars have lower values around 10 –8 M /yr. Beckwith et al. (1990) have found that typical temperature
Some protostars such as the FU Orionis objects even ex- laws encountered in T Tauri disks are more likely given by
hibit episodic outbursts with accretion rates as high as a few ∝ r –0.65–0.5. However, Kenyon and Hartmann (1987) have
10 –4 M /yr (Hartmann and Kenyon, 1996). Assuming a shown that for a flaring disk, the temperature profile should
mass accretion rate of ~10 –8 M /yr, a T Tauri star of 0.5 M be as shallow as q = 0.5, closer to the observed values.
would accrete only 0.01 M in 1 m.y. Hence, most of the
accretion must occur in the protostellar phase. 2.3. Dust Content

2.2. Modeling the Spectral Energy Distribution Longward of ~100 µm wavelength, the dust emission
becomes optically thin. Observations at these wavelengths
Global properties of disks can be inferred from the SED, are adequately explained by a dust absorption coefficient
but because of the lack of angular resolution, the results are following κν = κo[ν/1012(Hz)]β with β = 0.5–1 and κo =
strongly model dependent and there is usually no unique 0.1 cm2 g –1 of gas + dust (with a gas to dust ratio of 100)
solution. Moreover, many stars are binaries and SEDs are (Beckwith et al., 1990). The spectral index is significantly
not always individually resolved, leading to possible mis- lower than in molecular clouds, where β = 2. Compared to
interpretations. values found in molecular clouds, both β and κoshow that
 Dutrey et al.: Gas and Dust Components of Circumstellar Disks 83

a significant fraction of the grains have evolved and started with p = 1 has only 10% of its mass located within r =
to aggregate (Henning and Stognienko, 1996; Beckwith et 10 AU, while with p = 1.9, the same disk has 50% of its
al., 2000), grains may even have fractal structures (Wright, mass within the same radius.
1987). Dust encountered in protoplanetary disks seems to In summary, a significant fraction of the grains in proto-
be a mixture of silicate and amorphous carbon covered by planetary disks appear to be more evolved than in molecu-
icy mantles (Pollack et al., 1994). The exact composition lar clouds, and coagulation processes have already started.
is poorly known; recent VLT observations of broadband However, the vertical dust distribution is not yet constrained.
absorption features in the NIR begin to put quantitative con- Moreover, observations at a given frequency are mainly
straints on solid species located on grain mantles such as CO sensitive to grains of size a ≤ a few λ (absorption or diffu-
or H2O (Dartois et al., 2002; Thi et al., 2002). These re- sion cross-sections cannot significantly exceed the geo-
sults also confirm that many molecules may have condensed metrical cross-section, even for more complex grain features
from gas phases of grains (see also sections 2.4 and 3) in and aggregates) (Pollack et al., 1994; Krügel and Sieber-
the cold (~20–15 K) outer portion of the disk. Very close to morgen, 1994). Only multiwavelength analysis of resolved
the star, the dust mantles may be significantly different since images, from the optical to the centimeter domains, should
the disk is hotter (~1000 K at 0.1 AU). allow us to reach conclusions about the dust sedimentation.
Optical/NIR interferometry is a powerful tool to trace the Estimating the mass of the disks remains difficult. However,
innermost disk. Monnier and Millan-Gabet (2002) have continuum millimeter images suggest that the reservoir of
observed several disks around T Tauri and Herbig Ae/Be mass is located at a large distance, r ≥ 30–50 AU. Using a
stars. They found that the observed inner disk sizes (rin ~ gas-to-dust ratio of 100, analyses of the dust emission in-
0.1 AU) of T Tauri stars are consistent with the presence of dicate that the total (dust + gas) disk masses are in the range
an optically thin cavity for a NIR emission arising from sili- 0.001–0.1 M .
cate grains of sizes a ≥ 0.5–1 µm that are heated close to
their temperature of sublimation. 2.4. Gas Content
At NIR and optical wavelengths, small dust particles also
scatter the stellar light that impinges upon the disk surface, In protoplanetary disks, molecular abundances are de-
producing reflection nebulas imaged by optical telescopes. fined with respect to H2 since this is the main (gas) com-
Plate 2 shows in false color the HH30 disk seen edge-on, ponent, and the gas-to-dust ratio, which is not yet measured,
which appears as a dark lane. The star ejects a jet perpen- is assumed to be 100, as in the molecular clouds. Several
dicular to the disk plane and is highly obscured by the groups (Thi et al., 2001b; Richter et al., 2002) have recently
material along the line-of-sight (visual extinction up to Av ≥ started direct investigation of H2 (thanks to its quadrupolar
30 mag). Only the disk surface or atmosphere (Chiang and transitions in the near- and mid-IR region), but the most-
Goldreich, 1997) is seen. Due to the high opacity, these data used tracer of the gas phase remains CO.
cannot allow us to estimate the dust mass distribution with- Carbon monoxide is the most abundant molecule after
out making a priori (or external) assumptions about the molecular hydrogen. Its first rotation lines are observable
vertical distribution. However, grains with a typical size of with current millimeter interferometers, allowing astrono-
around a ~ 0.05–1 µm are responsible for scattering (Close mers to trace the properties of outer gas disks. The current
et al., 1998; Mac Cabe et al., 2002). Since forward scatter- sensitivity of millimeter arrays is limited and does not al-
ing is easier to produce than the backward scattering (e.g., low the observation of CO lines for r ≤ 30–50 AU. Since
GG Tau) (Roddier et al., 1996), the disk inclination usually the density is very high (n(H2) ≥ 106 cm–3), the J = 1–0 and
provides a simple explanation for the observed brightness J = 2–1 CO lines are thermalized by collision with H2 in the
asymmetry. whole disk. Hence, a simple model of Keplerian disk as-
Estimating the gas and dust mass of these disks is done suming LTE conditions is sufficient to derive the CO disk
by several methods (see also section 2.4) but is quite un- properties (Dutrey et al., 1994).
certain. Analyzing the SEDs in the optically thin part of the CO maps reveal that disks are in Keplerian rotation
spectrum leads to T Tauri disk masses (gas + dust) ranging (Koerner et al., 1993) and that many disks in Taurus-Au-
from 0.1 to 0.001 M (Beckwith et al., 1990). These deter- riga clouds are large, with typical radii Rout = 300–800 AU
minations suffer from many uncertainties such as the value (see Simon et al., 2000, their Fig. 1). Comparing resolved
of κo and the gas-to-dust ratio, which is usually assumed CO maps to disk models by performing a χ2 minimization
to have an interstellar value of 100. Moreover, the inner part of the disk parameters (Guilloteau and Dutrey, 1998, see
of the disk is still optically thick (up to radii of ~10–30 AU their Fig. 1) provides useful information about the density
at 3 mm). Resolved images of the thermal dust emission and temperature distributions. The temperature radial pro-
obtained with millimeter arrays allow a separation of pos- files deduced from 12CO images are consistent with stellar
sible opacity and spectral index effects. This procedure also heating in flared disks and the turbulence appears to be
estimates the surface density radial profile Σ(r) = Σ0(r/r0) –p. small, less than 0.1 km s–1 (Dutrey et al., 2004). Since the
Typical values of p are around 1–1.5 (Dutrey et al., 1996). 12 CO and 13CO J = 1–0 and J = 2–1 have different opaci-

Such low values imply that the reservoir of the mass is in ties, they sample different disk layers. A global analysis of
the outer disk traced by submillimeter images. Assuming a these lines permits the derivation of the vertical tempera-
single surface density distribution from 0.1 to 500 AU, a disk ture gradient. Dartois et al. (2003) have shown that in the
84 Comets II

DM Tau disk, the “CO disk surface,” traced by 12CO, is in the disk. The CO disk extends as far as the dust disk and
located around ~3 H above the disk midplane; the 13CO J = the velocity gradient is along the major disk axis, as ex-
2–1 samples material at about 1 H, while J = 1–0 is repre- pected for rotation. 12CO J = 2–1 emission is also observed
sentative of the disk midplane. They also deduce a vertical within the jet (extreme velocity). In the HH30 case the low
kinetic gradient that is in agreement with disk models (e.g., angular resolution of the data does not allow one to sepa-
D’Alessio et al., 1999); the midplane is cooler (~13 K) than rate between the 12CO J = 2–1 emission associated with the
the CO disk surface (~30 K at 100 AU). This appears in the outflow, the cloud, and the disk. This is a common problem
region of the disk where the dust is still optically thick to that cannot be fully solved by current interferometric ob-
the stellar radiation while it is already optically thin to its servations. Selecting sources that are located in a region
own emission, around r ~ 50–200 AU in the DM Tau case. devoid of CO emission of the molecular cloud minimizes
Beyond r ≥ 200 AU, where the dust becomes optically thin the confusion.
to both processes, the temperature profile appears vertically Since the disk is seen edge-on, the vertical distribution
isothermal. can be estimated from the optical observations of the dust
A significant fraction of the DM Tau disk has a tempera- (Burrows et al., 1996). The results are somewhat model
ture below the CO freezeout point (17 K), but enough CO dependent, but one can conclude that the disk is pressure
in the gas phase remains to allow the J = 2–1 line of the supported (dominated by the central star) with the best fit
main isotope to be optically thick. The chemical behavior given by H(r) ∝ r1.45. The authors estimate the surface den-
of molecules and coupling between gas and dust are poorly sity law to be Σ(r) ∝ 1/r and the disk mass ~6 × 10–3 M .
known. There have been only a few attempts to survey many CO observations reveal that the disk is in Keplerian rota-
molecules in protoplanetary disks (Dutrey et al., 1997; tion around a central star of mass 0.5 M and has an outer
Kastner et al., 1997; van Zadelhoff et al., 2001). Today, in radius of Rout = 440 AU. Interestingly, this is in agreement
addition to 13CO and C18O, only the more abundant species with the best fit of the optical data, which gives Rout ~
after the carbon monoxide are detectable, such as HCO+, 400 AU.
CS, HCN, CN, HNC, H2CO, C2H, and DCO+. By studying
the excitation conditions of the various transitions observed 2.6. Proplyds
in the DM Tau disk, Dutrey et al. (1997) deduced molecular
abundances indicating large depletion factors, ranging from The disks we described so far are found in low-mass star-
5 for CO to 100 for H2CO and HCN, with respect to the forming regions such as the Taurus-Auriga clouds. Physical
abundances in the TMC1 cloud. They also directly meas- properties of disks surrounding low-mass stars born inside
ured the H2 density; the total disk mass they estimated is a clusters forming massive stars may be significantly differ-
factor of 7 smaller than the total mass measured from the ent because they are exposed to the strong ambient UV field
thermal dust emission. Both results suffer from uncertain- generated by nearby OB stars and can be photoevaporated
ties; only a more detailed analysis will allow the conclu- by it (Johnstone, 1998). This is the case for the proplyds,
sion that the gas-to-dust ratio is lower than 100, even if such which are protoplanetary disks seen in silhouette against the
behavior is expected. strong H II region associated to the Trapezium cluster in
The chemistry of the gas phase in the inner disk is poorly Orion A (e.g., McCaughrean and O’Dell, 1996).
constrained because of limited sensitivity (Najita et al.,
2000). Models of nebulae irradiated by stellar radiation, in- 3. DISKS AROUND INTERMEDIATE-MASS
cluding X-ray emission, suggest a complex chemistry (Glass- STARS: HERBIG Ae/Be STARS
gold et al., 1997), even at relatively large radii (r ≥ 50 AU)
(Najita et al., 2001). With masses in the range 2–8 M , Herbig Ae/Be (HAeBe)
Plate 1 summarizes the observable properties of a proto- stars, massive counterparts of T Tauri stars, are the progeni-
planetary disk encountered around a T Tauri star of 0.5 M tors of A and B main-sequence stars. Since they are more
and located at a distance of 150 pc. luminous and massive than the T Tauri stars, the surrounding
material is submitted to stronger UV and optical stellar flux.
2. 5. Illustration Through HH30 Several Herbig Ae stars are isolated but located in nearby
star-forming regions (Taurus, R Oph); their observed prop-
The HH30 observations, shown in Plate 2, give one of erties can be directly compared with those of T Tauri stars.
the most complete pictures of the material surrounding a This is not the case for Herbig Be stars because most of
PMS star. Optical and millimeter observations clearly trace them are located at larger and uncertain distances (D ≥ 500–
the same physical object. In Plate 2, the HH30 dust disk 800 pc). Therefore, in this section we will mainly discuss
observed in the optical by the HST (Burrows et al., 1996) isolated Herbig Ae stars.
is close to edge-on and appears as a dark lane; only the disk Like T Tauri stars, SEDs of HAeBe stars exhibit strong
surface or atmosphere is bright. The jet emission is also seen, IR excesses. Optical and NIR observations (Grady et al.,
perpendicular to the disk plane. J. Pety (personal commu- 1999) reveal that many of these objects are surrounded by
nication, 2003) has superimposed in contours to this im- large reflection nebulae (e.g., more than 1000 AU for the
age the blueshifted and redshifted integrated emission (with A0 star AB Auriga), revealing envelopes or halos (Leinert
respect to the systemic velocity) of the 13CO J = 2–1 line et al., 2001). However, there is now clear evidence that
 Dutrey et al.: Gas and Dust Components of Circumstellar Disks 85

Herbig Ae stars are also surrounded by disks. In particular, from the optically thick 12CO J = 2–1 line (which probes
resolved CO maps from millimeter arrays reveal that the about three scale heights above the disk midplane) is T ~
circumstellar material is also in Keplerian rotation [e.g., 60 K at R = 100 AU; this is significantly larger than the
MWC480, an A4 star (Manning et al., 1997) and HD 34282, temperature of ~30 K found for T Tauri disks using the
an A0 star (Pietu et al., 2003)]. Millimeter continuum sur- same tracer. Interestingly, the disk is not detected in the NIR
veys also suggest that the total surrounding mass may have in scattered light. Augereau et al. (2001a) have deduced that
a tendency to increase with the stellar mass (see Natta et al., either the dust emission at 1.6 µm is optically too thin to be
2000, their Fig. 1). So far, one of the more massive Kepler- detected, or there is a blob of optically thick material close
ian disks (~0.11 M ) has been found around an A0 Herbig to the star that hides the outer disk from the stellar radia-
Ae star: HD 34282 (Pietu et al., 2003). tion. Knowledge of the disk scale height is required to
Since the medium is hotter than for T Tauri stars, one choose between these possibilities. The existence of such
would expect different behavior, in particular, a rich chem- blobs is also favored by SED models of several Herbig Ae
istry. The limited sensitivity at present of molecular surveys stars (Meeus et al., 2001, their Fig. 8).
at millimeter wavelengths does not allow one to distinguish Near-infrared and CO/millimeter detections are not nec-
significant differences, and outer disks (r ≥ 50 AU) of Herbig essarily linked: The T Tauri DM Tau has the best known
Ae stars appear similar to “cold” outer disks found around disk at millimeter wavelengths, but the disk was only re-
T Tauri stars. cently detected in the NIR by performing deep integration
However, most of the differences should appear in the with the HST (Grady et al., 2003). Keeping this in mind,
warm material, closer to the star. Optical/NIR interferometric the MWC 480 disk appears very similar to a T Tauri disk,
observations by Monnier and Millan-Gabet (2002) revealed at least for the outer part (r ≥ 50 AU), although it is hotter
that the observed inner radius of disks is usually larger for and perhaps somewhat more massive.
HAeBe stars than for T Tauri stars. This is understood in
term of truncation by dust sublimation close to the star. 3.2. UX Orionis Phenomenon
They also found that grain sizes are similar for T Tauri and
HAeBe stars. Dullemond et al. (2001) have shown that di- Some HAeBe stars, such as UX Orionis, have a very
rect irradiation of Herbig Ae disks at their inner radius can complex spectroscopic, photometric, and polarimetric vari-
explain the bump observed at IR wavelengths in the SEDs ability that has been, in some cases, monitored for years.
of Herbig Ae stars. In a few cases, as for HD 100546, direct The variability has usually a short periodicity on the order of
detection of H2 with the Far Ultraviolet Spectroscopic Ex- ~1 yr and can be as deep as two magnitudes in the V band.
plorer (FUSE) (Lecavelier des Etangs et al., 2003) reveals It is very tempting to link this phenomenon to planetary
the existence of warm (T = 500 K) molecular gas close to formation; the variability could be caused by clumps of ma-
the star (r ~ 0.5–1 AU). terial (such as clouds of protocomets) located in the inner-
The fact that HAeBe stars are hotter has also favored the most disk and orbiting the star. Natta and Whitney (2000)
use of the Infrared Space Observatory (ISO) to characterize have developed a model in which a screen of dust sporadi-
the geometry and the dust composition of the disk close to cally obscures the star; this happens when the disk is tilted
the star. Bouwman et al. (2000) have performed a detailed by about 45°–68° along the line of sight. One clearly needs
spectroscopic study from 2 to 200 µm of the circumstellar more sensitive multiwavelength data at high angular reso-
material surrounding AB Auriga (A0) and HD 163296 (A1). lution on a large sample of Herbig Ae stars to distinguish
Their analysis of the SEDs, assuming an optically thin dust among the various models.
model, has revealed the existence of both hot (T ~ 1000 K)
and cold (T ~ 100 K, most of the mass) dust components, 4. FROM PROTOPLANETARY
while the NIR emission at 2 µm can be explained by the TO PLANETARY DISKS
presence of metallic iron grains. As in T Tauri disks, sub-
stantial grain growth has occured, with grain size up to On one side, one finds massive gaseous protoplanetary
~0.1–1 mm. It is also important to note that comparisons disks around T Tauri and Herbig Ae stars, and on the other,
of the ISO spectrum of the Herbig Ae star HD 100546 with one finds dusty planetary disks around young main-se-
those of Comet Hale-Bopp have revealed many similarities quence stars. A natural question is then whether there are
(Waelkens et al., 1999). disks in an intermediate state. If so, what are their obser-
vational characteristics? Limited by the sensitivity of cur-
3.1. MWC 480: Similarities and Differences rent telescopes, we know of only a few examples of objects
with a T Tauri Disk that can be considered to be “transition” disks.

MWC 480 is located at D = 140 pc, in the Auriga cloud. 4.1. Surprising Case of BP Tau
CO observations by Manning et al. (1997) have revealed
that the surrounding disk is in Keplerian rotation around BP Tau is often considered as the prototype of CTTs. It
an A4 star (Simon et al., 2000). The disk is large (Rout = has a high accretion rate of ~3 × 10 –8 M /yr from its cir-
600 AU) and inclined by about 35° along the line of sight. cumstellar disk, which produces strong excess emission in
The stellar mass is around ~2 M . The temperature deduced the ultraviolet, visible, and NIR (Gullbring et al., 1998). It is
86 Comets II

also very young [6 × 105 yr (Gullbring et al., 1998)]. De- tentatively attributed to PAH (Sylvester and Skinner, 1996,
spite these strong CTT characteristics, its millimeter proper- and references therein) that are frequently observed in SEDs
ties are very different from those of other T Tauri stars sur- of HAeBe (e.g., Meeus et al., 2001). But the lack of ex-
rounded by CO disks. cess in the NIR, the lack of photometric variability, the faint
Recent CO J = 2–1 and continuum at 1.3-mm images from intrinsic measured polarimetry (Yudin, 2000), and most
the Institut de Radio Astronomie Millimétrique (IRAM) importantly, the low disk-to-star luminosity ratio (8.4 × 10–3)
array have revealed a weak and small CO and dust disk correspond to the description of a Vega-like star. Both
(Simon et al., 2000). With a radius of about =120 AU, the HAeBe and Vega-like classes show a large spread of ages.
disk is small and in Keplerian rotation around a (1.3 ± 0.2) With an age of 5 m.y. (Weinberger et al., 2000), HD 141569
(D/140 pc) M mass star. A deeper analysis of these CO J = falls at the common edge of the two categories.
2–1 data (Dutrey et al., 2003) also shows that the J = 2–1 HD 141569 is among the few stars that show a spatially
transition is marginally optically thin, contrary to what is resolved optically thin dust disk in the NIR. Contrary to the
observed in other T Tauri disks. The disk mass, estimated β Pictoris disk, the inclination of the HD 141569 disk on the
from the millimeter continuum emission by assuming a gas- line of sight offers the opportunity to investigate both the
to-dust ratio of 100, is very small (1.2 × 10–3 M ) (for com- radial and azimuthal profiles of the dust surface density in
parison, a factor of 10 below the minimum initial mass of the great detail. Using coronagraphic techniques, the HST iden-
solar nebula). By reference to the mass deduced from the tified a complex dust structure seen in scattered light of
continuum, the CO depletion factor can be estimated; this about 10 times our Kuiper belt size (~500 AU) (Augereau
leads to a factor as high as ~150 with respect to H2. Even et al., 1999). Mid-infrared thermal emission observations
taking into account possible uncertainties such as a lower only partly compensate for the lack of constraints on the
gas-to-dust ratio or a higher value for the dust absorption innermost regions (<1" ≡ 100 AU) masked by the HST coro-
coefficient, the CO depletion remains high compared to nagraph (Fisher et al., 2000). Both data help to sketch out
other CO disks. Finally, the kinetic temperature derived from the overall dust distribution, as summarized in Fig. 4 of
the CO data is also relatively high, about ~50 K at 100 AU. Marsh et al. (2002). The dust appears depleted inside ~150 AU
Both the relatively high temperature and the low disk compared to the outer regions. The outer disk has a complex
mass suggest that a significant fraction of the disk might shape dominated by two nonaxisymmetric and not accu-
be superheated (above the blackbody temperature), similar rately concentric wide annulii at 200 and 325 AU (Mouillet
to a disk atmosphere (e.g., Chiang and Goldreich, 1997) et al., 2001) respectively. Interestingly, the furthest ring is
(see also section 2). With reasonable assumptions for the made of grains smaller than the blowout size limit, which
dust grain properties and surface density, one can then es- theoretically points out the presence of cold gas in the outer
timate the fraction of small grains (a = 0.1 µm) still present disk (Boccaletti et al., 2003). Surprising, an arc that is ra-
in the disk to reach τV = 1 in the visible at the disk mid- dially thin but azimuthally extended over ~90° is located
plane. Since it corresponds to a total mass of small grains at about 250 AU, precisely between the two major ring-like
of about 10% of the total mass of dust derived from the structures. This information about the disk morphology is
millimeter continuum data (1.2 × 10 –5 M ), this is not in- very valuable because it indicates the impact of internal
compatible with the current data, but should be confirmed (planets?) and/or external gravitational perturbations (stel-
by optical and NIR observations. lar companions?) (Augereau and Papaloizou, 2004).
It is also interesting that the CO content of BP Tau is too The detection of a substantial amount of cold gas asso-
high to result from evaporation of protocomets [falling evap- ciated with an optically thin dust disk is also unusual (Zuck-
orating body (FEB) model; see also section 5]. Considering erman et al., 1995). Recent millimeter interferometric obser-
the total number of CO molecules in the disk and the CO vations of HD 141569 reveal the gaseous counterpart of the
evaporation rate of an active comet such as Hale-Bopp, a extended disk resolved in scattered light (see Plate 3). The
few times 1011 large comets similar to Hale-Bopp would be CO gas in rotation shows a velocity gradient consistent with
simultaneously required to explain the amount of CO gas the major axis of the optical disk. Interestingly, hot gas (CO)
present in the BP Tau disk. This is well above the number of is also detected by high-resolution mid-IR spectroscopy,
FEBs falling on β Pictoris per year (a few hundred). which reveals the gaseous content of the inner disk (Brittain
Taken together, the unusual millimeter properties suggest and Rettig, 2002) at a few tens of AU from the stars.
that BP Tau may be a transient object in the phase of clear- The HD 141569 disk possesses NIR properties close to
ing out its outer disk. those of the β Pictoris disk and mid-IR and millimeter prop-
erties close to those of an Herbig Ae disk, so it seems rea-
4.2. Ambiguous Case of HD 141569 sonable to consider it as a transition disk.

HD 141569 is a B9 star located at ~100 pc. The position 4.3. Puzzle of Weak-Line T Tauri Stars
of the star close to the ZAMS in the HR diagram and the
presence of an IR circumstellar excess lead many authors Weak-line T Tauri stars (WTTs) have a SED that presents
to classify it as an HAeBe star. This was reinforced by the a weak IR excess; unlike CTTs, they do not exhibit strong
presence of circumstellar gas later detected by Zuckerman optical emission lines (with WHα ≤ 10 Å). As such, they are
et al. (1995) and by the identification of emission features usually considered to be the evolved counterpart of the
 Dutrey et al.: Gas and Dust Components of Circumstellar Disks 87

CTTs stars and are classified as Class III objects surrounded stars with circumstellar material shows infrared excess above
by an optically thin NIR disk (a few ~107 yr). ~10 µm, from which it is possible to have some indication
However, several studies show that a significant fraction about the dust size, spatial distribution, and total mass, or
of the WTTs have ages on the same order as those of CTTs simply information about the fraction of stars harboring such
(Stahler and Walter, 1993; Grosso et al., 2000). Among planetary disks (Backman and Paresce, 1993). More recent
them, one interesting example is the case of V836 Tau: This ISO surveys of nearby stars show that about 20% of the
star presents the optical properties of WTT stars; its milli- stars have infrared excess attributed to circumstellar material
meter characteristics are very similar to those of BP Tau (Dominik, 1999) with a typical lifetime of about 400 m.y.
since it is also surrounded by a compact CO disk (Duvert (Habing et al., 1999, 2001).
et al., 2000). Its observed properties are also very similar to For an extremely small fraction of these disks, it is pos-
those of the BP Tau disk. More recently, Bary et al. (2002) sible to image the dust. These images are produced by the
have reported H2 detection around DOAr 21, a WTT located scattered light at visible wavelengths, or by images of the
in ρ Oph that is even more puzzling. infrared thermal emission of the warm part of the disk at 10
We have only a few examples of transition disks, and or 20 µm. The first historical image of such a disk was the
each of them exhibits very different properties that are de- image of the disk of β Pictoris obtained with coronographic
pendent upon the observational approach (optical vs. milli- observations of the scattered light (Smith and Terrile, 1984).
meter/submillimeter observations). This clearly demonstrates Imaging is difficult; indeed, β Pictoris remained the only
that only multiwavelength studies can allow the retrieval of disk imaged until the late 1990s (see, e.g., Lecavelier des
the physical properties of these objects. The scenario by Etangs et al., 1993; Kalas and Jewitt, 1995; Mouillet et al.,
which massive disks dissipate and perhaps form planets is 1997a; Heap et al., 2000), when new instruments allowed
poorly constrained today. observers to image a few other disks by the detection of the
scattered light (Schneider et al., 1999) (Fig. 1) or by the
5. PLANETARY DISKS detection of the thermal emission in the infrared [around
HR 4796 (Jawardhana et al., 1998; Koerner et al., 1998)]
Since the lifetime of massive protoplanetary disks is or in the submillimeter [images of Vega, Fomalhaut, and
observed to be less than a few ~107 years, we should not β Pictoris have been obtained by Holland et al. (1998), and
a priori expect disk structure beyond that age. As circum- images of ε Eridani by Greaves et al. (1998)].
stellar disks evolve, their mass decreases. When the disks Observations of the dust provide important constraints
dissipate, the material becomes less bright, less dense, and on the spatial structure of the disks. For example, the mor-
apparently more difficult to detect. Infrared excess detection phology of the β Pictoris disk and the inferred spatial dis-
of material around nearby main-sequence stars (Aumann et tribution have been analyzed in great detail (Artymowicz et
al., 1985) leads to the conclusion that the lifetime of the al., 1989; Kalas and Jewitt, 1995). Images revealed unex-
thin disks is longer than that of massive disks. Since the time pected properties, such as the presence of a break at
spent at these late stages is longer, this provides the oppor- ~120 AU in the radial distribution of the dust, the warp of
tunity to detect evolved disks in the solar neighborhood (less the disk plane, and various asymmetries. All asymmetric
than ~100 parsecs) around stars older than few 107 years. features are often attributed to gravitational perturbation of
These disks are less dense than protoplanetary disks, but massive bodies such as Jupiter-mass planets (Lecavelier des
their proximity allows us to observe them in great detail. Etangs et al., 1996; Lecavelier des Etangs, 1997b; Augereau
The disks seen around main-sequence stars are now believed et al., 2001b).
to be the visible part of more massive systems in which most
of the mass is preserved in the form of planetesimals and
even planets. There, planetary formation is either at the end
or already finished (Lagrange et al., 2000).
The duration of the “planetary disk” phenomenon is so
long (see below) that by nature they are obviously not the
remaining material of the protoplanetary disks. It is now
clear that these planetary disks have been replenished with
material from a preexisting reservoir. As we will see below,
the basic process needed to sustain these disks is based on
the release of dust and/or gas by colliding asteroids and/or
by evaporating planetesimals. These disks are thus also de-
scribed as debris disks or second-generation disks.

5.1. Dust in Planetary Disks

First detected by IRAS because of their infrared excess,

the dust component of planetary disks is the easiest part to Fig. 1. Image of dust scattered light in the HR 4796 ring ob-
detect. The spectral energy distribution of main-sequence served with the Hubble Space Telescope (Schneider et al., 1999).
88 Comets II

The most intriguing characteristic of the inner portion cases, below the detection limit of current instruments. Mo-
of the β Pictoris disk is the so-called “warp,” which consists lecular transitions at millimeter wavelengths are too faint
of a change of the inclination of the midplane of the disk to be detected. They give only upper limits on the gas con-
inside about 80 AU. This warp is explained by the presence tent (Dent et al., 1995; Liseau, 1999). Detections of infra-
of a planet on an inclined orbit with the same inclination as red emission of H2 at 17 and 28 µm around main-sequence
the tilt of the inner disk (Mouillet et al., 1997b). The meas- stars have been reported by ISO (Thi et al., 2001a,b). How-
ured warp distance allows one to constrain Mp × D2p, where ever, these detections have been challenged by groundbased
Mp and Dp are the mass and the distance of the perturbing observations at 17 µm, which show no detection with three
planet. In the case of β Pictoris we have times better sensitivity (Richter et al., 2002). FUSE obser-
vations also showed that if the ISO detection of H2 emis-
MpD2p ≈ 2 × 10 –3 M*(10 AU)2(t/107 yr)–1 sion around β Pictoris is real, then this H2 is not distributed
widely throughout the disk (Lecavelier des Etangs et al.,
If the age of the system is t ~ 2 × 107 yr (Barrado y Navas- 2001). The HST detection of Fe II emission lines in the disk
cués et al., 1999), then a Jupiter-mass planet at 10 AU and of β Pictoris is marginal and yet to be confirmed (Lecavelier
inclined by 5° from the disk plane can easily explain the des Etangs et al., 2000). Finally, the only strong detection
observed warp. of emission from the gaseous component in a planetary disk
Similarly, in the case of HR 4796, sharp truncation of has been performed by Olofsson et al. (2001). With high-
the ring structure is observed (Fig. 1) (Schneider et al., resolution spectroscopy of the β Pictoris disk, they clearly
1999). The presence of a ring is expected to shed light on detected the resonantly scattered Na emission through the
the physical phenomena that occurs at places where plan- Na I doublet line at 5990 and 5996 Å. The gas can be traced
ets are typically supposed to form. However, there is still from less than 30 AU to at least 140 AU from the central
no general agreement on the interpretation of this trunca- star. Unfortunately, this observation remains unique. This
tion, which could be produced by the gravitational pertur- definitely presents a new field of observation with an origi-
bations of a planet (e.g., Wyatt et al., 1999) or by drag of nal technique. Although emission spectroscopy of tenuous
the dust by the gas component of the disk (Klahr and Lin, gas disks is difficult, absorption spectroscopy is much more
2001; Takeushi and Artymowicz, 2001). sensitive. In planetary disks seen nearly edge-on, the cen-
A key point concerning disks around main-sequence stars tral star can be used as a continuum source, and the detec-
is that the lifetime of the dust is shorter than the age of these tion of absorption lines offers the opportunity to scrutinize
systems (see Artymowicz, 1997, p. 206, Fig. 8). In the β Pic- the gaseous content in details.
toris disk, dust particles are destroyed by collisions between A few months after the discovery of the dust disk around
grains, which produce submicrometer debris quickly elimi- β Pictoris, its gaseous counterpart was discovered through
nated by the radiation pressure. In the less-dense disks, such the Ca II absorption lines (see Fig. 2) (Hobbs et al., 1985;
as the ε Eridani ring (Greaves et al., 1998), the Pointing- Vidal-Madjar et al., 1986). Because one absorbing component
Robertson drag is the dominant process, which also elimi- is seen identically in all observations and at the same radial
nates the dust on a timescale shorter than the disk age. As velocity as the star (20 km s–1), it is called the “stable” gas
the lifetime of the dust is very short, one must consider that component. This stable gas is composed of small amounts
the observed dust is continuously resupplied (Backman and of neutral Na and Fe, as well as large amounts of singly
Paresce, 1993). It is generally thought that the debris disks ionized species such as Ca+, Fe+ Mg+, Mn+, and Al+. The
are substantial disks of colliding planetesimals [see Back- overall composition is close to solar (Lagrange et al., 1998).
man et al. (1995) for an analogy with a collision in the solar Ultraviolet spectroscopy leads to the detection of two very
system Kuiper belt]. These disks can thus be considered as peculiar elements: C I and the CO molecule, which both
the signature of complete planetary systems that, like our have short lifetimes. On the other hand, the OH molecule
own solar system, contain interplanetary dust, asteroid-like was not detected with a relatively tight upper limit (Vidal-
kilometer-sized bodies, and probably comets and planets. Madjar et al., 1994). The numerous electronic transitions
The visible part of these disks is only the fraction of mate- of CO in the ultraviolet give constrains on the column den-
rial having the largest cross section, showing the presence sity, temperature (~20 K), and a very unusual isotopic ratio
of invisible but more massive objects. 12CO/13CO = 15 ± 2 (Jolly et al., 1998; Roberge et al., 2000).

Circumstellar gas signatures similar to those of β Pictoris

5.2. Gas Disks Around Main-Sequence Stars ones are also seen around some other main-sequence stars.
It should be noted, however, that in the rare cases where a
Although apparently more difficult to interpret, the gas Ca II (or, e.g., Fe II) line at the star radial velocity has been
component of the planetary disks provides the opportunity detected toward other stars like HR 10, these stars have been
for the most detailed modeling of circumstellar processes. identified because they also show either spectral variabil-
In particular, the β Pictoris spectroscopic variability is now ity, or the presence of over-ionized species, or redshifted
well explained in many details by the evaporation of com- optically thick absorption lines. This lack of detection of
etary objects close to the star (see section 5.3). only the circumstellar absorption at the systemic velocity
In contrary to emission from more massive disks, emis- may be caused by possible confusion with the interstellar
sion lines from the gaseous planetary disks are, in most medium. The first main-sequence star discovered to have a
 Dutrey et al.: Gas and Dust Components of Circumstellar Disks 89

et al., 1997b). Links between these gas and dust features

have yet to be understood.

5.3. Beta Pictoris Disk: A Cometary Disk

The β Pictoris disk has certainly been the most fruitful for
surprises and discoveries. In addition to the gaseous stable
component, variable absorption features have been detected
and surveyed since 1984 (Fig. 2). Features that are slowly
variable are confined most of the time to one or two compo-
nents redshifted by 10–30 km s–1 relative to the star. Al-
though such structures seem to be changing in both velocity
and strength (by about ±10 km s–1 in velocity and large fac-
tors in strength), they nevertheless remain very comparable
during a few consecutive hours, often from one day to the
next and even sometime over weeks.
Some other components present strong variability, in par-
ticular in the Mg II and Al III lines. These components are
also observed in the Ca II and Fe II line as weak and broad
absorptions spread over a few tens of kilometers per sec-
ond. The changes are observed on a very short timescale,
hours or even less. These features are mostly strongly red-
shifted, with shifts that could reach 300–400 km s–1. These
highly varying features were detected only in ionized spe-
cies, including highly (over-)ionized ones like Al++ and
C+++, completely unexpected in such a relatively “cool”
stellar environment. The rapid changes make these features
difficult to track.
These spectral variations are interpreted with a scenario
of star-grazing comets. The presence of strong redshifted
ionized gas is difficult to understand, since the very high
Fig. 2. (a) Ca II spectrum of β Pictoris (Lecavelier des Etangs, radiation pressure should expel it very quickly. The vari-
2000). The stable component is visible at 20 km s–1 heliocentric able absorption lines are almost always redshifted, corre-
velocity. This spectrum shows two variable redshifted components: sponding to infalling gas seen in absorption against the
one sharp absorption at low velocity and one broad absorption stellar continuum (in an edge-on disk). The gas must then
line at high velocity (>100 km s–1). (b) Simulation of Ca II absorp- be injected with very high inward radial velocity. There is
tion lines produced by a FEB at large distance. The line is red-
only one simple way to produce this situation, namely the
shifted and sharp, with a profile very similar to the profile of the
evaporation of grains moving toward the star. Since the
redshifted variable lines observed in the β Pictoris spectrum.
radiation pressure acts on grains, they must be injected with
high velocity, through the evaporation from more massive
bodies for which the gravitation is much larger that the ra-
diation force. This model has been developed in great de-
very similar spectroscopic behavior to β Pictoris is HR 10 tail (Beust et al., 1990, 1991a,b), and can be referred to as
(Lagrange et al., 1990). This star shows variable redshifted the “evaporation of star-grazing comets.” Indeed, the strong
or blueshifted absorption lines (Lagrange et al., 1990; Welsh variability in the circumstellar lines of the ionized elements
et al., 1998), and a central component seems relatively like Fe+, Al++, C+++, and Mg+ is now attributed to the evapo-
stable. Very highly excited levels of Fe+ have been detected, ration of kilometer-sized, “cometary-like” bodies falling to-
proving that the gas is not interstellar but circumstellar. Red- ward the star; this is the “falling evaporating bodies (FEB)”
shifted optically thick Mg II lines have also been detected scenario. The over-ionized variable species Al++ and C+++
and interpreted as small clouds of excited gas falling toward cannot be produced by photoionization, but Beust and Tag-
the star (Lecavelier des Etangs, 1998). ger (1993) showed that they can be formed by collisional
51 Oph is an interesting case because circumstellar dust ionization in the coma surrounding these FEBs.
is present simultaneously with the gas: 51 Oph presents a Among the different phenomena that can be explained
complex system with dusty infrared excess due to cold dust, by this model, one can stress the observation of abnormal
silicate emission features, absorption lines by overionized line ratio in doublet features. For example, although the
species (Grady and Silvis, 1993), Fe+ at excited levels, an Mg II doublet has an intrinsic oscillator strength ratio of 2,
abnormal Mg II line-intensity ratio, and finally a possible de- the measured ratio is exactly 1, even for unsaturated lines
tection of C I in the circumstellar gas (Lecavelier des Etangs (Vidal-Madjar et al., 1994). This proves that the absorbing
90 Comets II

gas cloud is optically thick (ratio = 1) but does not cover the 1994; Roberge et al., 2000). CO and C I are destroyed by
total stellar disk (the lines are not saturated). This behavior is ultraviolet interstellar photons (extreme UV flux from the
directly explained by the FEB model, which produces clump- star is negligible). Like the dust, they have lifetimes shorter
iness of the absorbing clouds (Beust et al., 1989). Similar than the age of the star (tCO ~ tCI ~ 200 yr). A mechanism
ratios have also been detected in redshifted absorptions to- must replenish CO with a mass rate of MCO ~ 1011 kg s–1.
ward other “β Pictoris-like stars.” The corresponding dust/CO supplying rate is Mdust/MCO ≈ 1.
With several hundreds of FEBs per year, the frequency is This is very similar to the dust/CO ratio in the material sup-
several orders of magnitudes higher than that of Sun-graz- plied by evaporation in the solar system. This similarity pro-
ing comets in the solar system. Planetary perturbations are vides an indication that the β Pictoris dust disk could be
thought to be the process responsible. Direct scattering by supplied by evaporating bodies orbiting at several tens of
close encounters with a massive planet does not seem to be AUs from the star, much in the same way as Chiron evapo-
efficient unless the planet eccentricity is very high (Beust et rates at dozen of AUs from the Sun.
al., 1991b). Beust and Morbidelli (1996) proposed a generic
model based on a mean-motion resonance with a single mas- 5.4. Toward a Global Picture
sive planet on a moderately eccentric orbit (e = 0.05). In-
deed, a test particle trapped in the 4 : 1 resonance with such Disks around main-sequence stars are probably related
a planet becomes star-grazing after =10,000 planetary revo- to the presence of young planetary systems in a phase of
lutions. This model explains not only the preferred infall strong activity. They show that the planetary systems are
direction, but also the radial velocity-distance relation ob- still active and evolve after their formation.
served in the FEBs. There are still many unknowns. This new field of as-
Many other stars show redshifted absorption lines (HR tronomy is still a collection of different objects that do not
2174, 2 And, etc.). All these detections of redshifted absorp- correspond to an evolutionary scheme, and a global picture
tion lines raise the question of the explanation for the quasi- is still to be created. It is clear that the many different names
absence of blueshifted events. In the β Pictoris case, it is used for these disks, which we elected to call the “plane-
believed that the orbits of the star-grazing comets always tary disks,” show that there is not an unique understanding
present approximately the same angle to the observer (be- of the phenomenon. Some authors refer to the “Vega phe-
cause the gas is seen in absorption against the stellar con- nomenon,” often to explain the infrared excess. The term
tinuum in an edge-on disk). However, when observed on “β Pictoris phenomenon,” used because of the number of
several stars, some blueshifted orientation should be ex- different phenomena observed around that star, is even more
pected. Given the very impressive fit between the β Pictoris confusing. “Kuiper disk,” “cometary disk,” or alternatively
observations and the FEB model, it is likely that the β Pic- “debris disk” refer to evidence concerning the different ori-
toris FEB phenomenon is somehow particular, and that other gins of these disks. It is not yet clear if the many pieces
stars present either real infall on the star or their evaporating shown here correspond to the same puzzle. New observa-
bodies may be generally destroyed before they reach the tions and theoretical works will be needed to resolve these
periastron (Grinin et al., 1996). In the latter case, the pro- issues in the next decade.
cess needed to place these bodies on very eccentric orbits in
less than one orbital timescale remains to be discovered. 6. FUTURE OBSERVATIONS
Another class of cometary-like object might also be pres-
ent around β Pictoris. Collision of planetesimals are believed The examples given in the previous sections clearly dem-
to continuously resupply most of the dusty disks around onstrate that the frontier between the different classes of ob-
main-sequence stars. In the case of β Pictoris, a significant jects is not well constrained, partly because the statistics are
part of the disk can be also produced by the evaporation of still too poor to provide a quantitative understanding of some
kilometer-sized bodies located at several tens of AU from of the observed properties. Since very few disks have been
the central star (Lecavelier des Etangs et al., 1996). Indeed, resolved so far, deriving a timescale and a detailed evolu-
in the β Pictoris disk, CO evaporates below 120 AU from tionary scheme from protoplanetary to planetary disks re-
the star. If bodies enter that region, they start to evaporate mains speculative. Moreover, when it comes to the proto-
and eject dust particles. These particles are subsequently planetary phase, our understanding is crudely limited to the
spread outward in the whole disk by the radiation pressure. cold outer disks (r ≥ 50 AU).
The distribution of their eccentric orbits gives a dust surface Throughout this chapter, the examples used have illus-
density similar to that observed around β Pictoris. This alter- trated that only multiwavelength studies of disk properties
native scenario for the production of dust in the β Pictoris will allow astronomers to properly incorporate in their
disk easily explains any asymmetry even at large distances, models all the physical processes involved in the observed
because a planet in the inner disk can influence the distribu- phenomena.
tion of nearby parent bodies, producing the outward spread
of dust (Lecavelier des Etangs, 1998). 6.1. Challenge for Protoplanetary/Transition Disks
The observed CO/dust ratio is another argument in favor
of this scenario. An important characteristic of the β Pictoris In protoplanetary disks, most of the material lies in the
disk is the presence of cold CO and C (Vidal-Madjar et al., relatively cold outer part of the disks. Hence resolved sub-
 Dutrey et al.: Gas and Dust Components of Circumstellar Disks 91

millimeter observations, obtained with large millimeter ar- disk. Protoplanetary disks are indeed H2 disks, and direct
rays such as ALMA, will provide the best tool to investi- investigation of the H2 distribution and mass remains the
gate this reservoir of mass (r > 20–50 AU). In particular, most direct way to study how protoplanetary disks dissipate.
ALMA will observe large samples, providing statistics on This domain will strongly benefit from satellites such as the
disk properties and frequency. Of course, to study the hotter Space Infrared Telescope Facility (SIRTF)/Spitzer Space Tele-
inner disk, where planets form (0.1 ≥ r ≥ 10 AU), optical, scope (SST) and the James Webb Space Telescope (JWST).
NIR, and mid-IR interferometry techniques are required. As Finally, the current knowledge of protoplanetary disks is
soon as they will be able to produce images (even with a biased by the sensitivity limitations, and we can image only
few baseline numbers), instruments such as AMBER and the brighter disks. Disk clearing is poorly constrained. The
MIDI on the Very Large Telescope Interferometer (VLTI), ALMA sensitivity will allow many other objects similar to
or the Optical Hawaiian Array for Nanoradian Astronomy BP Tau, and even optically thin dust disks in the NIR, to
(OHANA), will add to our understanding of the dust prop- be imaged in the submillimeter.
erties and composition. Images (or a reasonable UV cover-
age) are necessary in order to choose between all the exist- 6.2. Challenge for Planetary Disks
ing models of dust disks; in particular, they should allow us
to disentangle the geometry, temperature, and opacity ef- By extrapolation from ISO results on the occurrence of
fects. Figure 3 summarizes which part of the disk can be debris disks around main-sequence stars, and according to
investigated, depending on the instrument used. A combina- the Hipparcos catalog, one can predict ~102 and ~103 plan-
tion similar to “ALMA and VLTI” would efficiently sample etary dust disks around (hypothetical) stars younger than
the global disk properties. A necessary step to understand about 0.5 G.y. within 20 pc and 50 pc radii of the Sun re-
how planets form is to view the gaps that are created by spectively. These stars are close enough that they are not
protoplanets. For this purpose, images are definitely re- limited by angular resolution considerations, but their disks
quired, either at submillimeter or NIR wavelengths. In its are simply too tenuous to be detected with current instru-
large configuration, ALMA will have baselines up to 14 km, ments. This points out a crucial need for an enhancement in
providing an angular resolution of ~0.03" (or 4 AU at the sensitivity combined with high-angular-resolution techniques.
Taurus distance) at λ = 1.3 mm. Hydrodynamics coupled Precise disk shapes, fine structures, and asymmetries as re-
to radiative transfer simulations of the dust emission at vealed by imaging may indeed be signposts of undetected
350 GHz by Wolf et al. (2002) show that ALMA will be able gravitational companions, such as planets perturbing the un-
to resolve a gap created by a proto-Jupiter, located at 5 AU derlying disk of kilometer-sized bodies that release the ob-
from a star at D = 150 pc. Concerning the gas content, in served short-lived dust.
spectral lines near λ = 1.3 mm, ALMA will be about 30 The observational techniques discussed below are sum-
times more sensitive than the IRAM array and quantitative marized in Plate 4. In the NIR, high-contrast imaging with
chemical studies could begin. Multitransition analyses would single-aperture telescopes is required to detect faint dust
even allow observers to measure abundance gradients in the disks very close to a bright star. For instance, new genera-
tions of adaptive optics systems and new concepts of corona-
graphic masks are currently under study, with the prime goal
being detection of faint objects from the ground, ideally
down to planets (e.g., VLT/Planet Finder). At these wave-
lengths (but also in the mid-IR), the innermost regions of
planetary disks will nevertheless remain unreachable with-
out the help of interferometry (e.g., Keck I and VLTI). Re-
solving the material within the very first AU around young
main-sequence stars and ultimately producing images by
NIR and mid-IR interferometry are attractive challenges in
the near future. In the mid-IR, single-aperture telescopes
suffer an unavoidable decrease in spatial resolution. The pre-
dominant gain at these wavelengths will mostly come from
future spacebased telescopes, particularly the 6-m JWST
and SST, with increases of two or three orders of magni-
tudes in detection thresholds. While current high-resolution
imagers in the mid-IR are limited to disks around nearby
stars younger than a few tens of millions of years, JWST’s
Mid-Infrared Instrument (MIRI) should resolve debris disks
around 1-G.y.-old A-type stars at 50 pc. In the millimeter,
Fig. 3. This montage summarizes the observable properties of a ALMA will permit the detection of an unresolved (but op-
protoplanetary disk encountered around a T Tauri star located at tically thin) clump of dust of 10 –2 M orbiting a star up to
150 pc. This illustrates which region of the disk is sampled de- 100 pc away in only 1 h of observing time (see also ALMA,
pending on the telescope in use. 2004).
92 Comets II

More and more observational efforts will certainly be Bary J. S., Weintraub D. A., and Kastner J. H. (2002) Detection of
focused on the gas in order to provide a better understand- molecular hydrogen orbiting a “naked” T Tauri star. Astrophys.
ing of its timescales and dissipation processes. Since the gas J. Lett., 576, L73.
content of young planetary disks is yet badly constrained, Beckwith S. V. W., Sargent A. I., Chini R. S., and Guesten R.
(1990) A survey for circumstellar disks around young stellar
anticipating future results might be very speculative. How-
objects. Astron. J., 99, 924.
ever, the ALMA sensitivity would allow to detect, in 1 h
Beckwith S. V. W., Henning T., and Nakagawa Y. (2000) Dust
of observing time, a CO column density of a few 1012 cm–2 properties and assembly of large particles in protoplanetary
in a beam of 2.5" (planetary disks are close to us, and hence disks. In Protostars and Planets IV (V. Manning et al., eds.),
angularly extended) assuming a linewidth of 3 km/s. This is p. 533. Univ. of Arizona, Tucson.
well below the CO column density of 1015 cm–2 detected Beust H. and Morbidelli A. (1996) Mean-motion resonances as a
by Vidal-Madjar et al. (1994) in β Pictoris. Depending on source for infalling comets toward β Pictoris. Icarus, 120, 358–
the gas geometry, the distance and the evolutionary status 370.
of the disk, ALMA would allow astronomers to place some Beust H. and Tagger M. (1993) A hydrodynamical model for
important constraints on various gas model distributions in infalling evaporating bodies in the β Pictoris circumstellar disk.
planetary disks. Icarus, 106, 42.
Beust H., Lagrange-Henri A. M., Vidal-Madjar A., and Ferlet R.
(1989) The β Pictoris circumstellar disk. IX — Theoretical
Acknowledgments. We thank A.Vidal-Madjar for fruitful com-
results on the infall velocities of Ca II, Al III, and Mg II. Astron.
ments. Figure 3 has been reproduced with the kind permission of
Astrophys., 223, 304–312.
H. Beust. A.D. would like to thank S. Guilloteau for a long term
Beust H., Vidal-Madjar A., Ferlet R., and Lagrange-Henri A. M.
and fruitful collaboration. M. Simon is also acknowledged for a
(1990) The β Pictoris circumstellar disk. X — Numerical simu-
careful reading of the manuscript. Many thanks to J. Pety, who
lations of infalling evaporating bodies. Astron. Astrophys., 236,
provided material for HH30 (Plate 2 and recent millimeter results).
202–216.
J.C.A. thanks the CNES for financial support.
Beust H., Vidal-Madjar A., Ferlet R., and Lagrange-Henri A. M.
(1991a) The β Pictoris circumstellar disk. XI — New Ca II ab-
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96 Comets II
 Weidenschilling: From Icy Grains to Comets 97

From Icy Grains to Comets

S. J. Weidenschilling
Planetary Science Institute

Comets formed from icy grains in the outer region of the solar nebula. Their coagulation
into macroscopic bodies was driven by differential motions induced by nebular gas drag. The
hierarchical growth by collisions produced “rubble pile” structures with sizes up to ~100 km
on timescales on the order of 1 m.y. Two-dimensional models of this growth, including orbital
decay due to drag, show radial mixing that lessens the tendency seen in one-dimensional mod-
els for components of a single characteristic size. Radial migration causes redistribution of con-
densed matter in the outer nebula, and produces a sharp outer edge to the Kuiper belt.

1. INTRODUCTION 2. PARTICLE MOTIONS IN

THE SOLAR NEBULA
Cometary nuclei are planetesimals that formed in the
outer reaches of the solar nebula. Presumably, they were The motions of solid particles in the solar nebula are
produced by the same process that formed planetesimals in dominated by drag forces due to gas; this is true even in the
the region of the terrestrial planets and the asteroid belt, but outermost region, where the density is low, and solids are
incorporated volatiles (notably water ice) that were in solid relatively more abundant due to condensation of volatiles at
form in the cold outer nebula. While comets may not be low temperatures. The radial pressure gradient partially sup-
pristine, they are probably the least-altered objects surviv- ports the gas against the Sun’s gravity, causing it to rotate
ing from the origin of the solar system. While much can at slightly less than the local Kepler velocity (Whipple,
be learned about their formation from their chemistry, they 1972). The fractional deviation from Keplerian rotation is
may also provide a unique record of the physical processes approximately the ratio of the thermal energy of the gas to
involved in their accretion. The material now present in any its orbital kinetic energy. One can show that ∆V, the differ-
comet originally existed in the solar nebula as microscopic ence between the gas velocity and Kepler velocity Vk, is
grains, probably a mixture of surviving interstellar grains proportional to the temperature T and the square root of the
and nebular condensates. Somehow, these submicrometer- heliocentric distance R (Weidenschilling, 1977). A typical
sized particles were assembled into bodies of sizes at least magnitude for ∆V is ~50 m s–1 for plausible nebular mod-
tens to hundreds of kilometers. It is clear that comets are els. As T decreases with R, ∆V does not vary strongly; for
not uniform aggregates of grains, but have structure on a plausible temperature gradient of T ∝ R–1/2, ∆V is inde-
larger scales. They display complex behavior that varies pendent of R. Thus, the deviation from Keplerian motion
both temporally and spatially (outbursts and jetting), and is larger in proportion to the orbital velocity at larger he-
implies inhomogeneities on scales of tens to hundreds of liocentric distances. Typically, ∆V/Vk is a few times 10–3 in
meters (Mumma et al., 1993; Weissman et al., 2004). On the region of the terrestrial planets, but can exceed 10 –2
the other hand, imaging of the nuclei of Comets Halley and beyond Neptune’s distance.
Borrelly at comparable resolution did not reveal obvious Solid particles are not supported by pressure forces. As
larger structural units; although both bodies were irregular a consequence, no particle can be at rest with respect to the
in shape, they did not appear to be lumpy on kilometer gas, but always has some components of radial and trans-
scales. Comets are structurally weak, as demonstrated by verse velocity. Their magnitudes depend on the particle size
shedding of fragments, occasional splitting, tidal disruption (more precisely, area/mass ratio) and drag law (Adachi et
of Shoemaker-Levy 9 during its encounter with Jupiter al., 1976; Weidenschilling, 1977). A small particle moves
(Asphaug and Benz, 1996), and the spontaneous disruption with the angular velocity of the gas (negligible transverse
of Comet LINEAR (Weaver et al., 2001). The observed component), but drifts radially inward at a rate that increases
properties of nuclei are consistent with “rubble pile” struc- with size. A large body pursues a Kepler orbit, experienc-
tures with components ~100 m in size that are very weakly ing a transverse “headwind” that causes its orbit to decay;
bonded, or perhaps held together only by gravity. These the rate of decay decreases with size. The peak radial ve-
properties are the expected result of formation by accretion locity, equal to ∆V, occurs at the transition between these
in the solar nebula. regimes. The size at which this peak velocity is reached

97
98 Comets II

the turbulent velocity (Weidenschilling and Cuzzi, 1993).

Unless the turbulence is very strong, the dominant source
of relative velocities is differential motion due to gas drag.

3. COLLISIONAL COAGULATION

If collisions between particles are to result in growth,

there must be some mechanism that allows them to stick
together. Perfect sticking is not required (and is unlikely
under most conditions for real materials), but at least some
collisions must yield net growth for bodies of all sizes. This
is not a problem for the initial stage of coagulation, involv-
ing micrometer-sized grains. For small particles, the rela-
tive velocities (thermal or drift) are low enough to allow
sticking by van der Waals surface forces. Theoretical mod-
Fig. 1. Particle velocities as functions of size in a model solar els (Dominik and Tielens, 1997) and laboratory experiments
nebula. The nebular parameters at 31.5 AU are: gas density 1.5 × (Blum and Wurm, 2000) confirm that coagulation under
10 –13 g cm–3, T = 57 K, ∆V = 52 m s–1. Particles are assumed to such conditions produces fluffy, fractal-like aggregates with
have fractal structures to diameter 1 cm, and density 1 g cm–3 at densities that decrease with increasing size.
d > 20 cm. Shown are radial and transverse components of sys- Under zero-gravity conditions in the solar nebula, this
tematic motions relative to the gas, thermal velocity, and gravita-
process may produce gossamer structures of macroscopic
tional escape velocity.
(approximately centimeter-sized) dimensions. However, this
type of growth cannot continue indefinitely; as the aggre-
gates become larger their drift velocities increase, and col-
does not vary strongly with heliocentric distance, and is lisions become energetic enough to allow some compaction
typically on the order of 1 m (Fig. 1). by rearranging bonds between grains. As the aggregates
The size dependence of the drag-induced velocity means become denser, their drift speeds increase further.
that any bodies that are not identical move relative to each Bodies of comparable size will collide rarely, and only
other and any ensemble of bodies having a range of sizes at low velocities. As shown in the simulations of Weiden-
will experience collisions. For small bodies (d < 1 m), only schilling (1997), most collisions occur between bodies of
radial drift is significant, and their relative velocities will quite different sizes. This circumstance favors growth, be-
be the difference between their radial velocities (far from cause the smaller “projectile” does not deliver enough ki-
the central plane of the nebula, their settling velocities may netic energy to disrupt the larger “target,” unless the latter
also be significant). Large bodies have high transverse ve- has very low impact strength. However, although a low
locity relative to the gas, but the same magnitude, ∆V, for probability of disruption is necessary for growth, it is not
all such bodies, so the relative velocity between any pair sufficient. The increase in drift velocities with size leads to
of large bodies is essentially the difference between their a problem: As can be seen from Figs. 1 and 2, meter-sized
radial velocities. The relative velocity between a small and bodies will have velocities relative to centimeter-sized par-
large body is essentially the latter’s transverse velocity. ticles as large as ∆V, i.e., tens of meters per second [if the
At the low temperatures of a few tens of degrees or less particles settle into a dense layer in the central plane of the
in the outer nebula, thermal motions dominate for microme- nebula, collective motion of particles and gas reduces the
ter-sized grains, but are negligible for larger bodies. Mu- effective value of ∆V (cf. Nakagawa et al., 1986)]. If such
tual gravitational perturbations are significant for bodies impacts do not result in net mass gain, then growth might
larger than about 1 km. Between those limits, gas drag stall before meter-sized bodies could form. If collisions (or
dominates. If turbulence is present, it can also induce rela- some other process) can produce bodies larger than this
tive motions. However, strong turbulence is unlikely to critical threshold, then further growth to kilometer size, at
persist at large heliocentric distances. In the outer nebula, which gravity can contribute to sticking, is assured. The
the surface density may be low enough to allow ionization centimeter-to-kilometer range is the critical stage of colli-
by cosmic rays, driving magnetorotational instability (Sano sional accretion.
et al., 2000), but the low gas density also favors dissipation It is not clear whether impacts at such speeds would
by ambipolar diffusion. The intensity of turbulence gener- result in net gain or loss of mass. This question cannot be
ated by this mechanism is unclear. In any case, the largest answered definitively, as we do not know the mechanical
eddies would have turnover timescales, imposed by the properties and impact strength of cometary material. Sirono
nebula’s rotation, comparable to the Kepler period. Bodies and Greenberg (2000) estimated the tensile and compres-
larger than about 1 m cannot respond to turbulent fluctua- sive strengths of porous aggregates of icy grains, and con-
tions on such timescales, while motions of smaller bodies cluded that compaction would dissipate a large fraction of
are correlated, leading to relative velocities smaller than energy during collisions, and would produce merged bodies
 Weidenschilling: From Icy Grains to Comets 99

Wurm et al. (2001) suggested that accretion of meter-

sized bodies would be aided by aerodynamic forces acting
on small grains. Grains would impact on the leading side,
brought by the “headwind” due to the body’s motion
through the gas. Grains or small aggregates striking at ve-
locities ~∆V would rebound (or displace grains from the
target) at speeds lower by perhaps an order of magnitude.
The gas flow would reverse their motion and return them
to the body’s surface, reimpacting at speeds low enough for
sticking by surface forces between the grains. This mecha-
nism could aid accretion at R ~ 1 AU, where plausible val-
ues for the gas density yield trajectories of only a few
centimeters for bouncing grains. However, it would not be
effective in the outer nebula, where impact speeds are com-
parable, but the gas density is lower by orders of magnitude;
the “turnaround distance” for grains would be correspond-
ingly larger, and their probability of reimpact on a meter-
sized target would be minuscule. Thus, particle coagulation
in the region of comet formation appears to require effec-
tive sticking in collisions.
Fig. 2. Contour plot of relative velocities between particles for
the same parameters assumed in Fig. 1. Particles of sizes <1 cm 4. GRAVITATIONAL INSTABILITY
have very low relative velocities, but bodies larger than ~1 m have
velocities ~50 m s–1. The “valley” in the central region shows that With the uncertainties attendant upon the messy and
bodies of nearly equal size have low relative velocities due to drag. poorly constrained mechanism of collisional sticking, the
Gravitational stirring dominates at sizes larger than about 1 km.
possibility of forming planetesimals by gravitational insta-
bility remains enticing. In the “classical” instability scenario
(Safronov, 1969; Goldreich and Ward, 1973), small particles
with substantial cohesion. Bridges et al. (1996) conducted settle to form a layer in the midplane of the solar nebula.
low-speed impact experiments involving frost-covered bod- When this layer reaches a critical density it becomes un-
ies. They concluded that the observed sticking was due to stable to density perturbations, which produce condensa-
interpenetration of irregular surfaces, and suggested that tions that collapse under their own gravity into solid bodies.
frost (of water ice and/or other volatiles) aided aggregation However, bodies formed by this mechanism in the outer
in the solar nebula. While this could not be the only mecha- nebula would be much larger than typical comets, and
nism (planetesimals evidently formed in the inner nebula, would not have any structure on macroscopic scales. In any
at temperatures too high for frosts), the mechanical prop- case, gravitational instability does not eliminate the need
erties of ices, especially their low elastic moduli, may have for particle coagulation. As pointed out by Weidenschilling
aided accretion in the outer solar system. Weidenschilling (1980), before the particle layer can reach the critical den-
(1997) emphasized that most collisions driven by gas drag sity, it drags the entrained gas at a velocity higher than that
would involve a small body impacting a much larger one. of the pressure-supported nebula. The resulting shear flow
If the bodies are porous aggregates, then the smaller one is unstable, and becomes turbulent, preventing further set-
might become embedded in the larger (it is not necessary tling. A layer of small (centimeter-sized or smaller) particles
to assume that the projectile survives intact). Weidenschil- cannot attain the critical density.
ling assumed that an impact added the projectile’s mass to If the bodies can accrete to sizes large enough to de-
the target, but removed an amount of material proportional couple from the shear-induced turbulence (>1 m), then they
to the impact energy; this is equivalent to the assumption can settle enough for the layer to attain the critical density.
that there is a critical impact velocity with net gain (loss) This condition is necessary for instability, but is not suffi-
of mass below (above) that threshold. An accreting body cient. The velocity dispersion must also be small enough
would experience impacts by smaller particles having a to allow density perturbations to grow. When the particle
range of sizes and relative velocities; as mentioned above, velocities are controlled by gas drag, they are not isotro-
bodies of comparable size would collide more gently. pic. As bodies of this size are too large to be stirred by
Whether a given body would grow or erode would depend turbulence, but too small for gravitational perturbations to
not only on the impact strength of the bodies, but on the be effective, their vertical velocity dispersion is very small;
size distribution of the ensemble, which would itself be a however, they may have a significant dispersion in radial
function of their strength. The impact strength assumed by velocity. If all particles were identical, then they would have
Weidenschilling resulted in net growth, but the range of the same radial velocity due to drag, but any real ensemble
allowable parameters remains to be determined. of particles produced by coagulation should have a range of
100 Comets II

sizes and corresponding velocities. The resulting dispersion transferred between levels, downward toward the midplane
inhibits gravitational instability (Weidenschilling, 1995). at rates proportional to their settling velocities, and by dif-
Ward (2000) showed that if the particle layer was bimodal fusion upward and downward along concentration gradients
with two different velocities, density perturbations in the where turbulence is present. Formation of a dense midplane
populations would be decoupled. For bodies larger than layer results in shear-induced turbulence, and the structure
about a meter, the radial velocity decreases with size (Fig. 1); of the layer is determined by a balance between settling and
the dispersion will diminish as the bodies grow, and the turbulent diffusion, with gravitational stirring included for
mean radial velocity decreases. The conditions for gravita- bodies large enough to decouple from the gas. The model
tional instability (density and velocity dispersion) can be parameters were chosen for a low-mass solar nebula at
attained, but only after collisional coagulation has produced 30 AU, with surface density of solids and gas of 0.4 and
bodies with mean size >10 m. As this is larger than the size 29 g cm–2, respectively. From the assumed initial state, with
of maximum radial velocity, there is no obstacle to further all solids present as micrometer-sized grains with a uniform
growth by collisions; gravitational instability becomes un- solids/gas mass ratio, the ensemble of particles evolved on
necessary by the time it becomes feasible. The instability a timescale of few times 105 yr, or a few thousand orbital
may still occur at that point, but its outcome will be differ- periods. This evolution could be divided into rather distinct
ent from the classical model. Bodies tens of meters in size stages. During the first few times 104 yr, thermal coagula-
are poorly damped by either drag or collisions, so the layer tion produced low-density, fractal-like aggregates, with sizes
maintains a significant velocity dispersion, which allows ~10 –2 cm, at all levels. As the aggregates in the upper levels
only density perturbations of long wavelength to grow settled toward the midplane, larger ones grew by sweeping
(Weidenschilling, 1995). The layer may break up into self- up smaller ones; this led to rapid growth and “rainout” of
gravitating clusters of particles, but these condensations are approximately centimeter-sized aggregates, which formed
too large (i.e., have too much angular momentum due to a layer with density greater than that of the gas. The shear
the rotation of the nebula) to collapse directly into solid between this layer and the surrounding pressure-supported
objects. Such condensations would probably be transient gas produced turbulence, which prevented settling of the
features, which would be torn apart by differential rotation. small aggregates within the layer. However, collisional
It is suggestive that for plausible values of the nebula’s growth continued, and a thinner sublayer of larger bodies
surface density, the characteristic wavelength of instability developed. This sublayer attained a density much higher
corresponds to condensation masses equal to those of com- than the classical threshold for gravitational instability (sol-
pact bodies with diameters ~100 km, about the size of typi- ids/gas ratio ~103), but the velocity dispersion was large
cal Kuiper belt objects. However, this may be coincidental; enough to prevent instability until the mean size was tens
it will be shown below that bodies of this size could grow of meters. With the assumption that instabilities in a poorly
by collisions within the lifetime of the solar nebula. damped system would not collapse, the collisional evolu-
tion was continued until bodies tens of kilometers in size
5. MODELING THE GROWTH accreted, after a model time of 2.5 × 105 yr. By that point,
OF COMETESIMALS gravitational stirring became effective and the velocity dis-
persion increased, with a significant vertical component.
5.1. One-Dimensional Models This caused the particle layer to become thicker, and its
density decreased; presumably still larger bodies would
Weidenschilling (1997) applied a numerical model of continue to grow by gravitational accretion.
particle coagulation and settling in the solar nebula to The size distribution of the accreting bodies (Fig. 3)
cometary formation; details of the model are described developed a distinct peak in the size range of tens to hun-
therein, and will be summarized only briefly here. That dreds of meters. The cause of this peak was the dependence
model is one-dimensional in the vertical direction, treating of radial velocity on size (Fig. 1) and the fact that collisions
the particle population in a series of levels at a single he- were due primarily to differences in radial velocity. The
liocentric distance. In each level, the particle size distribu- bodies with the largest velocities were quickly depleted by
tion is modeled by the mass in logarithmic diameter bins impacting larger bodies, opening a “valley” in the size dis-
from 10 –4 cm to >100 km. The evolution of the size distri- tribution at meter sizes. Bodies in the size range from tens
bution is computed in each of a series of levels, with colli- of meters to about a kilometer still had velocities larger than
sion rates due to thermal motion, differential settling, and their escape velocities, so there was no gravitational en-
radial and transverse motions due to gas drag. Particle den- hancement of their collision rates. Because their radial ve-
sities are assumed to vary with size, to simulate fractal struc- locities decreased with size, the larger bodies grew more
ture of small aggregates and compaction of macroscopic slowly, allowing smaller ones to catch up, and keeping the
bodies. Collisional outcomes depend on particle sizes and peak narrow. Eventually, the largest bodies began to have
impact velocities, consistent with an assumed impact significant gravitational enhancement of their collision rates,
strength. At each timestep, the number of collisions between and the peak became broader. During this stage of growth
particles of various sizes and the consequent changes in the the mean collision velocities decreased with increasing size,
size distribution are computed within each level. Bodies are reaching a minimum value at the transition from drag-con-
 Weidenschilling: From Icy Grains to Comets 101

accretion disk. The properties of the particle layer are av-

eraged through its thickness, so their model is effectively
one-dimensional in the radial direction, and complementary
to that of Weidenschilling (1997). They do not compute a
size distribution, but only a mean particle size as a func-
tion of time at a given radius. This approach neglects dif-
ferential drift motions among bodies of different sizes, and
allows only collisions due to turbulence, so their model
breaks down for disks with low turbulence. Despite these
limitations, they demonstrated that orbital decay due to gas
drag during particle growth could substantially alter the
radial distribution of solids relative to the gas during the
~106–107-yr lifetime of the solar nebula.

5.2. Two-Dimensional Models

Fig. 3. Computed size distribution in the nebular midplane at
various times, using the one-dimensional model of Weidenschilling In order to overcome the limitations of one-dimensional
(1997). After 105 yr, a “valley” forms in the range 1–10 m; bodies approaches, Weidenschilling (in preparation, 2003) has de-
of this size are near the peak in radial velocity, and are rapidly veloped a fully two-dimensional model of planetesimal forma-
depleted by collisions with larger bodies. Mass piles up in a peak tion. Its operation is similar to the one-dimensional model
at sizes ~100 m, where the radial velocity and collision rate are described above, but the vertical structure of the particle
decreasing with size. layer and its size distribution are computed in a series of
zones over a range of heliocentric distance. Bodies are trans-
ferred between zones at rates corresponding to their radial
velocities. The model also includes collective radial motion
trolled growth to gravitational accretion. This transition of the particle layer due to turbulent shear stress acting in
occurred when kilometer-sized bodies were accreting bod- the boundary layer (Goldreich and Ward, 1973) and radial
ies ~100 m in size. Larger bodies experienced more ener- diffusion by turbulence, but for macroscopic bodies these
getic collisions as impact velocities became dominated by are generally unimportant compared to orbital decay due
their escape velocities. Weidenschilling (1997) speculated to the drag of the “headwind.” Application of this two-di-
that cometary nuclei originated as “rubble piles” that were mensional model reveals some significant differences from
rather well-compacted at meter scale, but with more void the one-dimensional case.
space on larger scales, with a tendency to preserve struc- Figure 4 shows the size distribution in the range result-
ture on the scale of ~100 m. ing from a two-dimensional simulation from 30 to 90 AU,
The results of the one-dimensional coagulation model at model time of 5 × 105 yr. The innermost zone at this time
are consistent with observable physical properties of com- corresponds to the final stage reached by the one-dimen-
ets. However, that model has one significant shortcoming. sional simulation in Fig. 3. While the size distributions are
The peak radial velocity of ~50 m s–1 corresponds to 1 AU/ similar, in the two-dimensional case the “valley” around
century; this is approached only by bodies in a narrow range ~1 m is much shallower, and the peak at ~100 m is broader
of sizes (roughly 0.1–10 m), but even the lower radial ve- and more subdued. The apparent reason for this difference
locities of larger and smaller bodies could still result in is the dependence of the growth time on heliocentric dis-
substantial migration on the computed growth timescale. tance. It can be seen that large bodies form more slowly at
The one-dimensional model conserves mass locally; it in- larger values of R, due to the lower surface density. Recall
cludes the effects of radial velocities on the collision rate, that in the one-dimensional model, once bodies with sizes
but does not account for movement of mass into or out of of tens of meters formed, meter-sized bodies were depleted
the region of calculation at a given heliocentric distance. by colliding with the larger ones due to their high radial
This movement has two effects on the physical modeling: velocities; this is the cause of the gap in the size distribu-
At any location the total mass may increase or decrease tion.
relative to the starting value, and the size distribution may In the two-dimensional model, meter-sized bodies that
be altered by different rates of migration by bodies of vari- form at larger distances migrate inward, continually replen-
ous sizes. In addition, there may be compositional effects ishing the population at that size and filling the gap. The
as material that condensed at a range of heliocentric dis- addition of these bodies also keeps the median size smaller.
tances and temperatures is mixed during accretion. The model for gravitational stirring scales the out-of-plane
Stepinski and co-workers (Stepinski and Valageas, 1996, random velocity to the escape velocity of the median-sized
1997; Kornet et al., 2001) recognized that radial migration body in the midplane; the smaller median size in the two-
due to gas drag could be significant. They produced a model dimensional case results in a more flattened particle layer
for particle coagulation and migration in a circumstellar than in the one-dimensional model.
102 Comets II

of kilometer-sized or larger bodies that resist orbital decay.

These grow by catching the smaller bodies migrating in-
ward from larger distances. The gradient of the surface
density of solids becomes much steeper, and develops a
rather sharp “edge” in the range 40–50 AU, at about half
the radius of the nebula. The reason for this behavior is due
to the fact that the peak radial velocity induced by gas drag,
and the size at which this peak occurs, do not vary signifi-
cantly with heliocentric distance. Most of the migration
occurs during growth from about 0.1 to 10 m diameter. This
growth takes longer at the lower densities found at greater
distances, so a body that begins to accrete at a larger dis-
tance moves inward by a greater amount. Empirically, the
growth time varies approximately as R3/2, so the fractional
change of distance increases with R, causing the surface
density gradient to steepen. Because the particle layer is
highly flattened, small bodies migrating inward are effi-
Fig. 4. Results of a two-dimensional simulation performed in 20 ciently captured by larger bodies that have stopped their
zones from 30 to 90 AU, with an R–1 variation in surface density. orbital decay. Mass tends to pile up at the outermost dis-
The assumed surface density in the innermost zone is about half tance where kilometer-sized bodies grow, which further
that in the one-dimensional simulation, approximately doubling steepens the gradient of surface density. A similar “pileup”
the evolution timescale. After 5 × 105 yr, the innermost zone con- occurs in the radial one-dimensional model of Stepinski and
tains bodies larger than 100 km, while no bodies larger than 1 km
Valageas (1997), so this effect is not sensitive to details of
have formed beyond ~40 AU. In the inner zones, the “valley” at
the model. This transition is also accompanied by a steep
~1–10 m is less distinct due to inward migration of bodies of this
size that formed at larger distances. decline in the mean size of planetesimals. It can be seen in
Fig. 4 that no bodies larger than ~1 km have accreted be-
yond 50 AU. Continuation of the simulation to later times
would not produce any large bodies at this distance, as
The gaseous component of the solar nebula is assumed the surface density of solid material is too low for further
to remain constant, but radial migration results in signifi- growth.
cant redistribution of the solid matter (Fig. 5). The inner This simulation assumed a laminar nebula, i.e., the only
zones are initially depleted by orbital decay of the first- turbulence is that produced locally near the central plane
formed meter-sized bodies, After ~2 × 105 yr the surface by shear between the particle layer and the surrounding gas.
density in the inner region rises again due to the formation If there is an additional source of turbulence, e.g., magneto-
rotational instability, then its main effect would be to in-
crease the thickness of the particle layer. The lower density
would cause accretion to be slower, allowing more migration
during growth. Thus, the initial extent of the nebula would
have to be even greater to yield an edge at this distance.

6. FORMATION TIMESCALES

Motions induced by drag lead to relatively rapid forma-

tion of sizable bodies, compared with purely gravitational
accretion in the absence of gas. Kenyon (2002) modeled
planetesimal accretion in the Kuiper belt. His simulations
included gravitational stirring and fragmentation; most did
not include gas drag, or considered only damping of ec-
centricities and inclinations without orbital decay. The as-
sumed surface density of the planetesimal swarm was
comparable to the cases discussed above, but the initial size
Fig. 5. Evolution of the surface density of solids for the case
distribution was quite different: a power law with most of
shown in Fig. 4. At t = 0, when all condensed matter is in the form
the mass in bodies of radius ~100 m. Kenyon’s model re-
of dust, the surface density varies as R–1. Inside ~45 AU, the
growth of meter-sized bodies causes initial depletion by orbital quired ~10 m.y. to accrete 100-km bodies while drag-driven
decay, but this loss is replenished by matter coming in from greater accretion produces such in <1 m.y. in regions that are not
distances that is captured by larger bodies. The region beyond depleted by radial migration. Part of this difference can be
~45 AU suffers net depletion; the surface density and mean par- ascribed to the starting conditions. Gravitational accretion
ticle size decline steeply from 30 to 50 AU. would be faster for smaller initial sizes, which produce less
 Weidenschilling: From Icy Grains to Comets 103

stirring and lower velocities, with earlier transition to run- include radial migration, as growth timescales and sizes
away growth. However, gravitational stirring is isotropic, vary too gradually with heliocentric distance to produce
producing out-of-plane velocities that thicken the layer and such a sharp transition (Kenyon and Luu, 1998, 1999).
reduce the collision rate as the mean size increases. Drag- While there are other possible explanations for truncation
induced motions are more favorable to accretion because of the Kuiper belt, such as a stellar encounter during for-
they are parallel to the nebular midplane. Turbulent stirring mation of the solar system (Kobayashi and Ida, 2001), drag-
is ineffective for meter-sized and larger bodies, so the par- induced migration during planetesimal formation provides
ticle layer can attain high density, while the radial and trans- a plausible — perhaps unavoidable — mechanism for pro-
verse velocities are high enough to allow frequent collisions. ducing a sharp edge. The increasing difficulty of accretion
In contrast, the inner zones in the simulation experience a with distance also puts in doubt the existence of a massive
net increase in surface density of solids over the initial primordial belt of material in the region ~50–100 AU, as
value, allowing more rapid growth there. suggested by Stern (1996). The solar nebula probably had
The rapid formation of 100-km-sized bodies may have to extend to such a distance simply to account for the
consequences for their thermal evolution. If short-lived ra- present extent of the Kuiper belt, but most of the condensed
dionuclides such as 26Al were present in the outer part of matter originally present there was removed by gas drag
the solar nebula, accretion times ~1 m.y. imply that Kuiper before it could form bodies of significant size. Bodies in
belt objects of this size probably experienced enough heat- the region of the current Kuiper belt (40–50 AU) probably
ing to undergo melting and differentiation in their interiors contain a substantial fraction of material that originally
(Prialnik et al., 2004). In that case, they might be rather condensed (or survived from the presolar cloud) at much
compact bodies with low porosity and moderately high larger distances, possibly beyond 100 AU. In the denser
density and strength. However, modeling of the collisional inner region of the nebula, accretion times were shorter and
evolution of the Kuiper belt since its formation (Farinella the migration distance was less. Comets that formed in the
et al., 2000) shows that fragmentation of such large bodies region of the giant planets probably comprise material de-
is rare, and implies that most objects with sizes of a few rived from a smaller range of heliocentric distances.
kilometer are derived from smaller parent bodies a few tens
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7. CONCLUSIONS
Asphaug E. and Benz W. (1996) Size, density, and structure of
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Farinella P., Davis D. R., and Stern S. A. (2000) Formation and
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 Lunine and Gautier: Evolution of Volatiles in the Protoplanetary Disk 105

Coupled Physical and Chemical Evolution of Volatiles

in the Protoplanetary Disk: A Tale of Three Elements
Jonathan I. Lunine
University of Arizona

Daniel Gautier
Observatoire de Paris-Meudon

Volatiles contained within comets have been subjected to a range of physical and chemical
properties within the protoplanetary disk out of which the solar system formed. Here we focus
on three elements — O, N, and S — that occur in molecular forms of widely varying volatility.
These molecular forms play distinct roles in the disk, ranging from fundamentally determining
opacity and oxidation state (water), to being a passive tracer of the O chemistry (hydrogen
sulfide) and the amount of unprocessed molecular cloud material incorporated in grains (am-
monia). The interactions among the various molecular species are complex, reflecting numer-
ous physical processes in the disk, only some of which are well enough understood to model
in detail with confidence.

1. THE IMPORTANCE OF VOLATILES building blocks of planets and comets throughout the solar
AS TRACERS OF DISK PROPERTIES system, and is thus of especial value. Nitrogen is a key ele-
ment because it is well measured in comets and in Jupiter
Some of the details of planet formation are hidden in the and may have existed in planetesimals as highly volatile mo-
abundances of the elements and isotopes, now present in lecular nitrogen, N2, or as ammonia, NH3 (or related com-
the planets themselves, in the small bodies of the solar sys- pounds), or both. Molecular nitrogen is extremely volatile;
tem, and in the meteorites. Constraints imposed by these NH3 is only modestly more volatile than H2O ice. Which
abundances are more powerful if they are based on mul- of the two forms was more abundant in outer solar system
tiple elements, or more than one isotopic ratio. Models that solids can be constrained by jovian and cometary data, and
simulate the history of volatiles that may condense or ad- in turn this provides constraints on the conditions under
sorb in different ways as a function of position or time in which the icy planetesimals that seeded the giant planets
the disk are difficult to construct because they must con- formed.
sider processes occurring on a broad range of spatial and Galileo probe and remote sensing data from flybys, or-
temporal scales. Yet, a full understanding of the processes biters, and Earth-based observatories provide a detailed set
by which our solar system formed will not be gained until of elemental abundances for Jupiter unrivalled by that for
these processes are quantified to a sufficient extent, and this any of the other giant planets (Atreya et al., 2003), and il-
has yet to be achieved. lustrate the motivation for trying to understand the coupling
Oxygen, S, and N are elements that are abundant of dynamics and chemistry for multiple volatile species.
(Table 1) and of particular importance. Water drives the oxi- Noble gas (Ar, Kr, Xe) and three major element (S, N, C)
dation state of the disk where it occurs in the gas phase, abundances in the sensible atmosphere are remarkably uni-
and is a primary planet-building material in the outer part of form, being roughly 2–4 times the solar value; He is solar,
the disk. The icy nature of comets, many of the moons of while Ne and O are depleted relative to solar (Niemann et
the giant planets, and of the Kuiper belt attest to H2O ice as al., 1998). The elemental O depletion is in fact a depletion
a principal planet-building material. Water is dominant as a of H2O, because H2O is the primary carrier of O in Jupiter.
solid, and thus it affects the energy balance of the proto- The depletion is almost certainly associated with the me-
planetary disk, rather than being a passive tracer. Sulfur’s teorology of the atmosphere through which the probe flew
complex chemistry is coupled to the H2O abundance in the (Atreya et al., 2003). Observations of jovian moist convec-
inner disk; the diversity of volatilities of S compounds them- tion by the Galileo solid-state imaging (SSI) camera as well
selves mean that some will be found in the rocky (refractory) as spectra obtained by the Galileo Near-Infrared Mapping
primitive material of the chondrites, while others (notably Spectrometer (NIMS) support a deep H2O abundance in
H2S) will be trapped in H2O ice. H2S was also found in a excess of solar (Gierasch et al., 2000). [The Ne depletion
number of comets originating from the Oort cloud. This is more problematic, since the abundance is much less than
variety means that S has left clues to the assembly of the one would expect for a simple solar composition gas, and

105
106 Comets II

TABLE 1. Solar elemental abundances (Cox, 2000). factor of 4 relative to solar (Atreya et al., 2003). The clath-
rate model, because it is much less efficient in trapping
Element Abundance* volatiles, predicts a much larger accretion of H2O to explain
Oxygen 8.5 × 10 –4 the pattern of heavy elements, leading to an elemental O
Carbon 3.6 × 10 –4 abundance 9 times solar (Gautier et al., 2001). Determina-
Nitrogen 1.1 × 10 –4 tion of the deep H2O abundance will have to await a deep
Magnesium 3.8 × 10 –5 probe or microwave sounding mission.
Silicon 3.5 × 10 –5 The two models also differ in their assumptions about
Iron 3.2 × 10 –5 the elements N and S. The amorphous model explains the
Sulfur 1.8 × 10 –5
jovian abundance of H2S, hence the element S, in the con-
*Abundances are normalized to that of atomic H. text of the overall enrichment pattern, starting with a solar
abundance of S in the gas phase from which the ices were
formed. In order to fit the observations, the clathrate model
condensation is excluded for this volatile noble gas. It is requires that S in the gas phase in the vicinity of Jupiter,
possible that the Ne is dissolved in an immiscible phase of where the clathrate formed, was about half the solar value.
He deep in Jupiter’s interior (Roulston and Stevenson, The principal S compound in the gas phase in either model
1995).] is assumed to have been hydrogen sulfide (H2S). As dis-
Two models to explain the pattern of major elements and cussed below, the depletion around 5 AU required by the
noble gases in Jupiter have been offered. Both are based clathration model could be explained by a combination of
on the accepted inference that Jupiter’s interior is heavily radial redistribution of H2O, chemical reactions in the hot
enriched in “heavy” (non-H or non-He) elements relative inner disk, and outward transport by turbulent mixing. In the
to solar values (Fortney and Hubbard, 2003). The source amorphous model for Jupiter, most of the N is molecular
of the heavy elements cannot be the gas in the disk itself, (N2); in the clathrate model it is both in N2 and in NH3.
which supplies the heavy elements in solar proportion to Thus the three elements O, N, and S are coupled in terms
H and He. It must come, instead, from a condensed phase of the molecular forms required for consistency with jovian
of dust and planetesimals that accreted onto Jupiter as the composition under these two diverse views. But they are
giant planet grew (Pollack et al., 1996). The two models necessarily also coupled to the details of the physical pro-
draw on different sources of solids to achieve the heavy cesses by which they came to be trapped in the solids that
element abundance pattern seen in the Jupiter atmosphere. seeded Jupiter. In the remainder of this short chapter we
Because of the high abundance of O and hence H2O in the focus on protoplanetary disk processes that have affected
protoplanetary disk (which is assumed to have solar elemen- the partitioning of O, S, and N among compounds and
tal composition overall), H2O ice is likely to have been the phases, the interactions (chemical and physical) among
principle carrier of the volatiles that supplied the heavy these compounds and phases, and the resulting record left
elements. In one model Jupiter accreted solid material behind in comets. The examination is necessarily sketchy,
formed in a cold molecular cloud environment in which intended to give a flavor for the state of knowledge rather
volatiles were indiscriminately adsorbed onto amorphous than provide a complete model for the co-evolution of
H2O ice at temperatures below 30 K; this material was de- volatiles and disk. In section 2 the infall of primitive solid
livered by infall to the protoplanetary disk and accreted by matter to the disk, and the resulting sublimation of volatiles,
Jupiter (Owen et al., 1999). We call this the “amorphous” is examined. Transport and chemistry within the disk itself
model. The second (“clathrate”) model invokes formation is the subject of section 3, while the overall implications
of planetesimals local to the formation zone of Jupiter in a for cometary and planetary formation are covered in sec-
cooling disk, so that volatiles are progressively trapped in tion 4. Section 5 provides a brief list of upcoming missions
clathrate hydrate from 150 K down to 38 K (Gautier et al., and groundbased facilities that can provide additional data
2001). (In this chapter we use the terms “protoplanetary to test some of the ideas engendered by existing data and
disk”or just “disk” rather than “nebula” or “solar nebula.” modeling.
These last two terms refer to the epoch in the formation of
our own solar system when the protoplanetary disk was 2. INFALL AND MODIFICATION
largely gaseous, and it is this part of the evolution we focus OF VOLATILES
on in the present chapter. For clarity we prefer the more
astronomical term “disk” here.) The protoplanetary disk out of which the planets formed
Because the trapping conditions and hence mechanism was almost certainly the product of the collapse of a larger
of volatile trapping in the H2O ice differs in the two mod- region of material within a molecular cloud complex (Du-
els, the ratio of H2O ice to trapped volatiles differs in the trey et al., 1997). To what extent this occurred in a low- vs.
two cases. The amorphous model predicts that, in order to high-mass star-forming region has recently become contro-
produce the observed enrichments of 2–4 times solar in S, versial again as a result of the timescale problem for the
N, C, and the heavier noble gases, enough H2O must have formation of the giant planets — particularly Uranus and
entered Jupiter to enrich the elemental O abundance by a Neptune (Boss, 2003). However, in either case molecular
 Lunine and Gautier: Evolution of Volatiles in the Protoplanetary Disk 107

cloud material was accelerated to large velocities as it fell certain, large variations in the extent to which grains des-
into the nascent protoplanetary disk, and as a result solids tined for the outer solar system (beyond 5 AU) sublimate
were heated and perhaps sublimated before reaching the are obtained in numerical models, but the general pattern is
protoplanetary disk. Indeed, even before this the material nearly complete sublimation of H2O and more volatile spe-
was likely warmed by radiation from the proto-Sun, residing cies in the Jupiter-Saturn region and very little at orbits
as it was far above the center of the disk and hence outside corresponding to the Kuiper belt (Lunine et al., 1991).
of the shielding effects of the optically thick disk itself. Sublimated material reincorporated in grains according
The extent to which heating and sublimation of molecu- to the local temperature-pressure environment. At 5 AU
lar cloud grains occurred during infall is a matter of both temperatures declined relatively slowly during the time of
theoretical and observation debate. From the theoretical giant planet formation, and hence much of the sublimated
point of view, imagine a grain coming into the protoplanet- H2O ice recondensed not as amorphous ice, but rather in
ary disk from a region high above the midplane. Analyses crystalline form (Kouchi et al., 1994). Volatiles released
of protoplanetary disk models indicate that the presence of from amorphous ice by sublimation were progressively
shocks will generally create a dependence of the gas density trapped in the crystalline ice as temperatures dropped, likely
on altitude above the disk midplane that decouples all but in the form of clathrate hydrate. (Gautier et al., 2001). At
the smallest grains from the gas, leading to heating and sub- 30 AU, persistently low temperatures ensured rapid recon-
limation of the grains. Turbulence in the gas associated with densation of amorphous H2O ice with simultaneous trapping
the collapse process enhances the collision rate between of volatiles in the newly formed grains. Thus, the physical
grains and, if collisions are not predominantly destructive, effects on grains of radiative and gas-dynamical heating
growth to 1-µm solid particles or 100-µm fluffy aggregates associated with infall suggest an important dichotomy be-
(from an assumed starting size of 0.1 µm) is possible (Wei- tween H2O ice and trapped volatiles at 5 AU, vs. that at
denschilling and Ruzmaikina, 1994). Existence of millime- 30 AU, with intermediate properties in the intervening realm
ter-sized grains is suggested from the spectral energy of the outer planets.
distribution of some young stars (Beckwith et al., 2000), al- To what extent is this dichotomy reflected in the prop-
though populations of small grains are certainly present as erties of comets, whose sources range over the entire outer
well (Li and Lunine, 2003). It is thus likely that some solar system realm from 5 AU to 30 AU and beyond? Be-
amount of grain-gas decoupling, and consequent gas-dy- cause the compositional and isotopic information for short-
namical (i.e., roughly, frictional) heating of the grains oc- period comets, the origin of which appears to lie in the
curs in the disk (Ziglina and Ruzmaikina, 1999). Direct Kuiper belt, is rather poor compared to that for long-period
radiative heating of the grains associated with certain kinds comets, which formed well inward of 30 AU, comparison
of shock boundaries is also possible. is difficult. The abundance of elemental N is modestly de-
Thus grains were heated during their passage into the pleted in comets, and that of N2 and related volatile N spe-
protoplanetary disk, but the extent to which this happened cies strongly depleted (see Bockelée-Morvan et al., 2004).
depends on several factors, including the final distance of One possible explanation for this depletion is that tempera-
the grains from the proto-Sun but most importantly the tures in the region where the grains of long-period comets
accretion rate (Neufeld and Hollenbach, 1994). Because the formed was relatively high, cooling slowly, and the conse-
accretion rate controls the disk luminosity as well as the quent incorporation of volatiles involved a fractionation
strength of the shock, the problem is a coupled one that process akin to, or in fact corresponding to, the formation
must be solved numerically (Chick and Cassen, 1997). Two of clathrate hydrates (Iro et al., 2003). In such a process,
endmember cases have been considered in the literature. For even though temperatures become low enough to allow the
a disk in a relatively low-luminosity state (total luminosity trapping of N in H2O ice, the competition for void spaces
of disk plus protostar equal to 1–2 times that of the Sun), among species favors carbon monoxide over N2, so that, if
silicates, metals, and refractory organics survive the heat- H2O ice is not abundant enough to clathrate both species,
ing within the 1-AU terrestrial planet region; volatile organ- the latter is preferentially excluded from the icy grains.
ics survive to within a few AU, and H2O ice would be fully Much of the N in comets is then the result of condensation
vaporized within 5 AU. Alternatively, higher accretion rates of NH3 into the H2O ice as a stochiometric hydrate, with
onto the disk are possible (Chick and Cassen, 1997), for the N2 being secondary or absent.
which the luminosity may be 1 to 2 orders of magnitude This picture has a number of implications. First, the
higher, and then H2O ice grains could be vaporized to a dis- progressive trapping of volatile species in the crystalline
tance of 30 AU. clathrate hydrate requires that the icy component of mo-
Of concern here is the fate of the volatiles contained lecular cloud grains, with their indiscriminant mix of vola-
within the H2O ice. The original grains likely were com- tile and nonvolatile species, largely or fully sublimated in
posed of amorphous ice in which volatile molecular spe- the 5–10-AU region. Comets formed of grains from this
cies were adsorbed. Thus the sublimation rate during heat- region — Oort cloud comets — should exhibit a composi-
ing should be largely controlled by the H2O ice latent heat tional pattern in which the relative abundances of the most
as well as the grain size, which determines the thermal emis- volatile species are altered from molecular cloud values.
sivity. Since the grain size and extent of fluffiness are un- Short-period comets, on the other hand, which had their
108 Comets II

origin in the Kuiper belt at 30 AU and beyond, where sub- tween the two classes of comets as well. In particular, D/H
limation was absent or limited, ought to have a grain com- in three long-period comets is twice that of terrestrial ocean
position that reflects a cold molecular cloud origin. H2O (Meier et al., 1998b; Bockelée-Morvan et al., 1998),
Second, the model of Iro et al. (2003) weakly suggests which imposes stringent constraints on the source of the
a variation in the H2O ice abundance at 5 AU and beyond Earth’s oceans in dynamical models (Morbidelli et al.,
relative to that obtained assuming the solar composition of 2000). However, these models assume a constant D/H ra-
elemental O, because the CO abundance seems highly vari- tio in H2O in comets from the long-period comets of the
able from comet to comet. Iro et al. explain the CO varia- giant planet realm to the short-period Kuiper belt comets
tion as a consequence of the altered number of adsorption at 30 AU. The lack of grain heating and sublimation at
sites available for CO caused by fluctuating amounts of H2O 30 AU suggests this assumption may not be realistic; per-
ice. In fact, the clathrate trapping model to explain the abun- haps, e.g., D/H in H2O in short-period comets is even larger
dance of volatiles in Jupiter requires that the amount of H2O than in the long-period bodies.
ice at 5 AU be double the value implied by a solar abun-
dance of elemental O, while the amount of S be half its solar 3. EFFECTS OF TRANSPORT WITHIN THE
elemental value (Gautier et al., 2001), and the N values in DISK ON VOLATILE DISTRIBUTION
several well-measured comets also require an elevated H2O
abundance (Fig. 1). Thus, the N abundance in long-period The complex evolution of volatile species does not end
comets is tied, albeit indirectly, to the history of H2O and with the sublimation and reformation of solid grains. Trans-
S-bearing species in the 5 AU region. A mechanism for en- port processes in the disk bring grains and gas-phase spe-
riching H2O ice in the 5 AU region, namely through cold cies into warmer realms close to the disk center, and then
trapping of H2O vapor mixed outward from the hot inner outward again. Those grains that cross the phase boundary of
disk as suggested originally by Morfill and Volk (1984), is a major component of their composition will experience dra-
presented in the next section. matic changes, e.g., the sublimation of H2O ice. Gas phase
Third, if the histories of cometary grains embedded species that cross boundaries corresponding to changes in
within long- and short-period comets are as different as this thermodynamically (or kinetically) preferred molecular spe-
picture implies, then we expect distinct isotopic ratios be- cies will have their compositions altered in complex ways —
this is especially the case with S. In the present section we
describe the coupling between the physics of transport in
the disk and the chemistry/thermodynamics of phase transi-
tions and reactions for H2O and S. In the preceding section
we established that the N abundance and its molecular form
in grains is tied to the H2O abundance directly, and to S in-
directly, so at the end of the section we more closely ex-
amine possible similar effects for the molecular carriers of
elemental N. The question of transport processes in disks,
specifically their nature and origin in dissipative processes,
is a complex one for which the reader is referred to other
reviews (Stone et al., 2000).

3.1. Water

The condensation of H2O is a fundamentally important

process in protoplanetary disks, affecting the visible and
Fig. 1. The N+2 to CO+ ratios [nearly equal to the N2/CO values] infrared opacity, the abundance of solids, and the accretion
measured in four long-period comets. Bracketing these values are rate of planets embedded in the disk. But the gaseous and
the predicted N2/CO ratios from the Iro et al. (2003) model with solid abundances of H2O as a function of the distance from
(bottom line) a roughly solar H2O-to-H2 ratio and (top line) a H2O- the disk center are altered as well by condensation when
to-H ratio 2.8 times solar. See the text for discussion of a mecha- radial transport is considered (Morfill and Volk, 1984). In
nism for enriching the H2O abundance in the outer protoplanetary particular, imagine that some mixing process acts to carry
disk at the expense of the inner disk. The gas-phase N2/CO value
H2O vapor along a radius at the disk midplane. The pro-
in the protoplanetary disk — unaltered by grain trapping — is just
cess could involve macroscopic motions associated with
above but nearly coincident with the 2.8 times solar line. Thus
roughly doubling the H2O abundance in the region of long-period large-scale turbulence (turbulent diffusion) or instabilities
comet formation could explain the N2 to CO ratio in comets. Fig- of some sort. (From a practical point of view, microscopic
ure from Iro et al. (2003); for a discussion of the relationship of diffusion in the disk is too slow to generate the effects con-
the observed ions to the total neutral populations of N2 and CO, sidered here.) Absent condensation, adsorption, or chemical
see Bockelée-Morvan et al. (2004). creation/destruction, the transport mechanism will not alter
 Lunine and Gautier: Evolution of Volatiles in the Protoplanetary Disk 109

the radial distribution of the vapor abundance because any

transient spatial gradients created by the motions are quickly
eliminated by the same mechanisms. In the presence of
chemical/thermodynamic processes, the outcome is quite
different.
We consider condensation as a simple sink, or loss pro-
cess, for H2O occurring at a discrete radial distance from
the Sun at a given time in the evolution of the protoplanetary
disk. Condensation of a particular species occurs when the
partial pressure of that species exceeds the saturation va-
por pressure; since the latter is steeply dependent on tem-
perature, this criterion simply translates into a distance from
the disk center at which the species is saturated. For ex-
ample, the H2O condensation front (sometimes called the
snowline) might occur at 5 AU at a given time in the disk,
then move inward to 3 or 4 AU as the disk ages and cools.
There is no special requirement on the properties of the disk
to possess such a condensation front, other than that the
temperature must decline with radial distance and time.
Water vapor inward of the condensation front will be trans-
ported radially by whatever process, and when it passes Fig. 2. Water vapor abundance is plotted as a function of dis-
through the snowline it will condense out in the form of tance in a cylindrically-symmetric and turbulent protoplanetary
microscopic grains. (Supercooling of the vapor is a distinct disk, where the snowline is initially at 5 AU, for various times in
possibility because of the low temperatures involved, ~150– the evolution of the disk. Top panel assumes that ice grains formed
160 K at typical gas pressures in the disk. However, this at the snowline do not drift inward. Bottom panel allows inward
drift of the grains as they grow and decouple from the gas; the
does not change the argument; it simply means the effec-
snowline evolves inward as well. “Solar H2O” refers to the start-
tive snowline is pushed outward somewhat relative to the
ing abundance of H2O, uniform through the disk, and based on the
formal thermodynamic line that is defined as above.) solar O abundance. From Cyr et al. (1998).
In principle the condensation changes nothing, because
the microscopic grains of ice are embedded in the gas and
move with it, just as does the H2O vapor itself. But the
grains grow, and decouple from the disk gas when they under half of the starting value as disk transport processes
reach radii exceeding on the order of 0.1 cm (Cyr et al., deliver H2O to the snowline. This H2O is accumulated be-
1998). When this happens, although grains will spiral in- yond the snowline, leading to an excess of H2O ice there.
ward as a result of gas drag, the effective inward radial Water abundances double the starting value may be accu-
velocity is smaller than the turbulent velocity. The inward mulated in that region.
radial drift velocity declines as the grain size increases. The implications of the redistribution of H2O are inter-
Hence, the grains effectively are “left behind” in the 5-AU esting. The peculiar geochemistry of the enstatite meteor-
region, while the H2O vapor continues to obey the standard ites might be a signature of the depletion of H2O inward
diffusive mechanics associated with the gas phase. The of the disk snowline (Hutson and Ruzicka, 2000). The abun-
snowline becomes a cold trap, and over time the H2O abun- dance of organics increases dramatically and the mix of
dance inward of that line declines (Stevenson and Lunine, organic species changes in the inner disk with decreasing
1988). The precise history of the decline depends upon O (H2O) abundance (Cyr et al., 1999). The long timescales
detailed assumptions about grain growth rates, mechanisms required for the formation of Jupiter in the core accretion
of vapor transport, and position of the snowline, among model (Lunine et al., 2003) might be reduced dramatically
others (Cyr et al., 1998). Disruptive collisions presumably if the abundance of solids were enhanced over solar (Lis-
play an important role, considering that dusty circumstel- sauer, 1987), as would happen were H2O ice to accumu-
lar disks are observed at ages of several millions of years late beyond the snowline (Stevenson and Lunine, 1988). An
(Beckwith et al., 2000). A typical model result for a cylin- enrichment in H2O ice of a factor of 2 beyond the snowline
drically symmetric disk, with transport processes in the disk is required if the crystalline clathrate model of the enrich-
parameterized as turbulent diffusion, is shown in Fig. 2. ment of Jupiter is to be consistent with the interior abun-
Define the “starting value” as the abundance of H2O in the dances of the major elements in the solar system’s largest
absence of condensation processes, a value determined by planet, as noted above. Likewise, the depletion of N in com-
the elemental O abundance and partitioning of O among ets can be explained by the same model if H2O ice were
H2O, CO and other compounds (Cyr et al., 1999). Water enriched where the long-period comets formed. Whether the
vapor abundances inward of the snowline can drop to well enrichment of ice at the snowline is carried far enough
110 Comets II

beyond 5 AU to make this plausible has not been quantita- dial mixing. The data in Table 1 suggests that this process
tively evaluated. is too efficient; there is enough Fe to remove all the S and
Alternatively, one might argue that the protoplanetary prevent the formation of any but a very small trace of H2S.
disk was quiescent enough that H2O ice delivered from the However, many of the elements that would otherwise react
molecular cloud did not sublimate in the 5 AU region. While with S (Si, Mg) are locked up by reaction with O. Hence
this appears to be a difficult proposition based on the infall H2S is the primary carrier of S and has essentially the full
models described in the last section, it cannot be ruled out, solar abundance of the elemental S itself.
and in particular “contamination” of the 5–10-AU region The situation is different when the depletion of H2O
from cold solid matter delivered relatively pristine to more inward of the snowline is considered, and hence the elemen-
remote disk regions, then transported inward, is another tal O abundance there is reduced. In an extremely-O-poor
intriguing possibility that bears further study. case (10% solar), Si, Mg, and other elements are available
To assess whether indeed the evolution of H2O in the to bind with S as SiS and MgS, and thus drive down the
disk included establishment of a cold trap, with enrichment abundance of H2S to very low levels (Pasek et al., 2003).
beyond and depletion inward of that point, we must exam- The molecule HS also coexists with the SiS and MgS, but
ine other volatiles to assess whether the signature of this is still only 10% or less of the total S abundance. [Interest-
process might be written upon their abundances. ingly, SiS is seen in the mass-loss envelopes of carbon stars;
that is, stars with low O abundance relative to C (Bieging,
3.2. Sulfur 2001).] Given the much lower volatility of compounds like
SiS and MgS compared to HS and H2S, only the latter two
Sulfur occurred in a variety of chemical forms of widely are likely to be seen in the gas phase of the cold outer disk
varying volatility in the protoplanetary disk. The most vola- where the giant planets formed. At intermediate O abun-
tile abundant form was likely H2S, and it is this molecule dances, perhaps more likely to obtain in the disk, the chem-
that would have represented the bulk of the S trapped in istry becomes even more complex, with CaS and MgS “fin-
H2O ice. The S abundance in nine long-period comets in gers” over narrow ranges of temperature and hence radial
the form of H2S seems to vary from 0.4% to 1.5% relative distance (Pasek et al., 2003).
to H2O ice, and this is generally less than what is predicted What this complex chemistry implies for the H2S abun-
from the trapping of a solar complement of H2S in clath- dance in the outer part of the disk requires folding in cal-
rate hydrate in the disk (Iro et al., 2003). Likewise, the S culations of the kinetics of the S reactions (Fegley, 2000),
abundance in Jupiter cannot be reproduced by the model including the “poisoning” of the iron grains via the buildup
unless H2S is depleted in the feeding zone (the region from of layers of sulfides (Lauretta et al., 1996), and a realistic
which the planet acquires material) of Jupiter relative to transport model in a turbulent disk. This has not yet been
solar abundance (Gautier et al., 2001), but here the con- done. Since the chemical calculations suggest that the time-
straint is more severe: The depletion must be relative to the dependence of the H2O — hence O — abundance in the
background H2. Thus simply augmenting the amount of inner disk might act to destroy H2S there, the S abundance in
H2O ice by — for example — cold-trapping is not sufficient. the region of Jupiter- and comet-formation could have been
[Note that the mass M of gas within a ring of width ∆R, depressed as well. More generally, the histories of O-bear-
centered at a heliocentric distance R, is defined by dM/dR = ing and S-bearing volatile species in the disk are strongly
2π R q Σ, where Σ is the surface density of H and q the coupled.
mixing ratio of the considered species. Since the radial
dependence of surface density is weaker than r –2 (Beckwith 3.3. Nitrogen
et al., 2000), the mass of a molecular species with constant
mixing ratio as a function of radial distance increases as Little has been done to quantify the coupling to the O
one moves outward in the disk. Hence most of its mass is abundance of the chemistry of N-bearing species, in par-
located in the outer disk [see, for example, Fig. 14 of Her- ticular, NH3 and N2. Like carbon monoxide and methane,
sant et al. (2001)]. Therefore, the mass of S that was trapped there is a relationship between the abundances of the oxi-
in solid form in the feeding zone of Jupiter, and that subse- dized and reduced forms dependent on temperature and H
quently enriched the planet in elemental S, was small com- pressure. At very low temperature (200–300 K) the reduced
pared to the total mass of S in the disk.] (NH3) form of N is preferred, but the conversion timescale
A depletion of H2S in the feeding zone implies a loss proc- between the oxidized and reduced phases is so long at such
ess for H2S somewhere else in the disk — most plausibly temperatures that, in the disk, the oxidized form (N2) pre-
in the inner region. Indeed, some elemental S is trapped in dominated (Prinn, 1993). That NH 3 is seen in comets
the warm inner disk in refractory forms such as FeS (troi- (Wyckoff et al., 1991) suggests a source from the nascent
lite), SiS, MgS, CaS, and other related compounds. Such molecular cloud, where NH3 is known to exist (van Di-
S-metal combinations occur fairly rapidly at disk tempera- shoeck and Blake, 1998); other sources associated with giant
ture above about 500 K, and one might imagine some of planet formation seem less promising (Mousis et al., 2002).
the S being excluded from regions farther out in the disk The presence of a mix of NH3 and N2 derived all or in part
by this process if turbulent diffusion causes significant ra- from molecular cloud values is not in conflict with the grain
 Lunine and Gautier: Evolution of Volatiles in the Protoplanetary Disk 111

sublimation processes considered above; while both are lib- cometary H2O in the disk to temperatures significantly
erated into the gas phase by the sublimation process, am- above 30–50 K. At face value, the comets for which this
bient temperatures in the disk are too low for chemical has been measured — Halley, Hale-Bopp, Hartley-2, and
exchange of N between N2 and NH3 to occur. Hence the Wilson — ought to be composed of ice that has not seen
total molecular ratio (that in the gas and the grains) is the inner protoplanetary disk. However, the kinetics of the
largely preserved, with the exception of a small amount of exchange are very poorly known, and there is also a possi-
NH3 transported to the very innermost, hot part of the disk bility that the ortho/para value is reset later in the comae
where reaction kinetics are fast enough to convert it to N2. of comets by ion chemistry (Irvine et al., 2000).
Because NH3 readily forms so-called stochiometric hy- The N abundance in comets seems to be well explained
drates with H2O, there is no condensation front of solid NH3 by a model in which N2 is not indiscriminately trapped in
in the same sense as for H2O. Ammonia hydrates form in amorphous ice, but instead must compete for void sites with
H2O ice grains at temperatures above 70 K for typical disk other volatiles. This too implies a thermal cycling of the
temperature-pressure profiles (Iro et al., 2003). Kinetic in- H2O in the grains, up to a temperature that might be incon-
hibition of this process is unlikely because the NH3 abun- sistent with the ortho-to-para ratio if the latter reflects the
dance is significantly less than that of H2O ice (i.e., a few disk environment of the H2O ice grains.
percent), so that relatively little fresh ice must be exposed The S abundance in icy grains is also coupled to the H2O
to the gas to induce hydrate formation. The infall of NH3 abundance — more accurately, the oxidation state — in the
in molecular cloud grains over a broad range of disk semi- inner disk, because the latter determines the amount of H2S
major axes, and the stability of the molecule against trans- in the gas phase vs. the abundance of other S-bearing com-
formation to N2, makes it unlikely that a well-defined gradi- pounds. Since H2S appears to be the dominant S-bearing
ent in the NH3 abundance was present in icy grains that species in comets but is below the solar S/O ratio (Irvine
remained cooler than 70 K. et al., 2000), it may have been depleted by chemical pro-
cessing in the inner disk. Radial mixing brings H2S sup-
4. IMPLICATIONS FOR WATER ICE, plied from the molecular cloud inward, destroys some of
SULFUR, AND NITROGEN it, then mixes the H2S depleted gas outward. How much
COMPOUNDS IN COMETS H2S depletion occurs — i.e., how much of the original
molecular cloud complement is altered in this way — must
The processes discussed above are a subset of those that await more detailed models in which not only are the chem-
acted in the solar system’s protoplanetary disk on species of istry and physics coupled, but the time history of the gas
varying volatility. They illustrate that the processes of con- oxidation state is folded in as well. All we can say now is
densation, sublimation, adsorption, and chemical reactions that a depletion of S at 5 AU, implied by one interpretation
worked in a coupled fashion with dynamical mechanisms of the Galileo data, seems to be a plausible outcome of S
of mixing and heating in the disk. Grains experienced vary- chemistry in the inner disk (Pasek et al., 2003).
ing extents of heating and destruction during disk infall, and
then generation of H2O ice at the snowline engendered a 5. FUTURE KEY DATASETS
complex history of fluctuating H2O vapor levels in the in-
ner disk. These in turn affected the chemistry of the disk In this chapter we have sketched a coupled history of
in a wide variety of ways — the abundance of organics, the the volatile carriers of three elements: O, N, and S. There
relative abundance of metal sulfides to H2S, and the abun- is, of course, much more about cometary chemistry than
dance of H2O ice — hence giant planet formation time- just these three elements, and in particular the story of the
scales. Further, the abundance of H2O ice beyond 5 AU de- organics is a rich one that is covered elsewhere in this book.
termined the abundance of N2 trapped in grains destined for But the origin and evolution of the compounds bearing these
comets and the giant planets, through the availability of void elements provides a sufficiently complex and coupled pic-
sites in the recondensed crystalline ice. ture that a list of measurements required to test some of the
Isotopic evidence for these effects in comets is scanty. ideas presented here (and those not presented as well!) is
The D/H value in H2O in long-period comets is elevated over daunting. Such measurements will require spacecraft sam-
that in carbonaceous chondrites (Robert, 2001), but less ex- pling of comets, telescopic observations from the ground,
treme than D/H in other molecules observed in molecular and Earth- or solar-orbiting telescopes covering wavelengths
clouds (Bockelée-Morvan et al., 1998). The enrichment has not accessible from the ground.
been used to argue that the H2O in comets has not been sub- Direct sampling of comets is required to measure the
jected to warm temperatures in the inner disk, where re- abundances of relatively refractory species containing N and
equilibration with H and hence lowering of D/H might oc- S, as well as determine isotopic ratios that are impractical
cur. However, grain sublimation and vapor cycling through to measure spectroscopically. Deuterium abundances in H-
the disk might have modestly reduced the D/H value rela- bearing species other than H2O ice, with the exception of a
tive to some starting value in the molecular cloud. few like HCN (Meier et al., 1998a), remain poorly known,
The ortho-to-para ratio in H in cometary H2O is some- and would help constrain the thermal history of the H2O
what more constraining, challenging any model that heats ice. Likewise, measurement of the O isotopes — much more
112 Comets II

difficult spectroscopically — would be of value in this re- Acknowledgments. Some of the work described herein was
gard. We also wish to know how the volatiles are trapped supported by the NASA Origins of Solar Systems Program.
in comets, although the thermal cycling of comets as they
pass close to the Sun might have destroyed this record
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114 Comets II
 Ehrenfreund et al.: Interstellar Material to Cometary Particles and Molecules 115

From Interstellar Material to Cometary

Particles and Molecules
P. Ehrenfreund
Leiden Observatory

S. B. Charnley and D. H. Wooden

NASA Ames Research Center

The birthplace of stars, planets, and small bodies are molecular clouds consisting mainly of
H and He gas as well as tiny amounts of solid particles. Dust and gas from such an interstellar
cloud collapsed to form a central condensation that became the Sun, as well as a surrounding
disk — the solar nebula. In this protoplanetary disk innumerable submicrometer particles —
icy and refractory in nature — agglomerated to larger planetesimals and subsequently into
planets. Comets were formed from remnant inner disk material that was not incorporated into
planets. Comets assembled beyond the orbit of Jupiter and may therefore provide a record of
some pristine material from the parent interstellar cloud. Our knowledge of the composition of
comets is predominantly based on evaporation of volatile species and thermal emission from
siliceous and carbonaceous dust when bright comets approach the Sun. The investigation of
outgassing curves from bright comets has provided a general link with abundances of ices and
gas phase molecules detected in dense interstellar clouds. Theoretical models indicate that bulk
material in cometary nuclei is stratified in density, porosity, and composition and contains
coexisting ice phases, possibly clathrates and trapped gases. It is therefore apparent that the
outgassing of species from cometary nuclei will not essentially mimic that expected from pure
sublimation of ices of interstellar composition. The current lack of astronomical data related to
solar-type star-forming regions, and the statistically small sample of comets studied to date,
are the major obstacles to be overcome before a coherent link between interstellar and solar
system material can be established. This chapter attempts to compile the current knowledge on
the connection between interstellar and cometary material, based on observations of interstel-
lar dust and gas, observations of cometary volatiles, simulation experiments, and the analysis
of extraterrestrial matter.

1. INTRODUCTION material within the solar nebula must have occurred in one
way or another. A pivotal epoch of processing is when inter-
In the 1950s comets were described by Whipple (1950) stellar material is first accreted. However, no detailed stud-
as “dirty snowballs” made up of water ice and small rock ies of the chemistry at the accretion shock exist (cf. Neufeld
particles. Cometary observations and related investigations and Hollenbach, 1994). With this caveat, we can consider
between then and now strongly improved our knowledge two limiting cases of processing. First, interstellar material
and view on these precious and most pristine solar system entering far out in the nebula, where the accretion shock is
objects. For a historical perspective on comets the readers weak (100 AU), should be largely unmodified when first
are referred to Festou et al. (1993a,b, 2004). The appari- incorporated. In this case, chemical reactions will proceed as
tion of unusually bright comets in the last 2–3 decades and this material is transported radially inward (Aikawa et al.,
the observations using advanced instrumentation allowed us 1999; Gail, 2001). Second, accretion closer to the protosun
to get important insights into the coma chemistry (Bockelée- will lead to complete dissociation and destruction of inter-
Morvan et al., 2004; Hanner and Bradley, 2004) and their stellar molecules. In this case, the molecules will subse-
relation to the parent interstellar cloud (Irvine and Lunine, quently form solely from nebular chemistry (e.g., Fegley
2004). and Prinn, 1989) and these can be radially mixed outward.
The origin of comets and the content of pristine inter- Today results indicate that presolar material has been chemi-
stellar material incorporated in them are far from being cally and physically processed according to the distance
understood. The assumption that cometary nuclei are ag- from the protostar (Chick and Cassen, 1997; Fegley, 1999).
gregates of pristine interstellar ices and dust (Greenberg, Comets are therefore a mixture of interstellar and processed
1982; Li and Greenberg, 1997) is clearly a gross simplifi- material and their initial composition will differ according
cation. Processing of infalling interstellar medium (ISM) to their place of formation.

115
116 Comets II

The “long-period” comets probably formed across the C in the interstellar medium (Ehrenfreund and Charnley,
giant planet formation region (5–40 AU) with the majority 2000; Mennella et al., 1998). The same trend is observed in
of them originating from the Uranus-Neptune region. For meteorites, where macromolecular material takes up more
a detailed discussion of cometary reservoirs and cometary than 80% of the C (Sephton et al., 2000; Gardinier et al.,
evolution the readers are referred to Jewitt (2004), Dones 2000). The link between macromolecular C in the solar sys-
et al. (2004), and Meech and Svoren (2004). Given the gra- tem and the interstellar macromolecular C is yet to be under-
dient in physical conditions expected across this region of stood, but it is tempting to assume that such a material is
the nebula, chemical diversity in this comet population is to also present in comets.
be expected, as has been inferred for short-period comets Cometary nuclei are a highly porous agglomeration of
(A’Hearn et al., 1995). Processing and dynamical exchange grains of ice and dust and they appear stratified in density,
of icy planetesimals in the comet-forming region could have porosity, ice phases, and strength. For a detailed discussion
contributed to chemical heterogeneity, or may have “homo- on cometary structure and properties, the readers are re-
genized” cometary nuclei before their ejection to the Oort ferred to Prialnik et al. (2004) and Weissman et al. (2004).
cloud (Weissman, 1999), where they could have experienced The nuclear ice component probably consists of different
further material processing and evolution (Stern, 2003). coexisting ice phases, including amorphous ice, crystalline
Remote infrared observations of parent volatiles in six Oort ice, and clathrates, with gases trapped in bulk and clathrate
cloud comets (including Hyakutake and Hale-Bopp) showed hydrates (see Fig. 12 in Prialnik et al., 2004). The structure
that they have similar volatile organic compositions (Mumma of the nucleus and the internal processes lead to certain sub-
et al., 2003), appear to be more pristine, and display a rea- limation characteristics and outbursts of ice, dust, and gas
sonable similarity to interstellar cloud material. when the nucleus approaches the Sun (Meech and Svoren,
The noble gas differentiation, deuterium enrichment, and 2004; Prialnik et al., 2004; Colangeli et al., 2004). Monitor-
low ortho-para ratio measured in water are all consistent ing the sublimation pattern of cometary material provides a
with formation of precometary ices at ~30 K, similar to the powerful tool to obtain more information on their composi-
conditions in the Uranus-Neptune region (Bockelée-Morvan tion. However, from observations it is not possible to achieve
et al., 2004). Comet-forming material in the Jupiter-Saturn a direct correspondence between the heliocentric distance
region (5–10 AU) experienced higher temperatures and may and the volatility of species as defined by their sublimation
also have been exposed to a much higher degree of radiation temperatures, e.g., as pure ices (Capria, 2002). The size
processing before its assembly into comets. Extrapolating distribution of grains in cometary bulk material extends over
from the case of C/1999 S4 (LINEAR), there is some evi- several orders of magnitude, including the pores in between.
dence that such comets should exhibit depletions and differ- The effect of pore size distribution seems to be important
ent abundance ratios compared to those formed at 30 AU for the thermal conductivity. Shoshany et al. (2002) show
and beyond (Mumma et al., 2001a). in their models that the thermal conductivity is lowered by
Comets are made of silicates (~25%), organic refractory several orders of magnitude at high porosities. The physics
material (~25%), small carbonaceous molecules (few per- of the processes responsible for driving sublimation and
cent), and ~50% water ice with small admixtures of other outbursts from the interior of cometary nuclei is described
ice species (Greenberg, 1998). Molecular ices and the gases by Prialnik et al. (2004). Heat waves from the surface or
released upon sublimation, silicate dust, and solid-state car- internal radioactive heating provide the energy within the
bonaceous materials are the major components of dusty cometary nucleus for water ice crystallization, which re-
cometary comae that can be studied by astronomical obser- leases latent heat. The trapped gaseous species, which are
vations and through laboratory simulations (Rodgers et al., released during the crystallization process, move through
2004; Hanner and Bradley, 2004; Colangeli et al., 2004). the pores and carry along small, detached dust particles.
Studying these compounds in comets, in the ISM, and in Another source of gas in the interior can be sublimation of
meteoritic materials allows us to reveal which processes volatile ices from the pore walls. Once gas is released from
occurred in the ISM and which occurred during the forma- the ice in the interior of the nucleus, its pressure will cause
tion of the solar nebula. For example, the appearance of Mg- it to flow to the surface. Free gases present in the cometary
rich crystalline silicates in some comets and the scarcity of interior are expected to affect the thermal and mechanical
crystalline silicates in the ISM [<5%, Li and Greenberg structure of the nucleus. The internal pressure may surpass
(1997), <0.5%, Kemper et al. (2004)] indicates cometary the tensile strength of the fragile grainy configuration. This
crystalline silicates are grains that condensed at high tem- results in cracking of the porous matrix and subsequent
peratures [~1400 K, Grossman (1972)] or were annealed outbursts of gas and dust (Prialnik, 2002). Internal pres-
from amorphous silicates at somewhat lower temperatures sure buildup by gas, thermal stress, and rotation may cause
[>900 K, Fabian et al. (2000)] in the solar nebula. The ori- disruption of the fragile material. On the contrary, sintering
gin of cometary solid-state carbonaceous materials is less (increase of contact area between grains — the Hertz fac-
clearly defined than the origin of the siliceous materials. The tor — due to heating or compaction) and pore blocking due
bulk of solid-state cosmic C in the interstellar medium is in to larger grains as well as recondensation of volatiles may
an unknown form. There is strong evidence that amorphous reconsolidate material. The complexity of internal processes
C and similar macromolecular material takes up most of the may produce an individual pattern for each comet.
 Ehrenfreund et al.: Interstellar Material to Cometary Particles and Molecules 117

Large-scale groundbased simulation experiments (e.g., formed, chemical conditions eventually evolved to the point
KOSI Kometen-Simulation) have been performed to study where almost all the heavy volatile material had condensed
the evolution of cometary nuclei (Kochan et al., 1998; as ice onto dust grains (Brown et al., 1988; Bergin et al.,
Colangeli et al., 2004). Sublimation experiments with ice- 2002). As cold interstellar gas and ice-mantled dust grains
mineral mixtures showed the metamorphosis of ice, the collapsed onto the protosolar nebula, they were heated by
reduction of volatiles in surface layers, and the formation radiation and gas-grain drag (e.g., Lunine, 1989). Nonrotat-
of a porous low-density (0.1 g/cm3) dust mantle (Grün et ing collapse calculations indicate that infall timescales can
al., 1993). The formation of a dust mantle on the surface become shorter than most chemical timescales. This results
and a system of ice layers below the mantle from the dif- in material from the cool envelope collapsing onto the cen-
ferent admixed materials have been detected after the in- tral protostar without significant chemical alteration (Rodgers
solation of the artificial comet. Those experiments allowed and Charnley, 2003). However, because of rotation of the
for studies of the mechanisms for heat transfer between the dense cloud core, infalling parcels of gas and dust far from
comet surface and its interior, compositional structural and the axis of rotation would have had sufficient angular mo-
isotopic changes that occur near the comet’s surface, and mentum to move along ballistic trajectories and become in-
the mechanisms of the ejection of dust and ice grains from corporated in a disk, rather than fall directly into the proto-
the surface (Kochan et al., 1998; Colangeli et al., 2004). sun (Cassen and Moosman, 1981; Terebey et al., 1984).
In the following sections we will emphasize the discussion Infalling matter passes through the accretion shock where
on the main components that provide insights into the inter- significant processing can occur. Far from the protosun, the
stellar–solar system connection and emphasize the processes lower nebular (preshock) densities and slower shock speeds
that could contribute (or not) to modifying interstellar ma- meant less processing of interstellar material. In this case,
terial as it becomes incorporated into comets. processing may simply involve removal and postshock re-
condensation of the ices (e.g., Lunine, 1989). Approaching
2. TRACING INTERSTELLAR CLOUD the protostar, higher postshock temperatures and enhanced
MATERIAL IN COMETS UV fields led to increasingly hostile conditions for the sur-
vival of interstellar ices, volatile and refractory organics, and
In cometary science, a central issue is elucidating and refractory dust grains (Neufeld and Hollenbach, 1994; Chick
quantifying which aspects of their chemical composition and and Cassen, 1997).
heterogeneity can be attributed to being either pristine or Compositional and isotopic evidence from analysis of
partially processed interstellar material, or material formed meteorites and IDPs suggests, however, that some volatile
purely from nebular processes (Irvine et al., 2000; Irvine interstellar molecules may have entered the nebula relatively
and Lunine, 2004). Astronomical observations now allow us unscathed (Messenger, 2000; Irvine et al., 2000). The phase
to follow in detail the chemical evolution of pristine interstel- of large-scale accretion of molecular cloud material lasted
lar material in a system analogous to that from which the proto- around a few hundred thousand years; most of this was
solar nebula formed (Mannings et al., 2000; van Dishoeck consumed by the protosun (Cameron, 1995). Comets be-
and Blake, 1998; Ehrenfreund and Charnley, 2000). The gan to be assembled in the 5–100-AU region of the nebula
meteoritic record, interplanetary dust particles (IDPs), and toward the end of the stage of nebular disk dissipation (last-
asteroidal observations all indicate that some interstellar ma- ing about 50,000 years), when viscous effects dominated
terial underwent a very significant degree of processing in nebular evolution. During this stage, the interstellar mass
the protosolar nebula (e.g., Ehrenfreund et al., 2002). Ob- accretion rate was probably about 10–100 times less than
servations of a cometary volatile inventory that is largely that occurring in the initial phase of accretion. Comet for-
consistent with the interstellar inventory, and dust grains mation ended after a further 1–2 m.y., when solar accumu-
indicative of nebular processing, are evidence for contribu- lation almost finished and when giant planet formation (at
tions from at least two sources. However, in many cases, it 5–40 AU) was almost complete.
is not a simple matter to discern which source is respon- During disk dissipation, there was large-scale inward
sible for a particular chemical or physical characteristic; a transport of most of the gas and dust and outward transport
plausible theoretical argument can usually be made for each. of most of the angular momentum (e.g., Ruden and Pollack,
Here we discuss several distinctive features of cometary 1991). Turbulent motions, whether convective or magneto-
composition. This is done in the context of the processes hydrodynamic in origin, produced an outward diffusion of
that may have acted to modify interstellar material incor- material from the inner nebula (Morfill and Volk, 1984).
porated in the protosolar nebula (see section 5.3 of Wooden This led to radial mixing of the products of two chemistries
et al., 2004). We attempt to evaluate the likelihood of each (Irvine et al., 2000; Markwick and Charnley, 2004). The
feature being symptomatic of either interstellar origin or cold outer protosolar nebula, where accretion favors reten-
complete nebular reprocessing, or some intermediate be- tion of ISM integrity, was in fact a chemically active re-
tween these extremes. gion (e.g., Aikawa and Herbst, 1999a; Aikawa et al., 1999).
For comets we can only compare their volatile compo- Cosmic rays (beyond about 10 AU) and other sources of
sition directly with that of interstellar ices. However, it ionization such as X-rays (Glassgold et al., 1997), UV pho-
appears that, in the dense core from which the protosun tons (Willacy and Langer, 2000), and radioactive decay [e.g.,
118 Comets II

26Al and 60Fe; Finocchi and Gail (1997)] can drive a non- precursor interstellar volatiles; the location, epoch, and
equilibrium chemistry involving ion-molecule and neutral- source of this processing is largely to be determined.
neutral reactions. In the hot inner nebula (within about Silicate and C-based micrometer-sized dust particles that
1 AU), material can be completely destroyed and lose its are produced in the outflows of late-type stars provide a
interstellar integrity (Fegley and Prinn, 1989). The compo- catalytic surface for a variety of reactions to occur when
sition of this region is governed by a gas-grain chemistry they are dispersed throughout the molecular cloud (Ehren-
in thermodynamic equilibrium. There is little direct chemi- freund et al., 2003). In dense clouds, ices are stable and
cal knowledge about the 5–40-AU regions of disks where efficiently formed on the surface of such dust particles. The
comets are formed. Infrared observations of CO can probe formation of interstellar ices has been discussed in Wooden
the hot innermost regions of disks but these regions are not et al. (2004). An extended inventory of interstellar ice spe-
at present easily accessible to radioastronomical observa- cies has only been established for bright high-mass star-
tions (Dutrey et al., 2004). forming regions (e.g., Gibb et al., 2000). Whether those
Radial mixing offers a means of transporting crystalline abundances are relevant for a comparison with cometary
silicates, be they condensates or annealed grains, outward composition in low-mass systems is strongly questioned.
from the inner nebula into the 5–40-AU region where they There are only incomplete datasets available for solar-type
were incorporated into comets (Gail, 2001; Bockelée-Morvan stars. Most of them are characterized by a low flux and were
et al., 2002). However, nebular shocks at around 5–10 AU therefore difficult to observe by satellites such as the Infra-
are another possible candidate (Harker and Desch, 2002) red Space Observatory (ISO). Groundbased observations
and, if correct, would place constraints on the efficiency of allow us only to observe small wavelength regions in tel-
radial mixing and thermal convection in the nebula. Shocks luric windows (Boogert et al., 2002). Table 1 lists solid state
in icy regions of the nebula have also been proposed as the abundances measured in high- and low-mass (solar-type)
origin of chondritic fine-grained phyllosilicates (Ciesla et star-forming regions in comparison with cometary volatiles.
al., 2003). The detailed effects of such shocks on the volatile As discussed by Wooden et al. (2004), the spectrum of
organic inventory are probably extensive, and need to be interstellar clouds is very rich and shows some very strong
explored to coherently assess nebular processing of com- bands that mask the signature of a number of other spe-
etary materials. Inward transport of the products of “inter-
stellar chemistry,” or of similar chemistry in the cold disk,
could account for the similarities between the volatile in-
ventory of comets and these products. The key question is
TABLE 1. Interstellar ice abundances measured toward high-
therefore how much radial mixing actually occurred (see
and low-mass (solar-type) star-forming regions (Gibb et al., 2000,
Lunine, 1997; Fegley, 1999, 2000; Lunine and Gautier,
Nummelin et al., 2001, Pontoppidan et al., 2003, Taban et al.,
2004). For a detailed discussion on the physical and chemi- 2003) are compared to measured abundances of cometary volatiles
cal processes of disks the readers are referred to Dutrey et in comet Halley, Hyakutake, Hale-Bopp, Lee, LINEAR and Ikeya-
al. (2004), Boss (2004), and Lunine and Gauthier (2004). Zhang (see Bockelée-Morvan et al., 2004, Table 1).

2.1. Is There Interstellar Cloud High-mass Solar-type Comet

Material in Comets? Stars Stars Average
H2O 100 100 100
The gases observed in cometary comae originate from CO 9–20 5–50 1.8–30
the nuclear ices and so offer insight into the nucleus com- CO2 12–20 12–37 3–6
position. Coma molecules can either have a “native” source, CH3OH 0–22 0–25 1.8–2.5
and so have been sublimed directly from the nucleus itself, CH4 1–2 <1 0.14–1.5
or they may appear throughout the coma from an “ex- H2CO 1.5–7 — 0.4–4
tended” source, probably due to the decomposition of large OCS 0–0.3 <0.08 0.1–0.4
organic particles or molecules. For a detailed discussion on NH3 0–5 — 0.5–1.5
HCOOH 0.4–3 — 0.09
cometary volatiles and coma chemistry, the readers are re-
C2H6 <0.4 — 0.11–0.67
ferred to Bockelée-Morvan et al. (2004) and Rodgers et al.
HCN <3 — 0.1–0.3
(2004). A comparison with the inventory of interstellar ices, C2H2 — — 0.1–0.5
as well as with the gases found in dark molecular clouds and
in regions of massive and low-mass star formation, suggests The strong diversity of abundances among the main species CO,
CO2, and CH3OH, even within high- and low-mass star-forming
a direct link. Apparent evidence for the retention of an inter-
regions, hampers the search for an interstellar/cometary link. The
stellar origin are the facts that the major ice components,
lack of data for the low flux solar-type stars adds to those uncer-
and many of the trace molecular species, are also found in tainties. In contrast to cometary observations, there is no evidence
cometary comae. However, as briefly discussed here, there for the presence of C2H6, HCN, and C2H2 nor S-bearing species
are differences in the relative abundances of some cometary (apart from tiny abundances of OCS) in interstellar ices. H2CO
species when compared to their interstellar values. Thus, and HCOOH are only tentatively measured in interstellar ices and
there is some circumstantial evidence for processing of the need a more firm abundance determination.
 Ehrenfreund et al.: Interstellar Material to Cometary Particles and Molecules 119

cies. After H2O and CO (which may have multiple sources the inner nebula could not explain the cometary CH3OH
in comets), species such as CO2, CH3OH, OCS, NH3, and abundances. In this region an additional possible source of
CH4 seem to be among the only molecules that could pro- methanol is Fischer-Tropsch-type (FTT) synthesis (Fegley
vide constraints on an interstellar/cometary link. Most of and Prinn, 1989). Perhaps the simplest explanation is that
the other weak features may escape detection or their abun- these molecules are interstellar but have had their original
dance remains poorly determined in the ISM. This applies populations partially depleted in the nebula. For example,
to C2H2, C2H6, and HCN, of which none have been ob- CO2 (and H2CO) are very susceptible to destruction by H
served in the interstellar solid phase. The only molecules atoms in warm gas (Charnley and Kaufman, 2000). This
that show a similar abundance in comets and some low- may point to CO2 molecules being partially destroyed at
mass star-forming regions [such as “Elias 29” (Boogert et the accretion shock or in nebular shock waves. The situation
al., 2000)] are CH4 and CH3OH. is less clear for CH3OH since the direct detection of metha-
The ice phases within interstellar grain mantles will — nol in a protostellar disk [at <100 AU (Goldsmith et al.,
when incorporated into comets — contribute to the outgas- 1999)] indicates a large fractional abundance of 3 × 10–7,
sing properties, as do the structures of cometary nuclei that apparently at the disk surface, but a lower value deeper in
are stratified in temperature, porosity, density, and compo- the disk of 2 × 10–8. This lower value may simply arise from
sition (Prialnik et al., 2004). Interstellar icy grains are char- depletion onto dust, in which case the abundance of metha-
acterized by different ice phases, amorphous, crystalline, nol in any precometary ices could in fact be similar to that
segregated boundary layers and possibly clathrates (Ehren- found in comets.
freund et al., 1999). The current interstellar ammonia abundances, which are
In particular, some CO, CO2, and CH3OH seem to be much lower than originally estimated (Taban et al., 2003), are
present in pure form [e.g., “apolar” CO layers in cold clouds more compatible with cometary measurements (see Table 1).
or segregated boundary phases of CO2 and CH3OH in Both interstellar and nebular chemistries will produce N2
warmer cloud regions (Ehrenfreund et al., 1999)], which efficiently (e.g., Owen et al., 2001). Thus perhaps one of the
would allow sublimation at a much lower temperature than most perplexing problems in making a definite connection
when trapped in an H2O ice matrix. Sublimation of such between the major interstellar volatiles and those in comets
species at large heliocentric distances could provide evi- is widespread depletion/lack of N2 as measured by N+2 obser-
dence for such ice layers. No attempt has ever been made vations of the latter (Cochran et al., 2000; Cochran, 2002).
to correlate the outgassing pattern of cometary volatiles with This may simply be a volatility issue.
the different ice phases present in interstellar grain mantles. Molecular N may have been more readily evaporated
Carbon dioxide and CH3OH are the most important ice relative to CO due to modest warming of precometary ices
species (after H2O and CO) that can be used as a tracer for (e.g., Irvine et al., 2000). A further possibility is that CO
the interstellar/cometary link. ISO identified CO2 ice as one was selectively trapped during formation of clathrate hy-
of the major components in interstellar ice mantles with an drates, whereas N2 was not (Iro et al., 2003). Alternatively,
average abundance of ~15–20% relative to water ice. Re- this deficiency could have an origin in the prestellar phase
cently, CO2 ice abundances of up to 37% (relative to water (Charnley and Rodgers, 2002), in which case (and if pro-
ice) have been measured toward low-mass protostars (Num- duction and/or mixing of N2 in the nebula is inefficient) all
melin et al., 2001). Whereas CO2 ice is ubiquitous in the comets may to some degree show this deficiency relative
interstellar medium (every target measured has CO2 abun- to the ISM value.
dances above 10% relative to water ice), the measured abun- The problem in comparing the abundances of S-bearing
dance of CH3OH is highly variable and in fact is undetected compounds is that the cometary parents CS2 and H2S are
toward many sources. Among high-mass and low-mass pro- not detected in interstellar ices; although gaseous H2S is ob-
tostars, the CH3OH abundance ranges from small upper lim- served to be abundant in star-forming regions. CS2 and S2
its to 25% relative to water ice (Dartois et al., 1999; Pontop- are unknown in the ISM. The most abundant of the inter-
pidan et al., 2003). The cometary abundance of methanol stellar S-bearing compounds have all been detected in comets.
is appreciable but generally much smaller (~2%) when com- However, some of them are photoproducts of other com-
pared to interstellar ices (5–25%). Similarly, CO2 appears pounds (e.g., CS2 and CS, SO and SO2), or may have a dis-
to be much less abundant in comets than in molecular tributed (polymeric?) source (e.g., CS, OCS). These con-
clouds (Feldman et al., 2004). Both these observations sug- siderations make it very unlikely that cometary sulfuretted
gest either partial degradation of the interstellar molecules species represent pristine interstellar material.
or complete production of them in the solar nebula. If ener- The simple hydrocarbons CH4, C2H2, and C2H6 also
getic processing of molecular ices is an efficient means of present ambiguity. Methane is the only molecule among
forming CO2 (Wooden et al., 2004), and given the more these three that is present in interstellar ices (~1% relative to
energetic environment of the protosolar nebula, it is surpris- water ice); acetylene has a cometary abundance similar to
ing that CO2 is not at least as abundant as in molecular the interstellar gas (e.g., Lahuis and van Dishoeck, 2000). It
clouds. This may rule out energetic processing of ices in is therefore tempting to identify them as being of interstellar
the outer nebula as the source of these compounds. Gail origin where ethane forms by reduction of acetylene on cold
(2002) has shown that radial mixing of oxidized C dust from (10 K) grains. Alternatively, these hydrocarbons could have an
120 Comets II

origin in nebular chemistry, probably involving some form whose resolution should shed light on chemical differen-
of gas-grain chemistry. For example, Gail (2002) showed tiation and the place of origin of particular comets. Helbert
that mixing of oxidized C dust could explain the abundances et al. (2002) have shown that the abundances of these mole-
of CH4 and C2H2 in comets, but not the presence of C2H6. cules could be derived from C2H2, CH3CCH, and C3H8 in
If this particular nebular chemistry was the origin of these a coma chemistry driven by electron-impact dissociations.
hydrocarbons, then it requires outward radial mixing of CH4 However, methylacetylene and propane have not yet been
and C2H2 and inward transport of C2H6 from the outer neb- detected in comets. In this picture, the same uncertainties
ula, where it perhaps formed on grains. Alternatively, FTT in distinguishing interstellar and nebular contributions to the
synthesis would require that they all be transported outward hydrocarbons persist. Synthesis of long, unsaturated, C-
(Fegley and Prinn, 1989). Unfortunately, it is difficult to chain molecules appears to be one signature of interstellar
detect C2H6 in the ISM and therefore to definitively decide organic chemistry. There have been tentative detections of
on the origin of these compounds in cometary matter. C4H and its possible parent C4H2 in Halley and Ikeya-Zhang
Apart from the most abundant species, some organic respectively (Geiss et al., 1999; Magee-Sauer et al., 2002).
molecules found in molecular clouds have also been iden- The detection of a large suite of long C-chain molecules in
tified in the coma of Hale-Bopp (Bockelée-Morvan et al., comets, similar to the large ones found in molecular clouds,
2000, 2004). Simulations of interstellar ice analogs show would be strong evidence for an interstellar origin of these
increasing complexity on the molecular scale when ener- organics.
getic and thermal processing is applied (Allamandola et al., Of the many other small interstellar organics also found
1997; Moore and Hudson, 1998; Cottin et al., 2001a; Colan- in comets, HNCO, NH2CHO, CH3CHO, and HCOOH are ex-
geli et al., 2004). Those complex organics that have been pected, along with H2CO and CH3OH, to be products of inter-
observed in laboratory spectra of processed ice mixtures stellar grain-surface chemistry (Charnley, 1997). Although
may or may not be present at small abundance in interstellar there are differences between the interstellar and cometary
grain mantles. However, with current astronomical instru- abundances, the fact that these molecules are associated with
mentation they cannot be observed in the interstellar solid ices does suggest that they are products of interstellar chem-
phase. Their signatures will in most cases be too weak rela- istry. As these surface reactions involve low-temperature H-
tive to the continuum or they will be masked by the pres- atom additions, they cannot proceed efficiently on surfaces
ence of other strong bands. Thus, there will never be definite warmer than about 15 K since the H-atom residence time
proof for the presence of specific, large organic species in then becomes shorter than the timescales to migrate and
interstellar ice mantles; some indications may come from react, as shown experimentally (Watanabe et al., 2003). This
gas-phase measurements in hot cores that sample the ma- does not represent a problem in 10-K molecular clouds, but
terial evaporating from icy particles. greatly constrains the region of the nebula where such a
For molecules whose formation involves gas-grain chem- chemistry could occur. Any differences between the inter-
istry, we are generally comparing the abundances measured stellar and cometary abundances may then be due to selec-
toward regions of massive star formation, so-called hot mo- tive processing in the nebula (see the discussion on metha-
lecular cores. Such regions may also exist around low-mass nol above).
cores (Schoier et al., 2002) but these are generally less-well The other simple cometary organics, CH3CN, HC3N and
characterized. HCOOCH3, cannot be formed in the coma, and current theo-
The difficulties inherent in connecting observed com- ries of their formation require gas-phase reactions (Rodgers
etary volatiles with interstellar molecular cloud material can and Charnley, 2001b). The cometary abundances of CH3CN
be illustrated for the case of the HNC molecule. Cometary and HC3N are consistent with them being either the prod-
HNC was originally discovered in the coma of Hyakutake ucts of interstellar chemistry or similar processes in the outer
(Irvine et al., 1996); the high HNC/HCN ratio provided nebula. However, interstellar HCOOCH3 is believed to form
strong evidence that this HNC was preserved interstellar around protostars in an ion-molecule chemistry driven by
material. Subsequent calculations showed that the HNC/ evaporated ice mantles (Blake et al., 1987). The methyl
HCN ratios in Hyakutake and Hale-Bopp could apparently formate in comets may then have originated in a sequence
be produced by chemical reactions in the coma (Rodgers and involving the desorption of ices, an intervening period of
Charnley, 1998; Irvine et al., 1998). Further measurements ion-molecule chemistry, followed by recondensation. These
of HNC/HCN ratios in other comets, when confronted with conditions may have occurred upon the first accretion of in-
these models, demonstrated that gas-phase chemistry cannot terstellar material, or perhaps during alternating inward and
in general be the origin of HNC. The most likely source of outward radial mixing of interstellar material in the nebula.
HNC in the coma is the decomposition of a large organic, In summary, volatile cometary material shows a general
perhaps polymeric, compound (Rodgers and Charnley, 2001a; qualitative link with the interstellar ice phase and the in-
Irvine et al., 2003). ventory of identified interstellar molecules. It is unlikely that
The C chain radicals, C2 and C3, are widespread in com- these similarities reflect the wholesale incorporation of un-
ets and their abundances indicate a marked variation with altered interstellar ices into comets (cf. Greenberg, 1982).
the Tisserand parameter (A’Hearn et al., 1995). Identifi- As infalling interstellar material is decelerated at the accre-
cation of their chemical parent(s) is an important problem tion shock, it experiences chemical alteration to varying
 Ehrenfreund et al.: Interstellar Material to Cometary Particles and Molecules 121

degrees, depending upon the epoch and position of entry deuteration are in the gas phase, e.g., in IRAS 16293-2422
into the nebula. These changes range from those associated (Loinard et al., 2000).
with simple evaporation-recondensation of ices in the outer The fractionation ratio HDO/H2O has only been meas-
disk regions, to complete molecular dissociation in the inner ured in three comets (Halley, Hyakutake, and Hale-Bopp),
ones. We may also expect that the (interstellar) chemical where it was found to be around 3 × 10 –4. In Hale-Bopp,
clock can be further reset during the assembly of cometesi- the DCN/HCN ratio was determined to be about 0.002.
mals in the nebula. It is now realized that the chemistry Coma chemistry models demonstrate that these ratios are
occurring in the outer regions of protoplanetary disks closely truly those of the material residing in the nucleus (Rodgers
resembles that of dense interstellar regions. Hence, the pris- and Charnley, 2002). Gas-phase water D/H ratios measured
tinity of interstellar matter accreted under even the most in massive star-forming regions are generally low, around
benign conditions can become further adulterated. Elucidating 0.0003, and comparable with the cometary values. However,
in detail how the pristine inventory of available interstellar recent determinations of HDO/H2O in Orion suggest it could
volatiles can be corrupted will require careful modeling of be higher: ~0.004–0.011 (Pardo et al., 2001). Searches for
nebular chemistry, subject to the constraints that will be pro- HDO ice in low-mass protostellar cores yield only an upper
vided by future observations of disk and comet composition. limit on HDO/H2O of about 0.02 (Parise et al., 2002). Sur-
veys of low-mass protostellar cores consistently yield DCN/
2.2. Isotopic Fractionation: An Interstellar HCN ratios about a factor of 30 larger than the cometary
Signature in Comets? ratio (Roberts et al., 2002), the latter of which is comparable
to the value found in massive cores like Orion (0.003).
In cold interstellar clouds, both gas-phase and grain- Thus, it is difficult to elucidate the physical conditions
surface chemistries can lead to enhanced isotopic fractiona- under which cometary ices formed (and hence the probable
tion in molecules (Wooden et al., 2004). In comets, several location) by making analogies with interstellar sources, at
molecular isotopic ratios have been measured and these can, least for these two molecules. The D/H ratios measured in
in principle, provide important cosmogenic information massive cores appear to resemble cometary values best, but
(Table 3 in Bockelée-Morvan et al., 2004). It must, however, low-mass cores are more physically relevant to protoplane-
be stressed that conclusions drawn from such observations tary nebulae and thence, presumably, to comet formation.
may be biased due to the limited data available. It is possible that high molecular D/H ratios existed in the
Similar 18O/16O ratios, both close to the terrestrial value, protosolar natal cloud core and these were diluted by chemi-
were measured in Halley and Ikeya-Zhang (Balsiger et al., cal reactions during accretion and within the nebular disk.
1995; Lecacheux et al., 2003). The 13C/12C ratio has been Ideally, one would wish to compare D fractionation between
measured in C2, CN, and HCN for several comets and this is the envelope and disk of a forming protostar. Thus far, the
also apparently terrestrial (Wyckoff et al., 2000). From this only detection of a deuterated molecule in a disk, DCO+ in
data, one may draw the conclusion that either the natal cloud TW Hya, yields a D/H ratio of 0.035 (van Dishoeck et al.,
was of solar composition, or these ratios were set in the pro- 2003). This is comparable with that found in low-mass cores
tosolar nebula. However, the absolute interstellar fraction- but larger than found in massive cores. However, one must
ation expected in C and O isotopes is generally much less be careful in drawing conclusions based on a molecular ion.
than in other isotopes (Langer et al., 1984). Calculations This observation only provides information on the potential
demonstrate that C-isotopic fractionation by ion-molecule of disk chemistry to deuterate molecules (e.g., Aikawa and
reactions selectively enhances 13C in CO, whereas derived Herbst, 1999b) and gives no direct connection to the neutral
cometary 13C/12C ratios are not based on isotopes of CO. molecules observed in cometary nuclei.
Thus, it cannot be ruled out that other cometary mole- Thus, albeit based on just three measurements, comets
cules, perhaps derived from CO on dust, may possess higher appear to be less deuterated than the material from which the
13C/12C ratios. The 13C enhancements found in IDPs and car- protosolar nebula probably formed. This conclusion comes
bonaceous chondrites may have an origin in these species with the important caveat that the interstellar molecules with
(e.g., Cronin and Chang, 1993). the most distinctive D fractionation have not yet been meas-
Enhanced D fractionation is observed in many interstellar ured in comets (i.e., isotopomers of formaldehyde, ammonia,
molecules. The measured D/H ratios range from about 1 × and methanol).
10–4 for water to 0.5 for formaldehyde (Ceccarelli, 2002). There is some evidence that this may be the case since
Recently, there has been growing evidence for “superdeuter- it has been suggested that there may be differentiation in the
ation” in some molecules (H2CO, NH3), exhibited in high D/H ratios between nuclear HCN and the DCN and HCN
D/H ratios and the presence of multideuterated species: released into the coma from outgassing grains (Blake et al.,
D2CO, ND3, CHD2OH (Loinard et al., 2000; van der Tak 1999).
et al., 2002; Parise et al., 2002). Interestingly, this “super- Furthermore, the carbonaceous component of some IDPs,
deuteration” is observed in either low-mass prestellar cores, probably of cometary origin, exhibit D/H ratios close to the
where CO depletion onto dust may be responsible (van der interstellar range and higher than that found for HCN [D/H
Tak et al., 2002), or in cores where low-mass star forma- of 0.008 in “Dragonfly” (Messenger, 2000)]. Assuming that
tion has already occurred and the products of grain-surface similarly lower cometary D/H ratios will be found in formal-
122 Comets II

dehyde, ammonia, and methanol, the D/H ratios in comets two minerals — olivine and pyroxene or (Mgy,Fe(1 – y))2SiO4
could result from “erosion” of the pristine D/H ratios at the and (Mgx,Fe(1 – x))SiO3 — and are in two forms: amorphous
accretion shock or in nebular shocks. Ion-molecule chem- and crystalline (Colangeli et al., 2004).
istry in the outer nebula could also act to lower the original Thermal emission models of Comet 19P/Borrelly, one
interstellar fractionation (Aikawa and Herbst, 1999b). Al- of the few short-period comets with a silicate feature, fit
ternatively, it has been proposed that lowering of the water either a grain population dominated by discrete amorphous
fractionation may proceed by neutral exchange processes pyroxene and amorphous C grains (Hanner et al., 1996) or
in the nebula (Drouart et al., 1999), however, the value of core-mantle aggregate particles consisting of amorphous oli-
the solid HDO/H2O ratio assumed in this model is at present vine cores with amorphous C mantles (Li and Greenberg,
controversial (Texeira et al., 1999; Dartois et al., 2003). 1998a). Amorphous pyroxene and olivine are found in long
Important goals for future observations should be to deter- period comets in varying proportions (Hanner et al., 1994;
mine the D/H ratios of selected molecules, such as water Hanner and Bradley, 2004). In the core-mantle aggregate
and HCN, in disks, and also to measure D/H in cometary model (Hage and Greenberg, 1990), long-period comets are
molecules whose interstellar counterparts are known to have fitted with organic refractory mantles (Li and Greenberg,
large values (e.g., formaldehyde). 1998b), while short-period Comet Borrelly is better fitted with
Radio observations of HCN in Hale-Bopp indicate a 14N/ amorphous C mantles (Li and Greenberg, 1998a). These
15N ratio of around 300 (e.g., Jewitt et al., 1997; Crovisier comparisons suggest that parent-body processing and UV
and Bockelée-Morvan, 1999); as with C and O, this is con- irradiation do not change the silicate mineralogy while it
sistent with a terrestrial value (270). Recent measurements may carbonize the organic grain component (Li and Green-
of C15N and C14N in Comets Hale-Bopp and C/2000 WM1 berg, 1998a). In highly active long-period comets we can
(LINEAR) near perihelion by Arpigny et al. (2003) indi- compare the grain properties of particles dredged up from
cate that C14N/C15N is about 130, and significantly different deeper layers of the nucleus and entrained in jets with those
from that in HCN. For both molecules (HCN and CN) the particles released into the coma from the nuclear surface.
12C/13C ratios were found to be terrestrial. Some CN is cer- In Comet Hale-Bopp, grain mineralogy as revealed through
tainly coming from photodissociation of HCN but the ob- the shape of the 10-µm spectral resonances was uniform to
servations of Arpigny et al. (2003) indicate that there must within the measurement uncertainties at different positions in
also be another, probably polymeric, parent for CN that is the coma at a given epoch (Hayward et al., 2000), except
much more highly fractionated in 15N. Such low 14N/15N for a drop in the crystalline pyroxene resonance in the sun-
ratios are also detected in IDPs (Messenger, 2000) and can ward direction (Harker et al., 2002). The grain temperatures
be explained by interstellar chemistry theories (Charnley and the optical and near-IR polarization were significantly
and Rodgers, 2002). This emphasizes the crucial point for enhanced in Hale-Bopp’s jets (Hadamcik and Levasseur-
understanding the origin of cometary isotopic fractiona- Regourd, 2003), indicating a difference in grain morphology
tion — one must attempt to measure isotopic ratios of sev- or size (Levasseur-Regourd et al., 2002). Analysis of Hale-
eral different molecules. Bopp suggests that differences between surface and jet
particles can be attributed to grain morphology but not sili-
2.3. Silicates cate mineralogy. Studying the silicate mineralogy and crys-
tallinity therefore probes interstellar and nebular processes
Dust grains are entrained in the flow of escaping gases affecting silicate dust grains prior to their incorporation into
from the nucleus. Dust grains in the coma scatter and ab- comets (Hanner et al., 1996). The evidence, although not
sorb sunlight, reemitting the absorbed energy in the ther- unanimous, forms a consensus that cometary amorphous
mal infrared. At 1 AU, the highly refractory silicate grains silicates are of probable interstellar origin while crystalline
are warmed to radiative equilibrium temperatures well be- silicates are of probable nebular origin (Hanner and Brad-
low their melting or annealing temperatures. Therefore, the ley, 2004; Wooden, 2002).
properties of the silicate grain component of comae dust Amorphous silicates in comets probably are relic grains
probe the mineralogy and crystallinity of the silicate dust from the interstellar medium (cf. Hanner and Bradley,
in the nucleus. Cosmic-ray bombardment of surfaces of 2004). Formation of amorphous silicates requires very rapid
long-period comets while in the Oort cloud has the poten- cooling that is probable for an asymptotic giant branch
tial to alter the properties of the silicates on the nuclear (AGB) stellar outflow (Wooden et al., 2004; Tielens et al.,
surface. Collisional evolution of short-period comets in the 1997) but formation is unlikely under conditions in the solar
Kuiper belt and UV irradiation during their many perihe- nebula (Yoneda and Grossman, 1995). Amorphous or glassy
lion passages may also alter the grain properties. Compar- forms of minerals are relatively rare in meteoritic materi-
ing the dust properties in long- and short-period comets als compared to crystalline forms. Iron-bearing amorphous
compares the effect of minimal vs. significant parent-body olivine is fitted to the interstellar 10-µm absorption feature
processing. and interstellar extinction curve (Li and Greenberg, 1997).
As discussed in Hanner and Bradley (2004), IR spectra Iron-bearing amorphous olivine and pyroxene in a 5 : 1 ra-
of comets and laboratory studies of cometary interplanetary tio are fitted to the absorption feature in the line-of-sight
dust particles show that silicates in comets are dominated by to the galactic center (Kemper et al., 2004). By the relative
 Ehrenfreund et al.: Interstellar Material to Cometary Particles and Molecules 123

absence of amorphous silicates from highly processed solar

nebula materials (chondrules) and their ubiquity in the ISM,
amorphous silicates in comets are probably interstellar.
Further evidence of the interstellar source for cometary
amorphous silicates arises from the laboratory studies of
chondritic porous interplanetary dust particles (CP IDPs),
which are of probable cometary origin (Bradley, 1988; Han-
ner and Bradley, 2004). Chondritic porous IDPs are aggre-
gates of crystalline and amorphous silicates, the so-called
“GEMS” (Hanner and Bradley, 2004), in a matrix of car-
bonaceous materials (see section 2.4). Irradiation of GEMS
by high-energy particles during their residence time in the
ISM has been invoked to explain radiation tracks, compo-
sitional gradients with GEMS’ radii, and the presence of
nanophase Fe (Bradley, 1994).
Laboratory experiments demonstrate that ion bombard-
ment of 4-KeV He+ ions at fluxes typical of the ISM shocks Fig. 1. Infrared Space Observatory (ISO) short wavelength spec-
can amorphize crystalline olivine, increase porosity, reduce trometer (SWS) spectra of the pre-main-sequence Herbig Ae star
the Fe from its stoichiometric inclusion in the mineral to HD 100546 (Malfait et al., 1998), the O-rich post-AGB binary
embedded nanophase particles, and damage the chemistry star AC Her (Molster et al., 2002 a,b,c), and Comet Hale-Bopp
by reducing the O/Si and Mg/Si ratios, effectively increas- (Crovisier et al., 1997), showing the strong similarities in their
spectral features. The Mg-rich crystalline silicate resonances are
ing pyroxene at the expense of olivine (Carrez et al., 2002).
identified. Note the far-IR spectra are dominated by isolated crys-
Ion bombardment by 50-KeV He+ ions, characteristic of
talline silicate features of Mg-rich crystalline olivine with a few
supernovae shocks, does amorphize the crystalline silicates features of Mg-rich crystalline pyroxene.
but leaves the chemistry unaltered (Jäger et al., 2003). Thus,
ion bombardment can create the highly radiation damaged,
Mg-rich GEMS with nanophase Fe inclusions (Brownlee et
al., 2000) in CP IDPs whose spectra are very similar to the
amorphous silicates observed in cometary emission spec- 2002a), where crystallization is attributed to a low-tempera-
tra (Hanner and Bradley, 2004; Bradley et al., 1999a,b). ture mechanism that occurs over longer times in the spheri-
Therefore, morphology and mineralogy indicates that the cal outflows of single AGB stars (Molster et al., 1999).
cometary amorphous silicates have an interstellar origin. In the solar system, only silicate crystals in CP IDPs and
Halley’s Fe/Mg ratio is 0.52 and the solar value is 0.84 in Antarctic micrometeorites have such high Mg contents
(Jessberger et al., 1988), so Halley’s Fe content is close to (Bradley et al., 1999c) as deduced for cometary crystals.
solar. However, only 30% of the Fe is in silicates while 70% Comet Halley’s silicates are also very Mg-rich compared to
is in FeS and Fe grains. Halley’s Fe grains are highly re- chondrules and meteoritic materials. The range of Fe con-
duced, as there is <1% FeO. This is also characteristic of the tents in silicate crystals in chondrules is due to the rapid
iron within GEMS in CP IDPs where it exists as nanophase melting of grain aggregates at high temperatures followed
Fe or FeS and where the nanophase Fe has been attributed by rapid cooling (Delany, 1995; Kracher et al., 1984). Since
to ion bombardment in the interstellar medium. cometary crystals have very little Fe, these crystals have not
The crystalline silicates in comets are of probable nebular suffered chondrule-like postformation heating events in the
origin. The existence of Mg-rich crystalline silicates in com- nebula and represent primitive solar nebula materials (Wooden
ets is revealed by the sharp resonances in cometary 10-µm et al., 2000).
spectra (Hanner and Bradley, 2004; Harker et al., 2002; The appearance of Mg-rich crystalline silicates in some
Wooden, 2002). Comet Hale-Bopp’s observed 10-µm sili- comets indicates that cometary crystalline silicates are grains
cate feature is best-fitted by Mg-rich pyroxene “Cluster” that condensed at high temperatures [~1400 K (Grossman,
(Messenger, 2000) CP IDPs (Wooden et al., 2000). In fact, 1972; Hanner and Bradley, 2004)] or were annealed from
all crystalline silicates observed by the ISO short wave- amorphous silicates at somewhat lower temperatures [>900 K
length spectrometer (SWS) in comets, stellar outflows, and (Hallenbeck et al., 1998, 2000; Fabian et al., 2000; Hanner
protoplanetary disks are Mg-rich (Bouwman et al., 2001; and Bradley, 2004)] in the solar nebula. If annealing pro-
Molster et al., 2002a). Figure 1 presents from the ISO-SWS cesses occurred in the inner nebula (Mousis et al., 2002;
database the best comparison between a pre-main-sequence Bockelée-Morvan et al., 2002), then such temperatures
Herbig Ae star with a protoplanetary disk, an O-rich AGB occurred early (<300,000 yr) and radial diffusion rapidly
star, and Comet Hale-Bopp. The clear contrast of strong transported a uniform concentration of crystals to beyond
crystalline peaks is seen in many but not all Herbig Ae stars the snow line where comets formed (5–40 AU) (Bockelée-
(Meeus et al., 2001). Crystalline silicates are preferably de- Morvan et al., 2002). Annealing also may have occurred
tected in binary AGB stars that possess disks (Molster et al., in shocks in the nebula in the 5–10-AU region, producing
124 Comets II

local enhancements in the crystalline concentration (Harker Bopp (Harker et al., 2002; Li and Greenberg, 1997), is
and Desch, 2002). Annealing temperatures are not reached similar to what is plausible for both interstellar material (Iati
in the accretion shock between outer disk surface and the pre- et al., 2001; Vaidya and Gupta, 1999) and grain aggregates
natal cloud (Chick and Cassen, 1997; Neufeld and Hollenbach, in the solar nebula (Dominik and Tielens, 1997). Thus,
1994). Future observations may reveal differences in the crys- grains of probable cometary origin are aggregates of sili-
talline-to-amorphous ratios between long- and short-period cate and carbonaceous materials that have seen significantly
comets that will help to constrain solar nebula models. The different environments in the solar nebula prior to both their
detection of cometary crystals in long- and short-period com- aggregation into a single porous particle and their incorpora-
ets, however, may not only depend on their concentration tion into comets.
but also on grain properties such as grain size and porosity
(Hanner and Bradley, 2004). 2.4. Carbonaceous Matter
Challenges to the interpretation that cometary amorphous
silicates are interstellar and cometary crystals are primitive Our knowledge on carbonaceous material of comets is
solar nebula grains comes from recent discoveries using the rather limited. In situ measurements of a few nanograms of
nanoSIMS (secondary ion mass spectrometry). NanoSIMS Halley’s coma show C-rich grains that are apparently com-
is an ion microprobe, allowing elemental and isotopic analy- ponents of various types, including pure C particles, poly-
sis of small features of solid samples. Six out of more than cyclic aromatic hydrocarbons (PAHs), branched aliphatic
1000 subgrains in nine CP IDPs have anomalous 17O/16O hydrocarbons, C-O or C-N polymers, and more complex com-
and 18O/16O ratios and clearly carry presolar isotopic sig- pounds containing all four C, H, O, and N atoms (Fomenkova,
natures (Messenger et al., 2003). Three of the six presolar 1997). CHON organic compounds were first described as
grains are identified with mineral phases and have AGB being similar to kerogens (Jessberger et al., 1988). Hetero-
isotopic ratios: one forsterite crystal and two GEMS. About polymers or complex organic molecules also are proposed
1% by mass of the CP IDPs have distinct presolar signa- (Kissel et al., 1997). Some of the species remain very specu-
tures. The detection of a presolar forsterite crystal (Messen- lative due to the limited resolution of the mass spectrom-
ger, 2000) contradicts the concept that Mg-rich cometary eters that flew through Halley’s coma.
crystals are solar nebula grains. The mass fraction, however, The in situ measurements of Halley reveal that 25% by
is within the range estimated for the ISM [<0.5% (Kemper et mass are siliceous-free CHON grains, 25% are carbona-
al., 2004)]. The measured mass fraction of presolar GEMS, ceous-free silicate grains, and 50% are mixed carbonaceous
however, is significantly less than the cometary high mass and silicate grains. Mixed grains of greater mass exist in the
fraction of amorphous silicates of probable interstellar ori- innermost parts of the coma, while carbonaceous-free silicate
gin [Hanner and Bradley (2004); Hale-Bopp, Harker et al. grains are dominant further out in the coma (Fomenkova,
(2002)]. At this time, the nanoSIMS instrument detects only 1999). This suggests that the organic material is the “glue”
the subgrains with large isotopic anomalies. Higher-preci- that holds the silicates together and that the organic material
sion measurements on CP IDPs are required to improve our desorbs in the inner coma (Boehnhardt et al., 1990; Fomen-
understanding of the range of isotopic ratios that are con- kova, 1997), freeing the isolated silicate mineral phases. This
sidered to be interstellar and of the processes in the ISM that scenario is also proposed for Comet Hale-Bopp near peri-
may alter the signatures of the origins of dust grains. helion (≤1.5 AU) when its amorphous grains showed an in-
The presence of silicate crystals in comets implies mix- crease in porosity, a steeper size distribution (more smaller
ing of high-temperature and low-temperature materials in grains), and slightly higher relative mass fraction of crystal-
the comet-forming zone. The presence of silicate crystals in line silicates (Harker et al., 2002). Furthermore, within this
comets implies that processed nebular materials were incor- same heliocentric range (≤1.5 AU), Comet Hale-Bopp has a
porated with volatile-rich icy material. This implies a signi- strong distributed source of CO, i.e., the CO spatial distri-
ficant degree of radial transport and/or mixing in the nebula. bution is more radially extended than the distribution of the
In CP IDPs of probable cometary origin, the close proximity dust and other gas components; only 50% of the CO origi-
of oxidized, reduced, and metallic mineral phases, i.e., min- nated from the nucleus (DiSanti et al., 2001).
eral phases in contact with but far from equilibrium with The other 50% of the CO is deduced to arise from the
each other, indicates that these micrometer-sized aggregates desorption of an unknown organic component of the dust. A
of submicrometer units suffered minimal alteration after the possible candidate for the distributed CO is polyoxymethyl-
grains accreted their constituent parts. “The fact that (post- ene (POM), which is a polymer of formaldehyde (Boehn-
accretion) alteration of aggregate IDPs hardly reached ther- hardt et al., 1990). The desorption of POM first into formalde-
modynamic equilibrium at sub-micrometer scales supports hyde followed by photodegradation into CO would, how-
the view that energy for alteration was either scarce or ever, create far more formaldehyde (Cottin et al., 2001b)
unavailable for sufficiently long periods of time, or both” than detected in Hale-Bopp’s coma (Bockelée-Morvan et al.,
(Rietmeijer, 1998). Porosity distinguishes primitive but not 2000). Following the heliocentric dependence of both dust
necessarily presolar origin. The high porosity of cometary properties and distributed CO sources is currently one of
grains, including CP IDPs (Rietmeijer, 1998) and the high the best observational strategies for studying the organic
porosity deduced from thermal emission models of Hale- component of cometary dust.
 Ehrenfreund et al.: Interstellar Material to Cometary Particles and Molecules 125

Infrared observations of dusty comae ubiquitously de- sible presence of functional groups associated with alde-
tect a strong near-IR spectrally featureless thermal emission hydes, ketones, and organic acids.
that is well-fitted by amorphous C. The spectroscopic detec- Amorphous C in comets and CP IDPs is likely of inter-
tion of solid state CHON particles if they are made of kerogen- stellar origin. In situ measurements of Comet Halley reveal
like material is difficult in the near- and mid-IR because both discrete and mixed mineral assemblages. Of the total
kerogen is about 30 times less absorptive than Fe-bearing grains, ~8–10% by mass is elemental C that is of AGB
amorphous silicates, and even less absorptive than amor- origin based on its 13C/12C ratio (Fomenkova, 1999). Amor-
phous C; spectroscopic resonances are weak compared to phous C is invoked to fit the near-IR emission in comets
the other grain species. Unidentified gas phase lines are seen (e.g., Hanner et al., 1994; Harker et al., 2002), although
in comets at very high spectral resolution in the near-IR highly absorbing organic refractory mantles on silicate cores
(Magee-Sauer et al., 2002; Mumma et al., 2001b) and may can also produce this observed emission in some comets
be relevant to the mystery of the form of cometary organic (Greenberg and Hage, 1990; Li and Greenberg, 1998b). Of
gas-phase molecules. The detection of phenantrene (C14H10), Halley’s particles, the elemental C component best repre-
a gas-phase PAH macromolecule, in Halley is suggested sents the amorphous C that is abundant in CP IDPs and that
based on UV spectroscopic data (Moreels et al., 1994). The is invoked to produce the near-IR thermal emission from
emission band at 3.28 µm in a few comets suggests the pres- comets [20% by mass of the submicrometer grains in Hale-
ence of aromatics (Bockelée-Morvan et al., 1995; Colangeli Bopp (Harker et al., 2002)]. Models of the near-IR reflec-
et al., 2004); the unambiguous detection of the 3.28-µm tance spectra of Centaurs and Kuiper belt objects utilize, by
feature in moderate resolution IR spectra requires the decon- number, an amorphous C abundance of 1–20% (D. Cruik-
volution of emission from gas species in the same spectral shank, personal communication, 2003). Elemental C is,
range. No PAHs have been detected in the ISO IR spectra however, <<1% by mass in carbonaceous chondrites and 3–
of C/1995 O1 Hale-Bopp (Crovisier et al., 1997, Crovisier, 5% of aqueously altered primitive meteorites (Brearley and
1999), which may be due to the large heliocentric distance Jones, 1998). The depletion of amorphous C in inner solar
at the time of observation. Polycyclic aromatic hydrocar- system bodies relative to outer solar system bodies may be a
bons are very strong absorbers of UV radiation and emitters result of the oxygenation of C into CO and CO2 in the chon-
of IR photons, and as such, represent the observable “tip drule-formation process (Ash et al., 1998; Wooden, 2002;
of the iceberg” of cometary organics. Cuzzi et al., 2003).
Chondritic porous IDPs are cometary grains that contain Comparing the soluble fraction of carbonaceous mete-
both presolar and solar isotopic materials. [For in-depth dis- orites with cometary volatiles indicates that CI chondrites
cussions on the connection between properties of CP IDPs can be strongly related to comets. From the analyses of
and comets, see Hanner and Bradley (2004), Sykes et al. amino acids in different meteorites it was recently con-
(2004), Wooden (2002), and Messenger and Walker (1998).] cluded that the formation of an extensive number of amino
Chondritic porous IDPs have high entrance velocities rela- acids made through processes such as Strecker-Cyanohydrin
tive to asteroidal particle trajectories (into Earth’s strato- synthesis and Michael addition, as observed in the Murchi-
sphere where they are collected by high-flying aircraft), son meteorite, requires the presence of a number of alde-
high porosity and fragility (indicative of minimal process- hydes and ketones, as well as ammonia, water, HC3N, and
ing in the solar nebula), high Mg contents (in comparison HCN (Ehrenfreund et al., 2001). All the small molecules
with meteoritic materials), contain D-rich organic material required to make amino acids are in the current inventory
(Keller et al., 2000, 2002) and isotopic anomalies in N and of cometary volatiles. However, no ketones and only form-
C in the C phase (Messenger, 2000), and contain highly aldehyde and acetaldehyde (0.02%) are detected in comets
radiation damaged amorphous silicate spherules (GEMS) (Bockelée-Morvan et al., 2004). The low number of amino
in a C-rich matrix (Bradley et al., 1999a). In fact, most of acids and peculiar abundance ratio in CI chondrites (such
the CP IDPs have remarkably high C abundances, typically as Orgueil) is more compatible with cometary chemistry
several times higher than those of CI chondrites. Carbon is than with chemistry on asteroidal bodies (Ehrenfreund et
so abundant that it can be directly observed in ultramicro- al., 2001).
tome sections where it is often seen as regions of pure amor- In the ISM, the distribution of C is still an unsolved ques-
phous C covering areas as large as 1 µm across (Brownlee tion. In dense molecular cloud material a reasonable frac-
et al., 2002). Infrared spectroscopy of the ~3.4-µm CH- tion of C is incorporated into CO gas (20%) and a small
stretching region in CP IDPs shows the presence of aliphatic percentage (~5%) is present in C-bearing ice species (dis-
hydrocarbons (Brownlee et al., 2000; Flynn et al., 2002). cussed in section 2.1). Diffuse interstellar clouds are ex-
Recent laboratory data show that the abundant organic ma- posed to UV radiation and show very low levels of CO gas.
terials, specifically the aliphatic and aromatic materials, in In such environments about 15% of the cosmic C is attrib-
the CP IDP “Dragonfly” are responsible for the extremely uted to PAHs. Polycyclic aromatic hydrocarbons seem to
high D/H relative to terrestrial material and indicate a pre- be prevalent in the diffuse interstellar medium and on the
solar origin (Keller et al., 2002). edges of molecular clouds but may or may not be present
In this same “Dragonfly” particle, the CO carbonyl within molecular clouds. This leaves a large fraction (>50%)
stretch is observed (Flynn et al., 2002), indicating the pos- of the cosmic C unaccounted for in the interstellar medium.
126 Comets II

Laboratory simulations in combination with interstellar ob- the main component of comets, depend on the structural
servations argue that this missing C is incorporated into parameters of the material, such as porosity, grain size, ma-
solid-state macromolecular C (cf. Fig. 17 of Pendleton and terial strength, and local density. Organic molecules may act
Allamandola, 2002) such as amorphous and hydrogenated as glue within ice-dust mixtures that also enhances material
amorphous C (see Colangeli et al., 2004; Ehrenfreund and strength and thermal conductivity. Sublimation of material
Charnley, 2000; Mennella et al., 1998). from cometary nuclei is triggered by a complex system of
Though many different forms of C have been discussed, internal processes (Prialnik et al., 2004) and, even if these
hydrogenated (and dehydrogenated) amorphous C provide molecular ices were present in the same relative proportions
currently the best fit to observations of the UV bump at as interstellar ices, it is unlikely that the cometary outgas-
220 nm in the interstellar extinction curve and simultane- sing pattern would accurately reflect this.
ously the best quantitative solution for current dust models The infrared signatures of silicates in comets and in cir-
(Mennella et al., 1998). Note that graphite has been popu- cumstellar regions, as well as analyses of isotopic ratios in
larly invoked in the past to explain the UV 220-nm bump IDP silicates, have greatly improved our knowledge of dust
(Hoyle and Wickramasinghe, 1999; Li and Draine, 2001); in the early solar system and its link to that of comets. The
graphite does not comprise a significant mass fraction of existence of crystalline silicates in comets, as revealed by
CP IDPs (D. Brownlee, personal communication, 2003). cometary IR spectra and their apparent scarcity in the ISM,
Carbonaceous chondrites are known to contain a sub- has been invoked as an argument for mixing of “high-tem-
stantial amount of C, up to 3% by weight, and exhibit a perature” and “low-temperature” materials in the comet-
range of thermal and aqueous alteration believed to have forming zone. In particular, the appearance of Mg-rich crys-
occurred on their parent bodies. The major part of this C, talline silicates in some comets indicates that these grains
namely up to 90%, corresponds to a macromolecular or- originally condensed at high temperatures or were annealed
ganic fraction (Hayes, 1967). Solid-state 13C nuclear mag- from amorphous silicates at somewhat lower temperatures
netic resonance (NMR) investigation of the macromolecular in the solar nebula. This is proof that processed nebular ma-
material reveals a high level of branching of the aliphatic terials were incorporated into comets.
chains and shows that the aromatic units are highly substi- The overall picture shows that comets are a mixture of
tuted, especially in the Murchison meteorite (Gardinier et interstellar and nebular components (see Fig. 2). Based on
al., 2000). Given that macromolecular C is inferred to con- the molecular data available in sample comet populations,
stitute more than half the C in the interstellar medium, con- there is evidence both for chemical heterogeneity, as ex-
stitutes ~ 80% of the C in meteorites, and is present in com- pected, and also for some degree of chemical homogene-
ets, there probably exists a lineage between these reservoirs. ity. Cometary comae are now known to contain many mole-
Many small (organic) molecules observed in cometary co- cules identified in the interstellar medium; the majority of
mae originate wholly or partially from the decomposition these species emanate from the nuclear materials. These
of much larger molecules/particles. There is at present, how- facts are highly suggestive of cometary nuclei containing
ever, no direct or indirect evidence that large polymers simi- appreciable fractions of pristine or partially modified inter-
lar to those possibly present in comets (e.g., POM, PACM, stellar molecules, but are by no means definitive proof of a
HCN-polymers) reside in the interstellar medium. Obser- direct heritage. Compositional similarities do not provide
vations of interstellar organic compounds, laboratory simu- sufficiently accurate constraints; differences may be more
lations, and the analysis of extraterrestrial samples offer illuminating. Cometary nuclei contain at least two mole-
insights into the molecular forms of the cometary C. We cules not yet identified in molecular clouds: CS2 and C2H6.
await future in situ measurements and the return of comet- It would be of interest to definitively rule out the presence
ary samples by the Stardust mission to give a more conclu- of some common, relatively abundant, interstellar mole-
sive answer. cules. Current upper limits on possible candidates, such as
dimethyl ether, are not stringent enough (Bockelée-Morvan
3. CONCLUSIONS et al., 2004).
The molecular isotopic fractionation, measured in D and
The composition of comets provides important clues on heavy N, both suggest an origin in chemistry at very low
the processes that occurred during the formation of our solar temperatures. Whether this occurred in cold molecular
system. However, comets certainly evolve chemically and clouds or in the protosolar nebula cannot be decided based
physically as they visit the inner solar system frequently and on the available data. It could be argued that the D/H ratios
they are exposed to processing in their storage location. Any in water and hydrogen cyanide are not particularly strong
proposed similarities between interstellar and cometary discriminants of formation site. Detection of cometary mole-
material can be tested by astronomical observations, labora- cules with D/H ratios above 10%, as well as evidence for
tory simulations, and the analysis of extraterrestrial samples, multideuteration, would significantly favor a direct inter-
such as IDPs and carbonaceous chondrites. Comparison of stellar origin (Ceccarelli, 2002); however, the current up-
interstellar ice abundances to cometary volatiles shows a per limits on D/H in cometary formaldehyde and methanol
possible link between them. The physical properties of ice, (Table 3 of Bockelée-Morvan et al., 2004), although meager,
 Ehrenfreund et al.: Interstellar Material to Cometary Particles and Molecules 127

(a)

(b)

(c) (d) (e)

Fig. 2. Comets and their interstellar heritage. (a) Interstellar clouds collapse to form stars and protoplanetary disks from which plan-
ets, comets and asteroids form. Ices, amorphous silicates, and organics can be observed in dense and diffuse clouds. In protoplanetary
disks the infalling material is modified according to the distance from the protostar. Ultraviolet radiation and cosmic rays, shocks, and
turbulent mixing alter the original interstellar material before planetary and cometary formation. Image of Orion, courtesy of Robert
Gendler. (b) Comets are a mixture of interstellar and nebular components; the degree of mixing may be individual for each comet.
Their composition, as inferred from observations and the Comet Halley flyby missions, indicate ~50% ice (predominantly water),
25% silicates (amorphous and crystalline), and organic refractory material. Image of Comet Wild 2 Stardust encounter, courtesy of the
Stardust Team, Jet Propulsion Laboratory/NASA. (c) Interstellar icy grains are characterized by different ice phases — amorphous,
crystalline, segregated boundary layers, and possibly clathrates — and besides water, contain partly substantial amounts of CO2, CO,
and CH3OH. Sublimation of material from cometary nuclei is triggered by a complex system of internal processes and, even if these
molecular ices were present in the same relative proportions as interstellar ices, it is unlikely that the cometary outgassing pattern
would accurately reflect this. (d) Cometary amorphous silicates are of probable interstellar origin while crystalline silicates condensed
at high temperatures or were annealed from amorphous silicates at somewhat lower temperatures in the solar nebula. Image courtesy
of S. Balm. (e) Macromolecular carbon is inferred to constitute more than half of the carbon in the interstellar medium and ~80% of
the carbon in meteorites. A lineage between those reservoirs is expected, and such material should also exist in comets. Credit: Pendleton
and Allamandola (2002).

suggest otherwise. It is therefore of considerable importance on the isotopic ratios in comets, the detection of more com-
to know if low D/H fractionation ratios, of at most a few per- etary organics, and the compilation of detailed chemical
cent, are common in a statistically larger sample of comets. inventories of solar-type star-forming regions and their cor-
Future scientific endeavors aimed at improving our responding disks. Theoretical models of the chemical pro-
knowledge of the interstellar/solar system connection will cesses associated with the accretion of molecular cloud ma-
include ground- and spacebased telescopes using new and terial and radial mixing in the early solar nebula are vital
sensitive instrumentation. Such observations should focus for determining the starting material from which comets
128 Comets II

formed. Theoretical models of comet nuclei should aim to ral and synthetic chondrules: Evidence for insitu reduction by
reproduce the observed pattern in order to deduce internal carbon. Meteoritics & Planet. Sci., 33, A11.
properties of comet nuclei that are inaccessible to observa- Balsiger H., Altwegg K., and Geiss J. (1995) D/H and O–18/O –16
tions (Prialnik et al., 2004, and Fig. 13 therein). As empha- ratio in the hydronium ion and in neutral water from in situ ion
measurements in comet Halley. J. Geophys. Res., 100, 5827–
sized by Colangeli et al. (2004), laboratory simulations on
5834.
mixtures of refractory matter and ice will offer a new per-
Bergin Edwin A., Alves J., Huard T., and Lada C. J. (2002) N2H+
spective in the interpretation of cometary observations. and C18O depletion in a cold dark cloud. Astrophys. J. Lett.,
The analysis of extraterrestrial materials (in particular 570, L101–L104.
carbonaceous chondrites) remains a crucial method to study Blake G. A., Sutton E. C., Masson C. R., and Phillips T. G. (1987)
refractory matter, including silicates and organics. Isotopic Molecular abundances in OMC-1 — The chemical composition
data remain the most important tool to establish a link be- of interstellar molecular clouds and the influence of massive
tween regions in interstellar clouds and small solar system star formation. Astrophys. J., 315, 621–645.
bodies. Recent isotopic measurements have allowed the Blake G. A., Qi C., Hogerheijde M. R., Gurwell M. A., and
identification of presolar silicates in IDPs; their absence in Muhleman D. O. (1999) Sublimation from icy jets as a probe
meteorites indicates that they could not survive parent-body of the interstellar volatile content of comets. Nature, 398, 213–
216.
alteration (Messenger et al., 2002). New sensitive tech-
Bockelée-Morvan D., Brooke T. Y., and Crovisier J. (1995) On
niques, such as the nanoSIMS ion microprobe, can probe
the origin of the 3.2 to 3.6-micron emission features in comets.
isotopic ratios within tiny particles and will contribute sig- Icarus, 116, 18–39.
nificantly to our knowledge of presolar materials. Future Bockelée-Morvan D., Lis D. C., Wink J. E., Despois D., Crovisier
observations of more comets will enable a broader consen- J., Bachiller R., Benford D. J., Biver N., Colom P., Davies J. K.,
sus on cometary diversity to be established. The ultimate Gérard E., Germain B., Houde M., Mehringer D., Moreno R.,
goal of understanding cometary physics and chemistry, and Paubert G., Phillips T. G., and Rauer H. (2000) New molecules
their relation to the parent interstellar cloud, will be attained found in comet C/1995 O1 (Hale-Bopp). Investigating the link
by future space missions performing in situ experiments and between cometary and interstellar material. Astron. Astrophys.,
possibly bringing a cometary sample back to Earth. 353, 1101–1114.
Bockelée-Morvan D., Gautier D., Hersant F., Hure J.-M., and
Acknowledgments. Theoretical astrochemistry at NASA Ames Robert F. (2002) Turbulent radial mixing in the solar nebula as
Research Center (S.B.C.) is supported by NASA’s Exobiology, the source of crystalline silicates in comets. Astron. Astrophys.,
Planetary Atmospheres, and Origins of Solar Systems Programs 384, 1107–1118.
through funds allocated by NASA Ames under Interchange No. Bockelée-Morvan D., Crovisier J., Mumma M. J., and Weaver
NCC2-1412. P.E. is supported by VI/NWO, SRON, and ESA. We H. A. (2004) The composition of cometary volatiles. In Com-
thank F. Molster for preparation of Fig. 1. We are grateful to L. ets II (M. C. Festou et al., eds.), this volume. Univ. of Arizona,
Colangeli, J. Crovisier, M. Hanner, W. Irvine, and D. Prialnik for Tucson.
comments and discussion. Boehnhardt H., Fechtig H., and Vanysek V. (1990) The possible
role of organic polymers in the structure and fragmentation of
dust in the coma of comet P/Halley. Astron. Astrophys., 231,
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134 Comets II
 PART III:
NATURE AND EVOLUTION OF COMETARY ORBITS
 Yeomans et al.: Cometary Orbits and Nongravitational Forces 137

Cometary Orbit Determination and

Nongravitational Forces
D. K. Yeomans and P. W. Chodas
Jet Propulsion Laboratory/California Institute of Technology

G. Sitarski, S. Szutowicz, and M. Królikowska

Space Research Centre of the Polish Academy of Sciences

The accuracies of the orbits and ephemerides for active comets are most often limited by
imperfectly modeled rocket-like accelerations experienced by active comets as a result of the
outgassing cometary nucleus near perihelion. The standard nongravitational acceleration model
proposed by Marsden et al. (1973) has been updated by allowing the nucleus outgassing to act
asymmetrically with respect to perihelion, providing for time-dependent effects through the
precession of the cometary nucleus and accounting for the outgassing from discrete surface
areas on a rotating nucleus. While the most accurate nongravitational models will likely re-
quire a detailed a priori knowledge of a comet’s surface activity and rotation characteristics, it
is becoming possible to use only astrometric data to actually solve for some of the parameters
that describe the comet’s outgassing and rotational characteristics.

1. ASTROMETRY AND THE ORBIT log goes as deep as magnitude 16 and has an astrometric
DETERMINATION PROCESS accuracy better than 0.1 arcsec (http://ad.usno.navy.mil).
FOR COMETS Since cometary observations are influenced by random
errors, astrometric observations should be selected and
The accuracy of the orbit-determination process for com- weighted before they are used for orbit improvement. Bie-
ets depends on a number of factors, including the accuracy licki has elaborated objective criteria for the selection of
of the astrometric data, the interval over which these data cometary observations on the assumption that the distribu-
are available, the extent to which the position of the pho- tion of observational errors is normal (Bielicki and Sitarski,
tometric image represents a comet’s true center-of-mass, the 1991). Bielicki applied the process of selecting and weight-
incorporation of planetary and asteroidal perturbations, the ing the observations to those observations belonging to one
accuracy of the numerical integration and differential cor- apparition of the comet and thus he could obtain a value of
rection processes, and especially the correct modeling of the mean residual for observations of this apparition. Using
the accelerations due to the comet’s outgassing (i.e., non- the values of the mean residuals found for each of several
gravitational effects). These latter nongravitational effects, apparitions, one can calculate in advance the mean residual
which are due largely to the recoil effect from the vaporiza- a priori, µapr, which can then be compared with the mean
tion of water ices from the cometary nucleus, will be dis- residual a posteriori µapo that results from the model of the
cussed in later sections. comet’s motion when linking a number of apparitions. A
mathematical model of the comet’s motion used for the link-
1.1. Astrometric Data age of several apparitions may be regarded as satisfactory if
µapo ≈ µapr.
Optical astrometric positions for celestial objects most The most powerful astrometric optical positional data for
often consist of pairs of right ascension and declination val- improving an object’s orbit are taken when the object is
ues for a given time; these positions are determined using closest to Earth. Unfortunately, active comets have substan-
measured offsets from neighboring stars whose positions tial coma, or atmospheres, in the inner solar system and
have been accurately determined. Thus an object’s astro- these atmospheres have optical depths that prevent a direct
metric accuracy depends upon the measurement technique observation of the comet’s nucleus. As a result, the observer
and the accuracy of the reference star catalog employed. normally must assume that the object’s photometric center
For modern astrometric positions, the highest accuracy is (center-of-light) is also the comet’s center-of-mass, and this
achieved when the star catalog has been reduced with re- is not often the case. While linking a long data interval for
spect to Hipparcos reference star positions. One example Comet 26P/Grigg-Skjellerup, Sitarski (1991) found it nec-
of this type of catalog is the star catalog (UCAC2) from the essary to adjust the observations using a radial offset that
United States Naval Observatory (USNO), which includes varied as the inverse cube of the heliocentric distance. Yeo-
more than 60,000,000 stars, thus providing the high star mans (1994) outlined a procedure whereby this center-of-
density necessary for most astrometric reductions. This cata- mass/center-of-light offset at 1 AU from the Sun was

137
138 Comets II

included within the orbit-determination process. This off- unity (Marsden et al., 1973). The second term represents
set (So) is assumed to vary along the comet-Sun line with both the direct effects of the perturbing bodies on the comet
an inverse square dependence on heliocentric distance. For and the indirect effects of the perturbing bodies upon the
Comet Halley, the solution for the offset at 1 AU was about Sun. The perturbing bodies are often taken to be the plan-
850 km. In most cases, this offset is not easily determined ets and the three most massive minor planets. The second
from the available astrometric data. Of course, rather than line of the equation represents one form of the relativistic
trying to account for inaccurate observations of a comet’s effects (Anderson et al., 1975) that should be included be-
center-of-mass, it would be preferable if groundbased op- cause for many objects with small semimajor axes and large
tical observations actually observed the comet’s true posi- eccentricities, these effects introduce a nonnegligible radial
tion in the first place. In this regard, Chesley et al. (2001) acceleration toward the Sun (Sitarski, 1983, 1992c). In addi-
compared the groundbased optical astrometric positions for tion, these effects are required to maintain consistency with
Comet 19P/Borrelly in September 2001 with spacebased the planetary ephemeris (Shahid-Saless and Yeomans, 1994).
observations of the comet’s true nucleus taken by the Deep The accelerations are given in astronomical units/(ephemeris
Space 1’s optical imaging cameras prior to its close flyby day)2; k is the Gaussian constant; mj = the masses of the
on September 22, 2001. They concluded that the true nu- planets and Ceres, Pallas, and Vesta; r and r = |r| are the
cleus position of the comet was more accurately defined by heliocentric position vector and distance of the comet re-
groundbased observations if the brightest pixel were used spectively; rj = |rj| are the planetary distances from the cen-
rather than positions based upon a best-fitting two-dimen- ter of the Sun; and c is the speed of light in AU per day.
sional Gaussian fit to the photometric image. That is, the The third line of this equation gives the standard-model ex-
comet’s center-of-light should not be assumed to be the pressions for the outgassing accelerations acting on the
comet’s center-of-mass. We recommend that observers use comet in the radial (Sun-comet), transverse, and normal di-
the “brightest pixel” technique for reporting cometary astro- rections. These so-called nongravitational effects are dis-
metric observations. cussed in the following sections.
While the extraordinary power of radar observations to
refine an asteroid’s orbit has been documented several times 2. HISTORICAL INTRODUCTION TO
(for example, see Yeomans and Chodas, 1987; Yeomans et NONGRAVITATIONAL EFFECTS
al., 1992), radar observations are available for only five
comets (http://ssd.jpl.nasa.gov/radar_data.html). This pau- Comet 2P/Encke has played a central role in the histori-
city of radar observations for comets is primarily due to the cal evolution of ideas concerning the rocket-like thrusting
infrequency with which comets pass close enough to Earth. of an outgassing cometary nucleus and the attempts to
model these so-called nongravitational accelerations. First
1.2. Cometary Equations of Motion and the discovered by Pierre Mechain in 1786, Comet Encke was
Orbit Determination Process rediscovered by Caroline Herschel in 1795 and discovered
yet again by Jean-Louis Pons in 1805 and in 1818. Johann
The orbit-determination process is a linearized, weighted Encke provided the numerical computations to show that
least-squares estimation algorithm, in which astrometric the comets discovered in 1786, 1795, 1805, and 1818 were
observations are used to improve an existing orbit (Lawson one and the same object returning to perihelion at 3.3-year
and Hanson, 1974). At each time step of the numerical inte- intervals. After noting that the comet returned to perihelion
gration process, the dynamic model should include gravita- a few hours earlier than his predictions, Encke (1823) pos-
tional perturbations due to the planets and the larger minor tulated that the comet moved under the influence of a re-
planets, relativistic effects, and the accelerations due to the sisting medium that he envisaged as an extension of the
nongravitational effects. The partial derivatives necessary for Sun’s atmosphere or the debris of cometary and planetary
adjusting the initial conditions should be integrated along atmospheres remaining in space. Encke’s resisting medium
with the object’s equations of motion. The cometary equa- allowed him to successfully predict the perihelion returns
tions of motion can be written for the comet between 1825 and 1858.
Although the resisting medium theory seemed to be the
d2r k2r (rj − r) rj contemporary consensus opinion, Bessel (1836) noted that
dt2
= −
r3
+ k2 ∑m j
rj − r
3
−
r 3j
a comet expelling material in a radial sunward direction
j would suffer a recoil force, and if the expulsion of mate-
rial did not take place symmetrically with respect to peri-
k2 4 k2 r helion, there would be a shortening or lengthening of the
+ − (r ⋅ r )r + 4(r ⋅ r )r (1)
c2 r 3 r comet’s period depending on whether the comet expelled
more material before or after perihelion (see equation (2)).
+ A1g(r)r/ r + A2 g(r)t + A3g(r)n Although Bessel did not identify the physical mechanism
with water vaporization from the nucleus, his basic concept
The first term on the righthand side of the equation is the of cometary nongravitational forces would ultimately prove
solar acceleration where the Sun’s mass has been taken as to be correct.
 Yeomans et al.: Cometary Orbits and Nongravitational Forces 139

In the second half of the nineteenth century, the motion the bulk of solar insolation goes to sublimating the comet’s
of Comet Encke did not seem to behave in strict accordance ices. For water ice, ro = 2.808 AU and the normalizing con-
with Encke’s resisting medium hypothesis, and several al- stant α = 0.111262. The exponents m, n, and k equal 2.15,
ternate mechanisms were introduced to explain the phenom- 5.093, and 4.6142 respectively. The nongravitational accel-
ena (see Yeomans, 1991; Sekanina, 1991a). The final blows eration is represented by a radial term, A1g(r), and a trans-
to the resisting medium came when Kamienski (1933) and verse term, A2g(r), in the equations of motion. The radial
Recht (1940) found uniform decreases in the mean motion unit vector (r/r) is defined outward along the Sun-comet
of period Comets 14P/Wolf and 6P/d’Arrest respectively. line, while the transverse unit vector (t) is directed normal
With the discovery of mean motions that decreased with to r/r, in the orbit plane, and in the general direction of the
time, as well as some that increased, a successful hypoth- comet’s motion. An acceleration component normal to the
esis had to explain both phenomena. A resisting medium orbit plane, A3g(r), is also present for most active comets,
could only cause the latter phenomena. but its periodic nature often makes it difficult to determine
The breakthrough work that allowed a proper modeling because we are usually solving for an average nongravita-
of the nongravitational effects on comets came with Whip- tional acceleration effect over three or more apparitions. If
ple’s introduction of his icy conglomerate model for the the comet’s nucleus were not rotating, the outgassing in this
cometary nucleus (Whipple, 1950, 1951). Part of his moti- model would always be toward the Sun and the resulting
vation for this model was to explain the so-called nongravi- nongravitational acceleration would act only in the antisolar
tational accelerations that were evident in the motion of direction. The rotation of the nucleus, however, coupled
Comet Encke and many other active periodic comets. That with a thermal lag angle (η) between the nucleus subsolar
is, even after all the gravitational perturbations of the plan- point and the point on the nucleus where there is maximum
ets were taken into account, the observations of many ac- outgassing, introduces a transverse acceleration component
tive comets could not be well represented without the intro- in either the direction of the comet’s motion or contrary to
duction of additional so-called nongravitational effects into it — depending upon the nucleus rotation direction.
the dynamical model. These effects are brought about by Equation (2) represents the time derivative of the comet’s
cometary activity when the sublimating ices transfer mo- orbital semimajor axis (a) as a result of radial and transverse
mentum to the nucleus. The nongravitational effects become perturbing accelerations (Rp, Tp)
most evident as deviations in a comet’s perihelion passage
when compared with a purely gravitational orbit, and these 2[(e sinν)Rp + (p/r)Tp]
da
deviations are typically a fraction of a day per apparition, = (2)
although for Comet 1P/Halley it is as large as four days. dt n 1 − e2

2.1. Symmetrical Nongravitational Force Model In this equation, n, e, ν, and r denote, respectively, the or-
bital mean motion, eccentricity, true anomaly, and the com-
Whipple noted that for an active, rotating, icy cometary et’s heliocentric distance, while p is the orbital semilatus
nucleus, a thermal lag between cometary noon and the time rectum, a(1 – e2).
of maximum outgassing would introduce a transverse ac- Because of the thermal lag angle, a comet in direct rota-
celeration into a comet’s motion. In an attempt to model tion will have a positive transverse nongravitational accel-
these effects, Marsden (1968, 1969) first introduced a semi- eration component, and from equation (2), it is apparent that
empirical nongravitational acceleration model using what the comet’s orbital semimajor axis will increase with time
are now termed Style I nongravitational parameters. Style II (its orbital energy will increase). Likewise, a comet in retro-
parameters were added when Marsden et al. (1973) intro- grade rotation will be acted upon by a negative Tp and its
duced what has become the standard, or symmetric, non- semimajor axis will decrease with time. Because the non-
gravitational acceleration model for cometary motions; a gravitational acceleration is assumed to act symmetrically
rotating cometary nucleus is assumed to undergo vaporiza- with respect to perihelion, the time-averaged effect of the
tion from water ice that acts symmetrically with respect to periodic radial acceleration cancels out.
perihelion. That is, at the same heliocentric distance before When introducing the standard model, Marsden et al.
and after perihelion, the cometary nucleus experiences the (1973) included possible time dependences in the transverse
same nongravitational acceleration. The expressions for parameter (A2). Subsequently, however, the standard non-
these nongravitational accelerations can be written gravitational acceleration model was most often used solv-
ing only for the constant radial and transverse parameters
A1g(r)r/r + A2g(r)t (A1 and A2) over data intervals short enough that neglected
time dependences did not cause systematic trends in the
where residuals. Solutions for the nongravitational parameters
usually require astrometric data from at least three appari-
g(r) = α(r/ro) –m(1 + (r/ro)n) –k tions, and one can empirically determine their change with
time by comparing the nongravitational parameters deter-
The scale distance ro is the heliocentric distance inside which mined from several of these three-apparition solutions.
140 Comets II

The standard nongravitational parameters can be ex- of A1, A2, A3, even if A3 is poorly determined, to estimate
pressed as function of time by Ai(t) = A · Ci(t), i = 1, 2, 3, preliminary values of A, η, I, φ. These four parameters can
where A = (A12 + A22 + A23)1/2, and Ci(t) are direction cosines then be improved together with six orbital elements by the
for the nongravitational force acting on the rotating comet- least-squares correction process (Sitarski, 1990).
ary nucleus. The direction cosines Ci, derived by Sekanina Largely because of its success in allowing accurate ephem-
(1981) have a form eris predictions, the standard nongravitational force model
has been in use for three decades. More recently, it has be-
C1 = cosη + (1 – cosη) · sin2I · sin2λ come understood that, while this model is often successful
C2 = sinη · cosI + (1 – cosη) · sin2I · sinλ · cosλ in representing the astrometric observational data and allow-
C3 = [sinη · cosλ – (1 – cosη) · cosI · sinλ] sinλ ing the computation of accurate ephemeris predictions, the
standard model does not provide a completely accurate re-
where η is the lag angle, I = the equatorial obliquity, λ = ν + presentation of the actual processes taking place in the com-
φ, ν is the true anomaly of the comet, φ = the cometocentric etary nucleus.
longitude of the Sun at perihelion; the time dependence of Froeschlé and Rickman (1986) and Rickman and Froeschlé
Ci(t) is given by the true anomaly ν(t). Thus three param- (1986) used theoretical calculations to examine the secular
eters A1, A2, A3 can be replaced by four parameters A, η, I, evolution of the nongravitational parameters as a function
φ, which should be determined along with the corrections to of the heliocentric distance for various kinds of short-pe-
the six orbital elements in the orbit-determination process. riod comets and different assumed thermal inertias. In gen-
The angles η, I, φ describing the direction of the nongravi- eral, their values of these parameters did not correspond to
tational force vector in orbital coordinates are presented in those computed from the standard model. In fact, there was
Fig. 1. such a wide variation in the respective behavior of the A1,
Usually the radial and transverse components of the A2, and A3 parameters that no generally applicable model
nongravitational acceleration parameters (i.e., A1 and A2) are for the nongravitational effects was suggested. They noted
determined when investigating the motion of short-period that improved models would likely have to include the ef-
comets. In some cases the parameter A3 also has a meaning- fects of rotation pole orientation and seasonal heat flows.
ful contribution to the successful orbital solution. When For a more comprehensive outline of the earlier work
investigating the nongravitational motion of comets using the on cometary nongravitational forces, the reader is directed to
parameters A, η, I, φ it is necessary to first determine values previously published reviews (Marsden, 1968, 1969, 1985;
Marsden et al., 1973; Yeomans, 1994).

3. MODIFICATIONS TO THE
STANDARD NONGRAVITATIONAL
ACCELERATION MODEL

3.1. Normal Nongravitational Parameter A3

A nongravitational acceleration acting normal to the

comet’s orbit plane will affect the longitude of the ascend-
ing node and the orbital inclination, but neither of these per-
turbations is secular. Since these perturbations are modu-
lated by either sine or cosine functions of the true anomaly,
much of the nongravitational perturbations upon the two
orbital elements would average to zero even if the normal
perturbative forces remain positive or negative throughout
the orbit. Sekanina (1993c) noted that a meaningful solu-
tion for the normal nongravitational parameter (A3) would
be possible only for the special case where the perturba-
tions upon the ascending node and the inclination yield a
similar value of A3. Solutions for the A3 parameter are often
not useful but there are some notable exceptions. Meaning-
ful values of A3 were obtained for the 1808–1988 appari-
tions of 26P/Grigg-Skjellerup, the 1906–1991 apparitions
Fig. 1. Orientation of a spherical rotating nucleus. P is the north- of 97P/Metcalf-Brewington, and the 1958–1977 apparitions
ern orbital pole, S the northern pole of rotation. Angle I is the of 22P/Kopff (Sitarski, 1991, 1992a; Rickman et al., 1987a).
obliquity of the orbit plane to the comet equator, φ the solar longi- Over the four returns of periodic Comet 71P/Clark, Nakano
tude at perihelion, ν the true anomaly. The maximum outgassing (1992) found a value for A3 with a formal uncertainty of only
is shifted behind the subsolar meridian by the lag angle η. 3% and Sekanina (1993c) suggested that for this comet, the
 Yeomans et al.: Cometary Orbits and Nongravitational Forces 141

effective nongravitational perturbations on the ascending result of the cometary outgassing. To include this fact in
node and the orbital inclination are about equal. The rota- orbital computations, Sekanina (1988b) proposed taking
tion axis at perihelion is located in the plane defined by the into account the asymmetric outgassing of the comet’s
Sun-comet line at perihelion and perpendicular to the com- nucleus with respect to perihelion by replacing the g(r)
et’s orbit plane. The rotation axis is inclined about 45° with function with g(r') where r'(t) = r (t – τ). Thus the maximum
respect to the orbit plane. As seen from the comet, the ro- value of g(r), describing the comet’s maximum activity, is
tation axis at perihelion would be pointing in the general shifted by τ with respect to the perihelion time.
direction of the Sun but about 45° above it. In this configu- Using Sekanina’s idea, Yeomans and Chodas (1989)
ration, the cometary outgassing produces a noncanceling, analyzed the influence of asymmetric cometary activity with
nongravitational thrust in a normal direction and hence a respect to perihelion upon the orbit-determination process
valid solution for A3. In general, the extreme values for A3 for several comets. They examined the nongravitational
are reached when the single active region is located at a motion of a number of periodic comets and found that the
rotation pole and when the obliquity of the orbit plane to asymmetric nongravitational acceleration model usually
the equatorial plane is near 50° or 130°. The principal ac- improved an orbital solution when compared to the stan-
tive vent for Comet 19P/Borrelly is nearly aligned with the dard symmetric model. To find the best solution for an in-
rotation pole and Chesley and Yeomans (2002) found that dividual comet, the authors varied the value of τ in some
an inclusion of the A3 parameter in their solutions for this ranges to obtain the best fit to the astrometric observations.
comet’s orbit significantly improved the prediction ephem- However, τ may be treated as an additional nongravitational
eris for the successful flyby of the Deep Space 1 spacecraft parameter that can be determined along with other param-
on September 22, 2001. eters by the least-squares method.
Sitarski (1994a) elaborated upon the method of deter-
3.2. Asymmetric Nongravitational Force Models mining the values of τ as an additional parameter in the solu-
tion and for some comets repeated the cases done by Yeo-
From equation (2), we note that if the outgassing is mans and Chodas (1989), confirming their conclusions. The
asymmetric with respect to perihelion, a purely radial thrust asymmetric model of the comet’s outgassing can consider-
can introduce a secular change in a comet’s semimajor axis. ably change the values of A1 and A2 computed using the
This asymmetric nongravitational thrusting was first sug- standard symmetric model. In long intervals of time the shift
gested by Bessel (1836), and the modern version of this idea τ may change its value and sign. In the case of Comet 6P/
has become known as the asymmetric nongravitational force d’Arrest, it is about 40 d and is stable in many observed
model. Using the asymmetric light curve of Comet Halley, apparitions of the comet, but in the case of Comet 21P/
Yeomans (1984) attempted to employ the nucleus rotation Giacobini-Zinner τ = +14 days during 1959–1973 and τ =
parameters introduced by Sekanina (1981) to improve the –13 d in 1972–1987. Similarly in the case of Comet 22P/
nongravitational force model for Comet Halley. For this Kopff, τ changed its sign within the interval 1906–1990.
latter model, the outgassing was assumed to result from a Assuming that τ = τ0 + dτ/dt · (t – t0), where the new param-
subsolar active area, which is defined by its cometocentric eter dτ/dt denotes the daily change of τ, Sitarski found it
solar longitude at perihelion (φ), the obliquity of the nucleus possible to link all the apparitions of Comet Kopff over the
equator with respect to the orbit plane (I), and by a ther- interval 1906–1990, determining, along with the orbital ele-
mal lag angle (η) measured from the cometary subsolar ments, five nongravitational parameters: A1, A2, A3, τ0, dτ/dt.
point to the point of maximum outgassing. Although the Comet 6P/d’Arrest exhibits nearly time-independent
optimum lag angle and obliquity turned out to be small, in nongravitational effects and its visual light curves show an
apparent agreement with subsequent results, the orbital extraordinary asymmetry with respect to perihelion with a
solution did not improve upon the standard nongravitational peak about 40–50 d after perihelion. Replacement of the
force model. In an influential work, Rickman (1986) pointed standard function g(r) by the observed light curve led to a
out that the asymmetric outgassing observed for Comets 1P/ satisfactory orbital linkage of the positional observations
Halley and 22P/Kopff were the likely cause for the non- over the intervals 1910–1989 (Szutowicz and Rickman, 1993)
gravitational effects noted for these comets. and 1851–1995 (Szutowicz, 1999b).
Photometric observations of comets suggest that the
brightness behaviour of comets near the Sun is sometimes 3.3. Linear Precession Model (Spherically
strongly asymmetric with respect to perihelion. Festou et Symmetric Nucleus)
al. (1990) established an important statistical correlation
between the nongravitational effects and the perihelion One of the limitations of the standard nongravitational
asymmetries of the gas production curves. A linear relation- acceleration model is the lack of any long-term time de-
ship was devised between the nongravitational perturbation pendence that would allow the nongravitational parameters
of the orbital period, ∆P, and the difference, E, between the (A1, A2, A3) to change with time. Traditionally, this limita-
integrated gas production rate before and after perihelion. tion has been handled by solving for the nongravitational
The light curve can, in most cases, be used to indicate parameters using limited sets of observations that cover
whether orbital energy is being added or subtracted as a consecutive time intervals. Three apparitions is usually the
142 Comets II

minimum number of apparitions that allow a meaningful ten nongravitational parameters (A, η, I0, dI/dt, φ0, dφ/dt,
solution for the nongravitational parameters, so consecutive τ0, dτ/dt, t1, and t2) were determined along with six correc-
sets of three apparitions are often used for the orbit solu- tions to the orbital elements. Among those parameters it was
tions when these nongravitational parameters are changing possible to determine two critical moments for τ(t):
with time.
Partly to account for the long-term variations in the non- t1 = 1936.40 ± 0.32 and t2 = 1970.92 ± 0.24
gravitational parameters, Whipple and Sekanina (1979) and
Sekanina (1981, 1984) introduced a model in which sublimat- when
ing ices would provide a nongravitational force that was not
aligned with the nucleus’ center-of-mass and hence would τ1 = +27.63 d for t ≤ t1 and τ2 = –39.65 d for t ≥ t2
(except for locations on the equator and poles) exert a pre-
cessional torque on the rotation pole. Coupled with a lag but
angle between cometary noon and the time of the peak out-
gassing, this model can introduce a time-varying nongravi- τ = τ0 + dτ/dt · (t – tosc)
tational effect in a natural manner.
While the model was first applied to fit the secular de- when
crease of the nongravitational acceleration of Comet 2P/
Encke (Whipple and Sekanina, 1979), a slightly modified t1 < t < t2 and t0 = (–2.27 ± 0.57) d
version of this model was developed later and applied to a
number of other comets (Sekanina, 1984, 1985a,b; Sekanina for the osculating epoch tosc = 1951 December 20.0.
and Yeomans, 1985). There are examples of successful linkages of many appa-
Making the assumption that the spin axis of the rotating ritions of short-period comets using nongravitational mod-
nucleus should precess, one can take into account linear els of motion that include the rotating and precessing com-
terms of the precessional motion of the spin axis by assum- etary nucleus assuming a constant secular change of I and
ing that φ(t) = φ0 + dφ/dt · (t – t 0) and I(t) = I0 + dI/dt · (t – t 0), φ (Sitarski, 1991, 1994b). However, the linear model for the
where dφ/dt and dI/dt are constant. Thus, six nongravita- precession of the spin axis of the nucleus should be con-
tional parameters (A, η, I, φ, dφ/dt, dI/dt) must be deter- sidered as only a first approximation and it is often unsuit-
mined along with corrections to the six orbital elements able for extrapolations over long time intervals, especially
within the orbit-determination process. On that assump- when dI/dt is assumed to be constant.
tion, Bielicki and Sitarski (1991) linked four apparitions of The numerical models of nongravitational motion suc-
Comet 64P/Swift-Gehrels in the interval 1889–1991. For cessfully linking many apparitions of short-period comets
the standard model with A1, A2, A3 they got the mean re- are verified if extrapolations of their motions can be used
sidual a posteriori µapo = 1".94 and for the model with linear to recover the comets close to the predictions at subsequent
precession µapo = 1".75, whereas the mean residual a priori apparitions.
µapr = 1".67. For Comet 26P/Grigg-Skjellerup, Sitarski
(1991) obtained a satisfactory result linking 16 apparitions 3.5. Forced Precession Model
of the comet over the 1808–1988 interval using the model (Nonspherical Nucleus)
of a rotating cometary nucleus with linear precession, and
also including a displacement of the photometric center from Various interpretations have been proposed in an effort
the center-of-mass. In that case µapr = 1".31 but µapo = 1".60. to understand long-term variations in nongravitational per-
turbations. One of them is based upon the concept of a
3.4. Linear Precession Within an Asymmetric forced precession of a nonspherical cometary nucleus,
Nongravitational Acceleration Model caused by torques associated with the jet force of outgas-
sing. The phenomenon of the spin-axis precession of the
While using the linear precession model, one may also cometary rotating nucleus could explain the variations of
include a shift τ as an additional nongravitational param- A2 with time for Comet 22P/Kopff as found by Yeomans
eter to account for an asymmetry of the comet’s outgassing. (1974), who investigated the long-term nongravitational
This approach made it possible to link seven apparitions of motion of the comet. Sekanina (1984) used values of A2
Comet 45P/Honda-Mrkos-Pajdušáková over the interval obtained by Yeomans (1974) to determine a forced preces-
1948–1990 and the seven returns to the Sun of Comet 51P/ sion model for the rotating oblate nucleus of the comet.
Harrington in 1953–1994 (Sitarski, 1995, 1996). For Comet Thus Sekanina (1984) showed a relationship between the
22P/Kopff, Sitarski (1994b) found a successful solution physical parameters of the nucleus and its nongravitational
when linking 13 apparitions of the comet over the 1906– behavior.
1990 interval. However, he had to take into account a com- Assuming that the angles I and φ are functions of time
plicated function of the shift τ(t) that, according to the earlier as a result of the forced precession due to the asymmetric
investigations, had changed its sign within the interval con- gas ejection, Sekanina (1984) derived formulae for changes
sidered (Yeomans and Chodas, 1989; Sitarski, 1994a). Thus, of the spin-axis orientation of the cometary nucleus. The
 Yeomans et al.: Cometary Orbits and Nongravitational Forces 143

following formulae for the time-dependence of I and φ were

adopted for use in orbital computations (Królikowska et al.,
1998a)
t

∫
I = I 0 + dt ⋅ ϕ ⋅ cos(α + η)
0
t
φ = φ0 − ∫ dt ⋅ ϕ ⋅ sin(α + η) /sinI
0

j = A · fp · g(r) · (2 – s) · sinψ · cosψ ·

(1 – S1 sin2ψ)1/2(1 – S sin2ψ) –3/2

where j is the precession rate of the spin axis, and ψ and

α are the cometographic latitude and longitude of the sub-
solar point respectively. They are given by sinψ = sinI · sinλ,
and tanα = tanλ · cosI, respectively. S and S1 are defined as
S = s · (2 – s), S1 = S · (2 – S), and s denotes the nucleus
oblateness (s = 1 – Rb/Ra, where Ra and Rb are the equato-
rial and polar radii of the nucleus respectively).
The direction cosines Ci(t) for i = 1, 2, 3 have a more
complex form than those derived by Sekanina (1981) for
the spherically symmetric rotating nucleus since they are Fig. 2. Temporal variation of angle I due to the spin-axis forced
modified by terms containing the oblateness s. Variations precession of the comet’s nucleus for two short-period comets:
of I and φ depend on s and on the precession factor fp, which 26P/Grigg-Skjellerup (top), and 45P/Honda-Mrkos-Pajdušáková
is connected with the torque factor ftor, introduced by (bottom). The Grigg-Skjellerup forced precession model was con-
Sekanina (1984), by the relation fp = s · ftor. Preliminary structed on the basis of all positional observations taken during
1922–1991 (Sitarski, 1992b), and the model for Comet Honda-
estimates of A, η, I0, φ0 have to be determined from the
Mrkos-Pajdušáková was derived from the time interval 1948–1990
standard constant parameters Ai, while an initial estimate
(Sitarski, 1995). Dashed parts of the curve for Honda-Mrkos-
of the precession factor fp can be determined by setting fp = Pajdušáková indicate variation of I before the comet’s discovery.
0 and s = 0; the values of the six parameters A, η, I0, φ0, fp, Dotted horizontal lines divide models with prograde rotation (I <
and s can then be determined along with the six corrections 90°) from models with retrograde rotation (I > 90°) The same scale
to the orbital elements in the iterative orbit improvement on the vertical axes allows one to compare the dramatically dif-
process. The time shift τ could also be included as an addi- ferent amplitudes of the I variations due to the forced precession
tional parameter taking the more universal function g(r'), alone. Models of these two comets are very different. Forced pre-
r'(t) = r(t – τ) instead of the symmetric function g(r). cession models give a fast precession of the slightly prolate nu-
Sekanina’s forced precession model has been used for cleus of Grigg-Skjellerup and a very slow precession for the con-
investigations into the long-term nongravitational motion of siderably oblate nucleus of Honda-Mrkos-Pajdušáková (see also
Table 1).
Comets 26P/Grigg-Skjellerup and 45P/Honda-Mrkos-Pajdu-
šáková (Sitarski, 1992b, 1995). In both cases values of the
oblateness were determined. It was found that s = +0.437 ±
0.014 for Honda-Mrkos-Pajdušáková, and s = –0.373 ±
0.065 for Grigg-Skjellerup. This implies that the nucleus of sion model could link all the observations with an rms re-
Honda-Mrkos-Pajdušáková is oblate but for Grigg-Skjel- sidual of 2".21, the forced precession solution gave an
lerup the nucleus is a prolate spheroid rotating around its improved rms residual of 1".41.
longer axis. Solutions for the forced precession models can Królikowska et al. (1998b) applied the forced precession
be extended to determine the time variations of the angles model of the rotating cometary nucleus to examine the non-
I and φ. Figure 2 presents plots of I(t) for both comets. The gravitational motion of three comets (30P/Reinmuth 1, 37P/
noticeable peaks for Comet Grigg-Skjellerup correspond to Forbes, and 43P/Wolf-Harrington) over similar intervals of
rapid changes of I(t) during its perihelion passages. The about 70 years. For Comets Reinmuth 1 and Wolf-Harring-
sudden changes of I(t) for Comet Honda-Mrkos-Pajdušá- ton they found satisfactory solutions for the pure forced
ková are due to close approaches of the comet to Jupiter precession model, but for Comet Forbes they had to include
(e.g., in March 1983 to within 0.111 AU). For Comet an additional parameter, the time shift τ = –9.75 ± 0.76 d.
Honda-Mrkos-Pajdušáková, Sitarski (1995) compared two They concluded that the nucleus of Comet Reinmuth 1 is
solutions for the rotating nucleus, with the linear precession oblate (s = +0.198 ± 0.013) while the nuclei of Comets
and with the forced precession: Whereas the linear preces- Forbes and Wolf-Harrington are prolate (s = –0.047 ± 0.005
144 Comets II

TABLE 1. Orbital elements and nucleus physical parameters arising from

the forced precession models for six short-period comets.

Prolate Spheroid Models Oblate Spheroid Models

26P/Grigg- 43P/Wolf- 21P/Giacobini- 45P/Honda-Mrkos-
37P/Forbes Skjellerup Harrington 46P/Wirtanen Zinner Pajdušáková
Orbital elements
T 19990504.3758 20021129.7266 19970929.4341 20020826.6370 19981121.3214 20010415.4468
q 1.44602 1.11787 1.58183 1.056769 1.03375 0.53063
e 0.56811 0.63271 0.54398 0.65780 0.70647 0.82476
ω 310°.70 1°.62 187°.13 356°40 172°.54 323°.69
Ω 334°.37 211°.74 254°.76 82°.17 195°.40 91°.36
i 7°.16 22°35 18°.51 11.74 31°.86 3°.89

Forced precession parameters

A 0.5584 0.01746 +0.3634 0.6780 0.3944 0.3068
η 11°.89 28°.67 6°.36 15°.48 6°.53 12°.16
I0 121°.65 95°.63 130°.32 145°.15 29°.81 102°.92
φ0 12°.68 338°.20 136°.84 357°.58 260°.85 158°.96
fp –0.4623 –2.422 –0.3136 0.1234 0.3460 0.04210
s –0.0589 –0.0588 –0.0451 0.1019 0.2926 0.4396
τ –8.33 — –11.69 –23.48 –49.38 –13.65
Orbital elements are given for the epoch of the last perihelion passage T; angular elements ω, Ω, and i are refer to the equinox J2000.0.
Nongravitational parameter A is in units of 10 –8 AU/day2, the precession factor fp is in units of 107 d/AU, and the time shift τ is in days.

and s = –0.195 ± 0.032 respectively). The orbital elements variations of the nongravitational effects observed in erratic
and nucleus physical parameters arising from the forced pre- comets (see Fig. 3). However, it was sometimes necessary
cession model for six short-period comets are presented in to introduce several additional parameters — which to some
Table 1. extent simulated the wild behavior of the comet — to ob-
tain a reasonable solution for the numerical model of the
3.6. Erratic Comets comet’s motion. For example, to link the observations of
Comet Giacobini-Zinner over the 1900–1999 interval, the
Comet 32P/Comas-Solá belongs to a group of comets authors had to include A(1) before 1956 and A(2) after 1956
dubbed “erratic” by Marsden and Sekanina (1971). For (instead of one parameter A), τ1 before 1956, τ2 between
these comets, long-term nongravitational effects are irregu- 1956 and 1969, τ3 between 1969 and 1989, and τ4 after
lar and sometimes their values change rapidly. Nongravita- 1989 (see Fig. 4). Eleven nongravitational parameters [A(1),
tional effects in the motion of Comet 21P/Giacobini-Zinner A(2), η, I0, φ0, fp, s, τ1, τ2, τ3, and τ4] were therefore neces-
show an irregular behavior in time if we observe values of sary to link 1589 astrometric observations over a 100-yr
the parameter A2 as determined by linking three consecutive interval. It should be noted that the determined oblateness
apparitions of the comet: In the period 1900–1999, A2 s = +0.2926 ± 0.0055 for the nucleus of Comet Giacobini-
changed its sign after 1959 (Yeomans, 1971). Sekanina Zinner now seems physically reasonable.
(1985a) examined the nongravitational motion of Comet
Giacobini-Zinner, trying to explain its erratic character by 3.7. Case Study of Comet Comas Solá
the precessional motion of the spin axis of the comet’s
nucleus. However, he had to assume an unrealistically large Królikowska et al. (1998a) studied the nongravitational
oblateness for the nucleus equal to 0.88. Sekanina (1985b) motion of Comet 32P/Comas Solá during the 1927–1996
found a similarly unacceptable solution for Comet Comas- interval. This comet had been investigated earlier by Seka-
Solá, although in this case the irregular behavior of the nina (1985b), who applied the forced precession model and
comet was less dramatic than for Comet Giacobini-Zinner. found that this comet precessed more rapidly than any other
Królikowska et al. (2001) investigated the motion of six known comet. His model required a large oblateness of the
erratic comets: 16P/Brooks 2, 21P/Giacobini-Zinner, 31P/ nucleus, s = 0.57, and according to Sekanina gave “intol-
Schwassmann-Wachmann 2, 32P/Comas Solá, 37P/Forbes, erably large perturbations” in the spin-axis obliquity, which
and 43P/Wolf-Harrington. They showed it was possible to changed rapidly by about 90° after 1952. Królikowska et
link all apparitions of each comet on the basis of a forced al. (1998a) used new observations from the comet’s appa-
precession model with physically reasonable parameters. ritions in 1987 and 1996 and employed the forced preces-
Hence, one may conclude that the forced precession model sion model fit to 582 observations. They found three almost
of the rotating nonspherical cometary nucleus can explain equivalent models, two with the oblate nucleus and one with
 Yeomans et al.: Cometary Orbits and Nongravitational Forces 145

Fig. 4. Temporal variations in the nongravitational parameter A2

for two erratic comets: 37P/Forbes (top) and 21P/Giacobini-
Zinner (bottom). The open circles represent values of A2 deter-
mined as constants within sets of at least three consecutive appari-
tions. These circles lie in the middle of the time intervals (shown
as thin solid horizontal lines) taken for the calculations. The solid
circles are mean values of A2 (averaged over three consecutive
revolutions around the Sun) resulting from the forced precession
Fig. 3. Temporal variations of the angle I due to the spin-axis models. The thick horizontal lines represent the time intervals
forced precession of the comet’s nucleus for three erratic comets: taken into account for these averaged A2 values. Upright arrows
21P/Giacobini-Zinner (top), 37P/Forbes (middle), and 43P/Wolf- (Giacobini-Zinner case) indicate the assumed moments of changes
Harrington (bottom). The forced precession models were con- for the derived parameters: τ [time shift of the maximum of g(r)
structed on the basis of all the positional observations taken before with respect to the perihelion time] and A [level of activity; for a
the year 2000. There are 9 apparitions of Comets 37P/Forbes and detailed description of the Giacobini-Zinner model, see Króli-
43P/Wolf-Harrington, and 13 apparitions (almost 100 years) for kowska et al. (2001)]. These postulated moments for the discon-
Comet 21P/Giacobini-Zinner. The same scale on the vertical axes tinuities of τ (and A) were necessary to obtain a satisfactory forced
allows one to compare the amplitudes of the I variations. The precession model for Comet Giacobini-Zinner, and they model
dotted horizontal line divides the models with prograde rotation the actual changes of displacement of maximum activity with re-
(I < 90°) from the models with retrograde rotation (I > 90°). The spect to perihelion (and the level of activity) for almost 100 years
forced precession models give a slightly prolate shape for the of observations.
nucleus of Forbes and Wolf-Harrington, and quite an oblate shape
for the nucleus of Giacobini-Zinner (see also Table 1). The up-
right arrows have the same meaning as in Fig. 4.
cases it amounted to 2".11, whereas it dropped somewhat
to 2".05 for the prolate case: The a priori mean residual
the prolate nucleus. The oblate solutions (s = 0.35) were to was 1".41.
some extent similar to Sekanina’s solution, but I(t) now
showed rather moderate variations without rapid jumps. In 3.8. Case Study of Comet Wirtanen
all cases it was necessary to include two additional values
of the time shift, τ1 before 1940, and τ2 after 1940. The best Investigations into the motion of Comet 46P/Wirtanen
solution appeared to be that for the prolate nucleus where are especially interesting because this comet is one of a few
s = –0.105 ± 0.024 and τ1 = –55.05 ± 3.79 d. A solution for that have been considered for space flight rendezvous mis-
τ2 = +8.13 d was found by changing its value to find the sions. Until early 2003, it was the target body for the Euro-
best fit to the observations. Three solutions could be com- pean Space Agency’s Rosetta comet rendezvous mission.
pared by their rms mean residuals. In the oblate nucleus The comet, discovered in 1948, had only 67 positional ob-
146 Comets II

servations through 1991. In that period, the comet experi-

enced two close approaches to Jupiter, to within 0.28 AU
in 1972 and to within 0.47 AU in 1984, and both encoun-
ters changed the comet’s orbit considerably. Królikowska
and Sitarski (1996) undertook a preliminary investigation
of the comet’s nongravitational motion, applying the model
of the rotating and precessing cometary nucleus with lin-
ear precession of the spin axis. They found that the comet’s
nucleus should be oblate (fp was positive), but the poor
observational material did not allow a determination for the
value of s. The 1995–1997 apparition of Comet Wirtanen
yielded 247 new positional observations, and Królikowska
and Szutowicz (1999) again studied the comet’s motion
based on Sekanina’s forced precession model of the rotating
cometary nucleus. They were able to determine the value
of the oblateness s = +0.1019 ± 0.0342. However, to satis-
factorily adjust the solution to all the observations, they had
to introduce some additional parameters to the numerical
model of the comet’s motion: the time shift τ = –23.48 ±
1.25 d, and instead of the single parameter A, two param-
eters were required, AI = +0.802 ± 0.009 before 1989.0, and
AII = +0.678 ± 0.007 after 1989.0 (in the units of 10 –8 AU/
d2). This was the best solution (among others considered
in their paper) representing the observations with an rms
residual equal to 1".59 (the mean residual a priori was
1".38). Figure 5 shows the time dependence of I(t) and φ(t)
as well as the components of the nongravitational force per
unit mass Fi(t), extrapolated to 2015.

3.9. Nongravitational Accelerations Due to

Discrete Source Regions

The traditional view of nearly uniform outgassing from

any part of the nucleus surface when it is exposed to solar Fig. 5. Forced precession model of Comet 46P/Wirtanen based
insolation contrasts with the concept of localized active on an almost 50-yr interval of positional observations. For model
regions. Closeup images of the nucleus of Comet 1P/Halley details see Królikowska and Szutowicz (1999). Temporal variations
taken by the spacecraft Giotto in March 1986 revealed a are presented for the angle I (top), φ (middle), and components
few distinct dust jets, emanating from the sunlit side. Similar F1, F2, F3 of the nongravitational force per unit mass F (bottom)
due to the spin-axis forced precession of the comet’s nucleus.
distinct dust jets were evident in Comet 19P/Borrelly when
These latter three components are only meant to convey the quali-
the Deep Space 1 spacecraft flew past this comet on Sep-
tative changes in their magnitudes and directions near each peri-
tember 22, 2001 (Soderblom et al., 2002). The local out- helion passage. This model gives an oblate shape of the nucleus
gassing restricted to a few “active regions” evolving into with Prot/Ra = 4.9 ± 1.4 h/km, where Ra denotes the equatorial
craters has recently been incorporated into the physical radius. Assuming 6.0 ± 0.3 h for the rotational period Prot (Lamy
models of comets (Colwell et al., 1990; Colwell, 1997). The et al., 1998), the range of 0.9–1.7 km for the nucleus radius (con-
distribution of jets around the nucleus and their contribu- sistent with the photometric observations) is obtained. The vertical
tion to the total production rate also has implications for arrow denotes the time (1989) when the modeled levels of outgas-
the nongravitational effects in a comet’s orbital motion. For sing activity and perihelion asymmetry are assumed to change.
a nucleus with discrete outgassing regions (spotty nucleus),
the maximum sublimation rate will take place when the
subsolar point is closest to an active region, which may not
occur at perihelion. heat conduction into the nucleus. Hence there is no need
The effects of discrete outgassing on the shape of the for a thermal lag angle. The sublimation rate from a unit
gas production curve and on the nongravitational param- surface area on the nucleus is expressed as a function of
eters were discussed in detail by Sekanina (1991b, 1993a,c). heliocentric distance and the Sun’s zenith distance. The
In Sekanina’s model (1988a) the absorbed solar energy is model, as applied to Comet 2P/Encke (Sekanina, 1988a,b,
spent on sublimation and thermal re-radiation, but not on 1991a), allowed him to interpret its observed sunward fan-
 Yeomans et al.: Cometary Orbits and Nongravitational Forces 147

like coma as an effect of the northern and southern local- Wirtanen. The modeled gas production rate peaks before
ized vents on the comet’s nucleus (+55°N, –75°S); the perihelion in accordance with the nongravitational accelera-
comet’s spin axis was fixed. Sekanina (1991b, 1993a) noted tion (A2 < 0), but this is not consistent with the observed
examples of the rotation-averaged sublimation rates of light curve that peaks about one week after perihelion (Rick-
point-like sources at various locations on the nucleus sur- man and Jorda, 1998). Clearly there is not a one-to-one cor-
face calculated for a spherical nucleus with various axial respondence between a comet’s visual light curve and its
positions in an unperturbed heliocentric orbit. For the spotty gas production rates and it is the latter that controls the non-
model of the nucleus, the meaning of the nongravitational gravitational effects.
parameters is different than for the standard model. For the Chesley (2002) used the discrete jet model, averaged
spotty model, there is a correlation between the sign of A2, over one rotation period, to verify the two main active source
the asymmetry of the production curve, and the location of regions of 2P/Encke that Sekanina (1988a) had suggested
the active regions. In the standard model the sense of rota- (two sources at latitudes 55°N and –75°S). He found that
tion was directly correlated with the sign of A2 but this need these two source regions, together with Sekanina’s pole
not be true for the spotty model. Furthermore, a negative direction, provided a significant improvement over the stan-
value of A1, unrealistic in the standard model, can corre- dard nongravitational acceleration model in both the good-
spond to a circumpolar or high-latitude active source and ness of the orbit fit as well as in the orbit’s predictive capa-
certain combinations of the spin-axis orientation. Erratic bility. Going further, Chesley (2002) found that a pole po-
discontinuities in the nongravitational perturbations for three sition around RA = 220° and Dec. = +40° provided an even
comets and their long-term changes in A2 were interpreted better orbit fit and prediction than those obtained using the
by Sekanina (1993b) as the initiation of new active areas pole suggested by Sekanina.
or the deactivation of existing ones on the nucleus surface. It is a rare opportunity when one can test a cometary
Thus the proper modeling of the nongravitational effects nongravitational acceleration model with the help of astro-
should contain information on the true characteristics and metric imaging data provided by spacecraft. Chesley (2002)
locations of the comet’s active areas. noted that since the principal active vent for Comet 19P/
The rotational-averaged orbital components of the non- Borrelly was aligned with the rotation pole, this pole direc-
gravitational acceleration for a nucleus with active regions tion could be independently determined using the values of
were adopted for orbital computations and introduced di- A1, A2, A3, τ; the determined pole direction (RA and Dec. =
rectly into the equations of a comet’s motion by Szutowicz 208°, –4°) agreed with rotation pole values determined from
(2000). The lifetime of each active region was limited by long-term photometric studies (e.g., Farnham and Cochran,
time because of its activation and deactivation. The param- 2003) and had reasonable agreement with the pole position
eters of the model are three angles η, I, φ characterizing the determined from the spacecraft images themselves (Soder-
nucleus, the cometocentric latitude of the jth active region blom et al., 2002).
βj, and the constants Aj are proportional to Sj/M, where Sj
is the outgassing area of the jth source and M is the nucleus 4. INFERRING MASSES AND BULK
mass. These parameters can be determined along with the DENSITIES OF THE NUCLEUS USING
osculating orbital elements in the orbit-determination pro- NONGRAVITATIONAL EFFECTS
cess. The first attempt to introduce the spotty nucleus model
into orbital calculations was made to explain a dramatic It is important to note that there are no direct determi-
jump of the nongravitational effects in the motion of Comet nations for the mass or density of any comet and this is
71P/Clark (Szutowicz, 1999a). The spotty nucleus model likely to remain the situation until a spacecraft rendezvous
was successfully used to link all observations of Comet mission is carried out. Nevertheless, there have been many
46P/Wirtanen spanning the interval 1947–1997 (Szutowicz, studies suggesting that comets are rather low-density and
1999b) and of 43P/Wolf-Harrington over the period 1925– porous structures.
1997 (Szutowicz, 2000), with the rms residuals equal to Yau et al. (1994) found that the observations of Comet
1".57 and 1".39 respectively. For the former comet, the tem- 109P/Swift-Tuttle in 69 B.C. and in A.D. 188, 1737, 1862,
poral variations of the activity level are responsible for its and 1992–1993 were consistent with the complete absence
nongravitational behavior, whereas the orbital solutions for of nongravitational effects in this comet’s motion and that
the latter one involved a redistribution of the active areas. there have been no obvious changes in this comet’s abso-
From orbital solutions for 43P/Wolf-Harrington, it follows lute magnitude over two millennia. Because Comet Swift-
that the northern region (~38°N) was persistently active and Tuttle’s absolute magnitude has not changed significantly
the profile of the comet’s activity was modified by the ini- and there is a lack of significant nongravitational effects
tiation and disappearance of two southern regions (~–4°S, over the same period, constraints can be placed upon the
–51°S) in 1965, 1978, and 1991. According to the solutions, model for this comet’s nucleus. At 1 AU from the Sun, the
the time variation of the modeled sublimation rates is ac- outgassing activity of Swift-Tuttle is comparable with that
companied by parallel changes in the visual light curve. A of Comet Halley at the same heliocentric distance. Yet
contradictory result was obtained in the case of Comet 46P/ Comet Halley experiences an increase in its orbital period
148 Comets II

of four days per revolution due to nongravitational effects due to the ice halo in the coma, and some stochastic per-
while Swift-Tuttle has no perceptible change in its period. turbations like splitting or outbursts noted for both comets.
If the mass of Swift-Tuttle were significantly larger than The latter may cause stronger nongravitational effects than
Halley’s, however, one would not expect to be able to de- expected from the water sublimation rate alone.
tect a nongravitational acceleration in its orbital motion. Farnham and Cochran (2002) estimated the mass of
Based upon an analysis of their respective meteor stream Comet 19P/Borrelly by separately computing the nongravi-
characteristics, Hughes and McBride (1989) concluded that tational force and acceleration acting upon the comet’s
the mass of Comet Swift-Tuttle is about 10 times larger than nucleus. The force was computed from the observed gas
Comet Halley. production rate and the emission velocity while the non-
Rickman (1986) pointed out that radial outgassing forces gravitational acceleration was forthcoming from the orbital
that act asymmetrically with respect to perihelion were the computations. Dividing the comet’s determined mass by the
likely cause of the nongravitational effects upon Comets volume estimated from the Deep Space 1 spacecraft imag-
Halley and Kopff, and he went on to make estimates of their ing provided a bulk density for the comet’s nucleus of 0.49
masses and bulk densities. He noted that the water produc- (–0.20, +0.34) g/cm3.
tion curves for Halley and other comets show an asymme- Davidsson and Gutiérrez (2003) deduced a bulk density
try with respect to perihelion and therefore the effect of the for 19P/Borrelly of 0.10–0.30 g/cm3 by modeling the comet’s
radial component, integrated over one orbital period, would observed water production rates with nucleus surface activ-
be nonzero. The nucleus masses were estimated by com- ity maps based upon sophisticated thermophysical models.
paring nongravitational parameters with the rocket-like By requiring that the model reproduce the nongravitational
forces expected from the gas-production curves. In turn, the secular changes in the argument of perihelion and the longi-
gas-production curves were determined from the light tude of the ascending node, they were able to tighten the
curves using an empirical relationship developed by M. bulk density range to 0.18–0.30 g/cm3.
Festou. The bulk density for Comet Halley was estimated
to be 0.1–0.2 g/cm3 and that for Kopff was lower still. Rick- 5. NONGRAVITATIONAL EFFECTS AND
man et al. (1987b) continued this type of analysis and es- THE SOURCE REGION FOR
timated masses for 29 short-period comets. The change in LONG-PERIOD COMETS
the total orbital period per revolution results from the sum
of the contributions from the radial and transverse rocket Marsden and collaborators first reported the detections of
effects. The mass of each comet was determined as a func- nongravitational forces in the motion of long-period com-
tion of its estimated thermal and rotational properties. While ets in the late 1960s and early 1970s. In the Catalogue of
bulk densities for individual comets are very uncertain, the Cometary Orbits, Marsden and Williams (2001) gave non-
bulk densities of these objects as a group were estimated gravitational parameters A1 and A2 for 23 long-period com-
to be less than 0.5 g/cm3, suggesting that the cometary nu- ets. To determine these parameters, the authors applied the
cleus is a very porous structure. This type of analysis de- standard nongravitational model. It became evident that
pends upon the assumption that there is a correlation be- nongravitational accelerations affecting the orbital motion
tween the light curve and the assumed gas-production curve, of long-period comets (at 1 AU from the Sun) are a few to
that thermal lag angles are present, and that the surface of 10 times larger than the similar accelerations detected for
each object has an unmantled free sublimating area. Using short-period comets (Marsden et al., 1973). In the last de-
a similar approach for Comet Halley, Sagdeev et al. (1988) cade two famous long-period comets (1995 O1 Hale-Bopp
estimated a bulk density of 0.6 g/cm3 with error bars of +0.9 and 1996 B2 Hyakutake) offered unique opportunities for
and –0.4 g/cm3. After a rather complete discussion of the detailed investigation of the nongravitational effects on their
method and the uncertainties involved in this type of analy- orbital motion. The nongravitational effects play an essential
sis, Peale (1989) concluded that it is difficult to provide a role in the dynamical evolution of both comets. In particu-
meaningful constraint for the bulk density of Comet Halley. lar, the future orbital evolution, including nongravitational
The orbital nongravitational perturbations combined with effects, gives a significantly higher probability of these
the observed gas production rates were also employed to comets being ejected from the solar system than does the
estimate the masses of the two long-period comets: C/ pure gravitational orbital motion (Szutowicz et al., 2002a,b;
1995 O1 Hale-Bopp and C/1996 B2 Hyakutake (Szutowicz Królikowska, 2002).
et al., 2002a,b). The observed water production rates as a Nongravitational effects also play a role in the identifi-
function of the heliocentric distance were included into the cation of hyperbolic comets. The problem of a negative tail
nongravitational model represented by parameters: A (A is in the distribution of the reciprocals of original semimajor
proportional to Qm/M), η, I, φ, where Qm is the observed axis (1/aori) has been discussed in detail by many authors.
sublimation rate of water at 1 AU. The derived masses di- Marsden et al. (1973) speculated that neglecting the non-
vided by the volumes of both comets give bulk densities as gravitational effects tends to produce more hyperbolic origi-
low as 0.1 g/cm3 for Comet Hale-Bopp and 0.2 g/cm3 for nal orbits than really is the case. Subsequently, many
Comet Hyakutake. This kind of solution is limited by the authors (Yabushita, 1991; Bolatto et al., 1995) considered
thermal properties of the nucleus (i.e., the mean outflow the nongravitational perturbation in a comet’s energy per
velocity of the molecules), the excess of the production rate orbital revolution and concluded that these perturbations are
 Yeomans et al.: Cometary Orbits and Nongravitational Forces 149

too small to explain the negative excess of original bind- the true position of the cometary nucleus, are usually ac-
ing energy of “hyperbolic” comets. Misleading results can curate to the subarcsecond level. Yet multiple apparition
be obtained when the same osculating orbit is used as the orbital solutions for active short-period comets cannot often
initial orbit for backward integrations using nongravitational provide a root mean square (rms) residual (observed minus
effects and without these effects. Let us consider that the computed observational position) that is subarcsecond. It
same osculating orbit is integrated backward twice, first by is the improper modeling of the nongravitational effects that
setting the nongravitational terms equal to zero and then is the largest problem by far.
by including the nongravitational accelerations. The differ- Beginning with Encke’s first suggestion of an interplan-
ences in the resulting original reciprocals will then be sig- etary resisting medium to explain the anomalous motion of
nificantly smaller than 10 –4 AU–1. At first look, this seems the comet that bears his name, there have been many dif-
to suggest that nongravitational effects provide only mod- ferent models put forward to explain the accelerations in
est changes in the true original value for 1/aori. However, it the motions of active comets that are not due to the gravi-
is important to realize that an osculating nongravitational tational perturbations of neighboring planets or asteroids.
orbit determined from a set of observations would not be Although the notion of an icy conglomerate model for a
the same orbit as one determined from these same obser- cometary nucleus (Whipple, 1950, 1951) is still in basic
vations but under the assumption of purely gravitational agreement with the observations, there have been a num-
motion. Królikowska (2001) investigated the problem of the ber of recent modifications and refinements to this model.
original orbits of 33 comets considered as “hyperbolic” Largely as a result of the impressive images of Comet 1P/
comets (in the pure gravitational case). For the 16 cases for Halley’s nucleus taken by the Giotto spacecraft and those
which solutions for nongravitational effects could be carried taken more recently of 19P/Borrelly by the Deep Space 1
out, she showed that for almost all cases, the original orbits spacecraft, a “vent” model whereby the outgassing activity
changed from hyperbolic to elliptic. For the two comets for takes place from discrete active areas has replaced the pic-
which the original orbits remained hyperbolic (1996 E1, ture of an outgassing sunlit hemisphere.
1996 N1), their original orbits became less hyperbolic as a It seems likely that each comet has its own set of pecu-
result of solving for nongravitational effects and the result- liar jets located at various places on its surface and operating
ing negative original 1/aori values were rather modest. The at different strengths so that a completely accurate model
tendency for negative, original 1/aori values to become posi- for a particular comet’s nongravitational effects would re-
tive when nongravitational effects are taken into consider- quire a detailed knowledge of the comet’s surface outgas-
ation is due primarily to changes in the orbital eccentricity. sing features and rotation characteristics. Since this knowl-
Królikowska concluded that the nongravitational effects edge is available only for those few comets that are visited
could significantly affect the Oort peak for comets with by spacecraft, orbit practitioners will have to be content with
perihelion distance smaller than 3 AU. generic models that approximate the true situation. In this
At the other extreme from the nearly parabolic orbits regard the recent advances in bringing forth the asymmet-
from the Oort cloud comet lays 2P/Encke with its shortest ric nongravitational acceleration models, the forced nucleus
known cometary orbital period of 3.3 yr. The current orbit precession models, and especially the discrete active source
of 2P/Encke is completely interior to Jupiter’s orbit and is models are promising.
gravitationally decoupled from that planet. In trying to Many of the existing models solve for physical charac-
explain how Comet Encke arrived at this stable orbital po- teristics of the cometary nucleus (e.g., oblateness, thermal
sition, Steel and Asher (1996) noted that nongravitational lag angles, positions of sources, and the rotation pole). How-
effects on the comet, some four times larger than those that ever, the formal uncertainties computed for these quanti-
have recently been operative, would be enough to evolve ties that arise from the orbit-determination process alone
the comet from its current orbit into Jupiter-crossing orbits must be considered lower limits rather than realistic values.
and hence the same mechanism could have dropped the Whenever possible, these quantities should be confirmed
comet into its current orbit. The nongravitational effects can using spacecraft observations or a long series of photometric
cause the comet to drift across the jovian and saturnian groundbased observations. For example, the oblateness
mean-motion resonances in the asteroid belt and even if values and rotation pole positions derived from the orbit-
these nongravitational effects do not act in the same direc- determination process should be checked against the aspect
tion for extended periods of time, they can still strongly ratios and pole positions determined from groundbased
modify the orbit of an Encke-like object. photometric studies. As the astrometric datasets improve and
lengthen and as the modeling of the cometary nongravi-
6. SUMMARY tational effects becomes more realistic, there remains the
strong possibility that some physical characteristics of com-
Cometary orbit-determination problems are dominated ets will soon be accurately determined from the orbit-de-
by the proper modeling of the so-called nongravitational termination process alone. We are already beginning to see
perturbations that are due to the rocket-like thrusting of the signs that this is the case.
outgassing cometary nucleus. Modern astrometric positions, Acknowledgments. A portion of this work was carried out by
particularly those that are referenced to Hipparcos-based the Jet Propulsion Laboratory/California Institute of Technology
star catalogs and where the brightest pixel is employed as under contract to NASA.
150 Comets II

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152 Comets II
 Dones et al.: Oort Cloud Formation and Dynamics 153

Oort Cloud Formation and Dynamics

Luke Dones
Southwest Research Institute

Paul R. Weissman
Jet Propulsion Laboratory

Harold F. Levison
Southwest Research Institute

Martin J. Duncan
Queen’s University

The Oort cloud is the primary source of the “nearly isotropic” comets, which include new
and returning long-period comets and Halley-type comets. We focus on the following topics:
(1) the orbital distribution of known comets and the cometary “fading” problem; (2) the popu-
lation and mass of the Oort cloud, including the hypothetical inner Oort cloud; (3) the number
of Oort cloud comets that survive from the origin of the solar system to the present time, and
the timescale for building the Oort cloud; (4) the relative importance of different regions of the
protoplanetary disk in populating the Oort cloud; and (5) current constraints on the structure
of the Oort cloud and future prospects for learning more about its structure.

1. INTRODUCTION Halley-type comets (HTCs), and returning long-period com-

ets (LPCs) (e.g., Levison, 1996). The hyperbolic and para-
“They have observed Ninety-three different Comets, and bolic orbits, in turn, represent “new” long-period comets
settled their Periods with great Exactness. If this be true, (Oort, 1950; Levison, 1996). Lardner also noted that, with
(and they affirm it with great Confidence) it is much to be the exception of JFCs, there were roughly equal numbers of
wished that their Observations were made publick, whereby objects that revolved prograde (in the same direction as the
the Theory of Comets, which at present is very lame and de- planets) and retrograde around the Sun. [Note that the tra-
fective, might be brought to the same Perfection with other ditional dividing line between JFCs and HTCs is an orbital
Parts of Astronomy.” period P of 20 yr, with JFCs having P < 20 yr (semimajor
— Jonathan Swift, Gulliver’s Travels (1726) axes, a, less than 7.4 AU), and HTCs having 20 yr ≤ P <
200 yr (7.4 AU ≤ a ≤ 34.2 AU). Levison (1996) introduced
Recorded observations of comets stretch back more than the term “nearly isotropic comets” (NICs), which he divided
2000 years (Kronk, 1999). For example, Yau et al. (1994) into HTCs, which he took to have semimajor axes a < 40 AU,
showed that a comet noted in Chinese records in the year and the LPCs, which he defined to have a > 40 AU. The
69 B.C. was 109P/Swift-Tuttle, which most recently passed upper limit on the semimajor axis of an HTC at 34.2 AU
perihelion in 1992. However, it is only in the last 400 years or 40 AU is somewhat arbitrary, but Chambers (1997) later
that comets have been generally accepted as astronomical, showed that there is a dynamical basis for this upper limit.
as opposed to atmospheric, phenomena (e.g., Bailey et al., Chambers demonstrated that NICs with a < 22.5–39.6 AU,
1990; Yeomans, 1991). Even so, learned opinion until the with the upper limit depending upon orbital inclination, can
mid-twentieth century was divided on whether comets were be trapped in mean-motion resonances with Jupiter, while
interlopers from interstellar space (Kepler, Laplace, and bodies with larger orbits generally cannot.]
Lyttleton) or members of the solar system (Halley, Kant, Newton (1891) and van Woerkom (1948) performed early
and Öpik). studies of the effects of gravitational perturbations by Jupi-
By the mid-nineteenth century, it was well established ter on cometary orbits. In particular, van Woerkom showed
that most comets have orbits larger than the orbits of the in detail that the observed distribution of cometary orbital
known planets. Lardner (1853) stated “ . . . we are in pos- energies was inconsistent with an interstellar origin for
session of the elements of the motions of 207 comets. It comets. It then fell to Oort, who had supervised the latter
appears that 40 move in ellipses, 7 in hyperbolas, and 160 stages of van Woerkom’s thesis work (Blaauw and Schmidt,
in parabolas.” Lardner further divided the comets on ellip- 1993), to put the picture together. In his classic 1950 pa-
tical orbits into three categories that roughly correspond per, Oort wrote “There is no reasonable escape, I believe,
to what we would now call Jupiter-family comets (JFCs), from the conclusion that the comets have always belonged

153
154 Comets II

to the solar system. They must then form a huge cloud, of the planetesimals onto planet-crossing orbits in 10 m.y.
extending . . . to distances of at least 150,000 A.U., and or less (Gladman and Duncan, 1990; Holman and Wisdom,
possibly still further.” 1993; Levison and Duncan, 1993; Grazier et al., 1999a,b).
Interestingly, speculations by Halley (1705) in his famous The major exception to this rule is in the Kuiper belt, where
Synopsis of the Astronomy of Comets can be interpreted as some orbits remain stable for billions of years (Holman and
inferring a distant comet cloud. Halley was only able to fit Wisdom, 1993; Duncan et al., 1995; Kuchner et al., 2002).
parabolic elements to the 24 comet orbits he derived, but [Here, we define the Kuiper belt to encompass small bod-
he argued that the orbits would prove to be elliptical, writ- ies on low-eccentricity orbits with semimajor axes, a, greater
ing, “For so their Number will be determinate and, perhaps, than 35 AU. Long-term orbital integrations indicate that
not so very great. Besides, the Space between the Sun and some small bodies on near-circular orbits with a > 35 AU
the fix’d Stars is so immense that there is Room enough are stable for the age of the solar system. For example,
for a Comet to revolve, tho’ the Period of its Revolution be Duncan et al. (1995) found a stable region between 36 and
vastly long.” 39 AU, while Kuchner et al. (2002) found that most objects
This review will discuss what the observed cometary with a > 44 AU are stable for 4 G.y. The stability of objects
orbital distribution reveals about the structure of the spheri- with a between 39 and 44 AU depends upon their initial ec-
cal cloud of comets that now bears Oort’s name, and the centricities and inclinations. There are few stable orbits for
results of new dynamical simulations of the Oort cloud’s small bodies with a < 35 AU, except for Trojans of Jupiter
formation and subsequent evolution. In section 2 we de- and Neptune (Nesvorný and Dones, 2002) and main-belt
scribe the Oort cloud hypothesis and the evidence for why asteroids.] This quasistability explains the existence of the
we believe that there indeed is an Oort cloud. We then re- Kuiper belt and the low-inclination (“ecliptic”) comets,
view studies of the population and dynamics of the Oort which include the scattered disk, Centaurs, and JFCs (Dun-
cloud. In section 3 we discuss the hypothetical inner Oort can et al., 2004).
cloud, which has been proposed to possibly contain more The LPCs, by contrast, are thought to derive from the
comets than the classical Oort cloud, and “comet showers” planetesimals that did not remain on stable orbits, but be-
that might result from a stellar passage through the inner came planet-crossing. The first stage in placing a comet in
cloud. In section 4 we focus on modern studies of the for- the Oort cloud is that planetary perturbations pumped up
mation of the Oort cloud, assuming that comets started as the orbital energy (i.e., semimajor axis) of a planetesimal,
planetesimals within the planetary region. In section 5 we while its perihelion distance q remained nearly constant. If
discuss constraints on the Oort cloud based upon observa- the planets had been the only perturbers, this process would
tions of comets and the impact record of the solar system, have continued, in general, until the planetesimal’s orbit
and describe future prospects for improving our understand- became so large that it became unbound from the solar sys-
ing of the structure of the Oort cloud. Section 6 summarizes tem, and thereafter wandered interstellar space. However,
our conclusions. We refer the reader to other chapters in the very reason that a comet’s orbit becomes unbound at
this book for discussions of related topics, particularly the large distances — the presence of stars and other matter in
overview by Rickman and the chapters by Weidenschilling, the solar neighborhood that exert a gravitational force com-
Rickman, Yeomans et al., Morbidelli and Brown, Duncan et parable to that from the Sun — provides a possible stabi-
al., Harmon et al., Boehnhardt, Weissman et al., and Jewitt. lizing mechanism. Öpik (1932) and Oort (1950) pointed out
that once the comet’s orbit becomes large enough, passing
2. POPULATION AND DYNAMICS stars affect it. (As we describe below, gas in the solar neigh-
OF THE OORT CLOUD borhood now appears to be a slightly stronger perturber of
the Oort cloud than stars.) In fractional terms, stars change
2.1. Oort Cloud Hypothesis cometary perihelion distances much more than they change
the overall size of the orbit. (This is a consequence of the
We first give an overview of how we believe that LPCs long lever arm and slow speed of comets on highly eccen-
attained orbits at vast distances from the Sun, remained in tric orbits near aphelion.) If passing stars can lift a comet’s
such orbits for billions of years, and then came close enough perihelion out of the planetary region before the planets can
to the Sun that they began to sublimate actively. eject it from the solar system, the comet will attain an orbit
The early solar system is believed to have consisted of in the Oort cloud. The characteristic size of the Oort cloud
the planets, with their current masses and orbits, and a large is set by the condition that the timescale for changes in the
number of remnant small solid bodies (“planetesimals”) cometary semimajor axis is comparable to the timescale for
between and slightly beyond the orbits of the planets. We changes in perihelion distance due to passing stars. In es-
will assume there is no remaining gas in the solar nebula, sence, the comet must be perturbed to a semimajor axis
and will only discuss planetesimals in the region of the giant large enough that the orbit is significantly perturbed by
planets, which we will take to be 4–40 AU, where the plan- passing stars, but not so large that the orbit is too weakly
etesimals were likely to contain volatiles such as water ice. bound to the solar system and the comet escapes. This con-
Even if the small bodies started on orbits that did not cross dition yields a cloud of comets with semimajor axes on the
the orbits of any of the planets, distant perturbations by the order of 10,000 to 100,000 AU (Tremaine, 1993; see also
planets, particularly at resonances, would have excited most Heisler and Tremaine, 1986; and Duncan et al., 1987). The
 Dones et al.: Oort Cloud Formation and Dynamics 155

trajectories of the stars are randomly oriented in space, so iams, 2003). [The catalog contains 1516 single-apparition
stellar perturbations eventually cause the comets to attain a comets. Of these, only 386, or about one-quarter of the total,
nearly isotropic velocity distribution, with a median inclina- had observations that enable one to solve for the comet’s
tion to the ecliptic of 90° and a median eccentricity of 0.7. energy. For the other comets, the fits assume a parabolic
Subsequently, passing stars reduce the perihelion distances orbit.] We first introduce some terminology and notation.
of a small fraction of these comets so that they reenter the The symbol a represents the semimajor axis of a comet. The
planetary region and potentially become observable. quantity actually determined in orbit solutions is E ≡ 1/a,
The above description is similar to Oort’s vision of the which has units of AU–1. (We will assume these units im-
comet cloud. However, less than half the local galactic mass plicitly in the discussion below.) E, which we will infor-
density is provided by stars, the rest being in gas, brown mally refer to as “energy,” is a measure of how strongly a
dwarfs, and possibly a small amount of “dark matter” comet is held by the Sun. We distinguish three values of E,
(Holmberg and Flynn, 2000). We thus now recognize that which we denote Ei, Eo, and Ef. [For “original” and “fu-
the smooth long-term effect of the total amount of nearby ture” orbits of LPCs (see below), a is computed with re-
galactic matter, i.e., the “galactic tide,” perturbs comets spect to the center or mass, or barycenter, of the solar sys-
somewhat more strongly than do passing stars. The galac- tem, while “osculating” orbits of objects in the inner solar
tic tide causes cometary perihelion distances to cycle out- system are computed with respect to the Sun.] These de-
ward from the planetary region and back inward again on
timescales as long as billions of years (Heisler and Tre-
maine, 1986). In addition, rare, but large, perturbers such
as giant molecular clouds (GMCs) may be important for
the long-term stability of the Oort cloud.
Dynamically “new” comets typically come from dis-
tances of tens of thousands of AU, thereby giving the ap-
pearance of an inner edge to the Oort cloud. Hills (1981)
showed that this apparent inner edge could result from an
observational selection effect. The magnitude of the change
in perihelion distance per orbit, ∆q, of a comet due to ei-
ther galactic tides or passing stars is a strong function of
semimajor axis (a), proportional to a7/2. A dynamically new
comet with perihelion interior to Jupiter’s orbit must have
had q > 10 AU on its previous orbit; otherwise, during the
comet’s last passage through perihelion, Jupiter and/or Sat-
urn would have likely given it a large energy kick (typi-
cally much larger than the comet’s orbital binding energy)
that would either capture it to a much shorter period orbit
or eject it to interstellar space.
If we assume that a comet must come within 3 AU of
the Sun to become active and thus observable, ∆q must be
at least ~10 – 3 AU = 7 AU. It can be shown that, because
of the steep dependence of ∆q on a, this condition implies
that a > 28,000 AU (Levison et al., 2001). Comets with
semimajor axes of a few thousand AU could, in principle,
Fig. 1. Distribution of cometary orbital energies, E ≡ 1/a, where
be much more numerous than comets from tens of thou- a is the comet’s orbital semimajor axis in AU, from the 2003 Cata-
sands of AU, but they normally would not pass within the logue of Cometary Orbits. Only comets with –0.001 AU < E ≤
orbits of Jupiter and Saturn because of the “Jupiter barrier.” 0.002 AU are shown, i.e., only comets whose orbits are apparently
Such “inner Oort cloud” comets would only enter the in- weakly unbound (E < 0) or weakly bound to the solar system (a ≥
ner solar system following an unusually strong perturba- 500 AU). The catalog contains 386 “single-apparition” LPCs for
tion, such as a close stellar passage. Determining the pop- which the orbital energy could be determined. Of these, 268, 254,
ulation of the hypothetical inner Oort cloud is a major goal and 251 occupy the bins shown in (a), (b), and (c), respectively. All
of modern studies of the formation of the cometary cloud. panels have the same horizontal and vertical scales. (a) Osculat-
We now turn to a more detailed discussion of what is known ing value of “energy,” Ei. (b) Original value of energy, Eo. (c) Fu-
ture value of energy, Ef. The Oort cloud spike is not evident when
about the orbits of LPCs.
the histogram is plotted in terms of the orbital energies during or
after the comets’ passages through the planetary region [(a) and
2.2. Observed Orbital Distribution (c)]. However, when planetary perturbations are “removed” by cal-
culating the comet’s orbit before it entered the planetary region,
Figure 1 illustrates the orbital distribution of the 386 a spike of comets with a > 10,000 AU is evident [(b)]. The median
single-apparition LPCs whose energies are given in the semimajor axis of the comets shown in the spike is 27,000 AU.
2003 Catalogue of Cometary Orbits (Marsden and Will- See text for further discussion.
156 Comets II

note, respectively, the osculating (i.e., instantaneous) value led Oort to postulate the existence of the Oort cloud. Oort
of the comet’s 1/a value when it is passing through the plan- suggested that most new comets have aphelion distances of
etary region; the comet’s original 1/a before it entered the 50,000–150,000 AU, i.e., semimajor axes of 25,000–
planetary region (as determined by orbital integration); and 75,000 AU. More recent determinations give values about
the comet’s future 1/a after it passes outside the planetary half as large for the typical semimajor axes of new comets.
region. A comet with E > 0 is bound to the Sun, i.e., it fol- The median semimajor axis of the 143 comets in the 2003
lows an elliptical orbit. A comet with E < 0 is on a hyper- Catalogue of Cometary Orbits with Eo ≤ 10–4 (including
bolic orbit and will escape the solar system on its current those with Eo slightly less than 0, see below) is 36,000 AU,
orbit; colloquially, such a comet is called “ejected.” (Note and is 27,000 AU for the 112 comets with 0 ≤ Eo ≤ 10–4.
that a comet’s orbital energy per unit mass is –GM /2a, so Even these estimates of the typical value of the semimajor
the sign convention for E is the opposite of that used for axes may be too large, since these orbit fits do not take into
orbital energy.) We will also use the symbols q and i to de- account nongravitational forces.
note a comet’s perihelion distance and orbital inclination to Thirty-one comets shown in Fig. 1b have Eo < 0. Taken
the ecliptic, respectively. at face value, these comets could be intruders just passing
Osculating orbits of LPCs passing through the planetary through the solar system. It is more likely that most or all
region (Fig. 1a) indicated that many of the orbits were of these comets actually follow elliptical orbits, and that the
slightly hyperbolic, suggesting that those comets were ap- “hyperbolic” orbits are a consequence of observational er-
proaching the solar system from interstellar space. How- rors and/or inexact modeling of nongravitational forces. [If
ever, when the orbits were integrated backward in time to the comets with Eo < 0 were interstellar in origin, they
well before the comets entered the planetary system, yield- would likely have speeds at “infinity” comparable to the
ing the original inverse semimajor axis (denoted as Eo), the velocity dispersion of disk stars, or tens of kilometers per
distribution changed radically (Fig. 1b). The Eo distribution second (Fig. 1 in McGlynn and Chapman, 1989). Such a
is marked by a sharp “spike” of comets at near-zero but velocity would imply Eo ~ –1, much larger than the most
bound energies, representing orbits with semimajor axes negative value of Eo measured for any comet (Wiegert,
exceeding 104 AU; a low, continuous distribution of more 1996).]
tightly bound orbits; and a few apparently hyperbolic or-
bits. This is clearly not a random distribution.
Oort recognized that the spike had to be the source of
the LPCs, a vast, roughly spherical cloud of comets at dis-
tances greater than 10 4 AU from the Sun, but still gravita-
tionally bound to it. [Some researchers have noted that Öpik
(1932) anticipated Oort’s work by studying the effects of
stellar perturbations on distant meteoroid and comet orbits,
18 years earlier. Öpik suggested that stellar perturbations
would raise the perihelia of comets, resulting in a cloud of
objects surrounding the solar system. However, he specifi-
cally rejected the idea that comets in the cloud could ever
be observed, even indirectly, because he did not recognize
that stellar perturbations would also cause some orbits to
diffuse back into the planetary region. Öpik concluded that
the observed LPCs came from aphelion distances of only
1500–2000 AU. Though Öpik’s (1932) paper was a pioneer-
ing work on stellar perturbations, it did not identify the com-
etary cloud as the source of the LPCs or relate the observed
orbits to the dynamical theory.] Oort showed that comets
in the cloud are so far from the Sun that perturbations from
random passing stars can change their orbits and occasion-
ally send some comets back into the planetary system.
Oort’s accomplishment in defining the source of the LPCs is
particularly impressive when one considers that it was based
on only 19 well-determined cometary orbits, compared with Fig. 2. Distribution of original semimajor axes, ao. Comets are
sometimes classified as “new” or “returning,” depending on
the 386 high-quality orbits in the 2003 catalog.
whether ao is greater than or less than 10,000 AU, respectively.
In Fig. 1b, about 30% (112) of all 386 comets have 0 ≤
However, this classification is crude. To determine whether a par-
Eo ≤ 10 –4. [Another 87 of the comets have 1 × 10–4 < Eo ≤ ticular comet is “new,” it must be integrated backward one orbit,
2 × 10–3, with 132 comets off-scale to the right (i.e., with under the influence of the Sun and planets, galactic tides, and
semimajor axes <500 AU); see Fig. 2.] This region, which possibly nongravitational forces and nearby stars (Dybczynski,
corresponds to semimajor axes >104 AU, is the spike that 2001).
 Dones et al.: Oort Cloud Formation and Dynamics 157

Nongravitational forces make orbits (both “hyperbolic” orbit with a revolution period less than 200 yr, or collide
and elliptical) appear more eccentric (i.e., larger) than they with the Sun or a planet. [There are two classes of short-
actually are (Marsden et al., 1973, 1978; Królikowska, period comets, HTCs and JFCs. The HTCs encompass 41
2001). Marsden et al. (1973) estimate that if nongravita- known objects with a median orbital period of 70.5 yr and
tional forces were correctly accounted for, the average Eo a median inclination of 64°. Some or most HTCs may origi-
value of a comet would increase by 2 × 10–5. [This correc- nate in the Oort cloud (Levison et al., 2001). The JFCs in-
tion is up to 100 times larger for some “hyperbolic” com- clude 236 known comets with a median orbital period of
ets (Królikowska, 2001).] If this correction applied for all 7.5 yr and an median inclination of 11°. By contrast with
new comets, a comet with a nominal Eo value of 1 × 10 –5, HTCs, most JFCs probably do not originate in the Oort
corresponding to a semimajor axis of 100,000 AU, would cloud. The small inclinations of the JFCs argued for the
actually have a semimajor axis of 33,000 AU, and a comet existence of a low-inclination source region, i.e., the Kuiper
with a nominal ao of 20,000 AU would have a true semi- belt (Joss, 1973; Fernández, 1980a; Duncan et al., 1988,
major axis of 14,000 AU. Quinn et al., 1990; Fernández and Gallardo, 1994), but it
In addition, Marsden et al. (1978) showed that orbital now appears likely that most JFCs arise from the related
fits that neglect nongravitational forces give systematically structure called the scattered disk (Duncan et al., 2004). The
larger “original” semimajor axes for comets with smaller numerical data listed here were derived from the tables of
perihelion distances, for which nongravitational forces are HTCs and JFCs in the Web page of Y. Fernández (http://
typically more important. They derived an empirical rela- www.ifa.hawaii.edu/~yan/cometlist.html).]
tion 〈Eo 〉 = (4.63–2.37/q) × 10–5 for the average original In Fig. 2 we show the bound comets with a < 105 AU
semimajor axis for new comets with a perihelion distance on a logarithmic scale. This plot indicates that there are
of q measured in AU. In the limit of large q, for which about twice as many comets with “original” semimajor axes
nongravitational forces are less important, this relation gives (a) ranging from tens to thousands of AU, compared to the
an average original semimajor axis aave = 1/4.63 × 10–5 = number with a > 10 4 AU. Those with a < 10 4 AU are often
21,600 AU. Since new comets have e ~ 1, this implies a called “returning” comets; those with a > 10 4 AU are called
typical aphelion distance of 43,200 AU and a time-averaged dynamically “new” comets. The reason for this terminol-
distance aave (1 + 12 e2) ~ 32,000 AU. Thus a typical Oort ogy is as follows. The median value of Eo for the new com-
cloud comet resides some 30,000 AU from the Sun, which ets is 1/27,000 = 3.7 × 10 –5. The magnitude of the typical
it circles once every 3 m.y. energy change, |∆E|, which these comets undergo in one
Simulations by Heisler (1990) predict that during times perihelion passage is ~10–3, i.e., more than an order of mag-
of low comet flux, the energies of new comets should be nitude larger (Marsden and Williams, 2003; cf. van Woerkom,
peaked near Eo = 3.5 × 10–5, i.e., at a semimajor axis near 1948; Everhart, 1968; Everhart and Raghavan, 1970).
29,000 AU. Heisler assumed a local mass density of Since |∆E| >> Eo, about half the comets have Ef = Eo – ∆E ~
0.185 M /pc3. If the currently accepted value of 0.1 M /pc3 –∆E and the other half have Ef = Eo + ∆E ~ +∆E. The
is assumed instead (see discussion in Levison et al., 2001), former are ejected from the solar system; the other half are
the peak semimajor axis should be near 34,000 AU. Thus captured onto more tightly bound orbits with a ~ 1/∆E, i.e.,
Heisler’s model predicts a semimajor axis that is larger than semimajor axes of a few thousand AU.
the inferred location of the peak. This discrepancy could Thus comets with original values of a > 10 4 AU are
result from errors in orbit determination, contamination of unlikely to have passed within the orbits of Jupiter and
the “new” comet population with dynamically old comets Saturn, that is, within 10 AU of the Sun, in their recent past.
with a > 104 AU, or, as Heisler proposed, could indicate that (By contrast, the perturbations due to Uranus and Neptune
we are presently undergoing a weak comet shower (sec- are much smaller. Typical energy perturbations are propor-
tion 3). Neither the models nor data are yet adequate to tional to Mp/ap, where Mp is the planet’s mass and ap is its
determine which explanation is correct. semimajor axis.) The condition that a > 10 4 AU is only a
Figure 1c shows the “future” orbits of the comets; 96 of rough criterion for a “new” comet, since the distribution of
386 (25%) are slightly hyperbolic, indicating that they will energy changes is broad and centered on zero. Dybczynski
not return to the planetary region again and will leave the (2001) gives a detailed analysis of the past histories of LPCs
solar system. On their first pass through the planetary sys- with well-determined orbits. Some 55% of the observed
tem, the distant, random perturbations by Jupiter and the new comets (statistically consistent with the expected 50%)
other giant planets eject roughly half the “new” comets to have Ef < 0 and will not return. Only 7% of the returning
interstellar space, while capturing the other half to smaller, comets are ejected on their current apparition; since most
more tightly bound, less-eccentric orbits (van Woerkom, have recently traversed the planetary region a number of
1948); see below. Only about 5% of the new comets are times, they typically have Eo > |∆E| (Quinn et al., 1990;
returned to Oort cloud distances of 104–105 AU (Weissman, Wiegert and Tremaine, 1999). The most tightly bound comet
1979). On subsequent returns the comets continue to ran- in the plot has a = 40.7 AU and an orbital period 40.73/2 =
dom-walk in orbital energy until they are ejected, are de- 260 yr. (Conventionally, LPCs have been taken to be those
stroyed by one of several poorly understood physical mech- with orbital periods greater than 200 yr, since until the dis-
anisms (see section 2.3), are captured to a “short-period” covery of Comet 153P = C/2002 C1 Ikeya-Zhang = C/1661
158 Comets II

Fig. 3. Distribution of perihelion distances and inclinations to the ecliptic for the 706 historical (i.e., through 1995) single-apparition
comets (left panels) and the 680 recent (1996–February 2003) single-apparition comets (right panels) from the 2003 Catalogue of
Cometary Orbits. (b) shows a fit to an isotropic distribution for the non-Sun-grazers. The righthand panels are labeled 1996–2002
because the 2003 Catalogue is only complete through 2002, although it does include a few comets discovered early in 2003. The
differences between the left and right panels reflect observational selection effects in the discovery of comets. There was a distinct
change in the way comets were discovered in the mid-1990s because of (1) the discovery of numerous small Sun-grazing comets by
the SOHO spacecraft, which was launched in December 1995, and (2) increased numbers of discoveries of all classes of comets by the
automated searches for near-Earth objects begun around the same time.

C1 Hevelius, apparitions of a comet with P > 200 yr had historical comets. The observed perihelion distribution
never been definitively linked.) (Fig. 3a) is peaked near q = 1 AU because of two factors
Figure 3 shows the distribution of perihelion distances, with opposite dependences on heliocentric distance. First,
q, and inclination to the ecliptic, i, for the 1386 “single- historically, comets have only been discovered if they passed
apparition” LPCs tabulated by Marsden and Williams well within the orbit of Jupiter (5.2 AU), since water sub-
(2003). The lefthand panels plot 706 “historical” comets, limes more readily (and hence cometary activity is more
starting with C/-146 P1 and ending with C/1995 Y1. The vigorous) when comets are closer to the Sun (Marsden et
righthand panels show 680 recent comets, starting with C/ al., 1973). For comets with q < 3 AU, the total brightness
1996 A2 and ending with C/2003 B1. First consider the of an “average” comet typically scales as R–4∆–2, as com-
 Dones et al.: Oort Cloud Formation and Dynamics 159

pared with R–2∆–2 for a bare nucleus, where R is the comet’s 1951) on the inbound leg of their orbits, possibly because
distance from the Sun and ∆ is its distance from Earth. Thus of sublimation of some type of ice such as CO that is more
comets that closely approach the Sun or Earth are brighter volatile than water ice.
and therefore easier to discover (Everhart, 1967a). Second, Finally, Figure 3d shows the inclination distribution of
dynamical models suggest that the intrinsic number of com- the recently discovered comets. The peaks centered near 20,
ets per unit perihelion distance probably increases with 75, and 145° are due to the Marsden/Kracht, Meyer, and
increasing q throughout the entire planetary region (Weiss- Kreutz groups of Sun-grazers, respectively.
man, 1985; Dones et al., 2004).
Figure 3a also shows a smaller peak of comets with 2.3. Cometary Fading and Disruption
perihelion distances <0.01 AU (i.e., less than or approxi-
mately twice the radius of the Sun). These are Sun-grazing Oort pointed out in his 1950 paper that the number of
comets that have likely been driven onto small-q orbits by returning comets in the low continuous distribution (the
the secular perturbations of the planets (Bailey et al., 1992). “returning” comets) decayed at larger values of E. That is,
Most of these comets are members of the Kreutz family, as comets random-walked away from the Oort cloud spike,
which may be the remnants of a comet that broke up near the height of the low continuous distribution declined more
perihelion (Marsden, 1967, 1989). rapidly than could be explained by a purely dynamical
Figure 3b shows the inclination distribution of the his- model using planetary and stellar perturbations. [In a simple
torical comets, which roughly resembles an isotropic dis- model that considers only the effects of planetary pertur-
tribution (dashed curve). Everhart (1967b) showed that the bations, and in which comets survive for an infinite length
departures from an isotropic distribution due to observa- of time, the energy distribution of returning comets should
tional selection effects are small, with a ~ 10% preference be a constant for energies large compared to the magnitude
for discovery of retrograde comets. This indicates that the of a typical energy perturbation (see Oort, 1950; Lyttleton
observable Oort cloud is roughly spherical. The excess of and Hammersley, 1964) (Fig. 4).] This problem is com-
comets with 140° ≤ i ≤ 150° is primarily due to the Kreutz monly referred to as “cometary fading,” although “fading”
Sun-grazers. is a misnomer as it implies a gradual decline of activity. In
Figure 3c shows the perihelion distribution of comets fact, it is still not clear what the exact mechanism for fading
discovered since 1996. About two-thirds of the comets are is. Three physical mechanisms have been proposed to ex-
Sun-grazers (q < 0.01 AU), with a secondary peak centered plain the failure to observe as many returning comets as are
near 0.04 AU due to the Meyer, Marsden, and Kracht “near expected (Weissman, 1980a; Weissman et al., 2002). These
Sun” groups (Marsden and Meyer, 2002) [see the Web pages include (1) random disruption or splitting due to, e.g., ther-
of M. Meyer (http://www.comethunter.de/groups.html), J. mal stresses, rotational bursting, impacts by other small bod-
Shanklin (http://www.ast.cam.ac.uk/~jds/kreutz.htm), and ies, or tidal disruption (Boehnhardt, 2002, 2004); (2) loss of
the U.S. Naval Research Laboratory (http://ares.nrl.navy. all volatiles; and (3) formation of a nonvolatile crust or man-
mil/sungrazer/)]. Almost all these comets have been discov- tle on the nucleus surface (Whipple, 1950; Brin and Mendis,
ered by the Solar and Heliospheric Observatory (SOHO) 1979; Fanale and Salvail, 1984). In these three cases, the
spacecraft (Biesecker et al., 2002). From their apparent comet is referred to as, respectively, “disrupted,” “extinct,” or
failure to survive perihelion passage, the SOHO Sun-grazers “dormant.” Recently, Levison et al. (2002) argued that spon-
must be <0.1 km in diameter (Weissman, 1983; Iseli et al., taneous, catastrophic disruption of comets was the dominant
2002). physical loss mechanism for returning comets. In any case,
In contrast to the historical discoveries, the distribution the “fading” mechanism must be a physical one; the miss-
of recently discovered comets with q > 0.1 AU peaks not ing comets cannot be removed by currently known dynami-
near 1 AU, but rather about 3 AU from the Sun. The out- cal processes alone (Weissman, 1979, 1982; Wiegert and
ward march of this peak indicates that discovery of LPCs Tremaine, 1999).
with large perihelia is still severely incomplete. For example, Oort handled fading by introducing a factor, k, where k
Hughes (2001) concludes that LPCs are still being missed is “the probability that a comet is disrupted during a peri-
beyond 2.5 AU. The advent of electronic detectors and auto- helion passage.” (Note that Oort specifically called this
mated near-Earth object surveys has recently led to the dis- “disruption” rather than “fading.”) Oort adopted a value of
covery of a few LPCs with the largest perihelion distances k = 0.019, or 0.017 if “short-period” comets with orbital
ever found, including C/1999 J2 Skiff (LONEOS survey, q = periods <50 yr were omitted. However, Oort found that this
7.11 AU), C/2000 A1 Montani (Spacewatch, q = 9.74 AU), value removed comets too rapidly from the system, and thus
and C/2003 A2 Gleason (Spacewatch, q = 11.43 AU). (See suggested a slightly lower value of k = 0.014.
http://www.ifa.hawaii.edu/~yan/cometlist.html for a list of In Fig. 4 we show the distribution of original energies,
comets with q > 5 AU.) Inferring the true perihelion distri- Eo, for the 386 LPCs with the best-determined orbits. If
bution for active comets at large q would require correcting there were no “fading” (section 2.3), the distribution of Eo
for observational biases in comet discoveries. Performing should be approximately constant for Eo >> 10 –4 (dotted
this correction is difficult (and has not yet been attempted) line). The actual distribution (solid line) lies far below the
because dynamically new comets are often anomalously expected distribution, implying that many of the comets
bright at large heliocentric distances (Oort and Schmidt, must have “faded.” Models in which surviving comets have
160 Comets II

(Weissman, 1980a). Weissman’s simulations contained a

parameterization that accounted for cometary perturbations
by Jupiter and Saturn, and comets were also perturbed by
random passing stars and nongravitational forces. Comets
were removed by collisions, random disruption (splitting),
and loss of volatiles (sublimation of ices). A fairly good
match to the observed Eo distribution in Figs. 1b and 4 was
obtained. By tuning such a model to improve the fit, some
insight into the possible physical and dynamical loss mecha-
nisms was obtained. Weissman’s best fit was with a model
in which 10% of dynamically new comets randomly dis-
rupted on their first return and 4% of returning comets dis-
rupted on each subsequent return, with 15% of all comets
being immune to disruption.
Wiegert and Tremaine (1999) (see also Bailey, 1984)
investigated the fading problem by means of direct numeri-
cal integrations that included the gravitational effects of the
Sun, the four giant planets, and the “disk” component of
the galactic tide (see below). They carefully examined the
effects of nongravitational forces on comets, as well as the
gravitational forces from a hypothetical solar companion or
circumsolar disk 100–1000 AU from the Sun. However, like
Fig. 4. Distribution of original cometary orbital energy for all
previous authors, Wiegert and Tremaine found that the
386 comets in the 2003 Catalogue of Cometary Orbits with well-
determined energies. The histogram represents the observed dis- observed Eo distribution could only be explained if some
tribution. The dashed curves give theoretical distributions with and physical loss process was invoked. They found that they
without cometary “fading.” Oort (1950) developed a simple model could match the observed Eo distribution if the fraction of
in which the number of “old” comets passing perihelion in a given comets remaining observable after L passages was propor-
period of time with energy E is proportional to e–αE in the limit tional to L–0.6 ± 0.1, consistent with the fading law proposed
of large E. In this expression α = π(14−k k) ; the unit of E is the mean by Whipple (1962), or if ~95% of LPCs remain active for
magnitude of the energy perturbation per orbit produced by the only ~6 returns and the remainder last indefinitely.
planets, which we have taken to be 3.3 × 10 –4 AU–1; and k is the Historically, most comets have been discovered by ama-
probability of disruption per orbit, which we have taken to be teurs. Determining the true population of comets requires
either 0 (flat curve) or 0.014 (declining curve). If no fading is
a detailed understanding of observational bias, i.e., the prob-
assumed, the observed curve is far below the prediction of the
ability that a comet with a specified brightness and orbit will
model, while when a finite probability of fading is assumed, the
model agrees somewhat better with observations. More elaborate be discovered. Many sources of bias have been identified,
fading models (Weissman, 1979, 1980a; Wiegert and Tremaine, but have generally not been modeled in detail (Everhart,
1999) are in good agreement with the observations, but the re- 1967a,b; Kresák, 1982; Horner and Evans, 2002; Jupp et
sults are not necessarily unique. Although many authors have al., 2003). In recent years, telescopic surveys that prima-
modeled the fading problem, there is still not a definitive physi- rily discover asteroids have discovered both active comets
cal explanation for fading. See section 2.3 for further discussion. and inactive objects on comet-like orbits, which are some-
times called Damocloids. For example, the Near Earth As-
teroid Tracking (NEAT) system discovered 1996 PW (Helin
et al., 1996), an object of asteroidal appearance that has a =
a constant probability of disruption per perihelion passage 287 AU, q = 2.5 AU, and i = 30° (Weissman and Levison,
(dashed curve) or in which the number decays as a power 1997a). Discoveries by surveys are much better character-
law in the number of apparitions provide reasonable fits to ized than discoveries by amateurs, particularly for bodies
the actual distribution. that show little or no cometary activity. Using statistical
Whipple (1962) treated the problem somewhat differ- models of discoveries of inactive (extinct or dormant) com-
ently, modeling the expected cumulative “lifetime” distribu- ets by surveys (Jedicke et al., 2003), Levison et al. (2002)
tion of the LPCs as a power law, L–κ, where L is the number calculated the number of inactive, nearly isotropic comets
of returns that the comet makes. Whipple found that κ = 0.7 (NICs) that should be present in the inner solar system.
with an upper limit on the order of 104 returns gave the best Their study used orbital distribution models from Wiegert
fit to the observed orbital data. and Tremaine (1999) and Levison et al. (2001) that assumed
Weissman (1979) was the first to use a Monte Carlo no disruption of comets. Levison et al. (2002) then com-
simulation to derive the expected cometary orbital energy pared the model results to the 11 candidate dormant NICs
distribution, including realistic models of the expected loss (mostly HTCs) that had been discovered as of December 3,
rate due to a variety of physical destruction mechanisms 2001. Dynamical models that assume that comets merely
 Dones et al.: Oort Cloud Formation and Dynamics 161

stop outgassing predict that surveys should have discovered

~100 times more inactive NICs than are actually seen. Thus,
as comets evolve inward from the Oort cloud, 99% of them
become unobservable, presumably by breaking into much
smaller pieces that rapidly dissipate.
A complication in modeling fading arises because Oort
cloud comets on their first perihelion passage are often
anomalously bright at large heliocentric distances compared
to missing “returning” comets (Oort and Schmidt, 1951;
Donn, 1977; Whipple, 1978), and thus their probability of
discovery is considerably enhanced. Suggested mechanisms
for this effect include a veneer of volatiles accreted from
the interstellar medium and lost on the first perihelion pas-
sage near the Sun (Whipple, 1978), blow-off of a primor-
dial cosmic-ray-processed nucleus crust (Johnson et al.,
1987), or the amorphous-to-crystalline water ice phase trans-
formation that occurs at about 5 AU inbound on the first
perihelion passage (Prialnik and Bar-Nun, 1987). When
these Oort cloud comets return, they are generally not ob-
served unless they come within about 3 AU of the Sun,
where water ice can begin to sublimate at a sufficient rate
to produce an easily visible coma (Marsden and Sekanina,
1973). This is illustrated in Fig. 5. The failure to observe Fig. 5. Scatter diagram in original orbital energy and perihelion
many returning LPCs with q > 3 AU is likely to be an ob- distance for the observed LPCs. The vertical band of comets at
servational selection effect, as there is no known physical near-zero Eo is comets making their first perihelion passage from
and/or dynamical mechanism for preferentially removing the Oort cloud. Comets diffuse left and right in the diagram as a
them. Thus, in comparing the heights of the Eo spike and result of planetary perturbations, primarily by Jupiter (in general,
planetary perturbations do not significantly alter either the peri-
low distribution, one should only consider comets with q <
helion distance or the inclination of LPC orbits). Comets perturbed
3 AU. Considering only comets with q < 3 AU slightly al- to negative values of Eo escape the solar system. Note the low
leviates the fading problem; the ratio of the number of re- number of LPCs with perihelion distances q > 3 AU and values
turning to new comets is now 2.5, compared with 1.7 when of Eo > 10 –4. This deficit is likely an observational selection effect
all 386 high-quality orbits are used. Nonetheless, a return- due to the inability of these comets to generate visible comae
ing-to-new ratio of 2.5 is still more than 10 times smaller through water ice sublimation. Water ice sublimates poorly beyond
than predicted by models without fading (Wiegert and Tre- 3 AU from the Sun. Data from Marsden and Williams (2003).
maine, 1999).

2.4. Population and Mass of the Oort Cloud

the terrestrial planets region is undersupplied in LPCs as
To account for the observed flux of dynamically new compared with the outer planets region. This effect is known
LPCs, which he assumed to be about 1 per year within as the “Jupiter barrier.” We return to this topic in section 5.
1.5 AU of the Sun, Oort estimated that the population of Heisler (1990) performed a sophisticated Monte Carlo
the cometary cloud was 1.9 × 1011 objects. Oort stated that a simulation of the evolution of the Oort cloud, assuming it
“plausible estimate . . . of the average mass of a comet . . . is had formed with the centrally condensed density profile
perhaps about 1016 g . . . uncertain by one or two factors of found by Duncan et al. (1987) (hereafter DQT87; see sec-
10.” For an assumed density of 0.6 g/cm3, a cometary mass tion 4). Assuming a new comet flux of 2.1 comets/year with
of 1016 g corresponds to a diameter of 3.2 km. More recent q < 1 AU and “absolute magnitude” H10 < 11, Heisler (1990)
dynamical models (Heisler, 1990; Weissman, 1990a) have inferred that the present-day Oort cloud contains 5 × 1011
produced somewhat higher estimates of the number of com- comets with a > 20,000 AU and H10 < 11. Weissman (1996)
ets in the Oort cloud, by up to an order of magnitude. These relates H10, which is a measure of a comet’s total brightness
larger numbers come about in part from higher estimates that is generally dominated by coma, to cometary masses,
of the flux of LPCs throughout the planetary system, and using 1P/Halley to calibrate the relation (see also Harmon
in part from a recognition of the role of the giant planets et al., 2004). According to Weissman (1996), the diameter
in blocking the diffusion of cometary orbits back into the and mass of a comet with H10 = 11 are 2.3 km and 4 × 1015 g
planetary region (Weissman, 1985). Comets perturbed in- respectively. Assuming a broken power-law cometary size
ward to perihelia near the orbits of Jupiter and Saturn will distribution from Everhart (1967b) (see also Weissman and
likely be ejected from the solar system before they can dif- Levison, 1997b), and assuming that a comet’s luminosity
fuse to smaller perihelia where they can be observed. Thus, at a standard distance is proportional to its mass, Weissman
162 Comets II

(1996) infers that the average mass of a comet is 4 × 1016 g. encounter (interior to the inner edge of the Oort cloud) can,
Using Heisler’s (1990) modeled population, this implies a in principle, eject a large fraction of the comets in the entire
present-day mass of 2 × 1028 g or 3.3 M in comets with cloud, because the star pulls the Sun away from the cloud
a > 20,000 AU. Weissman (1996) estimated that there are (Heisler et al., 1987). Such drastic encounters have probably
1 × 1012 comets with a > 20,000 AU and H10 < 11, giving a not occurred in the past 4 b.y., but may have taken place in
mass for the outer Oort cloud (comets with a > 20,000 AU) the early solar system if the Sun formed in a cluster.
of 7 M . Weissman then assumed, based on DQT87, that García-Sánchez et al. (1999, 2001; see also Frogel and
the inner Oort cloud (a < 20,000 AU) contains about 5 times Gould, 1998) used Hipparcos and groundbased data to
as much mass as the outer Oort cloud, giving a total present- search for stars that have encountered or will encounter the
day Oort cloud mass of 38 M . However, this estimate is solar system during a 20-m.y. interval centered on the pres-
based upon a formation model and not on observations, ent. Correcting for incompleteness, García-Sánchez et al.
since (1) comets from the hypothetical inner Oort cloud are (2001) estimate that 11.7 ± 1.3 stellar systems pass within
not perturbed into the planetary region except during strong 1 pc (~200,000 AU) of the Sun per million years, so that
comet showers, which only occur some 2% of the time ~50,000 such encounters should have occurred over the
(Heisler, 1990), and (2) we are not presently undergoing a history of the solar system if the Sun had always occupied
strong comet shower (Weissman, 1993). We further discuss its current galactic orbit and environment. However, 73%
the population of the inner Oort cloud in sections 3 and 4. of these encounters are with M dwarfs, which have masses
less than 0.4 M . Strong comet showers are generally caused
2.5. Oort Cloud Perturbers by stars with masses ~1 M . Passages through the Oort
cloud by M dwarfs and brown dwarfs typically produce
Since first proposed in 1950, Oort’s vision of a cometary little change in the cometary influx to the planetary region
cloud gently stirred by perturbations from distant passing (Heisler et al., 1987).
stars has evolved considerably. Additional perturbers have It is now established that the galactic disk is the major
been recognized: GMCs in the galaxy, which were unknown perturber of the Oort cloud at most times (Harrington, 1985;
before 1970 (Biermann, 1978; Clube and Napier,1982), and Byl, 1986; Heisler and Tremaine, 1986; Delsemme, 1987),
the galactic gravitational field itself, in particular the tidal though stars and probably GMCs still play an important role
field of the galactic disk (Byl, 1983, 1986; Harrington, 1985; in repeatedly randomizing the cometary orbits. Galactic
Heisler and Tremaine, 1986). GMC encounters are rare, tidal perturbations peak for orbits with their line of apsides
occurring with a mean interval of perhaps 3–4 × 108 yr, but at galactic latitudes of ±45° and go to zero at the galactic
can result in major perturbations on the orbits of comets in equator and poles. Delsemme (1987) showed that the dis-
the Oort cloud. Hut and Tremaine (1985) showed that the tribution of galactic latitudes of the aphelion directions of
integrated effect of molecular clouds on the Oort cloud over the observed LPCs mimics that dependence. Although a
the history of the solar system is roughly equal to the inte- lack of comet discoveries near the galactic equator could
grated effects of all stellar passages. Atomic clouds have be the result of observational selection effects (e.g., confu-
much smaller effects on the Oort cloud than do stars or mol- sion with galactic nebulae), the lack of comets near the
ecular clouds (Hut and Tremaine, 1985). poles appears to confirm the importance of the galactic tidal
The galactic field sets the limits on the outer dimensions field on the Oort cloud.
of the Oort cloud. The cloud can be roughly described as a The galactic tide causes the cometary perihelia to oscillate
prolate spheroid with the long axis oriented toward the on timescales on the order of 1 b.y. (Heisler and Tremaine,
galactic center (Antonov and Latyshev, 1972; Smoluchowski 1986; DQT87). In general, the effect of the tide is stronger
and Torbett, 1984). Maximum semimajor axes are about 1 × than that of passing stars because (1) the typical magnitude
105 AU (i.e., 0.5 pc, or almost 40% the distance to the near- of galactic tidal perturbations is greater than the perturba-
est star) for direct orbits in the galactic plane, decreasing tion from stars for comets at a particular semimajor axis;
to about 8 × 10 4 AU for orbits perpendicular to the galac- and (2) the tide produces a regular stepping inward of com-
tic plane, and increasing to almost 1.2 × 105 AU for retro- etary perihelia, in contrast to the random-walk nature of
grade orbits (opposite to galactic rotation). stellar perturbations. As a result, tides bring comets into the
In addition, stars will occasionally pass directly through observable region more efficiently, making it somewhat
the Oort cloud, ejecting some comets and severely perturb- easier to overcome the dynamical barrier that Jupiter and
ing the orbits of others (Hills, 1981). A star passage drills Saturn present to cometary diffusion into the inner planets
a narrow tunnel through the Oort cloud, ejecting all com- region.
ets within a radius of ~450 AU, for a 1 M star passing at a Hut and Tremaine (1985) estimated that the dynamical
speed of 20 km s–1 (Weissman, 1980b). Over the history of half-life of comets in the Oort cloud due to the effects of
the solar system, Weissman estimated that passing stars have passing stars is about 3 G.y. at 25,000 AU and about 1 G.y.
ejected about 10% of the Oort cloud population. The ejected at 50,000 AU (see also Weinberg et al., 1987). Hut and
comets will all be positioned close to the path of the perturb- Tremaine (1985) estimated that the effects of GMCs on the
ing star, as will be many of the comets that are thrown into Oort cloud are comparable to those of stars, though there
the planetary system in a “cometary shower” (Weissman, are many uncertainties in how to treat clouds. Thus, due to
1980b; Dybczynski, 2002a,b). An extremely close stellar stellar perturbations, only about 5% of the comets should
 Dones et al.: Oort Cloud Formation and Dynamics 163

survive at 50,000 AU for 4.5 G.y., while 5% should survive the “pressure” due to the random motions of the comets bal-
at 30,000 AU if the effects of clouds are included. Some ances the inward attraction due to solar gravity), this as-
authors have estimated even shorter lifetimes (e.g., Bailey, sumed velocity distribution determines the density profile
1986). This led to suggestions that the observable, “outer” n(r) (comets/AU3) in the Oort cloud (see, e.g., Spitzer, 1987;
Oort cloud must be replenished, for example, by capture of Binney and Tremaine, 1987). Oort’s profile is given by
comets from interstellar space, as suggested by Clube and n(r) ∝ (R0 /r – 1)3/2 (Oort, 1950; Bailey, 1983; Bailey et al.,
Napier (1984). However, cometary capture is an unlikely 1990). For r << R0, n(r) ∝ r –γ, with γ ≈ 1.5. (The median
process because a three-body gravitational interaction is cometary distance in this model is 0.35 R0; at this distance,
required to dissipate the excess hyperbolic energy. Valtonen the effective value of γ is ~1.7.) Density distributions with
and Innanen (1982) and Valtonen (1983) showed that the γ < 3 have most of the mass in the outer regions of the
probability of capture is proportional to V∞–7 for V∞ > 1 km/s, cloud, so Oort’s model predicts that there should be few
where V∞ is the hyperbolic excess velocity. Capture is pos- comets with r << R0, i.e., the population of the inner Oort
sible at encounter velocities ≤1 km s–1, but is highly unlikely cloud should be small. However, Oort’s assumption of an
at the Sun’s velocity of ~20 km s–1 relative to the local stan- isotropic velocity distribution may not be valid in the in-
dard of rest (Mignard, 2000). ner parts of the cloud. For instance, if the orbits are pre-
More plausibly, the outer Oort cloud could be resupplied dominantly radial (i.e., orbital eccentricities ~1), γ should
from an inner Oort cloud reservoir, i.e., comets in orbits be ~3.5, implying a centrally condensed cloud.
closer to the Sun (Hills, 1981; Bailey, 1983) that are pumped Hills (1981) showed that the apparent inner edge of the
up by passing stars to replace the lost comets. However, due Oort cloud at a semimajor axis a = aI ≈ (1–2) × 10 4 AU
to uncertainties in cloud parameters and the history of the could be a selection effect due to the rarity of close stellar
solar orbit, it may be premature to conclude that the outer passages capable of perturbing comets with a < aI. Hills
Oort cloud has been so strongly depleted during its lifetime speculated that γ > 4, so that many comets (and perhaps the
that a massive inner Oort cloud is required to replenish the great majority of comets) might reside in the unseen inner
outer cloud. In particular, existing models of the effect of Oort cloud at semimajor axes of a few thousand AU. Besides
molecular clouds on the Oort cloud make highly idealized its possible role as a reservoir that could replenish the outer
assumptions about the structure of molecular clouds, and cloud after it was stripped by a GMC (Clube and Napier,
are sensitive to assumptions about the history of the Sun’s 1984), inner Oort cloud comets might be an important
orbit (e.g., the extent of its motion out of the galactic plane). source of impactors on the giant planets and their satellites
Finally, molecular clouds are part of a “fractal” or “multi- (Shoemaker and Wolfe, 1984; Bailey and Stagg, 1988; see
fractal” continuum of structure in the interstellar medium also Weissman, 1986, and section 5). However, the density
(Chappell and Scalo, 2001). The resulting spatial and tem- profile of the Oort cloud is not known a priori, but depends
poral correlations in interstellar gas density will result in a in large part upon the formation process.
much different spectrum of gravitational potential fluctua- During rare passages of stars through the inner Oort
tions experienced by the Oort cloud, compared to an inter- cloud, comet showers could result (Hills, 1981; Heisler et
stellar model that has clouds distributed independently and al., 1987; Fernández, 1992; Dybczynski, 2002a,b). Heisler
randomly (J. Scalo, personal communication, 2003). We (1990) simulated the LPC flux from the Oort cloud into the
now turn to a more detailed discussion of the hypothetical planetary region, under the influence of stellar perturbations
inner cloud. and a constant galactic tide. She found that the flux is con-
stant within the statistical limits of her dynamical model,
3. INNER OORT CLOUD AND except when a major perturbation of the cometary orbits
COMET SHOWERS occurs as a result of a penetrating stellar passage. A hypo-
thetical example of the flux vs. time into the terrestrial plan-
In Oort’s original model, he assumed that the velocity ets region (q < 2 AU) from Heisler (1990) is shown in Fig. 6.
distribution of comets in the Oort cloud is given by an iso- The extreme increases in the cometary flux caused by a
tropic distribution of the form f(v) = 3v2/v3max for v < vmax penetrating stellar passage through the inner Oort cloud are
and f(v) = 0 for v > vmax. The velocity vmax is a function of of particular interest. Hut et al. (1987) used a Monte Carlo
distance from the Sun, r, determined by an assumed outer simulation to show that a 1 M star passage at 20 km s–1 at
edge of the cloud at distance R0. Specifically, 3000 AU from the Sun would perturb a shower of ~5 × 108
comets into Earth-crossing orbits, raising the expected im-
2GM R0 pact rate by a factor of 300 or more, and lasting 2–3 × 106 yr
vmax = −1 (this model assumed a massive inner Oort cloud with a
R0 r
population five times that of the outer cloud, as predicted
with limiting cases by DQT87). Comets from the inner Oort cloud make an
average of 8.5 returns each (allowing for disruption) dur-
vmax → 2GM /r ing a major cometary shower. The flux is very high, in part,
because the shower comets from the inner Oort cloud start
(i.e., the local escape velocity) for r << R0 and vmax → 0 for from shorter period orbits than outer Oort cloud comets,
r → R0. Assuming that the Oort cloud is in equilibrium (i.e., with typical periods in the inner cloud of 2–5 × 105 yr vs.
164 Comets II

are shown in Fig. 7. The dynamical evolution of cometary

showers was also modeled by Fernández and Ip (1987).
Farley et al. (1998) presented the best evidence to date that
at least one comet shower has occurred in the past. Specif-
ically, they showed that the flux to Earth of extraterrestrial
3He, a tracer of interplanetary dust, increased for 2.5 m.y.,

centered near the time of the large Popigai and Chesapeake

Bay impacts some 36 m.y. ago and the late Eocene extinc-
tion event. However, it is possible that some other mecha-
nism [e.g., an “asteroid shower” following the catastrophic
disruption of a main-belt asteroid (Zappalá et al., 1998)]
also might have produced the signature detected by Farley
et al. (1998).
Fortunately, major cometary showers, as a result of deep
(q < 3 × 103 AU), penetrating stellar encounters, are rare,
occurring perhaps once every 4 × 108 yr. Cometary show-
ers should also occur with a similar frequency due to ran-
dom encounters with GMCs, but with possibly an order of
Fig. 6. Number of new LPCs from the Oort cloud entering the magnitude less total flux into the planetary region (Morris
terrestrial planets region, q < 2 AU, vs. time, based on a Monte and Muller, 1986). Lesser showers from more distant, but
Carlo simulation that included random passing stars and galactic still penetrating stellar passages at heliocentric distances
tidal perturbations. The large spikes are comet showers due to ~104 AU occur more frequently, on the order of every 4 ×
random stars penetrating the Oort cloud. From Heisler (1990). 107 yr (Dybczynski, 2002a,b; Matese and Lissauer, 2002).
If there is a massive inner Oort cloud, random cometary
showers may actually dominate the time-averaged LPC flux
through the planetary region (Weissman, 1990b).
The suggestion that both biological extinction events
(Raup and Sepkoski, 1984) and impact craters (Alvarez and
Muller, 1984) on the Earth repeat with a period of approxi-
mately 26 m.y. led to several hypotheses that invoked peri-
odic cometary showers as the cause of the extinctions. These
hypotheses involved (1) a dwarf companion star to the Sun
(“Nemesis”) in a distant, eccentric, 26-m.y. period orbit
(corresponding to a ~ 90,000 AU) with its perihelion deep
in the Oort cloud (Whitmire and Jackson, 1984; Davis et
al., 1984); (2) a tenth planet circulating in a highly inclined
orbit at about 150 AU from the Sun with a precession pe-
riod of 26 m.y., so that it periodically passed through a
transneptunian disk of small bodies (Whitmire and Matese,
1985); or (3) the solar system’s epicyclic motion above and
below the galactic plane. In this last scenario, GMC encoun-
Fig. 7. Dynamical evolution of a shower of comets from the ters would occur near the times of galactic plane crossings
inner Oort cloud due to a close, penetrating stellar passage at (Rampino and Stothers, 1984), which occur every 26–37 m.y.
20 km s–1 at 3000 AU from the Sun. The solid histogram is the (Bahcall and Bahcall, 1985). The apparent coincidence be-
number of comets (arbitrary units) crossing Earth’s orbit vs. time; tween galactic plane crossings by the solar system and ter-
the dashed curve is the fraction of the original shower comets still
restrial extinction boundaries was originally pointed out by
evolving in the system. On the order of 5 × 108 comets brighter
Innanen et al. (1978). The Sun’s galactic motion was also
than H10 = 11 are expected to be thrown into Earth-crossing or-
bits by the 1 M star’s passage. Roughly 10 of these comets would suggested as the clock mechanism by Schwartz and James
be expected to strike Earth. From Hut et al. (1987). (1984), although they only speculated about the underlying
physical mechanism leading to the extinctions.
A variety of dynamical problems have been identified
with each of these hypotheses, and no evidence in support
3–5 × 106 yr in the outer cloud. Returning comets tend to of any of them has been found. As a result, periodic comet
be perturbed to even shorter period orbits, ~103–105 yr. shower hypotheses have not gained wide acceptance and are
They thus make many returns in a relatively short period of generally discounted today, although Muller (2002) recently
time. The temporal profile and fraction of surviving comets proposed a modified version of the Nemesis companion-
for a major cometary shower as found by Hut et al. (1987) star hypothesis. More detailed discussions of the relevant
 Dones et al.: Oort Cloud Formation and Dynamics 165

issues can be found in Shoemaker and Wolfe (1986), Tre- <35 AU might have been an important source of Oort cloud
maine (1986), and Weissman (1986). Questions have also comets. The Dones et al. (2004) simulations bear out this
been raised about the reality of the periodicity in the fossil conclusion. However, in these models, perturbations due to
extinction record. Criticism has been made of the statistical Pluto are not important.]
techniques used to claim that the periodicity is significant Later work (Whipple, 1964; Safronov, 1969, 1972) in-
(Hoffman, 1985; Heisler and Tremaine, 1989; Jetsu and dicated that Jupiter and Saturn tended to eject comets from
Pelt, 2000), and of the accuracy of the dated tie-points in the the solar system, rather than placing them in the Oort cloud.
geologic record, particularly prior to 140 m.y. ago (Shoe- The kinder, gentler perturbations by Neptune and Uranus (if
maker and Wolfe, 1986). these planets were assumed to be fully formed) thus ap-
Variations in the cometary flux into the planetary region peared to be more effective in populating the cloud. How-
as the Sun revolves around its galactic orbit are still the ever, their role was unclear because the ice giants took a
subject of research. For example, the solar system under- very long time to form in Safronov’s orderly accretion sce-
goes a near-harmonic motion above and below the galactic nario. Fernández (1978) used a Monte Carlo, Öpik-type
plane (Matese et al., 1995; Nurmi et al., 2001). This mo- code, which assumes that close encounters with planets
tion currently carries the planetary system some 50–90 pc dominate the orbital evolution of a small body, to calculate
out of the plane, comparable to the scale height of the disk the probability that a comet would collide with a planet,
(Bahcall and Bahcall, 1985). The full period of the oscil- be ejected from the solar system, or reach a near-parabolic
lation is ~52–74 m.y. Matese et al. (1995) showed that this orbit (i.e., an orbit of a body that might end up in the Oort
causes the cometary flux to vary sinusoidally by a factor cloud). He suggested that “Neptune, and perhaps Uranus,
of 2.5–4 over that period, with the maximum flux occur- could have supplied an important fraction of the total mass
ring just after passage through the galactic plane. However, of the cometary cloud.” Fernández (1980b) extended this
the dynamical model of Matese et al. did not include stel- work by following the subsequent evolution of comets on
lar perturbations. The solar system has passed through the plausible near-parabolic orbits for bodies that had formed
galactic plane in the last few million years, so the current in the Uranus-Neptune region (5000 ≤ a ≤ 50,000 AU;
steady-state flux is likely near a local maximum. 20 AU ≤ q ≤ 30 AU; i ≤ 20°). He included the effects of
passing stars using an impulse approximation and included
4. SIMULATIONS OF THE FORMATION perturbations by the four giant planets by direct integration
OF THE OORT CLOUD for comets that passed within 50 AU of the Sun. Fernández
concluded that about 10% of the bodies scattered by Ura-
In his 1950 paper, Oort did not consider the formation nus and Neptune would occupy the Oort cloud at present,
of the comet cloud in detail, but speculated and that the implied amount of mass scattered by the ice
“It seems a reasonable hypothesis to assume that the giants was cosmogonically reasonable.
comets originated together with the minor planets, and that Shoemaker and Wolfe (1984) performed an Öpik-type
those fragments whose orbits deviated so much from circles simulation to follow the ejection of Uranus-Neptune plan-
between the orbits of Mars and Jupiter that they became etesimals to the Oort cloud, including the effects of stellar
subject to large perturbations by the planets, were diffused perturbations for orbits with aphelia >500 AU. They found
away by these perturbations, and that, as a consequence of that ~9% of the original population survived over the his-
the added effect of the perturbations by stars, part of these tory of the solar system, with ~90% of those comets in or-
fragments gave rise to the formation of the large cloud of bits with semimajor axes between 500 and 20,000 AU; 85%
comets which we observe today.” of the latter group had semimajor axes <10,000 AU. Shoe-
Oort proposed the asteroid belt as the source region for maker and Wolfe also found that the perihelion distribution
the LPCs on the grounds that (1) asteroids and cometary nu- of the comets was peaked just outside the orbit of Neptune,
clei are fundamentally similar in nature and (2) the aster- and estimated a total cloud mass of 100 to 200 M . Unfor-
oid belt was the only stable reservoir of small bodies in the tunately, their work was published only in an extended ab-
planetary region known at that time. Kuiper (1951) was the stract, so the details of their modeling are not known.
first to propose that the icy nature of comets required that The first study using direct numerical integrations to
they be from a more distant part of the solar system, among model the formation of the Oort cloud was that of Duncan
the orbits of the giant planets. Thus, ever since Oort and et al. (1987; hereafter DQT87). To save computing time,
Kuiper’s work, the roles of the four giant planets in populat- DQT87 began their simulations with comets on low-inclina-
ing the comet cloud have been debated. Kuiper (1951) pro- tion, but highly eccentric, orbits in the region of the giant
posed that Pluto, which was then thought to have a mass planets (initial semimajor axes, a0, of 2000 AU and initial
similar to that of Mars or the Earth, scattered comets that perihelion distances, q0, uniformly distributed between 5
formed between 38 and 50 AU (i.e., in the Kuiper belt!) and 35 AU). Gravitational perturbations due to the giant
onto Neptune-crossing orbits, after which Neptune, and to planets and the disk (z) component of the Galactic tide were
a lesser extent the other giant planets, placed comets in the included (see below). A Monte Carlo scheme from Heisler
Oort cloud. [Stern and Weissman (2001) have recently ar- et al. (1987) was used to simulate the effects of stellar en-
gued that the primordial Kuiper belt at heliocentric distances counters. Molecular clouds were not included.
166 Comets II

DQT87’s main results included the following: (1) The For the “cold” runs, the percentage of objects that were inte-
Oort cloud has a sharp inner edge at a heliocentric distance grated that currently occupy the classical “outer” Oort cloud
r ~ 3000 AU. (2) For 3000 AU < r < 50,000 AU, the num- (20,000 AU ≤ a < 200,000 AU) is only 2.5%, about a factor
ber density of the Oort cloud falls steeply with increasing of 3 smaller than found by DQT87. The percentage of ob-
r, going roughly as r –3.5. Thus the Oort cloud is centrally jects in the inner Oort cloud (2000 AU ≤ a < 20,000 AU)
condensed, with roughly 4–5 times as many comets in the is 2.7%, almost an order of magnitude smaller than calcu-
inner Oort cloud (a < 20,000 AU) as in the classical outer lated by DQT87. This result holds because most comets that
Oort cloud. (3) The present-day inclination distribution begin in the Uranus-Neptune zone evolve inward and are
should be approximately isotropic in the outer Oort cloud ejected from the solar system by Jupiter or Saturn. A small
and most of the inner Oort cloud. The innermost part of the fraction are placed in the Oort cloud, most often by Saturn.
inner Oort cloud, interior to 6000 AU, may still be slightly However, all four of the giant planets place comets in the
flattened. (4) Comets with q0 > 15 AU are much more likely Oort cloud. The Oort cloud is built in two distinct stages
to reach the Oort cloud and survive for billions of years than in the DLDW model. In the first few tens of millions of
are comets with smaller initial perihelia. For example, only years, the Oort cloud is built by Jupiter and Saturn, which
2% of the comets with q0 = 5 AU should occupy the Oort deliver comets to the outer Oort cloud. After this time, the
cloud at present, while 24% of the comets with q0 = 15 AU Oort cloud is built mainly by Neptune and Uranus, with the
and 41% with q0 = 35 AU should do so. This result appeared population peaking about 800 m.y. after the beginning of
to confirm that Neptune and Uranus, which have semimajor the simulation (Fig. 8). Objects that enter the Oort cloud
axes of 30 and 19 AU, respectively, are primarily responsible during this second phase typically first spend time in the
for placing comets in the Oort cloud. However, this find- “scattered disk” [45 AU ≤ a < 2000 AU, with perihelion
ing can be questioned, since the highly eccentric starting distance <45 AU at all times (Duncan and Levison, 1997)]
orbits had the consequence of pinning the perihelion dis- and then end up in the inner Oort cloud.
tances of the comets at early stages. This, in turn, allowed Plates 5 and 6 show the formation of the Oort cloud in
Neptune and Uranus to populate the Oort cloud efficiently terms of the orbital evolution in semimajor axis as a func-
because they could not lose objects to the control of Jupi-
ter and Saturn.
Dones et al. (2004; hereafter DLDW) repeated the study
of DQT87, starting with “comets” with semimajor axes
between 4 and 40 AU and initially small eccentricities and
inclinations. These initial conditions are more realistic than
the highly eccentric starting orbits assumed by DQT87.
DLDW integrated the orbits of 3000 comets for times up
to 4 b.y. under the gravitational influence of the Sun, the
four giant planets, the galaxy, and random passing stars.
Their model of the galaxy included both the “disk” and
“radial” components of the galactic tide. The disk tide is
proportional to the local density of matter in the solar neigh-
borhood and exerts a force perpendicular to the galactic
plane, while the radial tide exerts a force within the galac-
tic plane. These simulations did not include other perturbers
such as molecular clouds, a possible dense early environ-
ment if the Sun formed in a cluster (Gaidos, 1995; Fernán-
dez, 1997), or the effects of gas drag (de la Fuente Marcos
and de la Fuente Marcos, 2002; Higuchi et al., 2002).
DLDW performed two sets of runs with dynamically
“cold” and “warm” initial conditions. The results were very
similar, so we will focus on the “cold” runs, which included
2000 particles with root-mean-square initial eccentricity, e0,
and inclination to the invariable plane, i0, equal to 0.02 and
Fig. 8. Fraction of original cometary population placed in the
0.01 radians, respectively. DLDW assumed that the Sun re-
inner and outer Oort clouds and in the scattered disk in the DLDW
sided in its present galactic environment during the forma-
simulation. In these simulations the outer Oort cloud, which is
tion of the Oort cloud. originally populated by comets injected by Jupiter and Saturn,
We will take the results of these calculations at 4 G.y. forms more rapidly than the inner Oort cloud, which is primarily
to refer to the present time. For a comet to be considered a populated by comets injected by Uranus and Neptune. The simu-
member of the Oort cloud, we require that its perihelion lation predicts that at present, the populations of the inner and
distance exceeded 45 AU at some point in the calculation. outer Oort clouds are comparable.
 Dones et al.: Oort Cloud Formation and Dynamics 167

tion of perihelion distance and inclination to the invariable unobservable) inner Oort cloud. If we fit the entire Oort
plane of the solar system, respectively. We show six cloud at 4 G.y. in the DLDW model to a single power law,
“frames” from the DLDW integrations at various times in we find γ ~ 3, shallower than the value found by DQT87.
the calculations. (Animations showing these data every The shallow slope probably results because all the giant
1 m.y. throughout the simulation can be viewed at http:// planets inject comets into the Oort cloud, even though most
www.boulder.swri.edu/~luke.) Points in these plots are formed beyond 20 AU. A value of γ ~ 3 implies that the
color-coded by their formation location a0: Jupiter region inner and outer Oort clouds contain comparable numbers
comets (a0 between 4 and 8 AU) are magenta triangles; of comets at present in this model.
Saturn region comets (8–15 AU) are blue triangles; Uranus Finally, Fig. 8 shows the time evolution of the popula-
region comets (15–24 AU) are green circles; Neptune re- tions of the Oort cloud and scattered disk in the simula-
gion comets (24–35 AU) are red circles; Kuiper belt com- tion. The scattered disk is initially populated by comets
ets (35–40 AU) are black circles. scattered by Jupiter and Saturn, and peaks in number at
Plate 5a (0 m.y.) shows that the particles start with very 10 m.y. (off-scale on the plot). The predicted population of
small eccentricities, as represented by the diagonal line of the scattered disk in this model at the present time is roughly
particles that extends from ~4 to 40 AU. After 1 m.y. 10% the population of the Oort cloud.
(Plate 5b), the giant planets, particularly Jupiter and Sat- Likewise, the Oort cloud grows rapidly in the first few
urn, have scattered many comets into very eccentric orbits tens of millions of years due to comets injected by Jupiter
with perihelia still in the region of the giant planets. After and Saturn, and then undergoes a very prolonged period of
1 m.y., 76% of the test particles remain. Of the 24% lost in growth, primarily due to Uranus and Neptune, with the peak
the first million years, most were ejected from the solar population occurring around 800 m.y. From 150 m.y. to
system by Jupiter or Saturn. 4000 m.y., the fraction of comets in the Oort cloud ranges
At 10 m.y. (Plate 5c), we see the beginning of the forma- between 5% and 7.6%.
tion of the Oort cloud. Some particles with a > 30,000 AU Figure 8 also shows the populations of the inner and
have had their perihelia raised out of the planetary region outer Oort clouds individually. The population of the outer
by galactic tides and the effects of passing stars. In all, 48% Oort cloud peaks around 600 m.y. The inner Oort cloud
of the particles remain. At 100 m.y. (Plate 5d), the Oort peaks around 1.8 G.y. Because of the faster decline of the
cloud has begun to assume its current form. Twenty-eight outer Oort cloud, the ratio of numbers of inner to outer Oort
percent of the particles remain; 4.7% are in the Oort cloud, cloud comets increases with time, to 1.1 at present. None-
with the rest in the planetary region or scattered disk. From theless, this ratio is much smaller than was given by DQT87,
100 m.y. to 1000 m.y. (Plate 5e), particles continue to en- who found 4–5 times more comets in the inner Oort cloud
ter the Oort cloud from the scattered disk. The total num- than in the outer Oort cloud. Only 2.5% of the comets that
ber of particles continues to decline — 15% remain — but were initially in the simulation occupy the outer Oort cloud
the population in the Oort cloud peaks around 835 m.y. At at 4 G.y.
1000 m.y., 7.3% of the comets are in the Oort cloud. Finally, At face value, the low efficiency of Oort cloud forma-
at 4000 m.y. (Plate 5f), the structure of the Oort cloud re- tion in the DLDW simulation implies a massive primordial
mains nearly the same as at 1000 m.y., but its population has protoplanetary disk. Assuming an outer Oort cloud popula-
declined slightly. In total, 11% of the particles that DLDW tion of 5 × 1011–1 × 1012 comets (Heisler, 1990; Weissman,
integrated remain. Of these, about half revolve on orbits in 1996) and an average cometary mass of 4 × 1016 g (sec-
the planetary region (i.e., a < 45 AU), primarily in the Kui- tion 2.4), the original mass in planetesimals between 4 and
per belt, that have changed little. Most of the other survivors 40 AU was ~150–300 M , some 3–6 times the mass in sol-
reside in the Oort cloud, with nearly equal numbers of com- ids in a “minimum-mass” solar nebula. This amount of mass
ets in the inner and outer clouds. likely would have produced excessive migration of the gi-
Plate 6 shows the evolution of the particles’ inclinations. ant planets and/or formation of additional giant planets
Plate 6a (0 m.y.) shows that the particles’ inclinations to the (Hahn and Malhotra, 1999; Thommes et al., 2002; Gomes
invariable plane are initially small. After 1 m.y. (Plate 6b), et al., 2004). Since cometary masses are not well deter-
the planets have scattered the comets into moderately in- mined, it is not yet clear whether the large disk mass in-
clined orbits. After 10 m.y. (Plate 6c), the particles with a > ferred by DLDW presents a real problem.
30,000 AU have been perturbed by galactic tides and stars The results of the DLDW simulations appear inconsis-
into a nearly isotropic distribution of inclinations. As time tent with observations in another way. The population of
continues (Plates 6d–6f), tides affect the inclinations of the scattered disk that DLDW predict, on the order of 10%
particles closer to the Sun, so that at 4000 m.y. inclinations of the population of the Oort cloud, is much larger than the
are clearly isotropic for a > 7000 AU. inferred actual population of the scattered disk (Trujillo et
We now return to the issue of how centrally condensed al., 2000). Finally, the DLDW model of the Oort cloud
the Oort cloud is. Recall that DQT87 found a density pro- appears to be inconsistent with a model of the orbital dis-
file n(r) ∝ r –γ with γ ~ 3.5 for 3000 AU < r < 50,000 AU, tribution of the HTCs by Levison et al. (2001). Although
so that in their model most comets reside in the (normally the class of HTCs includes some objects on retrograde or-
168 Comets II

bits, such as Halley itself, the observed HTCs with perihelia the protoplanetary disk could populate the Oort cloud (Stern
<1.3 AU have a median inclination imed of only 58°. Levison and Weissman, 2001; Stern, 2003; Charnoz and Morbidelli,
et al. (2001), who took imed = 45°, using the data available at 2003).
that time, showed that the HTCs must originate in a some-
what flattened source region. Since the outer Oort cloud is 5. CONSTRAINTS ON THE STRUCTURE
known to be roughly isotropic, Levison et al. (2001) as- OF THE OORT CLOUD
sumed that most HTCs must come from a flattened inner
Oort cloud. However, because of the “Jupiter barrier” (sec- Barely one decade after the discovery of the first Kuiper
tion 5), the inner Oort cloud must contain many more com- belt object (besides Pluto), the number of known KBOs is
ets than the outer Oort cloud to provide enough HTCs. By comparable to the number of LPCs that have been discov-
contrast, in the models of DLDW, the inner Oort cloud does ered in recorded history. Full-sky surveys will likely tilt the
not contain such a large population, nor is it particularly balance decisively in favor of the Kuiper belt in the near
flattened. This discrepancy suggests some deficiency in one future (Jewitt, 2004). This disparity is, of course, a conse-
of the models. For example, the inner Oort cloud may not quence of the much greater distance to the Oort cloud and
be the source of the HTCs, or the DLDW model may not the r –4 heliocentric brightness dependence for distant bodies
be realistic enough because it neglects processes that were seen in reflected light. Thus a 200-km-diameter body with an
important in the early solar system. apparent magnitude of 23 in the Kuiper belt at 40 AU would
The assumptions of the DLDW model are highly ideal- have a magnitude of 42 in the inner Oort cloud at 3000 AU,
ized. Most importantly, the formation of the Oort cloud and a more typical 2-km comet at 20,000 AU, assuming an
needs to be studied in the context of a realistic model for albedo of 0.04, would have a magnitude of 60. Thus direct
planet formation. That is, the planets were still forming dur- imaging of comets at Oort cloud distances will not be pos-
ing at least the early stages of the formation of the Oort sible in the foreseeable future.
cloud. Planetary migration in the early solar system (Fer- There is no substitute for just counting comets in the Oort
nández and Ip, 1984) appears to have been important in cloud. In principle, comets, especially in the inner cloud,
shaping the Kuiper belt (Malhotra, 1995; Gomes, 2003; could be detected when they occult stars (Bailey, 1976). G-
Levison and Morbidelli, 2003; Gomes et al., 2004), and the or K-type main-sequence stars at a distance of 1 kpc
same is likely true for the Oort cloud. Uranus and Neptune (roughly twice the distance to the stars in Orion’s belt) have
may even have formed in the Jupiter-Saturn region (Thommes visual magnitudes of ~15–17. If the brightness of a mil-
et al., 1999, 2002), likely changing the fraction of comets lion such stars (about 10% of the number within 1 kpc) can
that ended up in the Oort cloud (see section 2). be monitored, occultations by 30-km comets at a distance
Tremaine (1993), Gaidos (1995), Fernández (1997), of 3000 AU can be detected in principle (e.g., Axelrod et
Eggers et al. (1997, 1998), Eggers (1999), and Fernández al., 1992; Brown and Webster, 1997). The Taiwan-America
and Brunini (2000) have discussed star formation in dif- Occultation Survey (TAOS) project, which will search for
ferent galactic environments. These authors point out that occultations by KBOs, will soon come online (Roques and
the Sun may have formed in a denser environment than it Moncuquet, 2000; Cooray and Farmer, 2003; Cooray, 2003),
now occupies (i.e., in a molecular cloud or star cluster), and and detections of Oort cloud comets remain a long-term goal
found that a more tightly bound Oort cloud would form. for occultation surveys (C. Alcock, personal communica-
For example, Eggers (1999) modeled the formation of the tion, 2003).
Oort cloud, assuming that the Sun spent its first 20 m.y. in For the present, our best hope is to try to infer the struc-
a star cluster with an initial density of 1000 or 10 stars/pc3, ture of the Oort cloud from the orbital distribution of known
as compared to the current density of ~0.1 stars/pc3. The comets. This is a difficult exercise because of the numer-
resulting cloud is produced primarily by Jupiter and Saturn, ous biases affecting discovery (section 2.2), and most im-
and its density peaks at a heliocentric distance of 6000– portantly, because the “Jupiter barrier” severely limits the
7000 AU in the 10 stars/pc3 case or at <1000 AU in the number of new comets from the inner Oort cloud that come
1000 stars/pc3 case. After the cluster dispersed, Uranus and within about 10 AU of the Sun (section 3).
Neptune would have placed comets in the cloud in more Bailey (1983) finds that for a > 28,000 AU, the Oort
or less the same way as they do with the Sun in its current cloud has a density profile n(a) ∝ a–γ, with γ = 2.4 ± 0.2.
environment. This assumes that the probability of discovery per year for
If the Sun remained in a dense environment for too long, a comet with a perihelion distance q well interior to Jupiter’s
the resulting Oort cloud might not be stable, and the orbits orbit goes inversely as the comet’s orbital period, which is
of Uranus and Neptune would have become eccentric and/ plausible. However, Bailey’s fits are based on only 37 “new”
or inclined (Gaidos, 1995; Ida et al., 2000; Adams and comets, a subset of those discussed by Marsden et al. (1978),
Laughlin, 2001; Levison et al., 2004). Drag due to residual with well-determined (“Class I”) orbits and q > 2 AU. (The
gas from the solar nebula may have been important in the condition on perihelion distance is imposed in order to
formation of the Oort cloud (de la Fuente Marcos and de minimize unmodeled nongravitational effects.) At face
la Fuente Marcos, 2002; Higuchi et al., 2002). Collisions value, Bailey’s result implies an outer Oort cloud that is
may have been important in determining which regions of more centrally condensed than in Oort’s original model (γ ~
 Dones et al.: Oort Cloud Formation and Dynamics 169

1.5) and less centrally condensed than in DQT87 or DLDW, maker, 1983; Bailey and Stagg, 1988; Shoemaker et al.,
both of whom find γ ~ 3.5 in the outer cloud. However, 1990; Weissman, 1990b; McKinnon et al., 1997; Levison et
since systematic effects due to nongravitational forces, even al., 2002; Morbidelli et al., 2002; cf. Rickman et al., 2001).
for comets with q > 2 AU, and unknown observational bi- Zahnle et al. (2003) estimate that ~1% of the impacts on
ases might be important, it will be important to reevaluate Jupiter are produced by NICs, including both active and
Bailey’s result by using a more homogeneous dataset. dormant cometary impactors. However, this percentage is
To better constrain the Oort cloud, we need well-defined higher for distant satellites, because the NICs experience less
surveys that detect a large number of dynamically new gravitational focusing than do ecliptic comets. For example,
LPCs with perihelia beyond Saturn, i.e., with q > 10 AU. Zahnle et al. (2003) suggest that NICs produce about 30%
(By “comets,” we mean bodies in highly eccentric long- of the 10-km craters on Jupiter’s prograde irregular satel-
period orbits. Such bodies may or may not be active.) The lite Himalia.
typical energy perturbations produced on comets by Ura- The rate of impacts on a planet by LPCs is R = N(q)〈p〉,
nus and Neptune are 10–100 times smaller than those pro- where N(q) is the number of comets that pass perihelion
duced by Jupiter and Saturn (Everhart, 1968; Fernández, within distance q of the Sun per year, and 〈p〉 is the mean
1981; Weissman, 1985; Duncan et al., 1987), so comets impact probability of the comets with the planet per orbit
with q > 10 AU suffer no “Uranus barrier” or “Neptune bar- of the comet. The biggest uncertainty in determining im-
rier” to produce a bias against comets from the inner Oort pact rates is in the cumulative perihelion distribution, N(q).
cloud. The perihelion distribution is only well-constrained for
A key aspect of surveys is having a long enough obser- 0.5 AU < q < 2.5 AU; over this range the number of comets
vational arc to be certain that an object is a long-period per AU rises with q. Zahnle et al. (2003) assumed N(q) ∝ q2
comet. At present, there is only one known LPC with q > throughout the region of the giant planets. However, because
10 AU, comet C/2003 A2 (Gleason), which was discovered they are partly or entirely exterior to the “Jupiter barrier,”
during Spacewatch observations taken in January 2003. At the saturnian, uranian, neptunian, and Pluto/Charon systems
the time of discovery the comet’s magnitude was 20 and are also subject to impacts by comets that originate in the
its heliocentric distance was 11.5 AU, a record. The IAU inner Oort cloud (Bailey and Stagg, 1988; Weissman and
Circular reporting the discovery noted that the comet’s in- Stern, 1994). DLDW find N(q) ∝ q3 in the giant planets
clination was only 8°, and stated “It seems likely that the region (also see Fernández, 1982; Weissman, 1985). As a
object is a Centaur, showing cometary activity as (2060) = result of this steeper dependence on q, DLDW estimate that
95P/Chiron has shown near perihelion” (Gleason et al., LPCs could contribute some 10% of the present-day im-
2003). However, a later fit incorporating prediscovery ob- pacts on Saturn, Uranus, and Neptune, and could dominate
servations indicated that C/2003 A2 is apparently a bona the impact rate by comets on the irregular satellites of these
fide dynamically new comet (Green, 2003). planets. [For some irregular satellites, collisions with other
Planned surveys should discover many LPCs with peri- such satellites probably dominate the current rates (Nes-
helia beyond 10 AU. The Large Synoptic Survey Telescope vorný et al., 2003, 2004).]
(LSST) was endorsed as a recommended “major initiative” Unfortunately, it is not straightforward to place limits on
by the most recent U.S. Decadal Survey in Astronomy and the population of the Oort cloud with the observed impact
Astrophysics (National Research Council Astrophysics Sur- record. However, the existence of distant irregular satellites
vey Committee, 2001). This 6–8-m optical telescope would of the giant planets, with sizes as small as 1 km, does con-
survey much of the visible sky weekly down to 24th mag- strain the population of impactors that have traversed the
nitude, beginning about one decade from now. Its objectives planetary systems since the irregulars formed. Small satel-
include studies of small bodies in the solar system (Tyson, lites are easier to disrupt, and their orbital periods are so
2002). In the shorter term, Pan-STARRS, a system consisting long that they cannot reaccrete after a catastrophic disrup-
of four 1.8-m telescopes, is planning to begin operations tion event. Nesvorný et al. (2004) have used arguments of
by 2007. Jewitt (2004) estimates that Pan-STARRS will this sort to rule out some combinations of total mass and
discover at least 400 comets per year (albeit mostly eclip- size distribution for the residual disk of planetesimals that
tic comets), including many with large perihelia. It also may remained after the giant planets formed.
provide interesting constraints on the number of interstellar Finally, if a very strong comet shower takes place due
comets passing through the solar system. Horner and Evans to the passage of a solar-mass star through the inner Oort
(2002) note that the GAIA astrometric satellite, which is cloud, the Jupiter barrier is temporarily eliminated, and a
scheduled to be launched in 2010, is expected to cover about large flux of comets will enter the entire solar system, in-
200 LPCs each year. cluding the region of the terrestrial planets. The number of
The final approach we will discuss for constraining the comets expected to strike Earth during such a shower is pro-
population of the Oort cloud involves the impact history of portional to the number of comets in the inner Oort cloud,
the planets and their satellites. At present, ecliptic comets so the cratering record of Earth can be used to constrain
appear to dominate impacts with the giant planets and their the population of the inner cloud. During the Phanerozoic
inner satellites (Zahnle et al., 1998, 2003), while asteroids (the last 543 m.y.), about one or two major showers would
dominate on Earth and the other terrestrial planets (Shoe- be expected, given the known frequency at which stars pass
170 Comets II

near the Sun (section 3). If the population of the inner cloud 2004). Most of the planetesimals that once orbited the Sun
were greater than about 100 times the population of the outer were probably ejected from the solar system. If most stars
cloud, even a single very strong shower would produce form comet clouds in the same way the Sun did, detection
more craters than Earth’s record allows (Shoemaker, 1983; of bona fide interstellar comets is likely in the near future
Grieve and Shoemaker, 1994; Hughes, 2000), and most of (McGlynn and Chapman, 1989; Sen and Rama, 1993).
the known craters on Earth would have formed during a Millennia after mankind first wondered what comets were,
period lasting only a few million years. This constraint re- we are on the verge of glimpsing their home.
fers to craters tens of kilometers in diameter. There is some
evidence that LPC nuclei have a flatter (i.e., more top- Acknowledgments. We thank C. Alcock, W. Bottke, S.
heavy) size distribution than do asteroids (Shoemaker et al., Charnoz, A. Cooray, P. Dybczynski, V. Emel’yanenko, T. Lee, A.
1990; Levison et al., 2002; Weissman and Lowry, 2003), so Morbidelli, D. Nesvorný, P. Nurmi, J. Scalo, A. Stern, and K.
considering only the largest known craters during the last Zahnle for discussions, and M. Festou, J. Fernández, and an
anonymous reviewer for helpful comments. The abstract service
half-billion years on Earth might yield a tighter constraint.
of the NASA Astrophysics Data System was indispensable in the
As we noted in section 3, the Popigai and Chesapeake Bay
preparation of this chapter. We acknowledge grants from the
craters (~100 km and 85 km in diameter, respectively), do NASA Planetary Geology and Geophysics program (L.D. and
seem to be associated with a comet shower 36 m.y. ago P.R.W.), the NASA Origins of Solar Systems Program (H.F.L.),
(Farley et al., 1998). and NSERC (M.J.D.). This work was performed in part at the Jet
Propulsion Laboratory under contract with NASA.
6. SUMMARY
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 Morbidelli and Brown: Kuiper Belt and Evolution of Solar System 175

The Kuiper Belt and the Primordial

Evolution of the Solar System
A. Morbidelli
Observatoire de la Côte d’Azur

M. E. Brown
California Institute of Technology

We discuss the structure of the Kuiper belt as it can be inferred from the first decade of
observations. In particular, we focus on its most intriguing properties — the mass deficit, the
inclination distribution, and the apparent existence of an outer edge and a correlation among
inclinations, colors, and sizes — which clearly show that the belt has lost the pristine structure
of a dynamically cold protoplanetary disk. Understanding how the Kuiper belt acquired its
present structure will provide insight into the formation of the outer planetary system and its
early evolution. We critically review the scenarios that have been proposed so far for the pri-
mordial sculpting of the belt. None of them can explain in a single model all the observed
properties; the real history of the Kuiper belt probably requires a combination of some of the
proposed mechanisms.

1. INTRODUCTION A primary goal of this chapter is to present the orbital

structure of the Kuiper belt as it stands based on the current
When Edgeworth and Kuiper conjectured the existence observations. We start in section 2 by presenting the various
of a belt of small bodies beyond Neptune — now known subclasses that constitute the transneptunian population.
as the Kuiper belt — they certainly were imagining a disk Then in section 3 we describe some striking properties of
of planetesimals that preserved the pristine conditions of the the population, such as its mass deficit, inclination excita-
protoplanetary disk. However, since the first discoveries of tion, radial extent and a puzzling correlation between or-
transneptunian objects, astronomers have realized that this bital elements and physical properties. In section 4 we
picture is not correct: The disk has been affected by a num- finally review the models that have been proposed so far
ber of processes that have altered its original structure. The on the primordial sculpting of the Kuiper belt. Some of
Kuiper belt may thus provide us with many clues to under- these models date from the very beginning of Kuiper belt
stand what happened in the outer solar system during the science, when only a handful of objects were known, and
primordial ages. Potentially, the Kuiper belt might teach us have been at least partially invalidated by the new data.
more about the formation of the giant planets than the plan- Paradoxically, however, as the data increase in number and
ets themselves. And, as in a domino effect, a better knowl- quality, it becomes increasingly difficult to explain all the
edge of giant-planet formation would inevitably boost our properties of the Kuiper belt in the framework of a single
understanding of the subsequent formation of the terrestrial scenario. The conclusions are in section 5.
planets. Consequently, Kuiper belt research is now consid-
ered a top priority in modern planetary science. 2. TRANSNEPTUNIAN POPULATIONS
A decade after the discovery of 1992 QB1 (Jewitt and
Luu, 1993), we now know 770 transneptunian objects (semi- The transneptunian population is “traditionally” subdi-
major axis a > 30 AU) (all numbers are as of March 3, vided in two subpopulations: the scattered disk and the Kui-
2003). Of these, 362 have been observed during at least two per belt. The definition of these subpopulations is not uni-
oppositions, and 239 during at least three oppositions. Ob- form, as the Minor Planet Center and various authors often
servations at two and three oppositions are necessary for use slightly different criteria. Here we propose and discuss
the Minor Planet Center to compute the objects’ orbital ele- a categorization based on the dynamics of the objects and
ments with moderate and good accuracy respectively. There- their relevance to the reconstruction of the primordial evo-
fore, the transneptunian population is gradually taking shape, lution of the outer solar system.
and we can start to seriously examine the Kuiper belt struc- In principle, one would like to call the Kuiper belt the
ture and learn what it has to teach us. We should not forget, population of objects that, even if characterized by chaotic
however, that our view of the transneptunian population is dynamics, do not suffer close encounters with Neptune and
still partial and is strongly biased by a number of factors, thus do not undergo macroscopic migration in semimajor
some of which cannot be easily modeled. axis. Conversely, the bodies that are transported in semi-

175
176 Comets II

Fig. 1. The orbital distribution of multiopposition transneptunian bodies, as of March 3, 2003. Scattered disk bodies are represented
as a cross, classical Kuiper belt bodies as dots, and resonant bodies as stars. In the absence of long-term numerical integrations of the
evolution of all the objects and because of the uncertainties in the orbital elements, it is possible that some bodies could have been
misclassified. The figure should thus be considered as an indicative representation of the various subgroups that compose the
transneptunian population. The dotted curve denotes q = 30 AU. The vertical solid lines mark the locations of the 3:4, 2:3, and 1:2
mean-motion resonances with Neptune. The orbit of Pluto is represented by a crossed circle.

major axis by close and distant encounters with Neptune gions of the (a, e, i) space with 32 < a < 50 AU that can
would constitute the scattered disk. The problem with pre- lead to a Neptune-encountering orbit within 4 G.y. Because
cisely dividing the transneptunian population into Kuiper dynamics are reversible, these are also the regions that can
belt or scattered disk is related to timescale. On what time- be visited by a body after having encountered the planet.
scale should we see semimajor axis migration resulting in Therefore, according to our definition, they constitute the
the classification of an object in the scattered disk? The scattered disk. For the a > 50 AU region, we use the results
question is relevant, because it is possible for bodies trapped by Levison and Duncan (1997) and Duncan and Levison
in resonances to significantly change their perihelion dis- (1997), who followed for a time span of another 4 G.y. the
tance and pass from a scattering phase to a nonscattering evolutions of the particles that encountered Neptune in
phase (and vice versa) numerous times over the age of the Duncan et al. (1995). Despite the fact that the initial condi-
solar system. tions did not cover all possible configurations, we can rea-
For this reason, we prefer to link the definition of the sonably assume that these integrations cumulatively show
scattered disk to its formation mechanism. We refer to the the regions of the orbital space that can be possibly visited
scattered disk as the region of orbital space that can be by bodies transported to a > 50 AU by Neptune encounters.
visited by bodies that have encountered Neptune within a Again, according to our definition, these regions constitute
Hill’s radius at least once during the age of the solar sys- the scattered disk.
tem, assuming no substantial modification of the planetary In Fig. 1 we show the (a, e, i) distribution of the trans-
orbits. We then refer to the Kuiper belt as the complement neptunian bodies that have been observed during at least
of the scattered disk in the a > 30 AU region. two oppositions. The bodies that belong to the scattered disk
To categorize the observed transneptunian bodies into according to our criterion are represented as crosses, while
scattered disk and Kuiper belt, we refer to previous work Kuiper belt bodies are represented by dots and stars (see
on the dynamics of transneptunian bodies in the framework explanation of the difference below).
of the current architecture of the planetary system. For the We believe that our definition of scattered disk and
a < 50 AU region, we use the results by Duncan et al. (1995) Kuiper belt is meaningful for what concerns the major goal
and Kuchner et al. (2002), who numerically mapped the re- of Kuiper belt science, i.e., to reconstruct the primordial
 Morbidelli and Brown: Kuiper Belt and Evolution of Solar System 177

evolution of the outer solar system. In fact, all bodies in tions, this is the one whose orbital properties are the most
the solar system must have been formed on orbits with very similar to those expected for the Kuiper belt prior to the
small eccentricities and inclinations, typical of an accretion first discoveries. We note, however, that the classical popu-
disk. In the framework of the current architecture of the lation is not that “classical.” Although moderate, the eccen-
solar system, the current orbits of scattered disk bodies tricities are larger than those that should characterize a proto-
might have started with quasicircular orbits in Neptune’s planetary disk. Moreover, several bodies have very large
zone by pure dynamical evolution. Therefore, they do not inclinations (see section 3.2). Finally, the total mass is only
provide any relevant clue to uncover the primordial archi- a small fraction of the expected pristine mass in that region
tecture. The opposite is true for the orbits of the Kuiper belt (section 3.1). All these elements indicate that the classical
objects with nonnegligible eccentricity and/or inclination. belt has also been affected by some primordial excitation
Their existence reveals that some excitation mechanism that and depletion mechanism(s).
is no longer at work occurred in the past (see section 4).
In this respect, the existence of Kuiper belt bodies with 3. STRUCTURE OF THE KUIPER BELT
a > 50 AU on highly eccentric orbits is particularly impor-
tant (five objects in Fig. 1, although our classification is un- 3.1. Missing Mass of the Kuiper Belt
certain for the reasons explained in the figure caption).
Among them, 2000 CR105 (a = 230 AU, perihelion distance The original argument followed by Kuiper (1951) to con-
q = 44.17 AU, and inclination i = 22.7°) is a challenge by jecture the existence of a band of small planetesimals be-
itself concerning the explanation of its origin. We call these yond Neptune was related to the mass distribution in the
objects extended scattered disk objects for two reasons: outer solar system. The minimum mass solar nebula inferred
(1) they do not belong to the scattered disk according to from the total planetary mass (plus lost volatiles) smoothly
our definition but are very close to its boundary and (2) a declines from the orbit of Jupiter until the orbit of Neptune
body of ~300 km like 2000 CR105 presumably formed much (see Fig. 2); why should it abruptly drop beyond the last
closer to the Sun, where the accretion timescale was suffi- planet? However, while Kuiper’s conjecture on the exist-
ciently short (Stern, 1996), implying that it has been sub- ence of a transneptunian belt is correct, the total mass in
sequently transported in semimajor axis until reaching its the 30–50-AU range inferred from observations is two or-
current location. This hypothesis suggests that in the past ders of magnitude smaller than the one he expected.
the true scattered disk extended well beyond its present Kuiper’s argument is not the only indication that the mass
boundary in perihelion distance. Given that the observa- of the primordial Kuiper belt had to be significantly larger.
tional biases rapidly become more severe with increasing
perihelion distance and semimajor axis, the currently known
extended scattered disk objects may be the tip of the ice-
berg, e.g., the emerging representatives of a conspicuous
population, possibly outnumbering the scattered disk popu-
lation (Gladman et al., 2002).
In addition to the extended scattered disk, we distinguish
two other subpopulations of the Kuiper belt. We refer to
the Kuiper belt bodies that are located in some major mean-
motion resonance with Neptune [essentially the 3:4, 2:3,
and 1:2 resonances (star symbols in Fig. 1) but also the 2:5
resonance (see Chiang et al., 2003)] as the resonant popu-
lation. It is well known that mean-motion resonances offer
a protection mechanism against close encounters with the
resonant planet (Cohen and Hubbard, 1965). For this rea-
son, the resonant population — which, as part of the Kuiper
belt, by definition must not encounter Neptune within the
age of the solar system — can have perihelion distances
much smaller than the other Kuiper belt objects, and even
Neptune-crossing orbits (q < 30 AU) as in the case of Pluto. Fig. 2. The mass distribution of the solar nebula inferred from
The bodies in the 2:3 resonance are often called Plutinos the masses of the planets augmented by the mass needed to bring
because of the analogy of their orbit with that of Pluto. We the observed material to solar composition (data from Lewis,
1995). The surface density in the Kuiper belt has been computed
call the collection of Kuiper belt objects with a < 50 AU
assuming a current mass of ~0.1 M (Jewitt et al., 1996; Chiang
that are not in any notable resonant configuration the clas-
and Brown, 1999; Trujillo et al., 2001; Gladman et al., 2001) in
sical belt. Because they are not protected from close en- the 42–48-AU annulus, and scaling the result by a factor of 70 in
counters with Neptune by any resonance, the stability cri- order to account for the inferred primordial local ratio between
terion confines them to the region with small to moderate volatiles and solids. The estimate of the total mass in the Kuiper
eccentricity, typically on orbits with q > 35 AU. The adjec- belt overwhelms that of Pluto, but still does not bring the mass to
tive “classical” is justified because, among all subpopula- the extrapolation of the ~r –3/2 line.
178 Comets II

Further evidence for a massive primordial Kuiper belt was distribution had to be steep enough that essentially all the
uncovered by Stern (1995), who found that the objects cur- mass was carried by these small bodies, while the number
rently in the Kuiper belt were incapable of having formed of bodies larger than ~100 km had to be basically equal to
in the present environment: Collisions are sufficiently in- the present number. Although this outcome seems consis-
frequent that 100-km objects cannot be built by pairwise tent with the suggestions of the accretional models, there
accretion of the current population over the age of the so- is circumstantial (but nonetheless compelling) evidence sug-
lar system. Moreover, owing to the large eccentricities and gesting the primordial existence of a much larger number
inclinations of Kuiper belt objects — and consequently to of large bodies (Stern, 1991). The creation of Pluto-Charon
their high encounter velocities — collisions that do occur likely required the impact of two approximately similar-
tend to be erosive rather than accretional, making bodies sized bodies that would be the two largest currently known
smaller rather than larger. Stern suggested that the resolu- bodies in the Kuiper belt. The probability that the two larg-
tion of this dilemma is that the primordial Kuiper belt was est bodies in the belt would collide and create Pluto-Charon
both more massive and dynamically colder, so that more is vanishingly small, arguing that many bodies of this size
collisions occurred, and they were gentler and therefore must have been present and subsequently disappeared. Simi-
generally accretional. larly, the existence of Triton and the large obliquity of Nep-
Following this idea, detailed modeling of accretion in a tune are best explained by the existence at one time of many
massive primordial Kuiper belt was performed by Stern large bodies being scattered through the Neptune system.
(1996), Stern and Colwell (1997a,b), and Kenyon and Luu The elimination of these large bodies (if they existed in the
(1998, 1999a,b). While each model includes different as- Kuiper belt) could not be due to the collisional activity, but
pects of the relevant physics of accretion, fragmentation, requires a dynamical explanation.
and velocity evolution, the basic results are in approximate Another constraint against the collisional grinding sce-
agreement. First, with ~10 M (Earth mass) or more of solid nario is provided by the preservation of the binary Kuiper
material in an annulus from about 35 to 50 AU on very low belt objects. The Kuiper belt binaries have large separations,
eccentricity orbits (e ≤ 0.001), all models naturally produce so it can be easily computed that the impact on the satel-
a few objects on the order of the size of Pluto and approxi- lite of a projectile 100 times less massive with a speed of
mately the right number of ~100-km objects, on a timescale 1 km/s would give the former an impulse velocity sufficient
ranging from several 107 to several 108 yr. The models sug- to escape to an unbound orbit. If the collisional activity was
gest that the majority of mass in the disk was in bodies strong enough to cause an effective reduction of the overall
approximately 10 km and smaller. The accretion stopped mass of the Kuiper belt, these kinds of collisions had to be
when the formation of Neptune or other dynamical phe- extremely common, so we would not expect a significant
nomena (see section 4) began to induce eccentricities and fraction of widely separated binary objects in the current
inclinations in the population high enough to move the col- remaining population (Petit and Mousis, 2003.)
lisional evolution from the accretional to the erosive regime Understanding the ultimate fate of the 99% of the ini-
(Stern, 1996). A massive and dynamically cold primordial tial Kuiper belt mass that is no longer in the Kuiper belt is
Kuiper belt is also required by the models that attempt to the first step in reconstructing the history of the outer solar
explain the formation of the observed numerous binary system.
Kuiper belt objects (Goldreich et al., 2002; Weidenshilling,
2002). 3.2. Excitation of the Kuiper Belt
Therefore, the general formation picture of an initial
massive Kuiper belt appears secure. However, a fundamen- An important clue to the history of the early outer solar
tal question remains to be addressed: How did the initial system is the dynamical excitation of the Kuiper belt. While
mass disappear? Collisions can grind bodies down to dust eccentricities and inclinations of resonant and scattered
particles, which are subsequently transported away from the objects are expected to have been affected by interactions
belt by radiation pressure and/or Poynting Robertson drag, with Neptune, those of the classical objects should have
causing a net mass loss. The major works on the collisional suffered no such excitation. Nonetheless, the confirmed
erosion of a massive primordial belt have been done by classical belt objects have an inclination range up to at least
Stern and Colwell (1997b) and Davis and Farinella (1997, 32° and an eccentricity range up to 0.2, significantly higher
1998), achieving similar conclusions (for a review, see than expected from a primordial disk, even accounting for
Farinella et al., 2000). As long as the planetesimal disk was mutual gravitational stirring.
characterized by small eccentricities and inclinations, the The observed distributions of eccentricities and inclina-
collisional activity could only moderately reduce the mass tions in the Kuiper belt are highly biased. High-eccentricity
of the belt. However, when the eccentricities and inclina- objects have closer approaches to the Sun and thus become
tions became comparable to those currently observed, bod- brighter and more easily detected. High-inclination objects
ies smaller than 50–100 km in diameter could be effectively spend little time at the low latitudes at which most surveys
destroyed. The total amount of mass loss depends on the take place, while low-inclination objects spend zero time
primordial size distribution. To reduce the total mass from at the high latitudes where some searches have occurred.
30 M to a fraction of an Earth mass, the primordial size (Latitude and inclination are defined with respect to the
 Morbidelli and Brown: Kuiper Belt and Evolution of Solar System 179

invariable plane, which is a better representation for the

plane of the Kuiper belt than is the ecliptic.)
Determination of the eccentricity distribution of the
Kuiper belt requires disentanglement of eccentricity and
semimajor axis, which is only possible for objects with well-
determined orbits for which a well-characterized sample of
sufficient size is not yet available. Determination of the
inclination distribution, however, is much simpler because
the inclination of an object is well determined even after a
small number of observations, and the latitude of discov-
ery of each object is a known quantity. Using these facts,
Brown (2001) developed general methods for debiasing
object discoveries to discern the underlying inclination dis-
tribution. The simplest method removes the latitude-of-dis-
covery biases by considering only objects discovered within
1° of the invariable plane equator and weights each object
by sin(i), where i is the inclination of each object, to account Fig. 3. The inclination distribution of the classical Kuiper belt.
for the proportional fraction of time that objects of differ- The points with error bars show the model-independent estimate
ent inclination spend at the equator (strictly speaking, one constructed from a limited subset of confirmed classical belt bod-
should use only objects found precisely at the equator; ies, while the smooth line shows the best-fit two-population model.
expanding to 1° around the equator greatly increases the
sample size while biasing the sample slightly against ob-
jects with inclinations between 0° and 1°). An important
decision to be made in constructing this inclination distribu- they are both valid from 6° to 10° and retrieve a correctly
tion is the choice of which objects to include in the sample. relatively calibrated high-inclination distribution.
One option is to use only confirmed classical objects, i.e., Brown (2001) developed a more general method to use
those that have been observed at least two oppositions and all objects simultaneously by comparing inclinations of all
for which the orbit is reasonably assured of fitting the defi- objects to those found from Monte Carlo observations of
nition of the classical Kuiper belt as defined above. The simple model inclination distributions at the latitudes of
possibility exists that these objects are biased in some way discovery. The simplest reasonable model distribution has
against unusual objects that escape recovery at a second a form where f(i)di, the number of objects between incli-
opposition because of unexpected orbits, but we expect that nations i and i + di, is proportional to sin(i) exp(–i2/2σ2) di
this bias is likely to be in the direction of underreporting where σ is a measure of the excitation of the population.
high-inclination objects. On the other hand, past experience The resonant and scattered objects are both well fit by this
has shown that if we use all confirmed and unconfirmed functional form with σ = 10° ± 2° and 20° ± 4° respectively.
classical bodies, we pollute the sample with misclassified The best single Gaussian fit for the confirmed classical belt
resonant and scattered objects, which generally have higher objects can be ruled out at a high level of confidence; the
inclinations and therefore artificially inflate the inclination observed inclination distribution of the classical Kuiper belt
distribution of the classical belt. We therefore chose to use is more complex than can be described by the simplest
only confirmed classical belt bodies, with the caveat that model. Guided by Fig. 3, we make the assumption that the
some high-inclination objects might be missing. Figure 3 inclination distribution between about 0° and 3° appears
shows the inclination distribution of the classical Kuiper belt adequately described by a single Gaussian times sine in-
derived from this method. This method has the advantage clination, and search for a functional form to describe the
that it is simple and model independent, but the disadvan- higher-inclination objects. The next simplest functional
tage that it makes no use of the information contained in form is one with a second Gaussian added to the distribu-
high-latitude surveys where most of the high-inclination tion: f(i)di = sin(i) [a1 exp(–i2/2σ12) + a2 exp(–i2/2σ22)]di.
objects are discovered. For example, the highest-inclination The best fit to the two-Gaussian model, found by model-
classical belt body found within 1° of the equator has an ing the latitudes and inclinations of all confirmed classical
inclination of 10.1°, while an object with an inclination of belt objects, has parameters a1 = 96.4, a2 = 3.6, σ1 = 1.8, and
31.9° has been found at a latitude of 11.2°. The two high- σ2 = 12 and is shown in Fig. 3. For this model ~60% of the
inclination points in Fig. 3 attempt to partially correct this objects reside in the high-inclination population.
deficiency by using discoveries of objects between 3° and A clear feature of this modeled distribution is the pres-
6° latitude to define the high-inclination end of the inclina- ence of distinct high- and low-inclination populations. While
tion distribution, using equation (3) of Brown (2001). Obser- Brown (2001) concluded that not enough data existed at the
vations at these latitudes miss all objects with lower inclina- time to determine if the two populations were truly distinct
tions, but we can linearly scale the high-latitude distribution or if the model fit forced an artificial appearance of two
to match the low-latitude distribution in the region where populations, the larger amount of data now available, and
180 Comets II

shown in the model-independent analysis of Fig. 3, confirms

that the distinction between the populations is real. The
sharp drop around 4° is independent of any model, while
the extended distribution to 30° is demanded by the pres-
ence of objects with these inclinations.

3.3. Physical Evidence for Two Populations

in the Classical Belt

The existence of two distinct classical Kuiper belt popu-

lations, which we will call the hot (i > 4°) and cold (i < 4°)
classical populations, could be caused in one of two gen-
eral ways. Either a subset of an initially dynamically cold
population was excited, leading to the creation of the hot
classical population, or the populations are truly distinct and
formed separately. One manner in which we can attempt
to determine which of these scenarios is more likely is to Fig. 4. Color gradient vs. inclination in the classical Kuiper belt.
examine the physical properties of the two classical popu- Color gradient is the slope of the spectrum, in % per 100 nm, with
lations. If the objects in the hot and cold populations are 0% being neutral and large numbers being red. The hot and cold
physically different, it is less likely that they were initially classical objects have significantly different distributions of color.
part of the same population.
The first suggestion of a physical difference between the
hot and the cold classical objects came from Levison and scattered objects at the 99.8% and 99.9% confidence level
Stern (2001), who noted that the intrinsically brightest clas- respectively, while the hot classical population appears iden-
sical belt objects (those with lowest absolute magnitudes) tical in color to these other populations. The possibility
are preferentially found with high inclination. Trujillo and remains, however, that the colors of the objects, rather than
Brown (2003) have recently verified this conclusion in a being markers of different populations, are actually caused
bias-independent manner from a survey for bright objects by the different inclinations. Stern (2002), for example, has
that covered ~70% of the ecliptic and found many hot clas- suggested that the higher average impact velocities of the
sical objects but few cold classical objects. high-inclination objects will cause large-scale resurfacing
The second possible physical difference between hot and by fresh water ice, which could be blue to neutral in color. If
cold classical Kuiper belt objects is their colors, which re- this hypothesis were correct, however, we would also expect
lates (in an unknown way) to surface composition. Several to see correlations between colors and semimajor axis or
possible correlations between orbital parameters and color eccentricity, which also determine impact velocities. These
were suggested by Tegler and Romanishin (2000) and fur- correlations do not exist. We would also expect to see cor-
ther investigated by Doressoundiram et al. (2001). The issue relations between color and inclination within the hot and
was clarified by Trujillo and Brown (2002), who quantita- cold populations. Again, these correlations do not exist.
tively showed that for the classical belt, inclination, and no Finally, we would expect to see correlations between color
other independent orbital parameter, is correlated with color. and inclination or semimajor axis or eccentricity for all
In essence, the low-inclination classical objects tend to be populations, not just the classical belt objects. Once again,
redder than higher-inclination objects. Hainaut and Delsanti no such correlations exist. While collisional resurfacing of
(2002) have compiled a list of all published Kuiper belt bodies may indeed affect colors, there is clearly no causal
colors that more than doubles the sample of Trujillo and relationship between average impact velocity and color
Brown (2002). A plot of color vs. inclination for the classi- (Thébault and Doressoundiram, 2003). In summary, the
cal belt objects in this expanded sample (Fig. 4) confirms significant color and size differences between the hot and
the correlation between color and inclination. This expanded cold classical objects implies that these two populations are
sample also conclusively demonstrates that no other inde- physically different in addition to being dynamically dis-
pendent dynamical correlations occur, although the fact that tinct. A confirmation of the surface composition differences
the low-inclination red classical objects also have low ec- between the hot and cold populations could be made with
centricities, and therefore high perihelia, causes an appar- infrared reflectance spectroscopy, but to date no spectrum
ent correlation with perihelion distance as well. of a cold classical Kuiper belt object has been published.
More interestingly, we see that the colors naturally di-
vide into distinct low-inclination and high-inclination popu- 3.4. Radial Extent of the Kuiper Belt
lations at precisely the location of the divide between the
hot and cold classical objects. These populations differ at Another important property of interest for understand-
a 99.9% confidence level. Interestingly, the cold classical ing the primordial evolution of the Kuiper belt is its radial
population also differs in color from the Plutinos and the extent. While initial expectations were that the mass of the
 Morbidelli and Brown: Kuiper Belt and Evolution of Solar System 181

Kuiper belt should smoothly decrease with heliocentric dis-

tance — or perhaps even increase in number density by a
factor of ~100 back to the level of the extrapolation of the
minimum mass solar nebula beyond the region of Neptune’s
influence (Stern, 1996) — the lack of detection of objects
beyond about 50 AU soon began to suggest a dropoff in
number density (Dones, 1997; Jewitt et al., 1998; Chiang
and Brown, 1999; Trujillo et al., 2001; Allen et al., 2001).
It was often argued that this lack of detections was the con-
sequence of a simple observational bias caused by the ex-
treme faintness of objects at greater distances from the Sun
(Gladman et al., 1998), but Allen et al. (2001, 2002) showed
convincingly that for a fixed absolute magnitude, the num-
ber of objects with semimajor axis <50 AU was larger than
the number >50 AU and thus some density decrease was
present.
Determination of the magnitude of the density drop be- Fig. 5. The radial distribution of the Kuiper belt. The light line
yond 50 AU was hampered by the small numbers of ob- shows the observed number of transneptunian objects per AU
jects and thus weak statistics in individual surveys. Trujillo interval (× 10), while the thick bold line shows the true radial dis-
and Brown (2001) developed a method to use all detected tribution inferred from this observed distribution taking into ac-
objects to estimate a radial distribution of the Kuiper belt. count biases due to brightness, distance, and size of the object. All
discovered transneptunian objects are considered in this analysis,
The method relies on the fact that the heliocentric distance
regardless of their dynamical class.
(not semimajor axis) of objects, like the inclination, is well
determined in a small number of observations, and that
within ~100 AU surveys have no biases against discover-
ing distant objects other than the intrinsic radial distribu-
tion and the easily quantifiable brightness decrease with to 80 AU (where a 1000-km object would be magnitude
distance. Thus, at a particular distance, a magnitude m0 will 22.7). Changes in the maximum object size assumed, smax,
correspond to a particular object size s, but, assuming a are equivalent to changing the outer limit of the validity of
power-law differential size distribution, each detection of the analysis by 80 AU (s max/1000 km)1/2. Alternatively, one
an object of size s can be converted to an equivalent number could further restrict the magnitude limits considered to
n of objects of size s0 by n = (s/s0)q – 1 where q is the differ- limit the maximum size while maintaining validity to a par-
ential power-law size index. Thus the observed radial distri- ticular distance. Different choices of minimum and maxi-
bution of objects with magnitude m0, O(r,m0)dr can be con- mum diameters have little effect on the final result unless
verted to the true radial distribution of objects of size s0 by extreme values for the maximum are chosen.
The analysis clearly shows that the known Kuiper belt
q −1 is a localized increase in number density. Several implicit
r(r − 1)10( m − 24.55) /5
R(r, s0 )dr = O(r, m 0 )dr assumptions go into the above method, but only extreme
15.60s0 changes in these assumptions substantially change the re-
sults. For example, a change in the object size distribution
where albedos of 4% are assumed, but only apply as a scal- beyond 43 AU could mimic a drop in object number den-
ing factor. Measured values of q for the Kuiper belt have sity, but only if, by 50 AU, the distribution is so extreme that
ranged from 3.5 to 4.8 (for a review, see Trujillo and Brown, most of the mass is either in a few (undiscovered) large ob-
2001). We will assume the steepest currently proposed value jects or a large number of (too faint) small objects. A physi-
of q = 4.45 (Gladman et al., 2001), which puts the strongest cal reason for such a change is not apparent. Likewise, a
constraints on the existence of distant objects. lowering of albedo beyond 50 AU could make it appear as if
Figure 5 shows the total equivalent number of 100-km there were a drop in number density, but, again, such a low-
objects as a function of distance implied by the detection of ering is not physically motivated. A change in the inclina-
the known transneptunian objects. One small improvement tion distribution beyond 50 AU could have the effect of
has been made to the Trujillo and Brown (2001) method. hiding objects if they are concentrated in low-inclination
The power-law size distribution is only assumed to be valid orbits close to the invariable plane, but repeating the analy-
from 50 to 1000 km in diameter, corresponding to an ex- sis considering only objects found within 1° of the invari-
pected break in the power law at some small diameter able plane still shows the sharp drop. While changing these
(Kenyon and Luu, 1999a) and a maximum object’s size. The assumptions could indeed invalidate the analysis method
effect of this change is to only use objects between magni- above, the much simpler conclusion is that the number den-
tudes 22.7 and 24.8, which makes the analysis only valid sity of the Kuiper belt peaks strongly at 42 AU and quickly
from 30 (where a 50-km object would be magnitude 24.8) drops off beyond that point.
182 Comets II

While the Trujillo and Brown (2001) method is good at 42 AU. This distribution can be ruled out at the many-sigma
giving an indication of the radial structure of the Kuiper levels. Assuming that the surface density drops as some
belt where objects have been found, it is less useful for power law, we model a range of different distribution r –α
determining upper limits to the detection of objects where and find a best fit of α = 11 ± 4 where the error bars are
none have been found. A simple extension, however, allows 3σ. This radial decay function should presumably hold up
us to easily test hypothetical radial distributions against the to ~60 AU, beyond which we expect to encounter a much
known observations by looking at observed radial distribu- flatter distribution due to the scattered disk objects.
tions of all objects found at a particular magnitude m0 in- It has been conjectured that beyond some range of Nep-
dependent of any knowledge of how these objects were tune’s influence the number density of Kuiper belt objects
found. Assume a true radial distribution of objects R(r)dr could increase back up to the level expected for the mini-
and again assume the above power law differential size dis- mum mass solar nebula (Stern, 1996; see section 3.1). We
tribution and maximum size. For magnitudes between m and therefore model a case where the Kuiper belt from 42 to
m + dm, we can construct the expected observed radial distri- 60 AU falls off as r –11 but beyond that the belt reappears at
bution of all objects found at that magnitude, o(r,m)drdm, by a certain distance δ with a number density found by extrapo-
lating the r –3/2 power law from the peak density at 42 AU
−q + 1 and multiplying by 100 to compensate for the mass deple-
r(r − 1)10( m − 24.55)/5
o(r, m) drdm = R(r)dr dm tion of the classical belt (Fig. 6). Such a model of the ra-
15.6s 0 dial distribution of the Kuiper belt can be ruled out at the
3σ level for all δ less than 115 AU (around this distance
where r ranges from that where the object of brightness m biases due to the slow motions of these objects also become
has a size of 50 km to that where the object of brightness important, so few conclusions can be drawn from the cur-
m has a size of smax. The overall expected observed radial rent data about objects beyond this distance). If the model
distribution is then simply the sum of o(r,m) over the val- is slightly modified to make the maximum object mass
ues of m corresponding to all detected objects. We can then proportional to the surface density at a particular radius, a
apply a K-S test to determine the probability that the ob- 100-times resumption of the Kuiper belt can be ruled out
served radial distribution could have come from the mod- inside 94 AU. Similar models can be made where a gap in
eled radial distribution. We first apply this test to determine the Kuiper belt exists at the presently observed location but
the magnitude of the dropoff beyond 42 AU. Standard as- the belt resumes at some distance with no extra enhance-
sumptions about the initial solar nebula suggest a surface ment in number density. These models can be ruled out
density drop off of r –3/2. Figure 6 shows the observed ra- inside 60 AU at a 99% confidence level.
dial distribution of objects compared to that expected if the While all these results are necessarily assumption de-
surface density of objects dropped off as r –3/2 beyond pendent, several straightforward interpretations are appar-
ent. First, the number density of Kuiper belt objects drops
sharply from its peak at around 42 AU. Second, a distant
Kuiper belt with a mass approaching that of the minimum
mass solar nebula is ruled out inside at least ~100 AU. And
finally, a resumption of the Kuiper belt at a density of about
1% expected from a minimum mass solar nebula is ruled
out inside ~60 AU.

4. PRIMORDIAL SCULPTING OF
THE KUIPER BELT

The previous section makes it clear than the Kuiper belt

has lost its accretional disklike primordial structure, some-
time during the solar system history. The goal of modelers
is to find the scenario, or the combination of compatible
scenarios, that can explain how the Kuiper belt acquired the
structural properties discussed above. Achieving this goal
would probably shed light on the primordial architecture
of the planetary system and its evolution.
Fig. 6. The observed radial distribution of Kuiper belt objects
Several scenarios have been proposed so far. Some of the
(solid histogram) compared to observed radial distributions ex-
Kuiper belt properties discussed in section 3 were not yet
pected for models where the surface density of Kuiper belt ob-
jects decreases by r –3/2 beyond 42 AU (dashed curve), where the known when some of these scenarios have been first pre-
surface density decreases by r –11 beyond 42 AU (solid curve), and sented. Therefore in the following — going beyond the orig-
where the surface density at 100 AU increases by a factor of 100 inal analysis of the authors — we attempt a critical reevalua-
to the value expected from an extrapolation of the minimum mass tion of the scenarios, challenging them with all the aspects
solar nebula (dashed-dotted curve). enumerated in the previous section. We divide the proposed
 Morbidelli and Brown: Kuiper Belt and Evolution of Solar System 183

Fig. 7. Final distribution of the Kuiper belt bodies according to the sweeping resonances scenario (courtesy of R. Malhotra). The
simulation is done by numerical integrating, over a 200-m.y. timespan, the evolution of 800 test particles on initial quasicircular and
coplanar orbits. The planets are forced to migrate (Jupiter: –0.2 AU; Saturn: 0.8 AU; Uranus: 3 AU; Neptune: 7 AU) and reach their
current orbits on an exponential timescale of 4 m.y. Large solid dots represent “surviving” particles (i.e., those that have not suffered
any planetary close encounters during the integration time); small dots represent the “removed” particles at the time of their close
encounter with a planet. In the lowest panel, the solid line is the histogram of semimajor axis of the “surviving” particles; the dotted
line is the initial distribution.

scenarios in three groups: (1) those invoking sweeping reso- outward. Malhotra (1993, 1995) realized that, following
nances, which offer a view of gentle evolution of the pri- Neptune’s migration, the mean-motion resonances with
mordial solar system; (2) those invoking the action of mas- Neptune also migrated outward, sweeping the primordial
sive scatterers (lost planets or passing stars), which offer Kuiper belt until they reached their present position. From
an opposite view of violent and chaotic primordial evolu- adiabatic theory (Henrard, 1982), most of the Kuiper belt
tion; and (3) those aimed at building the Kuiper belt as the objects swept by a mean-motion resonance would have been
superposition of two populations with distinctive dynamical captured into resonance; they would have subsequently
histories, somehow combining the scenarios in groups (1) followed the resonance in its migration, while increasing
and (2). their eccentricity. This model accounts for the existence of
the large number of Kuiper belt objects in the 2:3 mean-
4.1. Resonance Sweeping Scenarios motion resonance with Neptune (and also in other reso-
nances) and explains their large eccentricities (see Fig. 7).
Fernández and Ip (1984) showed that, while scattering Reproducing the observed range of eccentricities of the
primordial planetesimals, Neptune should have migrated resonant bodies requires that Neptune migrated by 7 AU.
184 Comets II

Malhotra’s (1993, 1995) simulations also showed that the obtained a ratio closer to 3. Chiang and Jordan (2002) also
bodies captured in the 2:3 resonance can acquire large in- noted that the positions of the five potential 1:2 resonant
clinations, comparable to that of Pluto and other objects. objects are unusually located with respect to a reference
The mechanisms that excite the inclination during the cap- frame rotating with Neptune, which may also have impli-
ture process have been investigated in detail by Gomes cations for migration rates and capture mechanisms.
(2000). The author concluded that, although large inclina- The migration of secular resonances could also have con-
tions can be achieved, the resulting proportion between the tributed to the excitation of the eccentricities and inclina-
number of high-inclination vs. low-inclination bodies and tions of Kuiper belt bodies. Secular resonances occur when
their distribution in the eccentricity vs. inclination plane do the precession rates of the orbits of the bodies are in simple
not reproduce the observations very well. ratio with the precession rates of the orbits of the planets.
The mechanism of adiabatic capture into resonance re- There are several reasons to think that secular resonances
quires that Neptune’s migration happened very smoothly. could have been in different locations in the past and mi-
If Neptune had encountered a significant number of large grated to their current location at about 40–42 AU. A grad-
bodies (1 M or more), its jerky migration would have jeop- ual mass loss of the belt due to collisional activity, the
ardized capture into resonances. Hahn and Malhotra (1999), growth of Neptune’s mass, and Neptune’s orbital migration
who simulated Neptune’s migration using a disk of lunar- would have moved the secular resonance with Neptune’s
to martian-mass planetesimals, did not obtain any perma- perihelion outward. Levison et al. (personal communication,
nent capture. The precise constraints set by the capture proc- 1997) found that the Kuiper belt interior to 42 AU would
ess on the size distribution of the largest disk’s planetesimals have suffered a strong eccentricity excitation. However, the
have never been quantitatively computed, but they are likely quantitative simulations show that the orbital distribution
to be severe. of the surviving bodies in the 2:3 resonance would not be
In the mean-motion resonance sweeping model the ec- similar to the observed one: The eccentricities of most
centricities and inclinations of the nonresonant bodies are simulated bodies would range between 0.05 and 0.1, while
also excited by the passage of many weak resonances, but those of the observed Plutinos are between 0.1 and 0.3.
the excitation that does occur is too small to account for Also, in this model there is basically no eccentricity and
those observed (compare Fig. 7 with Fig. 1). Some other inclination excitation for the Kuiper belt bodies with a >
mechanism (like those discussed below) must also have 42 AU, in contrast with what is observed.
acted to produce the observed overall orbital excitation of The dissipation of the primordial nebula would also have
the Kuiper belt. The question of whether this other mecha- caused the migration of the secular resonances. Nagasawa
nism acted before or after the resonance sweeping and cap- and Ida (2000) showed that the secular resonances involv-
ture process is unresolved. Had it occurred afterward, it ing the precession rates of the perihelion longitudes would
would have probably ejected most of the previously cap- have migrated from beyond 50 AU to their current position
tured objects from the resonances (not necessarily a prob- during the nebula dispersion. This could have caused ec-
lem if the number of captured bodies was large enough). centricity excitation of the Kuiper belt in the 40–50 AU re-
Had it happened before, then the mean-motion resonances gion. In addition, if the midplane of the nebula was not
would have had to capture particles from an excited disk. orthogonal to the total angular momentum vector of the
Another long-debated question concerning the sweeping planetary system, a secular resonance involving the preces-
model is the relative proportion between the number of sion rates of the node longitudes would also have swept the
bodies in the 2:3 and 1:2 resonances. The original simula- Kuiper belt, causing inclination excitation. The magnitude
tions by Malhotra indicated that the population in the 1:2 of the eccentricity and inclination excitation depends on the
resonance should be comparable to — if not greater than — timescale of the nebula dissipation. A dissipation timescale
that in the 2:3 resonance. This prediction seemed to be in of ~107 yr is required in order to excite the eccentricities
conflict with the absence of observed bodies in the former up to 0.2–0.3 and the inclinations up to 20°–30°. But if Nep-
resonance at that time. Ida et al. (2000a) showed that the tune was at about 20 AU at the time of the nebula disappear-
proportion between the two populations is very sensitive to ance — as required by the mean-motion resonance sweep-
Neptune’s migration rate and that the small number of 1:2 ing model — the disspation timescale should have been
resonant bodies, suggested by the lack of observations, ~108 yr, suspiciously lengthy with respect to what is ex-
would just be indicative of a fast migration (105–106 yr pected from current theories and observations on the evolu-
timescale). Since then, five objects have been discovered tion of protoplanetary disks. A major failure of the model
in or close to the 1:2 resonance (given orbital uncertainties is that, because only one nodal secular resonance sweeps
it is not yet possible to guarantee that all of them are really the belt, all the Kuiper belt bodies acquire orbits with com-
inside the resonance). There is no general consensus on the parably large inclinations. In other words, the model does
debiased ratio between the populations in the 2:3 and 1:2 not reproduce the observed spread of inclinations, nor their
resonances, because the debiasing is necessarily model- bimodal distribution. No correlation between inclination and
dependent and the current data on the population of the 1:2 size or color can be explained either. The same is not true
resonance are sparse. Trujillo et al. (2001) estimated a 2:3 for the eccentricities, because the belt is swept by several
to 1:2 ratio close to 1/2, while Chiang and Jordan (2002) perihelion resonances, which causes a spread in the final
 Morbidelli and Brown: Kuiper Belt and Evolution of Solar System 185

Fig. 8. Snap shots of the Kuiper belt under the scattering action of a 1-M planetesimal, itself evolving in the scattered disk. The
bold and the dash curves denote q = 30 AU and q = 35 AU respectively. The latter approximately defines the present limit for stability
in the Kuiper belt beyond 42 AU, and therefore marks the transition from the classical belt to the scattered disk. The test particles
(initially 500, uniformly distributed on circular and coplanar orbits between 35 and 55 AU) are plotted as an asterisk if q > 35 AU,
and as a cross otherwise. Neptune and the scattered planetesimal are shown by open circles. From Petit et al. (1999).

values. The secular resonance sweeping model cannot ex- inner belt (a < 40 AU) less than 1% of the bodies are found
plain the existence of significant populations in mean-mo- on what would become “stable orbits” once the massive
tion resonances, so that the mean-motion resonance sweep- planetesimal is dynamically removed. The depletion factor
ing model would still need to be invoked. in the 40–47 AU region is 74% after 20 m.y., 91% after
None of the models discussed above can explain the 50 m.y., and 96% after 100 m.y. This would completely
existence of the edge of the belt at ~50 AU. explain the mass deficit of the current belt. However, be-
yond 50 AU, ~50% of the original test particles are found
4.2. Scattering Scenarios on “stable orbits” (q > 35 AU) after 100 m.y., which is in-
consistent with the observed “edge.” In general terms, this
A radically different view has been proposed by Mor- model implies a quite steep positive gradient of the num-
bidelli and Valsecchi (1997), who first proposed that mas- ber density of bodies vs. semimajor axis, which is not ob-
sive Neptune scattered planetesimals (mass on the order of served in the real population. In particular, the relative
1 M ), temporarily on Kuiper belt-crossing orbits, could population in the 2:3 resonance would be much smaller than
have excited by close encounters the eccentricities and in- that (4% of the classical belt population) claimed from
clinations of the majority of Kuiper belt objects. This idea observations by Trujillo et al. (2001). In Petit et al. (1999)
has been investigated in details by Petit et al. (1999), who simulations the median eccentricity and inclination of the
made direct numerical simulations of the effects of scattered survivors after 100 m.y. are 0.19 and 8.6° in the 40–47 AU
massive planetesimals on test particles representing the ini- region and 0.27 and 7.4° beyond 47 AU. If the eccentricity
tially dynamically cold Kuiper belt. Figure 8 shows snap- distribution correctly reproduces the observations, the in-
shots of the status of the Kuiper belt after 20, 50, and clination distribution is not bimodal, and completely misses
100 m.y. respectively of evolution of an Earth-mass plan- objects with inclination larger than 20°, in contradiction
etesimal in the scattered disk. The test particles (initially with the observations. No correlation between inclination
500) were assumed at start on circular and coplanar orbits and colors could be explained within the framework of this
between 35 and 55 AU. The simulation shows that in the model.
186 Comets II

A variant of the Petit et al. scenario has been invoked excited to Neptune-crossing orbit, then Neptune would have
by Brunini and Melita (2002) to explain the apparent edge interacted with the full 50-M disk and therefore would
of the Kuiper belt at 50 AU. They showed with numerical have migrated much further. [This fact was not noticed by
simulations that a Mars-sized body residing for 1 G.y. on the simulations of Petit et al. (1999) and Brunini and Melita
an orbit with a ~ 60 AU and e ~ 0.15–0.2 could have scat- (2002), because the former considered a Kuiper belt of
tered into Neptune-crossing orbits most of the Kuiper belt massless particles and the latter a Kuiper belt whose total
bodies originally in the 50–70 AU range, leaving this re- mass was only ~1 M .] To limit Neptune’s migration at
gion strongly depleted and dynamically excited. Such a 30 AU, the total mass of the disk, including the Kuiper belt,
massive body should have been a former Neptune-scattered should have been significantly smaller. Our simulations
planetesimal that decoupled from Neptune due to the dy- show that even a disk of 15 M between 10 and 50 AU,
namical friction exerted by the initially massive Kuiper belt. once excited to Neptune-crossing orbit, would drive Nep-
The orbital distribution inside ~50 AU is not severely af- tune too far. Therefore, the scenario of a massive body scat-
fected by the massive planetesimal once on its decoupled tered by Neptune through the Kuiper belt is viable only if
orbit at a ~ 60 AU (see also Melita et al., 2002). However, the primordial mass of the belt was significantly smaller than
a strong dynamical excitation could be obtained during the usually accepted (accounting only for a few Earth masses).
transfer phase, when the massive planetesimal was trans- Motivated by the observation that the eccentricity of the
ported by Neptune encounters toward a ~ 60 AU, similar classical belt bodies on average increases with semimajor
to what happens in the Petit et al. (1999) simulations. Some axis (a fact certainly enhanced by the observational biases,
of the simulations by Brunini and Melita (2002) that in- which strongly favor the discovery of bodies with small
clude this transfer phase lead to an (a, e) distribution that perihelion distances), Ida et al. (2000b) suggested that the
is perfectly consistent with what is currently observed in structure of the classical belt records the footprint of the
the classical belt in terms of mass depletion, eccentricity close encounter with a passing star. In that paper and in the
excitation, and outer edge (see, e.g., their Fig. 10). The followup work by Kobayashi and Ida (2001), the resulting
corresponding inclination distribution is not explicitely dis- eccentricities and inclinations were computed as a function
cussed, but it is less excited than in the Petit et al. (1999) of a/D, where a is the original body’s semimajor axis and
scenario (M. Melita, personal communication, 2002). Simi- D is the heliocentric distance of the stellar encounter, for
larly, a correlation between inclination and size or color various choices of the stellar parameters (inclination, mass,
cannot be reproduced by this mechanism, and a distinctive and eccentricity). The eccentricity distribution in the clas-
Plutino population is not formed. Finally, our numerical sical belt suggested to the authors a stellar encounter at
simulations show that a 1-M planet in the Kuiper belt about ~150 AU. The same parameters, however, do not lead
cannot transport bodies up to 200 AU or more by gravita- to an inclination excitation comparable to the observed one.
tional scattering. Therefore, neither the Petit et al. (1999) The latter would require a stellar passage at ~100 AU or
scenario nor that of Brunini and Melita (2002) can explain less. From Kobayashi and Ida simulations we argue that a
the origin of the orbit of objects such as 2000 CR105. bimodal inclination distribution could be possibly obtained,
A potential problem of the Brunini and Melita scenario but a quantitative fit to the debiased distribution discussed
is that, once the massive body is decoupled from Neptune, in section 3.2 has never been attempted. A stellar encoun-
there are no evident dynamical mechanisms that would ter at ~100 AU would make most of the classical belt bod-
ensure its later removal from the system. In other words, ies so eccentric to intersect the orbit of Neptune. Therefore,
the massive body should still be present, somewhere in the it would explain not only the dynamical excitation of the
~50–70-AU region. A Mars-sized body with 4% albedo at belt (although a quantitative comparison with the observed
70 AU would have apparent magnitude brighter than 20, so distributions has never been done) but also its mass deple-
that, if its inclination is small (i < 10°), as expected if the tion, but would encounter the same problem discussed about
body got trapped in the Kuiper belt by dynamical friction, concerning Neptune’s migration.
it is unlikely that it escaped detection in the numerous wide- Melita et al. (2002) showed that a stellar passage at about
field ecliptic surveys that have been performed up to now, 200 AU would be sufficient to explain the edge of the clas-
and in particular in that led by Trujillo and Brown (2003). sical belt at 50 AU. An interesting constraint on the time at
Another severe problem, for both the Petit et al. (1999) which such an encounter occurred is set by the existence
and Brunini and Melita (2002) scenarios — as well as for of the Oort cloud. Levison et al. (2003) show that the en-
any other scenario that attempts to explain the mass deple- counter had to occur much earlier than ~10 m.y. after the
tion of the Kuiper belt by the dynamical ejection of a sub- formation of Uranus and Neptune, otherwise most of the
stantial fraction of Kuiper belt bodies to Neptune-crossing existing Oort cloud would have been ejected to interstellar
orbit — is that Neptune would have migrated well beyond space and many of the planetesimals in the scattered disk
30 AU. In Hahn and Malhotra (1999) simulations, a 50 M would have had their perihelion distance lifted beyond Nep-
disk between 10 and 60 AU drives Neptune to ~30 AU. In tune, decoupling from the planet. As a consequence, the ex-
this process, Neptune interacts only with the mass in the tended scattered disk population, with a > 50 AU and 40 <
10–35-AU disk (about 25 M ), and a massive Kuiper belt q < 50 AU, would have had a mass comparable or larger
remains beyond Neptune. But if the Kuiper belt had been than that of the resulting Oort cloud, hardly compatible with
 Morbidelli and Brown: Kuiper Belt and Evolution of Solar System 187

the few detections of extended scattered disk objects per- could be permanently trapped in the Kuiper belt. Thommes
formed up to now. An encounter with a star during the first et al. (1999) proposed a radical view of the primordial ar-
million years from planetary formation is a likely event if chitecture of our outer solar system in which Uranus and
the Sun formed in a stellar cluster (Bate et al., 2003). At Neptune formed in the Jupiter-Saturn zone. In their simu-
such an early time, presumably the Kuiper belt objects were lations, Uranus and Neptune were rapidly scattered outward
not yet fully formed (Stern, 1996; Kenyon and Luu, 1998). by Jupiter, where the interaction with the massive disk of
In this case, the edge of the belt would be at a heliocentric planetesimals damped their eccentricities and inclinations
distance corresponding to a postencounter eccentricity ex- by dynamical friction; as a consequence, the planets escaped
citation of ~0.05, a threshold value below which collisional from the scattering action of Jupiter before ejection on hy-
damping is efficient and accretion can recover, and beyond perbolic orbit could occur. In about 50% of the cases, the
which the objects rapidly grind down to dust (Kenyon and final states resembled the current structure of the outer solar
Bromley, 2002). The edge-forming stellar encounter could system, with four planets roughly at the correct locations.
not be responsible for the origin of the peculiar orbit of In this scenario Neptune experienced a high-eccentricity
2000 CR105. In fact, such a close encounter would also pro- phase lasting for a few million years, during which its aph-
duce a relative overabundance of bodies with perihelion dis- elion distance was larger than the current one. The planetesi-
tance similar to that of 2000 CR105 but with semimajor axis mals scattered by Neptune during the dynamical friction
in the 50–200-AU range. These bodies have never been dis- process therefore formed a scattered disk that extended well
covered despite the more favorable observational biases. In beyond its current perihelion distance boundary. When Nep-
order that only bodies with a > 200 AU have their perihe- tune’s eccentricity decreased down to its present value, the
lion distance lifted, a second stellar passage at about 800 AU large-q part of the scattered disk became “fossilized,” be-
is required (Morbidelli and Levison, 2003). Interestingly, ing unable to closely interact with Neptune again. This sce-
from the analysis of the Hipparcos data, Garcia-Sanchez nario therefore explains how a population of bodies, origi-
et al. (2001) concluded that, with the current stellar envi- nally formed in the inner part of the disk, could be trapped
ronment, the closest encounter with a star during the age in the classical belt. However, the inclination excitation of
of the solar system would be at ~900 AU. this population, although relevant, is smaller than that of
the observed hot population. This is probably due to the fact
4.3. Scenarios for a Two-Component Kuiper Belt that Neptune’s eccentricity is rapidly damped, so that the
particles undergo Neptune’s scattering action for only a few
None of the scenarios discussed above successfully re- million years, too short a timescale to acquire large incli-
produce the existence of a cold and a hot population in the nations. For the same reason, the “fossilized” scattered disk
classical belt (see section 3.2–3.3) and the correlation be- does not extend very far in semimajor axis, so that objects
tween inclination and sizes and colors. The reason is obvi- like 2000 CR105 are not produced in this scenario. Also, the
ous. All these scenarios start with a unique population (the high eccentricity of Neptune would destabilize the bodies
primordial, dynamically cold Kuiper belt). From a unique in the 2:3 resonance, so that the Plutinos could have been
population, it is very difficult to produce two populations captured only after Neptune’s eccentricity damping, during
with distinct orbital properties. Even in the case where it a final quiescent phase of radial migration similar to that
might be possible (as in the stellar encounter scenario), the in Malhotra’s (1993, 1995) scenario. Nevertheless, a Plutino
orbital histories of gray bodies cannot differ statistically population was never formed in the Thommes et al. (1999)
from those of the red bodies, because the dynamics do not simulations, possibly because Neptune’s migration was too
depend on the physical properties. The correlations between jerky owing to the encounters with the massive bodies used
colors and inclination can be explained only by postulat- in the numerical representation of the disk.
ing that the hot and cold populations of the current Kuiper Gomes (2003) revisited Malhotra’s (1993, 1995) model.
belt originally formed in distinctive places in the solar sys- Like Hahn and Malhotra (1999), he attempted to simulate
tem. The scenario suggested by Levison and Stern (2001) Neptune’s migration, starting from about 15 AU, by the
is that initially the protoplanetary disk in the Uranus-Nep- interaction with a massive planetesimal disk extending from
tune region and beyond was uniformly dynamically cold, beyond Neptune’s initial position. But, taking advantage of
with physical properties that varied with heliocentric dis- the improved computer technology, he used 10,000 particles
tance. Then, a dynamical violent event cleared the inner to simulate the disk population, with individual masses
region of the disk, dynamically scattering the inner disk roughly equal to twice the mass of Pluto, while Hahn and
objects outward. In the scattering process, large inclinations Malhotra used only 1000 particles with lunar to martian
were acquired. Most of these objects have been dynami- masses. In his simulations, during its migration Neptune
cally eliminated, or persist as members of the scattered disk. scattered the planetesimals and formed a massive scattered
However, a few of these objects somehow were deposited disk. Some of the scattered bodies decoupled from the
in the main Kuiper belt, becoming the hot population of the planet by decreasing their eccentricity through the interac-
classical belt currently observed. tion with some secular or mean-motion resonance. If Nep-
Two dynamical scenarios have been proposed so far to tune had not been migrating, as in Duncan and Levison
explain how planetesimals in the Uranus-Neptune zone (1997) integrations, the decoupled phases would have been
188 Comets II

A significant Plutino population is also created in Gomes’

simulations. This population is also the result of the super-
position of the population coming from Neptune’s region
with that formed further away and captured by the 2:3 reso-
nance during the sweeping process. Assuming that the bod-
ies’ sizes and colors varied in the primordial disk with
heliocentric distance, this process would explain why the
Plutinos, scattered objects, and hot classical belt objects,
which mostly come from regions inside ~30 AU, all appear
to have identical color distributions and similar maximum
sizes, while only the cold classical population, the only ob-
jects actually formed in the transneptunian region, has a dif-
ferent distribution in color and size.
Of all the models discussed in this paper, Gomes’ sce-
nario is the one that seems to best account for the observed
properties of the classical belt. A few open questions persist,
though. The first concerns the mass deficit of the Kuiper
belt. In Gomes’ simulations about 0.2% of the bodies ini-
tially in the Neptune-swept disk remained in the Kuiper belt
at the end of Neptune’s migration. Assuming that the pri-
mordial disk was ~100 M , this is very compatible with the
Fig. 9. The orbital distribution in the classical belt according to estimated current mass of the Kuiper belt. But the local
Gomes’ (2003) simulations. The dots denote the local population, population was only moderately excited and not dynami-
which is only moderately dynamically excited. The crosses de- cally depleted, so it should have preserved most of its pri-
note the bodies that were originally inside 30 AU. Therefore, the mordial mass. The latter should have been several Earth
resulting Kuiper belt population is the superposition of a dynami- masses, in order to allow the growth of ~100-km bodies
cally cold population and of a dynamically hot population, which
within a reasonable timescale (Stern, 1996). How did this
gives a bimodal inclination distribution comparable to that ob-
local population lose its mass? This problem is also unre-
served. The dotted curves in the eccentricity vs. semimajor axis
plot correspond to q = 30 AU and q = 35 AU. Courtesy of R. solved for the Thommes et al. (1999) scenario. The only
Gomes. plausible answer seems to be the collisional erosion sce-
nario, but it has the limitations discussed in section 3.1.
Quantitative simulations need to be done. A second prob-
lem, also common to the Thommes et al. scenario, is the
transient, because the eccentricity would have eventually existence of the Kuiper belt edge at 50 AU. In fact, in nei-
increased back to Neptune-crossing values, the dynamics ther scenario is significant depletion of the pristine popu-
being reversible. But Neptune’s migration broke the reversi- lation beyond this threshold obtained. A third problem with
bility, and some of the decoupled bodies managed to escape Gomes’ (2003) scenario concerns Neptune’s migration. Why
from the resonances, and remained permanently trapped in did it stop at 30 AU? There is no simple explanation within
the Kuiper belt. As shown in Fig. 9, the current Kuiper belt the model, so Gomes had to artificially impose the end of
would therefore be the result of the superposition of these Neptune’s migration by abruptly dropping the mass surface
bodies with the local population, originally formed beyond density of the disk at ~30 AU. A possibility is that, by the
30 AU and only moderately excited [by the resonance sweep- time that Neptune reached that position, the disk beyond
ing mechanism, as in Hahn and Malhotra (1999)]. Unlike 30 AU had already been severely depleted by collisions. A
in Thommes et al. (1999) simulations, the migration mecha- second possibility is that something (a massive planetary
nism is sufficiently slow (several 107 yr) that the scattered embryo, a stellar encounter, collisional grinding?) opened
particles have the time to acquire very large inclinations, a gap in the disk at about 30 AU, so that Neptune ran out
consistent with the observed hot population. The resulting of material and could not further sustain its migration.
inclination distribution of the bodies in the classical belt is
bimodal, and quantitatively reproduces the debiased inclina- 5. CONCLUSIONS AND PERSPECTIVES
tion distribution computed by Brown (2001) from the obser-
vations. For the same reason (longer timescale) the extended Ten years of dedicated surveys have revealed unexpected
scattered disk in Gomes’ (2003) simulations reaches much and intriguing properties of the transneptunian population,
larger semimajor axes than in Thommes et al. (1999) inte- such as the existence of a large number of bodies trapped
grations. Although bodies on orbits similar to that of 2000 in mean-motion resonances, the overall mass deficit, the
CR105 are not obtained in the nominal simulations, other large orbital eccentricities and inclinations, and the appar-
tests done in Gomes (2003) are suggestive that such orbits ent existence of an outer edge at ~50 AU and a correlation
could be achieved in the framework of the same scenario. among inclinations, sizes, and colors. Understanding how
 Morbidelli and Brown: Kuiper Belt and Evolution of Solar System 189

the Kuiper belt acquired all these properties would prob- dynamical process. The final position of Neptune would
ably constrain several aspects of the formation of the outer simply reflect the primitive truncation of the protoplanetary
planetary system and of its primordial evolution. disk. A bigger problem is the explanation of the different
Up to now, a portfolio of scenarios have been proposed physical properties of the cold and hot populations, because
by theoreticians. None of them can account for all the ob- they both originated within 35 AU, although in somewhat
servations alone, and the solution of the Kuiper belt primor- different parts of the disk. At the time of this writing, this
dial sculpting problem probably requires a sapient combina- innovative model has not yet been critically debated within
tion of the proposed models. The Malhotra-Gomes scenario the community of experts. But this scenario offers a simple
on the effects of planetary migration does a quite good job at prediction that will be confirmed or denied by future ob-
reproducing the observed orbital distribution inside 50 AU. servations: The edge of the cold classical belt is exactly at
The apparent edge of the belt at 50 AU might be explained the location of the 1:2 resonance.
by a very early stellar encounter at 150–200 AU. The origin Kuiper belt science is a rapidly evolving field. New ob-
of the peculiar orbit of 2000 CR105 could be due to a later servations change our view of the belt every year. Since the
stellar encounter at ~800 AU. discovery of the first transneptunian object 10 years ago,
The most mysterious feature that remains unexplained several review papers have been written, and most of them
in this combination of scenarios is the mass deficit of the are already obsolete. No doubt this will also be the fate of
cold classical belt. As discussed in this chapter, the mass this chapter, but it can be hoped that the ideas presented
depletion cannot be explained by the ejection of most of here can continue to guide us in the direction of further
the pristine bodies to Neptune-crossing orbit, because in this understanding of what present observations of the Kuiper
case the planet would have migrated well beyond 30 AU. belt can tell us about the formation and evolution of the
But the collisional grinding scenario also seems problem- outer solar system.
atic, because it requires a peculiar size distribution in the
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192 Comets II
 Duncan et al.: Dynamical Evolution of Ecliptic Comets 193

Dynamical Evolution of Ecliptic Comets

Martin Duncan
Queen’s University

Harold Levison and Luke Dones

Southwest Research Institute

Ecliptic comets are those with T > 2, where T is the Tisserand parameter with respect to
Jupiter. In this chapter, we review the enormous progress that has been made in our under-
standing of the dynamical evolution of these bodies. We begin by reviewing the evidence that
Jupiter-family comets (JFCs; those with 2 < T < 3) form a dynamically distinct class of comets
that originate in a flattened disk beyond Neptune. We present a model for the distribution of
comets throughout the JFC and Centaur regions that is consistent with current observations,
although further observations and numerical simulations in the Centaur region are called for.
We then discuss dynamical results (since confirmed by observations) that a significant amount
of material that was scattered by Neptune during the early stages of planet formation could
persist today in the form of a “scattered disk” of bodies with highly eccentric orbits beyond
Neptune. We describe the dynamical mechanisms believed responsible for the longevity of the
surviving bodies and argue that if objects in the Kuiper belt and scattered disk have similar
size distributions, then the scattered disk is likely to be the primary source of JFCs and Cen-
taurs. Finally, we describe the importance of understanding the ecliptic comet population for
the purposes of determining impact rates on the satellites of the giant planets and of age deter-
minations of the satellite surfaces. We present tables of impact rates based on the best cur-
rently available analyses. Further refinements of these rates and age determinations await better
observations of the Centaur population (including its size distribution), as well as a better un-
derstanding of the formation and early dynamical evolution of the outer solar system.

1. INTRODUCTION rates of ecliptic comets on planets and their moons are dis-
cussed, while section 7 contains a brief summary of the state
The dynamical and physical lifetimes of most observed of understanding of the origin of JFCs and the dynamical
comets are short compared to the age of the solar system. evolution of ecliptic comets.
Thus, comets must be coming from some reservoir or res-
ervoirs that slowly allow comets to leak out to regions where 2. COMETARY TAXONOMY
they can be detected. Although these reservoir(s) must be
stable enough to retain a significant number of objects for Historically, cometary taxonomy was based on orbital
billions of years, there must also be some currently active period, with comets of orbital period shorter than 200 yr
mechanisms that transport objects into the regions where being termed “short-period comets” and those with periods
they are more easily detected. less than 20 yr being further subdivided into the class called
It is currently believed that there are three main sources “Jupiter-family” comets. However, numerical integrations
of the known comets: the Oort cloud, the Kuiper belt, and such as those described below show that under such a
the scattered comet disk. The first of these is discussed in scheme a given short-period comet typically shifts in and
Dones et al. (2004). Here we discuss the Kuiper belt and out of the “Jupiter-family class” many times during its
scattered disk with regard to their role as the source of eclip- dynamical evolution. Carusi and Valsecchi (1987) first sug-
tic comets. The structure of these cometary reservoirs are gested that since the Tisserand parameter does not vary
discussed in more detail in Morbidelli and Brown (2004). substantially during a typical comet’s lifetime, a taxonomy
This chapter is organized as follows. In the next section based on this parameter might be more appropriate than one
we briefly review comet taxonomy and terminology. In based on orbital period.
section 3 we review numerical integrations of the orbits of Recall that the Tisserand parameter with respect to Ju-
observed Jupiter-family comets, and in section 4 we sum- piter, T, is defined as
marize results of simulations of the transport of comets from
the transneptunian region into the region typically inhab- T = aJ/a + 2 (1 – e2)a/aJ cos(i) (1)
ited by JFCs. Section 5 reviews the dynamical properties
of the long-lived tail of the distribution of Neptune-scat- where aJ is Jupiter’s semimajor axis, and a, e, and i refer
tered comets (the “scattered disk”). In section 6, the impact to an object’s semimajor axis, eccentricity, and inclination

193
194 Comets II

respectively. It is an approximation to the Jacobi constant,

which is an integral of the motion in the circular restricted
three-body problem. It is also a measure of the relative ve-
locity between a comet and Jupiter during close encounters,
vrel = vc 3 – T , where vc is Jupiter’s velocity about the Sun.
Objects with T close to, but smaller than, 3 have very slow,
and thus very strong, encounters with Jupiter. Objects with
T > 3 cannot cross Jupiter’s orbit in the circular restricted
case, being confined to orbits either totally interior or to-
tally exterior to Jupiter.
For this chapter, we will adopt a taxonomic scheme based
on that of Levison (1996), in which the most significant
division is based on the Tisserand parameter. In this scheme
comets with T > 2 are designated ecliptic comets because
most members have small inclinations. As we shall see
below, these objects most likely originate in the Kuiper belt
(Edgeworth, 1949; Kuiper, 1951; Fernández, 1980; Duncan
et al., 1988) or the scattered disk (Torbett, 1989; Duncan
and Levison, 1997). Comets with T < 2, which are believed
to be mainly comets from the Oort cloud (Oort, 1950; Ever-
hart, 1977) are designated nearly isotropic comets, reflect-
ing their inclination distribution (see Dones et al., 2004).
Independent of other classifications, a comet is said to be
“visible” if its perihelion distance is less than 2.5 AU.
Ecliptic comets can be further subdivided into three
groups. Comets with 2 < T < 3 are mainly on Jupiter-cross-
ing orbits and are dynamically dominated by that planet.
We call these Jupiter-family comets (hereafter called JFCs).
Comets with T > 3 (not Jupiter-crossing) are not considered
members of the Jupiter family. A comet that has T > 3 and Fig. 1. (a) The semimajor axes, a, of observed comets with pe-
a > aJ (orbit is exterior to Jupiter) is designated as Chiron- riods less than 200 yr as a function of their Tisserand parameter
type or a Centaur. A comet that has T > 3 and a < aJ is with respect to Jupiter, T. The dashed vertical lines represent the
designated an Encke-type. Note that this combination of T boundaries of the Jupiter family at T = 2 and T = 3. Objects fall-
and a implies that the orbit of this object is entirely interior ing above the solid curve must have perihelia greater than 2.5 AU.
(b) The inclination, i, of the same set of comets as in (a) as a
to Jupiter, i.e., the aphelion distance is less than aJ. How-
function of T. Again, the dashed lines represent the boundaries of
ever, it may be too severe to use a strict criteria of T < 3
the Jupiter family. The shaded areas represent regions that are
since there are a few comets with T slightly larger than 3 physically unattainable due to the relationship between i and T
that dynamically belong to the Jupiter family (i.e., they are assuming q ≤ 2.5 AU and Q ≥ aJ. (c) The same as (a) except for
not decoupled from Jupiter; they suffer frequent long-last- simulated comets when they first become “visible,” i.e., when their
ing encounters with the planet). These are the comets some- perihelia first drop below 2.5 AU. (d) The same as (b) except for
times called the “quasi-Hilda” type (see, e.g., Kresák, 1979; simulated comets when they first become visible. From Levison
Tancredi et al., 1990). This is a very interesting group since and Duncan (1997).
these objects experience frequent temporary satellite cap-
ture and occasional low-velocity impacts with Jupiter (like
Shoemaker-Levy 9) and Jupiter’s moons.
taxonomy. The strong clumpings of JFCs at values of T just
3. DYNAMICS OF OBSERVED less than 3 and at low inclinations are important clues to
JUPITER-FAMILY COMETS their origins, as we shall describe in section 4.
Pioneering integrations of the dynamical evolution of
Historically, researchers were interested in the origin and short-period comets spanning roughly 1000 yr were per-
evolution of the group of observed comets known as “short- formed by Carusi et al. (1985) and Carusi and Valsecchi
period” comets, (i.e., those with periods less than 200 yr). (1987). Further important numerical integrations in the early
The upper two panels of Fig. 1 show the distributions of 1990s include the “COSMO-DICE” project (Nakamura and
semimajor axis a and inclination i for these comets vs. Tis- Yoshikawa, 1992a,b), as well as the work of Tancredi and
serand parameter T. The dashed lines in both plots repre- Rickman (Tancredi and Rickman, 1992; Rickman, 1992; Tan-
sent the boundaries of the Jupiter family according to our credi, 1994), Lindgren (1992), and Emel’yanenko (1992).
 Duncan et al.: Dynamical Evolution of Ecliptic Comets 195

A comprehensive set of long-term integrations spanning perihelia beyond 2.5 AU are difficult to detect, this implies
up to 107 yr of the dynamical evolution of short-period com- that there are more than 10 times more undetected JFCs
ets was performed by Levison and Duncan (1994) (hereafter than there are visible JFCs. Of those visible now, half will
called LD94). In view of the chaotic nature of each indi- evolve to states with q > 2.5 AU in roughly 103 yr.
vidual orbit, LD94 integrated 4 orbits per comet (each with The very flattened inclination distribution of JFCs (i.e.,
slightly different initial orbital elements) for the 160 short- their concentration at small inclinations) was found to be-
period comets known in 1991. The orbits of the Sun, planets come more distended as it aged. Since JFCs are a dynami-
(except Mercury and Pluto), and comets were integrated cally distinct class, they must have an inclination distribution,
forward and backward in time for 107 yr. A comet was fol- when they first become visible, that is even more flattened
lowed until it either became unbound from the Sun and than that currently observed. Given this evidence that the
reached a distance of 150 AU or became a Sun-grazer with JFCs originate in a flattened distribution such as the Kuiper
pericenter less than 2 solar radii. Although the chaotic be- belt, we explore the dynamical transport from the transnep-
havior of individual orbits precluded an accurate determi- tunian reservoirs in the next section.
nation of the long-term fate of any individual comet, it was
appropriate to extract statistical information from this 4. FROM THE TRANSNEPTUNIAN REGION
sample that should resemble the evolution of the real en- TO JUPITER-FAMILY COMETS
semble of comets.
LD94 found that the Tisserand parameter, T, does not We turn now to the study of the origin and dynamical
vary substantially for most observed short-period comets: evolution of the class of objects that we referred to in sec-
Less than 8% of comets moved in or out of the JFC class dur- tion 2 as “ecliptic comets.” As noted in section 3, the ob-
ing the integration, and most of those that changed tended to served JFCs (which make up the bulk of the active ecliptic
remain near the Tisserand dividing line throughout. Thus, the comets) have a very flattened inclination distribution with
JFCs were found to be a dynamically distinct class within the a median inclination of only 11°. In the last 15 years or so,
short-period comets. research attempting to explain this inclination distribution
The currently observed perihelion distance distribution has been extremely active. Indeed, attempting to understand
of comets is strongly peaked toward small values. This is these comets stimulated one of the most important discov-
most likely due to a strong observational bias against the eries in planetary science in the last half of the twentieth
discovery of comets with large perihelion distances because century — the discovery of the Kuiper belt.
they are less active and do not pass close to the Earth. Quinn Ecliptic comets were originally thought to originate from
et al. (1990) define a “visible” comet as one with q ≤ 2.5 AU. nearly isotropic comets that had been captured into short-
If a comet has a q greater than this value then, they argue, period orbits by gravitational encounters with the planets
it is not likely to become bright enough to be discovered. (Newton, 1891; Everhart, 1977; Bailey, 1986). Joss [(1973),
Indeed, only 14% of the known short-period comets have see later work by Fernández and Gallardo (1994) and Levi-
q larger than this value, despite the fact that there is a large son et al. (2001)] argued that this process is too inefficient,
region of phase space with q > 2.5 AU available to objects and Fernández (1980) suggested that a belt of distant icy
being scattered by Jupiter. For this review, we adopt this planetesimals beyond Neptune could serve as a more effi-
definition of visibility. cient source of most of these comets. Duncan et al. (1988)
It was found that in the forward integration, 92% of strengthened this argument by performing dynamical simu-
comets were ejected from the solar system, and that ≈6% lations that showed that a cometary source beyond Neptune
were destroyed by becoming Sun-grazers. However, LD94 with small inclinations to the ecliptic was far more consis-
did not differentiate between JFCs and Halley-type comets tent with the observed orbits of most of these comets than
(HTCs) (T < 2, a < 40 AU) when considering Sun-grazers. the randomly distributed inclinations of comets in the Oort
A subsequent reexamination of those integrations found that cloud (see also Quinn et al., 1990). They named this source
half the objects that became Sun-grazers were Halley type, the Kuiper belt.
although HTCs represented only ~10% of the comets inte- The size, extent, and eccentricity of the cometary orbits
grated in LD94. A full 30% of the HTCs became Sun-graz- in this belt were left as open questions in Duncan et al.
ers, while only 3% of the JFCs shared the same fate in the (1988). Traditionally, this work was used to imply that the
integrations. Indeed, only ~1% of the objects that became source of these comets is a primordial population of low
visible eventually became Sun-grazers. eccentricity, moderately low-inclination objects beyond
The median lifetime of all known short-period comets Neptune (in what we call the Kuiper belt in this review).
from the current time to ultimate destruction or ejection is An alternative interpretation is that this disk was made up
approximately 4.5 × 105 yr: The median lifetime of JFCs of objects on moderately low-inclination, highly eccentric
is 3.25 × 105 yr. The median number of times that JFCs orbits beyond Neptune (in what we call the scattered disk).
changed from orbits with q < 2.5 AU to q > 2.5 AU was 10. The details of these interpretations are discussed below.
A typical comet spent less than 7% (median value) of its Nevertheless, the first transneptunian object (after Pluto and
dynamical lifetime with q < 2.5 AU. Since objects with Charon) was discovered in 1992 (Luu and Jewitt, 1993);
196 Comets II

now more than 800 transneptunian objects are known (for Plate 8 shows the distribution of the ecliptic comets
current lists see http://cfa-www.harvard.edu.edu/ps/lists/ derived from the simulations of LD97, assuming that the
TNOs.html and http://cfa-www.harvard.edu.edu/iau/lists/ rate of objects leaving the Kuiper belt has remained approxi-
Centaurs.html). mately constant over the last ~108 yr and that there was no
To date the only comprehensive simulation of the trans- huge influx at early epochs. The figure is a contour plot of
port of objects from the transneptunian region to the inner the fraction of comets per square AU in perihelion-aphelion
solar system is that of Levison and Duncan (1997) (here- (q–Q) space. The figure was generated by binning the q–Q
after LD97). They assumed that the source region was a values of all the comets at all output points in the integra-
dynamically very cold primordial Kuiper belt and that there tions, which occurred once every 104 yr before a comet be-
were enough objects leaking out of this belt, due to the came visible and once every 1000 yr after it become visible.
gravitational effects of the planets (e.g., Levison and Dun- The resulting matrix was then normalized so that the total
can, 1993; Holman and Wisdom, 1993; Nesvorny and Roig, number is 1. Note that we are not plotting, say, the relative
2000; Kuchner et al., 2002) to supply the JFCs. Although number of comets per square AU at a given distance from
this assumption is limiting in some respects (which we dis- the Sun, but rather presenting the more abstract density con-
cuss below), we believe that there are properties of the tours on a grid with pericentric distance q on one axis and
dynamics of these objects that are independent of the de- apocentric distance Q on the other. Also shown in Plate 8
tails of the source reservoir. Thus, we discuss the results of are curves of constant eccentricity and semimajor axis.
LD97 in some detail. There are two well-defined regions in Plate 8. Beyond
LD97 performed numerical orbital integrations of 2200 approximately Q = 7 AU, there is a ridge of high density
massless particles as they evolved from Neptune-encoun- extending diagonally from the upper right to the center of
tering orbits in the Kuiper belt for times up to a billion years the plot, near e ≈ 0.25. The peak of this ridge is near e = 0.2
or until they either impacted a massive body or were ejected at large Q and tends to increase to e ≈ 0.3 near Q ~ 7 AU.
from the solar system. The initial orbits for these particles As discussed in LD97, the eccentricities of objects that are
were chosen from a previous set of integrations of objects between the planets and not yet under Jupiter’s control are
that were initially in low-eccentricity, low-inclination orbits expected to be about 0.25 due to the constraints of the Tis-
in the Kuiper belt but evolved onto Neptune-crossing orbits serand parameter. The peak density in this ridge drops by
on timescales between 1 and 4 G.y. (Duncan et al., 1995). almost 2 orders of magnitude as it moves inward, having a
The median inclination of the particles at the time of en- minimum where the semimajor axes of the comets are the
countering Neptune was 4°. same as Jupiter’s. This population extends inward of Jupi-
LD97 found that as objects evolve inward from the ter’s orbit and terminates near the 2:1 mean-motion reso-
Kuiper belt, they tend to be under the dynamical control of nance with Jupiter. Indeed, we find that objects can be
just one planet. That planet will scatter the comets inward forced onto nearly circular orbits with semimajor axes as
and outward in a random walk, typically handing them off small as ~4 AU. This inner edge is coincident with the inner
to the planet directly interior or exterior to it. Therefore, the edge of Jupiter’s “crossing zone” at 3.88 AU. Gladman and
comets tend to have eccentricities of about 0.25 between Duncan (1990) defined Jupiter’s “crossing zone” as the re-
handoffs. However, once they have been scattered into the gion in which objects on initially circular orbits can become
inner solar system by Jupiter, they can have much larger Jupiter-crossing. Since this process is time reversible, it is
eccentricities as they evolve outward. not then surprising that Jupiter can drive comets into nearly
Plate 7 shows the evolution of a typical particle in the circular orbits in this region.
perihelion distance (q)–aphelion distance (Q) plane, as it Inside of Q ≈ 7 AU the character of the distribution is
evolves from the Kuiper belt (q > 30 AU) to a visible JFC quite different. Here there is a ridge of high density extend-
(the most populous of the visible ecliptic comets). The posi- ing vertically in the figure at Q ~ 5–6 AU that extends over
tions are joined by blue lines until the particle first became a wide range of perihelion distances. Objects in this region
“visible” (q < 2.5 AU) and are linked in red thereafter. Ini- are the JFCs. This characteristic of a very narrow distribu-
tially, the particle spent considerable time with perihelion tion in Q is seen in the real JFCs and is again a result of
near the orbit of Neptune (30 AU) and aphelion well be- the narrow range in T. Taken together, this distribution of
yond the planetary system. However, once its perihelion comets produces a surface distribution shown as the dashed
dropped to Uranus’ location, this particle, which was cho- curve in Fig. 2.
sen at random from LD97’s integrations, clearly shows the The median dynamical lifetime of the ecliptic comets
handoff behavior described above. It evolved at relatively was found to be 4.5 × 107 yr. (This is the time from the first
small eccentricity to visibility (cf. the lines of constant ec- encounter with Neptune to ejection from the solar system,
centricity e = 0.2 and 0.3 on Plate 7) and it spent consider- placement in the Oort cloud, which they took to include
able time with perihelion or aphelion near the semimajor comets with semimajor axes >1000 AU, or impact with the
axis of one of the three outer planets. Its postvisibility phase Sun or a planet). LD97 found that about 30% of the objects
is reasonably typical of JFCs, with much larger eccentrici- in the integrations became visible comets (q < 2.5 AU). Of
ties than the previsibility comets and perihelion distances those that became visible, 99.7% were JFCs at the time of
near Jupiter or Saturn. first visibility.
 Duncan et al.: Dynamical Evolution of Ecliptic Comets 197

tion distribution more extended than the observations unless

fading due to physical evolution is included. From this LD97
estimated that the physical lifetime of JFCs is between 3000
and 25,000 yr. The most likely value is 12,000 yr.
With this estimate of the physical lifetime, LD97 were
able to calibrate the total number of ecliptic comets by using
the number of observed JFCs. They thereby estimated that
there are roughly a million ecliptic comets with semimajor
axes less than 30 AU. This estimate refers to objects that
would produce active comets with total absolute magnitudes
brighter then 9 if they came within 2.5 AU of the Sun. We
discuss the conversion from limits based on absolute mag-
nitudes to those based on physical radii in section 5.
In the simulations of LD97, when the ecliptic comets first
became visible they were almost entirely members of the
Jupiter family. Although a small fraction of these comets
switched to visible HTCs, the orbital element distribution
of LD97’s simulated HTCs is not consistent with the ob-
served distribution. In particular, the semimajor axes of the
Fig. 2. The predicted surface density of Centaurs and JFCs as a simulated comets are generally too small. Since LD97 found
function of heliocentric distance. The dashed curve represents that it takes at least 105 yr and usually over 106 yr to become
objects initially on low-inclination Kuiper belt orbits in the inte- a visible HTC after the comet first becomes visible, most
grations of LD97. The solid curve is from a small number of of these comets have likely become extinct since this is
objects with initial inclinations of roughly 25°. longer then the typical physical lifetime estimated above.
Thus, although the Kuiper belt can be the source of at least
some of the HTCs, initially low-inclination bodies encoun-
tering Neptune are unlikely to provide a significant num-
In order to compare the results of the simulations to the ber of them.
distribution of real comets, Figs. 1c and 1d show the orbital Finally, we consider the Encke-type comets, which are
element distribution of all visible comets in the simulations low-inclination comets totally interior to Jupiter’s orbit (see
of LD97 when they first became visible. When making a section 2). Comet 2P/Encke is the only active member of
comparison between the real and simulated JFCs in Fig. 1 this population. Although 107P/Wilson-Harrington has a T
it is important to note that there are about five times as many consistent with this class, it is probably not a comet (Bottke
points in the simulated population as in the observed popu- et al., 2002). However, there are several kilometer-sized
lation. Thus, outlying data points in the simulated popula- asteroids known to be in similar orbits (Asher et al., 1993).
tion are less significant than they may otherwise seem. The These small “asteroids” could be extinct comets. Numeri-
distribution of comets in the simulation matches that for the cal integrations of its orbit show that 2P/Encke will hit the
real Jupiter-family remarkably well. Therefore, the simu- Sun in only 105–106 yr (Levison and Duncan, 1994) due
lations show that the Kuiper belt is an excellent potential to its close association with secular resonances (Valsecchi
source for the JFCs. However, the Kuiper belt does not et al., 1995).
produce very many HTCs (at least initially, see below). This The LD97 integrations did not produce any comets simi-
result is consistent with the results of earlier work (Quinn lar to 2P/Encke, but included neither the effects of the ter-
et al., 1990) that the Kuiper belt is the main source of JFCs, restrial planets nor nongravitational effects. Some of these
whereas another reservoir (possibly the inner Oort cloud) effects were considered by Steel and Asher (1996), Harris
is the most likely source for most of the HTCs (see Dones and Bailey (1998), and Asher et al. (2001). Fernández et
et al., 2004). al. (2002) integrated the orbits of a sample of real JFCs with
An interesting aspect of the distributions shown in Fig. 1 the terrestrial planets and nongravitational forces included.
is the very narrow range in T that JFCs occupy. Although They found that they could produce objects on Encke-like
we define a JFC as one with 2 < T < 3, the median T for orbits, but only when strong nongravitational forces (as
the family is 2.8. The narrow range in T is related to small strong as or greater than those that are estimated to be cur-
inclinations to the ecliptic seen for these comets: An ob- rently acting on Encke) are included.
ject on a Jupiter-crossing orbit with T > 2.8 and q < 2.5 AU
must have an inclination less than ~26°. 5. DYNAMICS OF THE SCATTERED DISK
The inclination distribution of JFCs when they first be-
come visible is more concentrated to small inclinations than Perhaps the most interesting result of the LD97 simula-
the observed population and was found to become more tions was that about 5% of the particles survived the length
distended as it aged. Indeed, this model predicts an inclina- of the integration (109 yr). All the survivors had semimajor
198 Comets II

Fig. 3. The temporal behavior of a long-lived member of the scattered disk. The black curve shows the behavior of the comet’s
semimajor axis. The gray curve shows the perihelion distance. The three dotted curves show the location of the 3:13, 4:7, and 3:5
mean-motion resonances with Neptune. From Duncan and Levison (1997).

axes outside the orbit of Neptune. This result implied that by Holman and Wisdom (1993), leads to an overall distri-
there may be a significant population of objects with highly bution of semimajor axes for the particles that is peaked
eccentric orbits in an extended disk beyond the orbit of near the locations of many of the mean-motion resonances
Neptune — a “scattered” comet disk. Although, the idea of with Neptune. Occasionally, the longevity is enhanced by
the existence of a scattered comet disk dates to Fernández the presence of the Kozai resonance (Kozai, 1962).
and Ip (1983) and Torbett (1989), it was the modern work In all long-lived cases, particles had their perihelion dis-
of LD97 and the followup paper, Duncan and Levison tances increased so that close encounters with Neptune no
(1997) (hereafter DL97), that demonstrated that the scat- longer occurred. Frequently, these increases in perihelion
tered disk should exist. DL97 extended the LD97 integra- distance were associated with trapping in a mean-motion
tions to 4 × 109 yr. It was found that 1% of the particles resonance, although in many cases it has not yet been pos-
remained in orbits beyond Neptune after 4 b.y. So, if at early sible to identify the exact process that was involved. On
times, there was a significant amount of material from the occasion, the perihelion distance can become large, but 81%
region between Uranus and Neptune or the inner Kuiper of scattered disk objects in the simulations have perihelia
belt that evolved onto Neptune-crossing orbits, then there between 32 and 36 AU.
could be a significant amount of this material remaining Figure 3 shows the dynamical behavior of a typical long-
today. [The first scattered disk object was discovered by Luu lived particle. This object initially underwent a random walk
et al. (1997) shortly after this prediction.] in semimajor axis due to encounters with Neptune. At about
DL97 found that some of the long-lived objects were 7 × 107 yr it was temporarily trapped in Neptune’s 3:13
scattered to very long-period orbits where encounters with mean-motion resonance for about 5 × 107 yr. It then per-
Neptune became infrequent. However, at any given time, formed a random walk in semimajor axis until about 3 ×
the majority of them were interior to 100 AU. Their lon- 108 yr, when it was trapped in the 4:7 mean-motion reso-
gevity is due in large part to their being temporarily trapped nance, where it remained for 3.4 × 109 yr. Notice the in-
in or near mean-motion resonances with Neptune. The crease in the perihelion distance near the time of capture.
“stickiness” of the mean-motion resonances, first mentioned While trapped in this resonance, the particle’s eccentricity
 Duncan et al.: Dynamical Evolution of Ecliptic Comets 199

became as small as 0.04. After leaving the 4:7, it was trivial conversion, since there is no good correlation be-
trapped temporarily in Neptune’s 3:5 mean-motion reso- tween the absolute magnitude of a comet (which is based
nance for ~5 × 108 yr and then went through a random walk on a comet’s activity) and its size (for discussions, see, e.g.,
in semimajor axis for the remainder of the simulation. Levison et al., 2001; Zahnle et al., 1998). Examples of
DL97 estimate the number of scattered disk objects that possible values for the number of comets in the scattered
their model would require if it was the sole source of the disk with diameters, D, >1 km range from ~5 × 108 [fol-
JFCs. They first computed the simulated distribution of lowing the calibration of Bailey et al. (1994)], through ~2 ×
comets throughout the solar system at the current epoch 109 [following the calibration of Weissman (1990)], to ~5 ×
(assuming the disk was created 4 × 109 yr ago, with the dis- 109 (following Levison et al.’s (2001) estimate, based on
tribution averaged over the last 109 yr for better statistical Kary and Dones (1996)].
accuracy). They found that the ratio of scattered disk objects If the scattered disk is the source of the Centaurs and
to visible JFCs (those with a perihelion distance <2.5 AU) JFCs, then the estimate of its population has implications
is 1.3 × 106. Since there are currently estimated to be 500 for planet formation. Since we employ the calibration of
visible JFCs (LD97; see also Fernández et al., 1999), there Weissman (1990) for this discussion, we note that there are
are presently ~6 × 108 comets in the scattered disk if this significant uncertainties in these numbers. It was shown
model is the sole source of the JFCs. Figure 4 shows the above that ~1% of the objects in the scattered disk remain
spatial distribution for this model. after 4 × 109 yr in the simulations of DL97, and that ~2 × 109
The above estimate is not particularly physically mean- comets with D > 1 km are currently required to supply all
ingful because it refers to comets with absolute magnitudes, the JFCs with the adopted calibration of Weissman (1990).
HT, brighter than 9 when they are visible. A more interest- Thus, a scattered comet disk requires an initial population
ing measure is the number of comets greater than some of only 2 × 1011 comets [or ~1 M (Weissman, 1990)] on
diameter, typically set to 1 km. Unfortunately, this is a non- Neptune-encountering orbits. Since planet formation is
unlikely to have been 100% efficient, the original disk could
have resulted from the scattering of even a small fraction
of the tens of Earth masses of cometary material that must
have populated the outer solar system in order to have
formed Uranus and Neptune. Thus, a disk that supplies the
current JFCs and Centaurs appears to have properties con-
sistent with that expected from our current understanding
of planet formation.
The first scattered disk object discovered was 1996 TL66,
found in October 1996 by Jane Luu and colleagues (Luu et
al., 1997). Current observations indicate that it has a semi-
major axis of 85 AU, a perihelion of 35 AU, and an incli-
nation of 24°. Dozens of other objects are currently known
(see http://cfa-www.harvard.edu/iau/lists/Centaurs.html for
a complete list.) The total number in 100-km-sized scattered
disk objects is estimated to be between 20,000 and 50,000
(Trujillo et al., 2000), comparable to the number of simi-
lar-sized Kuiper belt objects interior to 50 AU. The num-
ber in comet-sized (1–10-km) bodies remains to be obser-
vationally measured. However, using the size distribution
of Weissman and Levison (1997) and Trujillo et al.’s (2000)
number, we find that we should expect between 2 × 109 and
6 × 109 objects with D > 1 km. This number is consistent
with our estimates above for a scattered disk source of JFCs.
Fig. 4. The surface density of comets beyond Neptune for two Indeed, we believe that it can now be argued that the
different models of the source of JFCs. The dotted curve is the scattered disk is the primary source of the Centaurs and
required surface density assuming that a dynamically cold Kuiper JFCs. If the Kuiper belt were the source, we would expect
belt is the current source (Levison and Duncan, 1997). There are that the number of objects in the Kuiper belt would be more
7 × 109 comets with HT < 9 in this distribution between 30 and
than an order of magnitude larger than the number of ob-
50 AU. This curve ends at 50 AU because the models are uncon-
jects in the scattered disk because the average dynamical
strained beyond this point and not because it is believed that there
are no comets there. The solid curve is the model of Duncan and lifetime of scattered disk objects [2 × 108 yr (Levison et al.,
Levison (1997) assuming the scattered disk produced by their 2001)] is much shorter than that of a Kuiper belt object
integrations is the sole source of the JFCs. There are estimated to (Duncan et al., 1995; Kuchner et al., 2002). However, we
be 6 × 108 comets with HT < 9 currently in this distribution (see have just noted that Trujillo et al. (2000) found that the two
text). From Duncan and Levison (1997). populations of 100-km objects are comparable. Assuming
200 Comets II

that objects in the scattered disk and the Kuiper belt have ing ourselves to objects with 5.2 < a < 30 AU. For each of
similar size distributions, the fact that most scattered disk these we randomly choose an absolute magnitude, the dis-
objects are on less stable orbits (see Emel’yanenko et al., tribution of which is consistent with what is observed in
2003) and become planet-crossing at a greater rate implies the Kuiper belt [N(<H) ∝ 10αH, where H is the absolute
that the scattered disk is the primary source of the JFCs. magnitude, N is the total number, and α = 0.7 (Gladman et
This conclusion is also supported by the recent work of al., 2001; Trujillo et al., 2001). We run these objects through
Morbidelli et al. (2004), who performed a detailed com- the survey simulator, which calculates the probability that
parison between the two different dynamical models for the each object would have been discovered by the surveys that
scattered disk. They found that the orbital element distri- have thus far discovered real Centaurs. From this, we can
bution of observed scattered disk objects is not consistent generate an estimate of what the model predicts for the or-
with a scattered disk that is in dynamical equilibrium with bital element distribution of the known Centaurs. This re-
the Kuiper belt. Such a model predicts many more scattered sult is represented by the dark solid curves in Fig. 5. The
disk objects with semimajor axes between 50 and 60 AU dotted curves show the distribution of real, multiopposition,
(compared to objects with larger semimajor axes) than are Centaurs. The distributions in a, i, and q are very similar.
actually observed. However, a model invoking an ancient Thus, we can conclude that the models of LD97 do indeed
scattered disk, previously much more massive, is in good match the distribution of the currently observed Centaurs.
agreement with the observed scattered disk. Again, we can However, this result is a necessary but not sufficient
conclude that the scattered disk is old and is the most likely condition, because the observations may not sample enough
source of the Centaurs and JFCs. of the Centaurs to be a significant constraint on the overall
Very recently, strong evidence has emerged for the ex- distribution. For example, LD97 studied the evolution of a
istence of an “extended scattered disk” (Gladman et al., small number of objects leaving the Kuiper belt at inclina-
2002). This disk is comprised of bodies such as 2000 CR105 tions of ~25°. The solid curve in Fig. 2 shows the surface
that have very large semimajor axes and perihelia outside density distribution of this model compared to the standard
40 AU. These objects cannot have been placed on such LD97 model shown by the dotted curve. Note that there is
orbits by strong gravitational scattering off any of the giant roughly a factor of three difference between the curves in
planets in their current orbits. The mass in this population the outer solar system and a factor of 2 at Saturn. How-
is extremely uncertain due to the difficulty in finding such ever, they agree at Jupiter.
distant objects in the first place and due to the difficulty of We have run this “hot” model of the Centaurs through
determining their orbits without frequent and well-timed re- our synthetic survey simulator and the predicted orbital
covery observations. Their cosmogonic implications are sig- element distribution of discovered objects is shown as the
nificant and are discussed in Morbidelli and Brown (2004). blue curves in Fig. 5. There is reasonably good agreement
between this model, the original model, and the observa-
6. PLANETARY IMPACT RATES tions. The only exception is in the inclinations where ob-
FROM ECLIPTIC COMETS jects in this model have slightly (but not significantly) larger
inclinations. However, we conclude that the observations
An important aspect of the ecliptic comet population is cannot yet distinguish between these two reasonable mod-
that it is the primary source of impactors on the satellites els of the Centaurs. This fact should be considered when
of the giant planets (Zahnle et al., 1998). Thus, if it is pos- interpreting the impacts rates we present below.
sible to determine the total number and orbital distribution Having said this, we return to the issue of impact rates.
of these objects, it should be possible to estimate the ages Included in the analysis presented in LD97 was a crude
of the satellite surfaces. Given the importance of this topic, estimate of the impact rates on the planets from ecliptic
we dedicate this section to this issue. comets. Subsequently, Levison et al. (2000) have used the
As described in section 4, the best set of integrations for results of LD97 to present a more precise and detailed
this purpose remains those presented in LD97. However, analysis of the impact rates and characteristics of the im-
before we proceed with a discussion of their results with pacting bodies. Levison et al. (2000) used three different
regard to impact rates, we first need to ask whether the LD97 methods to compute the impact rates on the giant planets
model is a good representation of the Centaur (i.e., impact- (see section 2 of that paper for details). The main results
ing) population. We do this by comparing the orbital ele- of these calculations are given as the last three columns in
ment distribution of LD97’s synthetic Centaurs to real ob- their Table 1, which is reproduced here (see Table 1). For
jects. Unfortunately, the data suffer from significant obser- this discussion, we note that the authors recommend using
vational biases in semimajor axis (a), inclination (i), and the last column (Öpik II) as the standard impact rate: The
perihelion distance (q). Thus, to compare the LD97 model variation in the entries for each planet should be viewed as
to observations, we first run the model through a synthetic a measure of the uncertainty in the rate given in the last
survey simulator. Here we use one developed by Morbidelli column.
et al. (2004) for the transneptunian population. This simu- The impact rates were calculated assuming that the rate at
lator, in turn, was based on the work of Brown (2001). which comets evolve from their source region to the eclip-
Our basic procedure is as follows. We generate a set of tic comet population has been constant. This assumption is
synthetic Centaurs from the integration of LD97, restrict- clearly not correct, although the authors believe that it does
 Duncan et al.: Dynamical Evolution of Ecliptic Comets 201

Fig. 5. The orbital element distribution of the Centaurs. The dark solid curves are those derived from the simulations of LD97, while
the gray curves are derived from a subset that started with objects leaving the Kuiper belt with inclinations of roughly 25°. Both the
solid curves were generated using the synthetic survey simulator of Morbidelli et al. (2004). The dotted curves show the distribution
of observed, multiopposition, Centaurs.

TABLE 1. Impact rates of ecliptic comets with HT < 9 on the

planets according to Levison et al. (2000).

Number of Number of
Impacts Impacts Rate Direct Rate Öpik I Rate Öpik II
Planet Stage 1 Stage 2 (comets/yr) (comets/yr) (comets/yr)
Jupiter 7 114 6.3 × 10–4 5.0 × 10 –4 6.5 × 10 –4
Saturn 4 17 1.9 × 10–4 2.0 × 10 –4 2.7 × 10 –4
Uranus 10 0 3.4 × 10 –4 1.2 × 10 –4 1.6 × 10 –4
Neptune 10 0 3.4 × 10–4 2.6 × 10 –4 3.5 × 10 –4

Mercury — — — 4.8 × 10 –9 6.1 × 10 –9

Venus — — — 4.2 × 10 –8 5.4 × 10 –8
Earth — — — 6.2 × 10 –8 8.0 × 10 –8
Mars — — — 1.4 × 10 –8 1.8 × 10 –8

not have a large effect on the estimates of the current impact per year. In order to do this, Levison et al. (2000) find that
rates. However, most likely these impact rates were signifi- the values presented in Table 1 should be multiplied by a
cantly higher in the distant past. For example, if DL97’s factor of ~5, although there are great uncertainties in this
model of the scattered disk is correct, the impact rates on the number. For example, Bottke et al. (2002) use data from
giant planet satellites 2 × 109 yr ago were roughly a factor the Spacewatch Near Earth Asteroid survey to estimate that
of 2 larger than current rates. Any attempt to use the im- this scale factor should be 1.7 ± 1.2 rather than 5. How-
pact rates to estimate the ages of satellites should take this ever, this assumes that 100% of all JFCs become inactive
into account. rather than disintegrate once their active lifetime is over. If
The impact rates given in Table 1 are calibrated to ac- two-thirds of the JFC population self-destructed, the val-
tive JFCs with absolute magnitudes, HT, brighter than 9. As ues of the scale factor would agree.
describe above, a more common and standardized measure Zahnle et al. (1998, 2001, 2003) computed impact rates
of impact rates is to present them scaled to the number of on the satellites of Jupiter, Saturn, Uranus, and Neptune,
objects with diameters greater than 1 km striking a planet and on Pluto/Charon. Ecliptic comets appear to be the main
202 Comets II

impactors on all these bodies. In these papers, the (relative) more recent observations suggest is not the case for a large
spatial distribution of ecliptic comets was taken from the fraction of the transneptunian population. However, we
integrations of LD97 and DL97. However, the authors at- presented evidence in this review that suggested that many
tempted to perform a much more careful analysis of the of the properties of the distribution (such as the distribu-
uncertainties in the total number of comets in the system. tion interior to Jupiter) were independent of the detailed
Galileo observations of the galilean satellites indicate a structure of the source reservoir. Indeed, we showed that
paucity of small craters relative to an extrapolation of the the predicted Centaur orbital distributions in LD97 are con-
distribution at larger sizes (see Schenk et al., 2003, for a sistent with the distribution of the currently observed, multi-
discussion.) The most reasonable interpretation of this re- opposition Centaurs once observational biases are included.
sult is that there are relatively few subkilometer comets in We also noted, however, that the study of a small number
the JFC population (at least at Jupiter), which may have of objects leaving the Kuiper belt at inclinations of approxi-
important implications for the origins of these objects. mately 25° also produced a Centaur distribution in rough
Recently, Zahnle et al. (2003) argued that this relative pau- agreement with the observations despite differing in surface
city must exist all the way out to 30 AU because if not, life- density by a factor of 2–3 from the dynamically “colder”
times against collisional disruption by ecliptic comets would model in the outer planetary region. It is clear that further
be <<109 yr for a number of small moons around Saturn, observations, coupled with a better understanding of the
Uranus, and Neptune. formation and early dynamical evolution of the outer solar
However, if subkilometer comets really are under- system, will be required before these uncertainties can be
abundant in the outer solar system, this implies that either reduced.
(1) there are few such bodies in the source regions — the We have presented the dynamical results (since con-
scattered disk and/or (less likely) the Kuiper belt — or that firmed by observation) that a significant amount of mate-
(2) most small comets are destroyed at heliocentric distances rial that was scattered by Neptune during the early stages
greater than 30 AU. Both these explanations have problems. of planet formation could persist today in the form of a
The former seems unlikely because the transneptunian “scattered disk” of bodies with highly eccentric orbits be-
population is generally believed to have been collisional in yond Neptune. We described the dynamical mechanisms
the early days of the solar system, and therefore should have believed responsible for the longevity of the subset of ob-
produced many small fragments (Stern, 1995; Kenyon, jects that have survived to the current epoch. The results
2002; Stern and Weissman, 2001). The latter is unlikely of the integrations suggest that the dynamical lifetime of
because there is no obvious way to destroy the comets by scattered disk objects is much less than that of most cur-
thermal or other effects at such great distances from the Sun. rently observed Kuiper belt objects. Since the numbers of
However, the size distribution of comet precursors likely objects inferred from observations in the two groups are
will not be known until transneptunian occultation experi- comparable, then if the two groups have similar size distri-
ments such as TAOS (Alcock et al., 2003) are discovering butions, we argue that the scattered disk is likely to be the
kilometer-sized bodies in the region. primary source of JFCs and Centaurs.
Finally, we have described the importance of understand-
7. SUMMARY ing the ecliptic comet population for the purposes of deter-
mining impact rates on the satellites of the giant planets and
In the past 15 years there has been enormous progress of age determinations of the satellite surfaces. We have pre-
in our understanding of the dynamical evolution of eclip- sented tables of impact rates based on the best currently
tic comets, largely due to the ability of researchers to per- available analyses. Further refinements of these rates and
form orbital integrations of large numbers of comets for age determinations await better observations of the Centaur
timescales on the order of the age of the solar system. The population (including its size distribution), as well as a
study of the dynamics of comets has helped lead the way better understanding of the formation and early dynamical
to important discoveries about new structures in the solar evolution of the outer solar system.
system, including the Kuiper belt and the scattered disk.
We began this chapter by reviewing the evidence from
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turbations and the origins of short-period comets. Astrophys. the scattered Kuiper Belt. Astrophys. J., 529, 102–106.
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Rickman H. (1992) Structure and evolution of the Jupiter family. the trans-Neptunian belt: Statistics from the CFHT survey.
Cel. Mech. Dyn. Astron., 54, 63–69. Astron. J., 122, 457–473.
Schenk P. M., Chapman C. R., Zahnle K., and Moore J. (2003) Valsecchi G. B., Morbidelli A., Gonczi R., Farinella P., Froeschlé
Ages and interiors: The cratering record of the galilean satel- Ch., and Froeschlé C. (1995) The dynamics of objects in or-
lites. In Jupiter: The Planet, Satellites, and Magnetosphere (F. bits resembling that of P/Encke. Icarus, 118, 169–180.
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Stern S. A. (1995) Collisional time scales in the Kuiper disk and Weissman P. R. and Levison H. (1997) The population of the
their implications. Astron. J., 110, 856. trans-neptunian region The Pluto-Charon environment. In
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of comets during the formation of the Oort cloud. Nature, 409, Univ. of Arizona, Tucson.
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 Rickman: Current Questions in Cometary Dynamics 205

Current Questions in Cometary Dynamics

Hans Rickman
Uppsala Astronomical Observatory

We summarize the most important findings reported, and unanswered questions identified, in
the review chapters on cometary dynamics in this book. Comments are also offered on the signi-
ficance of these problems — and thus of cometary dynamics — for making progress on several
major issues of solar system cosmogony.

1. INTRODUCTION better astrometric accuracy and improved coverage of the

orbits. Moreover, this is getting used along with data on gas
Cometary dynamics involves the study of transfer pro- production rates and outflow kinematics to construct realis-
cesses between widely separated regions of the solar sys- tic models of the jet force, from which physical properties
tem. Essentially, it aims to understand how cometary orbits of the nuclei like their masses may be deduced.
change so that comets are brought between outer and inner We realize the important interconnection between com-
ranges of heliocentric distance (r). These provide, respec- etary physics and dynamics. It is not possible to fully under-
tively, cold storage of the cometary volatiles for billions of stand the thermophysical or chemical characteristics of a
years, and then the possibility to exhibit cometary activity cometary nucleus without reference to its orbital history and
while consuming those volatiles. One thus talks of distant formation region, and the details of the orbital motions pro-
reservoirs that are still active today, supplying new comets vide a promising tool to probe structural and evolutionary
for their first entries into orbits plunging into the water sub- properties of cometary nuclei — primarily density or poros-
limation zone (this has classically been considered as r < ity and dust coverage. In fact, cometary motions are affected
2.5–3 AU, but under some circumstances H2O may subli- by nongravitational forces that obviously depend on the
mate at significantly larger distances, and modern observa- physical properties of the nuclei, showing that cometary dy-
tional techniques have allowed the discovery of many com- namics is influenced by physical properties as well. More-
ets with perihelia around 5–10 AU). over, the fate of an individual comet arriving from the Oort
Of course, our interest in cometary dynamics extends cloud may take entirely different courses, depending on the
well beyond the currently operating mechanisms for bring- details of the nongravitational effects. Finally, dynamical
ing comets into “observable” orbits (i.e., orbits with small models for the transfer of comets into “observable” orbits
enough perihelion distance). It also incorporates the past have to be judged against the distribution of observed com-
evolution, and even formation, of the distant reservoirs. ets, and this involves a judgement of both observational
Thus the scope is ambitious enough to involve an attempt to biases and physical evolutionary effects. Hence cometary
link the orbital statistics of observed comets to critical fea- dynamics cannot be understood without reference to com-
tures of solar system cosmogony such as the origin of the etary physics.
giant planets and the transneptunian disk. Even though such The rest of this paper will focus on some of the most
studies are by necessity limited to statistical properties of interesting aspects of cometary dynamics, attempting to
the transfer processes, there is also the intriguing challenge highlight a number of unresolved problems and identify
of understanding the places of certain particular comets needs for continued research in the future. For references
within the resulting scenarios. Examples are the comets for to published literature the reader should primarily consult
which D/H ratios and a range of molecular abundances have the full review papers in this book, since in many cases the
been observed (1P/Halley, 1995 O1 Hale-Bopp, 1996 B2 relevant papers will not be cited here.
Hyakutake), and the target comet of ESA’s Rosetta mission
(67P/Churyumov-Gerasimenko). 2. ORIGIN OF COMETARY POPULATIONS
Most of the progress of research in these areas, reported
in the chapters of this book, is of relatively recent origin. In 2.1. Infeed and Capture
particular, it has important connections to the discovery and
characterization of the Edgeworth-Kuiper belt during the last It is now considered a well-established fact that the Jupi-
decade. But this book also describes much progress in the ter family (i.e., short-period comets with Tisserand param-
classical area of cometary dynamics that seeks to explain the eters T in the range 2 < T < 3) predominantly originates in
fine details of observed cometary motions and link as many multiplanet captures from the transneptunian population
apparitions of periodic comets as possible, while accurately (see Jewitt, 2004; Duncan et al., 2004). By contrast, the
representing all observations. There is thus a trend toward contribution from the Oort cloud, while not nil, should be

205
206 Comets II

rather small. Currently the most interesting question seems the current population size. Hence, while Jupiter-family
to concern the relative contributions of two possible source comets derived from the Kuiper belt would be collisional
populations: the “classical Kuiper belt” or the “scattered fragments (Farinella and Davis, 1996), those coming from
disk” (Duncan et al., 2004). the scattered disk may still be collisionally unevolved. As a
The classical Kuiper belt is a population of objects that consequence, the findings of the Rosetta mission will have to
formed well outside Neptune’s orbit and stayed there for be viewed in a framework that is quite different, depending
the age of the solar system; this population has undergone on which is the actual source population.
strong collisional evolution. The present infeed of such ob- Of course, it is of great importance to establish what
jects into Neptune-crossing orbits is due to resonant inter- chemical effects the collisional evolution would have. To
actions with the giant planets that increase the eccentricities what degree is the structure and composition of cometary
over a very long timescale, and those interactions should ice different, comparing a primordial nucleus with one that
affect only a fraction of the entire population. is a collisional fragment? Studies of differentiation effects in
On the other hand, the scattered disk consists of objects large transneptunian objects (Choi et al., 2002) shed some
that started out from encounters with Neptune and subse- light on this, but more work is needed.
quently reached a temporary asylum by resonant decrease There is also a third source, however, as already men-
of eccentricity (and thus increase of perihelion distance). tioned. The Oort cloud, and especially its inner core (with
In this case, the present infeed is to be seen as the inevitable semimajor axes a in the approximate range 5000 < a <
return of the refugees, and essentially the whole population 20,000 AU), is certainly contributing some — as yet un-
will eventually be affected, even though at present only a known — fraction of the Jupiter-family comets as well as
part of it is likely to be concerned. the Centaurs. Its contribution to the Halley-type comets (or-
Estimates based on the number of discoveries of objects bital periods P < 200 yr and T < 2) is undisputed, but the
with diameters D > 100 km indicate that the two popula- apparent preference for low-inclination orbits of Halley-type
tions are about equally numerous. If this holds true down to comets is a problem, if the classical Oort cloud with its iso-
D < 10 km, their relative contributions to both the Centaurs tropic orbital distribution is considered as the main source.
and the Jupiter family should be in inverse proportion to Thus a flattened inner Oort cloud has also been suggested as
the typical timescales of their respective infeed mechanisms. the principal source of Halley-type comets (Levison et al.,
The argument of Duncan et al. (2004) is that the infeed 2001), but a full treatment of the infeed and capture from
timescale is much shorter for the scattered disk, which is the inner Oort cloud remains to be made.
hence the dominating source of the Centaurs and the Jupi-
ter family. 2.2. Origin of Source Populations
This conclusion needs to be further scrutinized, as more
observations will yield improved estimates of population Considerable progress has been made in the modeling
sizes for both the Jupiter family, the Centaurs, the Kuiper of planetesimal scattering from the accretion zone of the
belt, and the scattered disk. In particular, the extrapolation of giant planets, and hence some insights into the formation
numbers of objects from D > 100 km to D < 10 km is risky, of the Oort cloud, Kuiper belt, and scattered disk have also
especially if collisionally evolved and unevolved popula- been reached (see Morbidelli and Brown, 2004; Dones et
tions are compared. At present, the estimated number (~100) al., 2004). Based on the most realistic simulations available
of D > 100 km Centaurs appears on the small side compared so far, it seems that the inner and classical parts of the Oort
with the infeed rates expected from the two transneptunian cloud should be about equal in mass and number of com-
reservoirs (10 –5–10 –4 yr –1 for a population of ~10 4 D > ets, and that the inner Oort cloud should be only slightly
100 km objects and infeed timescales of 108–109 yr), given “flattened,” i.e., show only a slight preference for prograde
a Centaur dynamical lifetime of ~107 yr. over retrograde orbits (Dones et al., 2004). However, ef-
However, on the one hand, better knowledge of the popu- fects that are likely significant have been neglected, so the
lation sizes may in fact remove any trace of a discrepancy, picture is not yet complete.
and on the other hand, it also seems necessary to spend Thus a comprehensive study of Oort cloud formation in
further effort on constraining the dynamical timescales. For combination with giant planet accretion, and with the young
instance, if large fractions of the Kuiper belt and scattered solar system placed in a dense environment of surround-
disk populations are immune to infeed toward Neptune over ing stars, remains to be performed. In parallel, understand-
much longer timescales, it is not even certain that the two ing the origin of the Kuiper belt and scattered disk is also
sources are rich enough to explain the Centaurs — or, in- presenting a growing challenge. Recent discoveries or sug-
deed, the Jupiter-family comets. gestions of a mixed Kuiper belt structure involving dynami-
Whether or not the current conclusion in favor of the cally hot and cold components with different size and color
scattered disk as the principal source holds up against such distributions, with an outer edge at a ~ 50 AU, are prompt-
efforts, the final answer is bound to have great cosmogonic ing investigations of more complex formation scenarios than
significance. This is because the scattered disk, presumably, used by the early models (Morbidelli and Brown, 2004).
is not collisionally evolved to the same degree as the clas- There may still be a long way to go, and some of the ob-
sical Kuiper belt — otherwise it would be hard to explain servational data — e.g., on size distributions and frequency
 Rickman: Current Questions in Cometary Dynamics 207

of occurrence of binaries — may need to be extended. But in the future. However, real breakthroughs may require the
the outcome in terms of a more solid picture of how the advent of new telescopes and instrumentation. When 30–
transneptunian structures formed along with the giant plan- 100-m telescopes come on line, imaging of the innermost
ets is eagerly awaited, to say the least! coma regions should, by resolving the dust jet structures,
allow the measurement of much more accurate positions of
3. NONGRAVITATIONAL EFFECTS the nuclei than previously possible. Likewise, this will yield
additional information on the main direction of outflow,
Among recent progress in the treatment of nongravita- thus further helping to constrain the nongravitational force
tional effects, let us first mention the self-consistent treat- models.
ment of such effects when calculating both the osculating When it comes to estimating nuclear masses, a main rea-
orbit near perihelion and the original orbit before entry into son for optimism is the prospect of measuring the nongravi-
the planetary system (see Yeomans et al., 2004). It has been tational precession of the perihelia with considerable accu-
found that the original reciprocal semimajor axes (1/a)orig racy (see Davidsson and Gutiérrez, 2003). In the framework
thus derived may differ quite significantly from the corre- of the standard model these are expressed by the param-
sponding quantities derived assuming purely gravitational eter A1. This parameter has a significant advantage over A2
motion, and thus the negative reciprocals found for a small (which similarly measures the delay of perihelion passage)
set of long-period comets may be mostly explained away in that the effect, to first order, does not depend on the peri-
by this effect (Królikowska, 2001). Important as that may helion asymmetry of the gas production curve but only on
be, it is equally important to realize that the comets with the total amount of gas produced from the nucleus. Hence,
positive (1/a)orig are subject to nongravitational forces as facing uncertainties over the actual amount of this perihe-
well. Neglecting this, one may significantly affect the width lion asymmetry, it is easier to interpret the A1 effect than the
of the Oort peak (Królikowska, 2001) and the apparent “in- A2 effect.
ner edge” of the infeed of new comets. Hence, the appar-
ent discrepancy between the inner edge at a = 20,000 AU 4. CONCLUSIONS
and the theoretically expected one at 28,000 AU (Levison
et al., 2001) may not be real, or the problem may be aggra- As in the past, cometary dynamics continues to tackle
vated — further research is necessary. problems of fundamental significance for understanding the
A related problem, also of importance, is what influence formation and evolution of the solar system. We have high-
the nongravitational effects may have on the capture of Oort lighted several examples of further progress to be expected,
cloud comets into short-period, Halley-type orbits. This con- as both numerical simulations and observations continue to
cerns comets with small perihelion distances q — typically, improve. This will involve sharpening our picture of how
q < 2.5 AU. From the fact that the typical, indirect jovian the giant planets formed and the transneptunian disk and
perturbation of 1/a for such a comet (Rickman et al., 2001) Oort cloud were shaped. It will also allow a better under-
is much larger than the typical nongravitational perturba- standing of how comets formed and evolved into their
tion, one would expect the latter to contribute very little. present orbits, and — hopefully — a more solid framework
But there is an important difference between the random- for interpreting the host of physical and chemical data al-
walk nature of the jovian perturbations and the systematic ready obtained and likely forthcoming with Rosetta and
progression of the nongravitational effect. Imagine that at other space missions.
least half the comets experience a decrease of the semima-
jor axis — for instance, due to an excess of outgassing on REFERENCES
the preperihelion branch of the orbit. In the absence of a
Choi Y.-J., Cohen M., Merk R., and Prialnik D. (2002) Long-term
nongravitational effect the comets start their random walk evolution of objects in the Kuiper belt zone — Effects of inso-
in 1/a dangerously close to the parabolic limit, and it is a lation and radiogenic heating. Icarus, 160, 300–312.
well-known fact that this is a severely limiting factor for Davidsson B. J. R. and Gutiérrez P. J. (2003) Estimating the nu-
the capture efficiency (Everhart, 1972). Even a slight ten- cleus density of comet 19P/Borrelly. Icarus, in press.
dency to walk away from this ejection limit might then have Dones L., Weissman P. R., Levison H. F., and Duncan M. J. (2004)
an important consequence by delaying the ejections and Oort cloud formation and dynamics. In Comets II (M. C.
thus increasing the chances for a decisive capture event by Festou et al., eds.), this volume. Univ. of Arizona, Tucson.
direct gravitational interaction with Jupiter. Duncan M., Levison H., and Dones L. (2004) Dynamical evolution
This possibility remains to be investigated. Let us only of ecliptic comets. In Comets II (M. C. Festou et al., eds.), this
volume. Univ. of Arizona, Tucson.
add that, should it be the case that nongravitational effects
Everhart E. (1972) The origin of short-period comets. Astrophys.
may indeed influence the capture of Oort cloud comets sig-
Lett., 10, 131–135.
nificantly, there will also be a dependence on physical prop- Farinella P. and Davis D. R. (1996) Short period comets: Primor-
erties. For instance, comets with small nuclei will be pref- dial bodies or collisional fragments? Science, 273, 938–941.
erentially affected. Jewitt D. C. (2004) From cradle to grave: The rise and demise of
The progress that has been achieved in detailed charac- the comets. In Comets II (M. C. Festou et al., eds.), this vol-
terization of the nongravitational effects is likely to continue ume. Univ. of Arizona, Tucson.
208 Comets II

Królikowska M. (2001) A study of the original orbits of “hyper- Rickman H., Valsecchi G. B., and Froeschlé Cl. (2001) From the
bolic” comets. Astron. Astrophys., 376, 316–324. Oort cloud to observable short-period comets. I. The initial
Levison H. F., Dones L., and Duncan M. J. (2001) The origin of stage of cometary capture. Mon. Not. R. Astron. Soc., 325,
Halley type comets: Probing the inner Oort cloud. Astron. J., 1303–1311.
121, 2253–2267. Yeomans D. K., Chodas P. W., Szutowicz S., Sitarski G., and
Morbidelli A. and Brown M. E. (2004) The Kuiper belt and the Królikowska M. (2004) Cometary orbit determination and non-
primordial evolution of the solar system. In Comets II (M. C. gravitational forces. In Comets II (M. C. Festou et al., eds.), this
Festou et al., eds.), this volume. Univ. of Arizona, Tucson. volume. Univ. of Arizona, Tucson.
PART IV:
THE NUCLEUS
 Keller et al.: In Situ Observations of Cometary Nuclei 211

In Situ Observations of Cometary Nuclei

H. U. Keller
Max-Planck-Institut für Aeronomie

D. Britt
University of Central Florida

B. J. Buratti
Jet Propulsion Laboratory

N. Thomas
Max-Planck-Institut für Aeronomie
(now at University of Bern)

It is only through close spacecraft encounters that cometary nuclei can be resolved and their
properties determined with complete confidence. At the time of writing, only two nuclei (those
of Comets 1P/Halley and 19P/Borrelly) have been observed, both by rapid flyby missions. The
camera systems onboard these missions have revealed single, solid, dark, lumpy, and elongated
nuclei. The infrared systems gave surface temperatures well above the free sublimation tempera-
ture of water ice and close to blackbody temperatures. The observed nuclei were much more
similar than they were different. In both cases, significant topography was evident, possibly
reflecting the objects’ sublimation histories. Dust emission was restricted to active regions and
jets in the inner comae were prevalent. Active regions may have been slightly brighter than
inert areas but the reflectance was still very low. No activity from the nightside was found. In
this chapter, the observations are presented and comparisons are made between Comets Halley
and Borrelly. A paradigm for the structure of cometary nuclei is also described that implies
that the nonvolatile component defines the characteristics of nuclei and that high porosity, large-
scale inhomogeneity, and moderate tensile strength are common features.

1. INTRODUCTION It is important to emphasize that prior to the spacecraft

encounters with Comet 1P/Halley in 1986, the existence of
The nuclei of most comets are too small to be resolved a nucleus was merely inferred from coarse observations.
by Earth-based telescopes. Even on the rare occasions when While the idea that a single, small, solid body was at the
a large, possibly resolvable, long-period comet, such as center of a comet’s activity (Whipple, 1950) was widely
Comet Hale-Bopp (C/1995 O1), enters the inner solar sys- accepted by the scientific community, it was only with the
tem, the nucleus is obscured from view by the dust coma. arrival of the Russian Vega 1 and 2 and European Space
Hence, the only means of studying the details of a cometary Agency’s Giotto spacecraft at Comet Halley in 1986 that
nucleus is by using interplanetary space probes. this could be confirmed and other concepts [e.g., the “sand-
Spacecraft passages to within 10,000 km allow many bank” model of Lyttleton (1953)] could finally be rejected.
different techniques to diagnose the properties of the nu- It was to be 15 years before another image of a cometary
cleus. The most obvious is high-resolution imaging. How- nucleus would be acquired, when NASA’s Deep Space 1
ever, there are several other remote sensing techniques that (DS1), a technology development mission, successfully im-
could give important information. Only visible and infrared aged the nucleus of Comet 19P/Borrelly in September 2001.
spectroscopy have been used, giving estimates of the surface Remarkably, the two nuclei observed by these missions
temperatures of both Comet 1P/Halley and Comet 19P/Bor- were extremely similar.
relly. Indirect measurements through analysis of the volatile Comet Halley is the most prominent member of comets
(gas) and nonvolatile (dust) components in situ, for example, on highly inclined (162.24°) and eccentric (0.967) orbits,
are also vital to our understanding of cometary nuclei since which are thought to have been members of the Oort cloud.
they give information on the composition and structure of Its period was 76.0 yr and its perihelion distance 0.587 AU.
the nucleus. Ion mass spectrometers have been particularly It is one of the most active short-period comets. Therefore,
useful in this respect for our current understanding. its appearance during the space age triggered the launch of

211
212 Comets II

TABLE 1. Cometary flybys.

Closest Date and Time Flyby Heliocentric Phase Angle Best Pixel Scale Comment on
Approach of Closest Velocity Distance of Approach Obtained Imaging Systems
Spacecraft Distance (km) Approach (km s–1) (AU) (degrees) (m/pixel) and Data
Vega 1 8890 06.03.1986 79.2 0.792 134 Out of focus
07:20:06 (FWHM = 10 pixels)

Vega 2 8030 09.03.1986 76.8 0.834 121 Saturated on nucleus

07:20:00

Giotto 596 14.03.1986 68.4 0.89 107.2 38 Little three-dimensional

00:03:02 information because of
reset 9 s before closest
approach

Deep Space 1 2171 22.09.2001 16.5 1.36 88.0 47 Some stereo information,
minimum phase angle
52°, no color

the “Halley Armada,” comprising five spacecraft that en- The Vega 2 TVS also experienced problems. The images
countered the comet in spring 1986. The Japanese probes, are saturated on the nucleus and the data of the coma that
Suisei and Sakegaki (Hirao and Itoh, 1987), did not pen- were returned are limited in dynamic range to effectively
etrate the comet’s inner coma and did not carry experiments only 5 bits (32 gray levels) digital resolution. While these
for studying the nucleus. The Vega 1 and 2 spacecraft made data are of little interest for direct studies of the nucleus
encounters on March 6 and 9, 1986, respectively (Table 1). surface, they do provide some information on the near-
Just after midnight on March 14, 1986, the Giotto space- nucleus jet structures of Comet Halley (Fig. 1). In particular,
craft made its closest approach (596 km). The Vega and the data indicate a sunward “fan” of dust emission (Larson
Giotto spacecraft all carried sophisticated remote sensing
experiments for determination of the properties of the nu-
cleus, and we discuss those results in turn in section 2. In
section 3, we discuss the results on the nucleus of Comet
10P/Borrelly obtained from the DS1 mission.

2. COMET HALLEY’S NUCLEUS

2.1. Vega Observations

The Vega cameras imaged the nucleus throughout their

encounters with Comet Halley. However, both imaging sys-
tems experienced severe problems. The Vega 1 television
system (TVS) system was out of focus. The point-spread
function (PSF) of the instrument was subsequently found
to be at least 10 pixels full-width half-maximum (FWHM),
caused by a displacement of the detector with respect to the
focal plane of about 0.5 mm (Abergel and Bertaux, 1995).
This effect degraded the effective resolution from around
150 m (at closest approach) to 1.5 km at best and made the
images appear extremely fuzzy. While the nucleus was re-
solved and observed over a range of phase angles, a huge
amount of work (e.g., Merényi et al., 1990) had to be in-
vested to correct the images for the degraded PSF and to
derive the basic shape of the nucleus. This has proven to Fig. 1. The Vega 2 image (#1690) from the Vega atlas of Comet
be important since the orientation of Comet Halley’s nu- 1P/Halley (Szegö et al., 1995) is cleaned and geometrically cor-
cleus at the time of the Vega 1 encounter provides a strict rected. It shows the nucleus and its vicinity from a distance of
constraint on models of the rotational state of the comet 8030 km (near closest approach) at a phase angle of 28° on
(Belton, 1990) (see below). March 9, 1986.
 Keller et al.: In Situ Observations of Cometary Nuclei 213

et al., 1987) that may have originated from a quasi-linear

“crack” in the surface (see also Szegö et al., 1995). The data
therefore suggest that activity is restricted to “active regions”
(confirmed by Giotto images). The lack of structure in the
comae of some short-period comets [e.g., Comet 4P/Faye
(Lamy et al., 1996)] may indicate a more homogeneously
active surface may be appropriate for some nuclei, but Vega,
Giotto, and DS1 images clearly show that this is not the case
for Comets Halley and Borrelly.
Further support for limited areas of activity comes from
the Vega IKS experiment, which determined the surface tem-
perature of Comet Halley’s nucleus. Temperatures in excess
of 350 K were recorded (Emerich et al., 1987a,b). A surface
undergoing free sublimation of water ice (at 1 AU helio-
centric distance) can only reach an equilibrium temperature
of about 220 K even for low albedo values. The IKS mea-
surement indicates that significant parts of Comet Halley’s Fig. 2. Six examples of HMC images of P/Halley in original
surface were inactive. Care in the interpretation is necessary, frame sizes. Image #3056 was taken 1814 s (distance to nucleus
however, because micrometer-sized dust particles from the 124,000 km) and image #3502 was taken 31 s (2200 km) before
surface rise in temperature rapidly once ejected. If the op- closest approach.
tical depth, τ, of these particles approaches 1, the effect is to
mask the thermal emission from the (possibly) lower tem-
perature surface. 2.2.2. Bulk properties of the nucleus. In the HMC im-
Indeed, the first impressions of the Vega TVS data sug- ages only ~25% of the surface area accessible to the cam-
gested τ ≈ 1 (based, to some extent, on the fuzziness of the era is illuminated by the Sun, owing to the large phase angle.
pictures now attributed to defocusing). This temperature Fortuitously, the outline of the dark limb is visible against
measurement has not been rediscussed subsequently, but the illuminated dust in the background. This unique circum-
support for high surface temperatures came from the DS1 stance provided a good enough constraint that the fuzzy
flyby (Soderblom et al., 2002) where optical depth was not Vega images taken from different solar and rotational phase
a problem because the activity of Comet Borrelly was more angles could be interpreted and the bulk properties (volume)
than one order of magnitude lower than that of Comet of the nucleus could be determined. The maximum length
Halley (at the encounters). These high temperatures con- of the nucleus from Vega images was 15.3 km. A compari-
firm that activity is restricted and most of the surface of both son with the length seen by HMC (14.2 ± 0.3 km) requires
comets is inert. the long axis of the nucleus to be 22° above or below the
After the Vega encounters the size and shape of the image plane. A major effort of the Vega team went into
nucleus of Comet Halley was not obvious. It was not even defining the orientation and illuminated outline of the nu-
clear that there was only a single nucleus. False color im- cleus for both of the flybys (Merényi et al., 1990; Stooke
ages artificially cropped at certain isophote levels [e.g., and Abergel, 1991). Additional constraints come from the
cover images of Sagdeev (1988) and Szegö et al. (1995)] are period(s) of the cometary brightness fluctuations derived
strongly misleading if interpreted as showing the nucleus. from Earth-based observations (see also section 2.2.5). Vari-
It took the observations of the subsequent Giotto flyby to ous solutions of the rotation axis and period(s) were sug-
provide the basic information for the interpretation of the gested [more elaborate interpretations come from Belton et
Vega images. al. (1991) and Szegö et al. (1995)], but none satisfies all the
constraints. The solution by Belton et al. (1991) needs the
2.2. Giotto Observations “thick and the thin” ends of the nucleus on the Vega 1 images
interchanged from the orientation derived by the Vega team.
2.2.1. Imaging by the Halley Multicolour Camera. In addition, the distribution of active areas on the nucleus
More than 2000 images of Comet Halley’s coma and surface does not satisfy the constraints derived from HMC
nucleus were acquired by the Halley Multicolour Camera images. A best fit triaxial ellipsoid with 7.2, 7.22, and 15.3 km
(HMC) onboard the Giotto spacecraft. A detailed descrip- for the axes was derived by Merényi et al. (1990) with an
tion of the observations and results is given by Keller et al. estimated error of 0.5 km in each figure. Taking into account
(1995). During approach, the phase angle was 107° and the deviations from this ellipsoid (with a volume of 420 km3)
changed only slightly up to the last good image taken from led to an estimated volume of 365 km3 and an overall surface
a distance of 2000 km with a resolution of 45 m/pixel. The of 294 km2 for Comet Halley’s nucleus. Combining this vol-
Giotto spacecraft was then hit by large dust particles and ume with a mass estimate of 1–3 × 1014 kg (Rickman, 1989)
lost contact to ground. A representative sample of images determined from nongravitational forces yields a density of
is shown in Fig. 2. the nucleus of 550 ± 250 kg m–3. Other estimates of the
214 Comets II

density yield a wider range, not excluding the “intuitive” The color of the nucleus was found to be slightly reddish
value of 1000 kg m–3 (Sagdeev et al., 1988; Peale, 1989). with a gradient of 6 (±3)% per 100 nm between 440 nm and
A surprisingly (at that time) low geometric albedo of 810 nm (Thomas and Keller, 1989), similar to P-type as-
0.04+0.02
–0.01 of the nucleus was derived from Vega images (Sag- teroids. The variation of the reflectivity over the visible sur-
deev et al., 1986) assuming a Moon-like phase function. face was moderate (Keller, 1989), somewhat in contrast to
Similar values are found for other comets from groundbased the results of the more detailed observations of the nucleus
visible and IR observations (Keller and Jorda, 2002; Lamy of Comet Borrelly (see section 3.1). No “icy” patches could
et al., 2004). Comets are among the darkest objects of the be seen, either on HMC or on Vega images. Active areas
solar system. This albedo of 0.04, measured directly for the may possibly be slightly brighter than their surroundings,
first time, has been widely used as a canonical value to de- but the increased dust density could confuse the issue. Pure
termine sizes from photometric observations. The reflectiv- water ice on the surface can be ruled out. However, small
ity of the illuminated surface derived from HMC images contaminations of the ice with carbon suffice to reduce the
for a phase angle of 107° was found to be less than 0.6% reflectivity to the observed low value.
(Keller et al., 1986). Fitting the observed reflectivity (I/F) 2.2.3. Topography and morphology. Two spheres, a
across the illuminated surface seen in the HMC images con- larger one on the south end (Fig. 3), connected to each other
firmed the Moon-like phase function and yielded a reflectiv- creating a “waist” would be a higher mode approximation
ity at zero phase angle between 0.05 and 0.08, in reasonable than the ellipsoid. The near 2 : 1 elongation of the nucleus
agreement with estimates of the peak reflectivity (Keller et is rather typical for cometary nuclei (Keller and Jorda,
al., 1995; Thomas and Keller, 1989). 2002; Lamy et al., 2004). Prominent large-scale features are

Fig. 3. Features on the surface of the nucleus of Comet 1P/Halley. Sections of the composite image (center bottom) are extracted
and expanded by a factor of 3 to show, in detail, notable features on the nucleus mentioned in the text. Nonlinear enhancement has been
applied to provide improved contrast. From Keller et al. (1988).
 Keller et al.: In Situ Observations of Cometary Nuclei 215

the northeastern limb that follows a straight line and ter-

minates in an almost rectangular corner (duck tail) that
protrudes by ∆R/R = 0.3 above the radius of the best-fit
ellipsoid. The terminator on the south (morning) side of the
central depression paralleled by a bright band (ridge) indi-
cates a large-scale feature such as a terrace. The central
depression tapers toward the mountain. Its illuminated tip
lies about 900 m above the best-fit ellipsoid. For more de-
tails, see Keller et al. (1995).
The roughness of the nucleus is visible down to the reso-
lution limit of the HMC observations (45 m/pixel). The
chain of hills are an example for the typical scalelength of
0.5–1 km; others are the structures inside the crater. It cov-
ers a projected area of 12 km2 and its depth was estimated
to be only 200 m (Schwarz et al., 1986). Most topographic
features may be shallow because of the large solar zenith
angle (long shadows) during the HMC observations. The
strongly irregular shape, the protrusions, the topographic
features, the high porosity and low gravity of the nucleus,
and the predominance of nonvolatile material all suggest
that the surface morphology is characterized by roughness Fig. 4. The directions of “filaments” seen in the dust emission.
down to small scales (Kührt et al., 1997). The filaments are small inhomogeneities (500 m in diameter at
2.2.4. Activity. their source). This fine structure in the emission would have been
2.2.4.1. Overall activity: Activity characterized by dust far too faint to be seen by simultaneous groundbased observers.
jets or cones can be directly observed at the illuminated area The filaments appear to criss-cross each other.
just below the northern tip of the nucleus around the sub-
solar point and in direction roughly toward the Sun. In this
region the maximum brightness of the images is observed other, obviously due to the influence of topography (Tho-
just above the limb. The strongest jet, however, does not mas et al., 1988; Huebner et al., 1988). A few filaments
originate from this location. At radial distances from the point away from the Sun, emerging behind the dark limb.
surface lager than the radius of the nucleus, the maximum They probably originate from the small insolated sliver of
of the dust column density shifts to an azimuth about 40° the nucleus apparently pointing, in projection, in the anti-
south of the projected comet-Sun direction, the direction solar direction. No indications of activity on the nightside
of the strongest dust jet. Dust emission into this direction of the nucleus were found.
is about three times stronger than the subsolar jet and domi- The interaction of jet features is also evidenced by the
nates the overall shape of the dust coma (compare the im- curved dark area in the dust just in front of the lower end
ages of Fig. 2). This strong jet originates from the illumi- of the bright patch. A three-dimensional gas dynamics
nated hemisphere turned away from the observer (Thomas calculation confirms this interaction, mainly caused by the
and Keller, 1988). A third rather weak jet is directed (in concavity (Fig. 3) at the waist (Crifo and Rodionov, 1999).
projection) about 90° off the comet-Sun direction toward In a series of papers, Crifo et al. (2002) and Rodionov et al.
the north. The overall shape of the dust isophotes can be (2002) have modeled the observations based on the assump-
well modeled by the superposition of these three jets with tion of a uniformly active homogenous nuclear surface
a cone width of ~40° (FWHM). Belton et al. (1991) iden- rather than on limited active areas within a predominantly
tified five jets from groundbased, Vega, and Giotto images. inert surface. They assume that the dust production is pro-
The position of their main jet, however, is not in agreement portional to the insolation. This leads to a strong concen-
with the HMC observations. tration of the dust production (and density) toward the
2.2.4.2. Structures and filaments and topography: The Sun-comet line and in the sunward hemisphere. The ratio
extent of the visible active area covers about 3 km along of the integrated dust of the sunward to that of the anti-
the bright limb. Here the highest-resolution images taken sunward hemisphere would then be about an order of mag-
show structures on the surface and in the dust jet above it. nitude larger than observed (section 3.2) (see Keller et al.,
Narrow filamentary structures can be discerned starting at 1995). While Comet Halley was active enough that the hy-
the surface with footprints about 500 m in diameter. Some pothesis of a homogenous surface activity could be justi-
of these filaments can be followed out to more than 100 km fied and tested, the jets observed during the flyby of Comet
(Thomas and Keller, 1987a,b). Overall, more than 15 nar- Borrelly (see section 3.3) obviously cannot be explained by
row jets and filaments, some strongly collimated with open- a homogenously active surface.
ing angles of a few degrees, were revealed by image proc- The limited width (FWHM ≈ 40°) of the major jets sug-
essing (Fig. 4). Some of the filament directions cross each gests that they do not originate from flat or convex active
216 Comets II

areas on an otherwise inert surface. Shallow indentations,

however, like the crater or larger concave topography (like
the bright patch) suffice to collimate the dust (Keller et al.,
1992). A crude axisymmetric gas-dynamics model that
describes the acceleration of dust particles (typically 10 µm)
from the surface (Knollenberg, 1994) was used to simulate
these jets. The narrow fine filaments with opening angles
of a few degrees cannot be explained by cavities that would
be too deep for the Sun to reach their bottoms. Rather than
by an enhancement of activity, the filaments can be formed
by reduction of activity in the center of an active area simu-
lating strong (axisymmetric) interactions of shock fronts
(Keller et al., 1995).
2.2.5. Nucleus rotation. Shortly after the encounters
with Comet Halley, the rotation period of the nucleus was
derived by comparing the various images during the three
flybys. In a first-order approach, a stable rotation around
the axis of maximum inertia (perpendicular to the long axis)
was assumed (Wilhelm, 1987; Sagdeev et al., 1989). Fits
were found for a period slightly above 50 h (2.2 d). Ground-
based observations of the coma brightness variations yielded
a period of about 7 d, but dynamical features (jets, shells)
were in agreement with the 2.2-d periodicity. It is now Fig. 5. The highest-resolution image of the Comet 19/P Borrelly.
widely assumed that the spin state of Comet Halley is ex- This image was taken at 3556 km from the comet and has a scale
cited, i.e., that the rotation is not in its energetic minimum of 47 m/pixel.
and includes nutation (Sagdeev et al., 1989; Samarasinha
and A’Hearn, 1991; Belton et al., 1991). There is no com-
mon understanding of the details (Keller and Jorda, 2002). veals coarse topographic information. Based on this digital
Three flybys and a long series of groundbased observations terrain model, morphological and photometric information
were not sufficient to pin down the rotational parameters. of the surfaces of various terrains can be derived. These
more detailed analyses and interpretations have recently
3. COMET BORRELLY’S NUCLEUS been published in a special volume of Icarus devoted mainly
to the DS1 flyby of Comet Borrelly. Here we provide a sum-
The next spacecraft close encounter with a comet oc- mary of those results.
curred on September 22, 2001 when the DS1 spacecraft Comet 19P/Borrelly is a Jupiter-family comet with an
flew by the Comet 19P/Borrelly. The DS1 mission was orbital period of 6.86 yr, a semimajor axis of 3.61 AU, an
primarily an engineering test of a solar-electric ion-propul- inclination of 30.24°, and a perihelion distance of 1.359 AU.
sion system, but part of the mission goals were to test space- The flyby occurred eight days after perihelion while the
craft instruments and software with close flybys of small comet was crossing the ecliptic. DS1 imagery showed an
bodies. The primary data for this paper comes from imagery 8.0 ± 0.1 km × 3.15 ± 0.08 km object shaped like a left
taken by the Miniature Integrated Camera and Spectrom- footprint with a heel at the bottom of Fig. 5 and the sole
eter (MICAS) instrument, which included a 1024 × 1024 toward the top. The rotation axis derived from Earth-based
frame-transfer CCD. The mission plan was to fly by Comet observations corresponds to the short axis exiting near the
Borrelly with a miss distance of approximately 2000 km on central mesa (see section 3.2). The pole obliquity and or-
the sunward side at a relative speed of 16.5 km s–1 (Soder- bital longitude are 102.7° ± 0.5° and 146° ± 1°, correspond-
blom et al., 2002). Because MICAS was in a fixed orienta- ing to RA = 214.01° and DEC = –5.07° (Schleicher et al.,
tion on the spacecraft, the whole spacecraft was rotated to 2003). The pole is pointed sunward, with a subsolar lati-
keep Comet Borrelly in the field of view. tude of ~60° during the encounter (Soderblom et al., 2002).
During the 90 minutes before closest approach, 52 vis- Comet Borrelly has an average disk integrated geometric
ible wavelength images were taken with MICAS at solar albedo of 0.029 ± 0.006 (Buratti et al., 2004), even slightly
phase angles between 88° and 52°. Shown in Fig. 5 is the lower than the value measured for Comet Halley (see sec-
highest-resolution image, taken at 3556 km from the comet, tion 2.2.2). The albedo values of Comet Halley and Comet
with a resolution of 47 m/pixel. Because Comet Borrelly Borrelly are comparable to those of other dark bodies in the
has a long rotation period of 25 ± 0.5 h, DS1 saw essen- solar system, including the low-albedo regions of Iapetus
tially only the illuminated part of one hemisphere of the (Buratti and Mosher, 1995), the uranian rings (Ockert et al.,
comet. The full shape and volume of the nucleus could not 1987), and the lowest-albedo C-type asteroids (Tedesco et
be revealed. Matching images taken between solar phase al., 1989), including several in comet-like orbits (Fernández
angles of about 60° and 52° provides stereo pairs and re- et al., 2001).
 Keller et al.: In Situ Observations of Cometary Nuclei 217

3.1. Disk-Integrated Photometry

The DS1 encounter with Comet Borrelly enabled the first

photometric modeling of a cometary nucleus. Physical at-
tributes of the surface of the nucleus, including the com-
paction state of the optically active portion of the regolith
and the macroscopic roughness, can be derived by fitting
photometric models to the observed brightness as a func-
tion of viewing geometry. The nucleus must be observed
over a range of solar phase angles to perform this type of
analysis.
Figure 6 shows a disk-integrated solar phase curve of
Comet Borrelly created from Earth-based observations
(Lamy et al., 1998; Rauer et al., 1999) and spacecraft mea-
surements, along with a disk-integrated fit to Hapke’s pho-
tometric model (Hapke, 1981, 1984, 1986). The derived
single scattering albedo w = 0.020 and the asymmetry of
the phase function g = –0.45 led to an opposition surge
amplitude of B0 = 1.0 and low compaction indicated by the
parameter h = 0.0084. The mean slope angle of 20 relates
to surface roughness on scales ranging from clumps of par-
ticles to mountains.
Comet Borrelly’s nucleus has surface physical proper-
ties similar to those of C-type asteroids (Helfenstein and
Veverka, 1989). The single-scattering albedo is lower than Fig. 7. Unit and feature map of Borrelly based on analysis of
measured for any other body. The phase integral derived the MICAS imagery, including stereo pairs.
from the data in Fig. 6 is 0.27 ± 0.01, to yield a Bond al-
bedo of 0.009 ± 0.02, again the lowest of any object in the
solar system so far measured. These values, however, de- 3.2. Surface Morphology
pend critically on the few Earth-based measurements.
The extremely low albedo values require high micro- Comet Borrelly has a complex surface with a range of
porosity of the surface that traps the light very efficiently. morphological features. Interpretations of these features
Appropriate modeling will have to show whether these based on analysis of the MICAS imagery, including stereo
values can be reached with realistic physical properties. pairs, are shown in Fig. 7. Four major morphological units
can be discerned — dark spots, mottled terrain, mesas, and
bright terrain — and two surface features — ridges and
fractures. One of the most interesting (but expected) results
is the absence of impact craters, commonly associated with
small bodies. The upper limit for their diameters is 200 m
(Soderblom et al., 2002). While there are a number quasi-
circular depressions visible, they are most abundant in the
mottled terrain and have roughly similar diameters and
sometimes regular spacing (cf. the chain of hills on the
surface of Comet Halley). Our analysis suggests that they
may be sublimation features. Using a simple shape model,
a Lommel-Seeliger photometric function, and the phase
curve illustrated in Fig. 6, a map of normal reflectances
(Buratti et al., 2004) illustrates variegations up to a factor
of almost four in albedo (from 0.012 to 0.045) that are
correlated with geologic terrains and features. For low-al-
bedo objects such as Comet Borrelly, normal reflectance
and geometric albedo are equivalent.
Dark spots: These are the darkest areas on the comet,
with a geometric albedo around 0.015. Photometric profiles
of the dark spots confirm that they are not shadowed and
Fig. 6. The disk-integrated solar phase curve of Borrelly created have photometric properties similar to the mottled terrain
from groundbased, spacebased (HST), and spacecraft (DS1) obser- (Nelson et al., 2004; Buratti et al., 2004). Dark spots ap-
vations. pear to overlie the mottled terrain and hence are the strati-
218 Comets II

graphically highest unit on Comet Borrelly. They probably

represent the oldest surface lags.
Mottled terrain: The mottled terrain is stratigraphically
below the dark spots and consists of areas rough at pixel
resolution with depressions, troughs, hills, and ridges. The
terrain is dominated by a mixture of quasicircular depres-
sions and low hills. The quasi-circular depressions are about
200–300 m in diameter and are most common on the heel
portion of the comet. Low hills tend to be roughly aligned
along the long axis of the comet and spaced approximately
300–400 m apart (cf. the chain of hills on Comet Halley;
see section 2.2.3). The morphology and albedo variations
suggest that the mottled terrain represents older surface lag
deposits that have been subjected to extensive sublimation
erosion leading to terrain softening and collapse (Britt et
al., 2004).
Mesas: Mesas consist of several areas of steep, bright-
appearing slopes surrounding darker, flat tops. These fea-
tures are primarily in the central portion of the comet and Fig. 8. The dominant dust emission on the sunward side is di-
appear, along with the smooth terrain, to be associated with vided into α and β jets. The α jet is aligned at the core of the
some of the active jets. Mesa formation is probably driven, main jet. The β jet shown here is one of several roughly parallel
like terrestrial mesas, by erosion (sublimation) on the steep smaller collimated jets. The range of this image is about 4825 km.
slopes. The mesa slopes are probably one of the most freshly
exposed areas on the comet and may be a source of signifi-
cant gas/dust loss. tion is accounted for by the jets, about 20% is from the fan,
Smooth terrain: Photometric analysis suggests that this and about 15% is in other fans. About 30% of the dust
unit is slightly rougher than average at subpixel scales with appears above the nightside hemisphere (Boice et al., 2002).
geometric albedos of typically 0.032 and in some spots as This may well be material emitted from the dayside hemi-
high as 0.045 (Buratti et al., 2004). The fine pattern of al- sphere, appearing on the nightside due to projection effects.
bedo variegations may indicate areas of differential activity The comet’s active area has been estimated at approximately
and/or surface age as part of the resurfacing processes from 8% of the total surface (Boice, 2002).
dust ejection. Hubble Space Telescope (HST) observations estimated
Ridges and fractures: Digital terrain models indicate that the water production rate to 3.0 ± 0.6 × 1028 s–1 at the time
the area of the heel is canted about 15° relative to the sole of encounter, or about 600 kg s–1 (Weaver et al., 2003).
(Soderblom et al., 2002; Oberst et al., 2004). Most of the Integrated over Comet Borrelly’s orbit the water mass loss
ridges and fractures are associated with the boundary of this per apparition would be approximately 2 × 1010 kg. Add-
canted area. These ridges of 1–2 km in visible length are ing a similar amount of dust suggests an average erosion
oriented normal to the long axis of the comet and could of the total surface between 0.5 and 1 m per apparition
indicate compressional shortening (Britt et al., 2004). If this based on a density of the nucleus <1.000 kg m–3. Water
interpretation is correct, the features require some tensile sublimation is strong enough to remove up to 10 m of sur-
strength of the nucleus. face layers at active areas (Huebner et al.,1986). For in-
stance, the mesa slopes could retreat 10–20 m per apparition
3.3. Jets and Active Areas (Britt et al., 2004). This level of erosion makes active com-
etary surfaces one of the most dynamic and rapidly chang-
DS1 observed dust and gas activity including collimated ing features in the solar system.
jets and fans (Soderblom et al., 2002). The largest central
jet, called the α jet, is a dusty beam a few kilometers wide 4. COMPARISONS OF COMETS HALLEY,
at the comet (cf. active areas of Comet Halley; see sec- BORRELLY, AND ASTEROIDS
tion 2.2.4.1), extending out to at least 100 km and canted
30° from the comet-Sun line (Fig. 8). This feature appears 4.1. Comets Halley and Borrelly
to emanate from the broad central area of the comet, which
includes the mesas and the smooth terrain. There are sev- The Vega, Giotto, and DS1 measurements of cometary
eral smaller parallel jets, called the β jets, which are about nuclei are far more similar than they are different. Both
200–400 m at the base [cf. filaments of Comet Halley (sec- Comets Halley and Borrelly are irregularly shaped, very
tion 2.2.4.2)], about 4–6 km in length, and canted about 15° dark, and active over minor fractions of their surfaces (pro-
from the direction of the α jet. The fan feature is diffuse ducing “jets”), and have surface temperatures close to those
dust apparently emanating from the smooth terrain unit at expected for a blackbody.
the end of Comet Borrelly’s heel and oriented roughly along The nuclei show surface features inconsistent with a
the Sun-comet line. About 35% of the comet’s dust produc- uniformly shrinking ellipsoid (or snowball) and some ten-
 Keller et al.: In Situ Observations of Cometary Nuclei 219

sile strength is apparent in protrusions such as the moun- are very different. Comets Halley and Borrelly are char-
tain or duck tail of Comet Halley or the canted low end of acterized by a lack of impact craters and the existence of
Comet Borrelly (see section 3.2). It is interesting that ob- complex and sublimation-driven erosional features such as
servations of structures have been interpreted by the DS1 mesas, hills, and mottled terrain. Disk-resolved analysis of
team using geological analogs — an approach not adopted Comet Borrelly’s roughness and particle phase function
by the Giotto team, for example. The stereo coverage re- suggests that the comet does not get rougher with age, and
sulting in a digital terrain model, better solar illumination, that regions of the comet are infilled with or mantled by
and less interference of the smaller dust production provide native dust. The surfaces of asteroids are dominated by
for a more detailed analysis of the surface features and impact craters. The energy to drive the asteroidal erosion
morphology in the case of Comet Borrelly. Nonetheless, process comes from episodic impact collisions, so this is
here too the similarities are more striking than the differ- necessarily a very slow process compared, e.g., to terres-
ences. The dark spots and ridges seen on Comet Borrelly trial erosive processes. Cometary erosion is driven by sub-
(Fig. 7) are very similar to the chain of hills seen at Comet limation of volatiles during the cometary perihelion passage
Halley (Fig. 3). The smooth terrain on Comet Borrelly is around the Sun. For Jupiter-family comets like Borrelly with
probably associated with activity and looks rather like the frequent perihelion passages, sublimation-driven erosion
central depression on Comet Halley, which also shows evi- alters landforms at rates that would be fast even by terres-
dence of activity (at least on its sunward extreme). The trial standards. Fundamentally, surfaces of comets are domi-
elevations on Comet Borrelly may be similar to the moun- nated by sublimation while the surfaces of asteroids are
tain feature on Comet Halley, while the mottled terrain is dominated by impacts.
reminiscent of the region between the big active area and
the chain of hills on Comet Halley. 4.3. The Nucleus Paradigm
Active regions appear to have slightly higher albedos
than inactive regions, but nowhere does the albedo exceed The spacecraft flybys revealed dark, evolved, solid
0.045 at the resolution of the images (around 50–100 m/ cometary nuclei. The nonvolatile compounds outweigh the
pixel). It cannot be completely ruled out that there are small ice (McDonnell et al., 1991), quite in contrast to what was
areas within these active regions that have (high) albedos considered before the Comet Halley flybys when an upper
closer to that of pure ice. The inhomogeneity of the sur- limit for the dust to gas ratio of 0.3 was used for the engi-
face activity and topography clearly influence the structure neering model (Divine, 1981). Hence, their overall physi-
of the inner coma, making it difficult to extract information cal properties are better characterized by the nonvolatile
about the nature of the source, the initial acceleration, and component and not by (water) ice (Keller, 1987). The ex-
particle fragmentation in the flow (Ho et al., 2003). While tremely low reflectivity argues for a surface of high poros-
some preliminary conclusions on the structure of the source ity in accord with the low bulk density of the whole nucleus.
region may be possible, neither dataset is really good enough The low tensile strength and porosity of the material is also
to distinguish between different surface emission models. reflected in the frequent fragmentation of the dust particles
The similarities of both cometary nuclei are striking. leaving the nucleus within the gas stream (Thomas and
There is no hint that comets originating from the Oort cloud Keller, 1990).
(Comet Halley) look different from nuclei originating in the The limited areas of activity can hardly be discerned
Edgeworth-Kuiper belt (Comet Borrelly) [see Dones et al. from the generally inert surface, but they do seem to be
(2004) and Duncan et al. (2004) for discussions on these slightly more reflective. An active region on a Jupiter-family
two cometary source regions]. comet with a perihelion distance near 1 AU will lose about
The fortuitous observations of the complete outline of 5–10 m depth of surface layer per revolution around the Sun
Comet Halley’s nucleus, including its unilluminated parts, (Huebner et al., 1986). Consequently, the interior (mate-
by HMC and the Vega 1 and 2 images provide a reasonable rial with volatiles that surfaces in active areas) looks simi-
shape model and the overall volume of the nucleus. This lar to the material of the (inert) surface. The nucleus consists
information is completely missing in the DS1 data. It took of a porous dust matrix that is in parts enriched with vola-
three flybys to model the complex rotation of Comet Halley, tiles producing the activity. The inert surface layers are a
even though the quality of the Vega images was not good crust of depleted matrix material that can form large topo-
enough to provide sufficient reference points for uncontro- graphic protrusions (the duck tail and mountain on Comet
versial interpretations. No information on the rotation of Halley and features such as mesas on Comet Borrelly). The
Comet Borrelly can be expected from the DS1 encounter. fact that the surface temperature of the inert regions (com-
prising 80–90% of the surface area) reaches that of a black-
4.2. Comet and Asteroid Surfaces body is then unsurprising. In an active region, any loose
mantle of dust (regolith) that might form would be blown
The images of Comets Halley and Borrelly highlight the away during perihelion passage (Kührt and Keller, 1994).
similarities and differences between comets and other small The present nuclei of Comets Halley and Borrelly are
bodies like asteroids and small moons. Photometric analy- the small remnants of frequent splittings and shedding of
sis of Comet Borrelly’s nucleus suggests that it has a rego- blocks of material. Estimates of the mass in Halley’s asso-
lith and that its surface looks similar to that of asteroids. ciated meteor streams show that its original mass 2000 to
However, the processes at work on the two classes of bodies 3000 revolutions ago was 5–10 times bigger (Hughes, 1985).
220 Comets II

The splitting is facilitated by the physical inhomogeneity

of the nucleus agglomerated from subnuclei. The observed
topography with typical scalelengths from 0.5 to 1 km
(chain of hills, mottled terrain, dark spots) to the highly
elongated shapes of the nuclei of Comets Halley and
Borrelly, with indications of a “waist,” reflects their inner
structure.
The difficult detection and first characterization of the
nucleus of Comet Halley in 1986 provided the fundamen-
tal data for our understanding of the nature of comets. It Fig. 9. The nucleus of Comet Wild 2 is shown in this image
took 15 years to confirm these observations and to extend taken by the Stardust nagivation camera during the spacecraft’s
the conclusions to a second object. closest approach to the comet on January 2, 2004. The largest
Comet Halley is the most productive short-period comet, visible dimension is about 5 km. The image was taken within a
but yet only a minor fraction of its surface is active. Typical distance of 500 km of the comet’s nucleus. (The image was pro-
duced for distribution via the Web, and does not represent the final
Jupiter-family comets display activity levels one or two
quality.) From the NASA Stardust Web page (Principal Investi-
magnitudes less than this, e.g., Comet Borrelly. How is ac-
gator D. Brownlee, University of Washington, Seattle).
tivity at this low level maintained over many revolutions
around the Sun? How does activity really work? The physi-
cal explanation of this phenomenon is a key to our under-
standing of comets. The answer will require new missions formation can be significantly improved with digital terrain
where the onset and details of activity can be studied in models derived from stereoscopic views. The overall size
depth. and shape of a cometary nucleus as well as its rotation
parameters can only be accessed by multiple flybys or, even
5. OUTLOOK better, by a comet rendezvous where the spacecraft orbits
the nucleus.
While Earth-based observations are now able to deter- The European Space Agency’s Rosetta mission is such
mine the sizes, approximate shapes, and possibly rotational a rendezvous mission. Originally, the Rosetta spacecraft was
characteristics of cometary nuclei (and hence may provide to be launched in January 2002 to meet with Comet 46P/
statistics), the next major step in the study of cometary Wirtanen at 3.5 AU from the Sun. Difficulties with the
nuclei will come from future space missions dedicated to launcher required a new orientation of the mission. The sec-
their detailed investigation. The first of these will be NASA’s ond launch attempt was successful in March 2004. Its new
Discovery mission, Stardust, which will provide informa- goal is Comet 67P/Churyumov-Gerasimenko. The Rosetta
tion on the nonvolatile composition of the nucleus of Comet spacecraft will deposit a science package on the surface of
81P/Wild 2. The physical structure of the particles, along the nucleus and then continue to monitor the nucleus right
with information on their strength, size, and shape, will through perihelion. If successful, this ambitious mission
provide us with some understanding of how structures on would study the nucleus surface down to a resolution of
the nucleus can form and how the nucleus as a whole came 2 cm/pixel from orbit and provide detailed measurements
together. The emphasis of this mission is on the sample at even higher resolution from the lander. A strong comple-
return. Nevertheless, the navigation camera produced im- ment of remote sensing (cameras, spectrometers, tomo-
ages of the nucleus of unprecedented quality, showing a graphic radio experiment) and in situ (ion and neutral mass
rough surface with a large number of crater-like features spectrometers, dust analyzer, charge particle analyzer) in-
(Fig. 9). struments will observe the nucleus and its activity.
The Deep Impact mission will crash a block of copper Activity could be monitored, compositional changes
into Comet 9P/Tempel 1 and study the effects of the im- followed, surface temperatures tracked, and the internal
pact. This will tell us about the tensile strength and poros- structure assessed. It is the activity that characterizes com-
ity of the nucleus. The impact will also expose pristine ets and leads us to think of them as relics from the forma-
material from the interior of the nucleus and we will be able tion of the solar system. Hence, the emphasis Rosetta places
to assess its chemical characteristics with a broad range of on studying the nuclear activity should be highly rewarded.
analytical instruments onboard the spacecraft. It is a testa- In the distant future, the ultimate objective will be a
ment to our lack of knowledge of the physical properties sample return mission that can place strong constraints on
of cometary nuclei that many widely different scenarios for the models of cometary origin and formation and, hence,
the impact are still being considered by the flight team as on studies of the evolution of the solar system as a whole.
plausible.
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 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 223

The Sizes, Shapes, Albedos, and Colors of Cometary Nuclei

Philippe L. Lamy
Laboratoire d’Astronomie Spatiale du
Centre National de la Recherche Scientifique

Imre Toth
Konkoly Observatory

Yanga R. Fernández
Institute for Astronomy of the University of Hawai‘i

Harold A. Weaver
Applied Physics Laboratory of The Johns Hopkins University

We critically review the data on the sizes, shapes, albedos, and colors of cometary nuclei.
Reliable sizes have been determined for 65 ecliptic comets (ECs) and 13 nearly isotropic comets
(NICs). The effective radii fall in the range 0.2–15 km for the ECs and 1.6–37 km for the NICs.
We note that several nuclei recently measured by the Hubble Space Telescope are subkilometer
in radius, and that only 5 of the 65 well-measured EC nuclei have effective radii larger than
5 km. We estimate that the cumulative size distribution (CSD) of the ECs obeys a single power
law with an exponent qS = 1.9 ± 0.3 down to a radius of ~1.6 km. Below this value there is an
apparent deficiency of nuclei, possibly owing to observational bias and/or mass loss. When
augmented by 21 near-Earth objects (NEOs) that are thought to be extinct ECs, the CSD flattens
to qS = 1.6 ± 0.2. The cumulative size distribution of NICs remains ill-defined because of the
limited statistical basis compared to ECs. The axial ratios a/b of the measured nuclei of ECs
have a median value of ~1.5 and rarely exceed a value of 2, although it must be noted that the
observed a/b values are often lower limits because of uncertainties in the aspect angle. The
range of rotational periods extends from 5 to 70 h. The lower limit is significantly larger than
that of main-belt asteroids and NEOs (~2.2 h, excluding the monolithic fast rotators), and this
has implications for the bulk density of cometary nuclei. By combining rotation and shape data
when available, we find a lower limit of 0.6 g cm–3 for the nucleus bulk density to ensure sta-
bility against centrifugal disruption. Cometary nuclei are very dark objects with globally aver-
aged albedos falling within a very restricted range: 0.02–0.06, and possibly even narrower.
(B-V), (V-R), and (R-I) color indices indicate that, on average, the color of cometary nuclei is
redder than the color of the Sun. There is, however, a large diversity of colors, ranging from
slightly blue to very red. While two comets have well-characterized phase functions with a
slope of 0.04 mag deg–1, there is evidence for steeper (2P/Encke, 48P/Johnson) and shallower
(28P/Neujmin 1) functions, so that the observed range is 0.025–0.06 mag deg–1. The study of
the physical properties of cometary nuclei is still in its infancy, with many unresolved issues, but
significant progress is expected in the near future from current and new facilities, both ground-
based and spaceborne.

1. INTRODUCTION planetesimals from which the cores of the outer planets

were built. Furthermore, the physical evolution of cometary
1.1. Motivation for Studying Cometary Nuclei nuclei over the past 4.6 G.y. must be explained within the
context of any unified theory of the solar system, and com-
There are many reasons why the investigation of comet- parative studies of cometary nuclei and dynamically related
ary nuclei can advance our understanding of the solar sys- bodies [e.g., transneptunian objects and Centaurs (see Jewitt,
tem, and this topic is discussed in detail by Weidenschilling 2004)] should provide insights into the physical and colli-
(2004) and by Lunine and Gautier (2004). Briefly, cometary sional histories of these objects.
nuclei are the most primitive observable objects remaining Through impacts over the age of the solar system, com-
from the era of planetary formation. As such, they provide etary nuclei have significantly affected the formation and
information on the thermophysical conditions of the proto- evolution of planetary atmospheres and have provided an
planetary disk and on the formation mechanism for the icy important source of volatiles, including water and organic

223
224 Comets II

material, to the terrestrial planets. Interest has been building We note that short-period Comets 8P/Tuttle (Porb = 13.51 yr,
recently in the contribution of cometary nuclei to the Earth TJ = 1.623), 96P/Machholz 1 (Porb = 5.26 yr, TJ = 1.953),
impact hazard, which has previously focused mainly on as- and 126P/IRAS (Porb = 13.29 yr, TJ = 1.987) are now classi-
teroids. Another important motivation for studying cometary fied as NICs.
nuclei is that their bulk properties may dictate what steps Because of their different origin, the question arises as
should be taken for hazard mitigation in the event of a pre- to whether the two populations (ECs and NICs) have in-
dicted collision. trinsically different physical properties, or whether they
reflect a continuous spectrum of planetesimals in the early
1.2. Origin and Evolution of Cometary Nuclei solar system, making them more similar than different. The
nuclei of ECs suffer significant heating episodes during their
Various scenarios have been proposed to explain how frequent passages through the inner solar system, where
cometary nuclei formed from the microscopic grains within sublimation processes erode the surface layers, devolatilize
the dusty disk of the solar nebula (Weidenschilling, 2004). the interior, and possibly alter the shape and structure of
Different formation mechanisms may have been operational the nucleus. Weissman (1980) showed that ~10% of the
at different places within the nebula, and this may have led NICs split on their first perihelion passage and Levison et al.
to diversity in the physical properties of cometary nuclei (2002) suggested that 99% of them are disrupted sometime
depending on where they formed. Even if there was a com- during their dynamical evolution. This may suggest differ-
mon formation mechanism for all cometary nuclei, diver- ent physical properties for the ECs and the NICs, although
sity could persist because of differences in the physical and convincing, direct evidence of such differences has not yet
chemical conditions at different heliocentric distances (e.g., been found.
collisional environment, chemical composition, radiation In summary, there are a variety of processes associated
environment, etc.). with the formation and evolution of comets that could affect
Dynamical arguments support the hypothesis that comet- the physical properties of cometary nuclei. There should be
ary nuclei originate from at least two different regions of no expectation that comets form a homogeneous group with
the solar system: The vast majority of the ecliptic comets respect to their physical properties, and it will be interest-
are thought to be collisional fragments of Kuiper belt ob- ing to investigate possible correlations of those properties
jects [the so-called transneptunian objects (see Duncan et with the comet’s place of origin and its subsequent history.
al., 2004; Barucci et al., 2004)], while most of the long-
period and Halley-type comets probably formed in the vi- 1.3. Historical Perspective
cinity of the giant planets and were subsequently ejected
to the Oort cloud where they were stored for most of their To understand how far we have progressed in the study
lifetimes (Dones et al., 2004). of cometary nuclei, we summarize briefly some of the im-
We follow the classification scheme proposed by Levison portant results of the twentieth century. As is commonly
(1996) and distinguish between ecliptic comets (ECs) and done, we define the border between “pre-history” and “re-
nearly isotropic comets (NICs). This scheme is not pro- cent history” to coincide with the publication of the classic
foundly different from the historical tradition, but it has the paper on cometary nuclei by Whipple (1950).
merit of being based on strict dynamical parameters, namely 1.3.1. Pre-history. Before 1950, the paradigm govern-
the Tisserand parameters of comets that are (nearly) con- ing the cometary “nucleus” did not involve a central, mono-
stants of motion with respect to Jupiter. ECs have 2 ≤ TJ ≤ 3 lithic body. Rather, the “nucleus” was envisaged as an un-
and are equivalent to the Jupiter-family comets (JFCs), in- bound agglomeration of meteoritic solids. In this sandbank
cluding 2P/Encke (although it is now practically decoupled model, described by Lyttleton (1953, 1963), all the particles
from Jupiter). ECs in general have orbital periods less than comprising a comet were on independent but very similar
20 years, hence the quasi-correspondence with the popula- orbits, and there was no gravitational binding. This model
tion of short-period comets. NICs have TJ < 2 and group was consistent with the observations of many cometary phe-
together the Halley-type comets (which have a lower limit on nomena, i.e., the morphological complexity of the inner
their periods, in general, of 20 years) and the long-period comae of comets, as well as (qualitatively) the odd behaviors
comets (old and new). Based on their dynamical histories, that comae sometimes display. The term “nucleus” itself
the population of NICs is further divided into two subpopu- was used with imprecision, as noted by, e.g., Bobrovnikoff
lations: (1) dynamically new NICs, which are on their first (1931) and Vorontsov-Velyaminov (1946). Most often, the
pass through the inner solar system and typically have semi- “nucleus” merely referred to the peak in the surface bright-
major axes, a, greater than ~10 4 AU, and (2) returning NICs, ness distribution, which is frequently called the “central
which have previously passed through the inner solar sys- condensation.”
tem and typically have a ≤ 10 4 AU. The returning NICs are The basic misconception of this era was a drastic over-
further divided into two subclasses: external returning com- estimation of the typical size of cometary nuclei, which
ets (ERCs) with periods greater than 200 years, and Halley- most researchers thought were tens of kilometers in size.
type comets (HTCs) with orbital periods less than 200 years. Reports of observers resolving disks of the “nuclei” prob-
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 225

ably provided the motivation for this misconception. In cometary nuclei as a population has been derived from ob-
hindsight, we now recognize that observers were merely servations made during the past decade.
seeing the steeply sloped surface brightness distribution of
the inner coma. However, a few researchers thought com- 1.4. Observing Cometary Nuclei
etary nuclei were monoliths, as small as 1 km in diameter or
even less, on the basis of the starlike appearance of Comet The overarching observational goal for studies of comet-
7P/Pons-Winnecke when observed close to Earth in 1927 ary nuclei is to understand their ensemble properties, which
(Slipher, 1927; Baldet, quoted by Vorontsov-Velyaminov, is accomplished in several ways. The most common obser-
1946). Further impediments to a proper understanding of vations involve visible-wavelength photometry, from which
cometary nuclei were the poorly constrained albedo and the color and the product of the cross-section and albedo
phase-darkening behavior. The idea of a nucleus, or dust can be measured. More detailed observations at these wave-
grains for that matter, with a very low albedo did not be- lengths, such as time series of data at multiple epochs, pro-
come acceptable until after the spacecraft flybys of 1P/ vide clues on the shape and rotation state of the nucleus.
Halley in 1986. Observations at wavelengths longer than ~5 µm, in the ther-
1.3.2. Recent history. The “dirty snowball” model pro- mal-infrared, provide data on both the size and albedo and
posed by Whipple (1950) envisaged the nucleus as “a con- constrain the thermal properties of the bulk material com-
glomerate of ices . . . combined in a conglomerate with me- prising the nucleus.
teoric materials.” Two significant improvements over the Contrary to popular belief, the optical depth, τ, of most
sandbank idea were the model’s ability to adequately ex- cometary comae is generally small enough to allow direct
plain both the cometary nongravitational motion and the gas detection of the nucleus, in principle. Possible exceptions are
production rate. unusually active comets, such as C/1995 O1 (Hale-Bopp),
With this paradigm established, the future interpretation for which τ may approach unity. For most comets, the real
of data established the relatively (compared to pre-1950) problem lies with the intrinsic faintness of the nucleus rela-
small sizes of nuclei. Photographic data taken by Roemer tive to the light scattered from dust grains in the coma, i.e.,
(1965, 1966, 1968) set constraints on the sizes of many nu- the contrast is usually too small to distinguish the nucleus
clei, although at this time the albedo was still thought to be clearly. Historically, planetary astronomers have attempted
much higher than the currently accepted mean. Furthermore, to overcome this obstacle by observing comets at large helio-
there was still the problem of unresolved comae around dis- centric distances, when the nucleus was assumed to be inac-
tant comets. Generally, Roemer’s photographic observations tive and coma-free. On the one hand, the activity level at
were not taken at sufficiently large heliocentric distances for large heliocentric distances is often so low that most of the
the comets to be inactive, and they were significantly con- observed light can be attributed to reflection from the nu-
taminated by unresolved coma. Delsemme and Rud (1973) cleus. On the other hand, many comets are known to be con-
tackled the problem of albedo by comparing the nuclear spicuously active at large heliocentric distances, preventing
brightness far from the Sun and the gas production rate such an observational approach. Another approach was to
close to the Sun, and derived albedos that seemed to confirm observe only relatively nearby, very low activity comets,
the high values of conventional wisdom. However, we now whose dust production rates were so small that the nucleus
know that nuclear sizes based on cometary activity are lower clearly stood out even when the spatial resolution was only
limits, making the derived albedos upper limits, owing to hundreds of kilometers, but this works well for only a hand-
the fact that typically only a small fraction of the nucleus ful of objects. Spacecraft encounters, of course, are the best
surface is active. way to obtain detailed information on the physical proper-
Several significant steps forward were taken in the 1980s. ties of cometary nuclei, and we have learned much from the
Simultaneous thermal-infrared and optical measurements spectacular encounter images of 1P/Halley and 19P/Borrelly
were made (discussed in section 3.3), establishing that nu- (see Keller et al., 2004). While spacecraft encounters pro-
clear albedos were low. In 1983 Comet IRAS-Araki-Alcock vide “ground truth” that cannot be obtained any other way,
made an extremely close approach to Earth, and the syn- this approach is necessarily limited to a small number of
thesis of data using modern observational techniques re- objects and cannot be used to determine the properties of
sulted in a fairly complete description of that nucleus [size, cometary nuclei as a population. Fortunately, recent im-
albedo, shape, and rotation (Sekanina, 1988)]. Finally, the provements in the resolution capabilities and sensitivities
flotilla of spacecraft flying by Comet 1P/Halley confirmed of ground- and spacebased telescopes now allow us to study
beyond any doubt that a single, solid body lies at the center the physical properties of a large number of cometary nu-
of a comet. clei, even in the presence of substantial coma.
The past decade has witnessed a major observational ef-
fort to study cometary nuclei using medium to large ground- 1.5. Scope of this Chapter
based telescopes and space telescopes outfitted with charge-
coupled device (CCD) detectors, and this has resulted in a Within the context of this chapter, “physical properties”
wealth of new data. Indeed, most of our understanding of refer to the size, shape, albedo, and color of the nucleus. All
226 Comets II

these properties can be observed directly, and in section 2 ally fainter signals, high thermal background with ground-
we describe in detail the techniques for doing so. In sec- based facilities, and inferior performance of IR detectors.
tion 3, we summarize the results for each individual comet Usually one has no choice but to observe the nuclei at close
for which data are available because a comprehensive and range, usually exploiting a close encounter with Earth. As
critical evaluation of the results cannot be obtained from with observations of reflected sunlight, a coma will usually
any other reference. After discussing techniques and results, be present and must be taken into account. Before the age
in section 4 we synthesize all the data to estimate the dis- of large-area infrared array detectors, this was difficult and
tribution of sizes, shapes, colors, and rotational periods of so, again, very low activity comets were the most popular
cometary nuclei as a population. In section 5 we discuss targets. However, new and improved thermal detectors, such
some outstanding, unresolved issues in the study of comet- as those on the Space Infrared Telescope Facility (SIRTF),
ary nuclei and comment on the direction of future research will relax the limitations of the technique.
on the physical properties of cometary nuclei. Some short, The sample of objects for which the thermal emission at
concluding remarks comprise section 6. radio wavelengths may be detected is even more restricted
Some physical properties of cometary nuclei are not cov- than in the infrared. The nucleus must be exceedingly close
ered in this chapter. The structure, strength, and bulk den- (e.g., C/1983 H1 IRAS-Araki-Alcock) or exceedingly large
sity are especially important, but, in general, these can only (e.g., C/1995 O1 Hale-Bopp). In addition, radar observa-
be estimated indirectly, as discussed by Weissman et al. tions have a ∆–4 limitation, where ∆ is the geocentric dis-
(2004) and by Boehnhardt (2004). Although we summarize tance, and only rarely do comets pass close enough to the
results on the rotational periods of cometary nuclei, mainly Earth to permit radar measurements of the nucleus (Harmon
because they are obtained from the same light curve data et al., 2004).
used to measure shapes, a comprehensive discussion of the Finally, we discuss rarely performed stellar occultation
rotational properties is given by Samarasinha et al. (2004). observations, which have the potential to provide detailed
The physical nature of the ice and dust contained within com- shape information on nuclei and their inner comae.
etary nuclei (e.g., crystalline vs. amorphous ice, thermal con-
ductivities and heat capacities of the ice and dust, etc.) is 2.2. Using the Reflected Light
very poorly constrained observationally and is discussed from
a modeling perspective by Prialnik et al. (2004). Finally, the 2.2.1. Observations. Detecting the solar light reflected
very interesting question of how comets are related to the by cometary nuclei remains the most powerful and efficient
other minor bodies in the outer solar system is not treated method to determine their size and to study their properties.
here, but rather is covered separately by Jewitt (2004). However, this technique requires knowledge of the albedo
and phase law, as discussed below.
2. TECHNIQUES FOR DETECTING AND At large heliocentric distances, e.g., rh > 4 AU, the activ-
CHARACTERIZING COMETARY NUCLEI ity of most ecliptic comets is very weak, and the coma may
become sufficiently faint (or possibly nonexistent) to reveal
2.1. General Considerations the “bare” nucleus. Thus, the best strategy for these comets
generally is to observe near aphelion. However, there are
Cometary nuclei are certainly among the most difficult two main problems: (1) the geometric conditions (large rh
objects of the solar system to detect and characterize, usu- and ∆) usually result in a very faint nuclear signal, and
ally suffering from the dual problem of being faint and im- (2) the criterion used to decide the nonexistence of a coma,
mersed in a coma. The techniques for their study are those namely the stellar appearance of the nucleus, is not robust
first developed for the investigation of asteroids, but with because an unresolved coma can still contribute substan-
the additional complexity caused by the presence of a coma. tially to the observed signal. The most well-known example
The primary technique, visible-wavelength imaging, uses is 2P/Encke, which has been anomalously bright at almost
reflected sunlight and takes advantage of high-performance every observed aphelion (Fernández et al., 2000, and refer-
detectors like CCDs. This technique has been most success- ences therein).
ful for relatively large and/or very low activity nuclei at For the NICs, cometary activity can continue well be-
large heliocentric distances, and for comets observed at yond this rough boundary for the ecliptic comets, probably
close range and with sufficient spatial resolution to sepa- due to the higher abundance of ices more volatile than water,
rate unambiguously the nuclear and coma signals. The pros such as CO. Many comets are known to be active beyond
and cons of these two cases will be discussed below. A third 5 AU (e.g., Szabó et al., 2001; Licandro et al., 2000; Lowry
method using this technique, the in situ spacecraft investi- and Fitzsimmons, 2001) and even beyond 10 AU (Meech,
gation, is discussed by Keller et al. (2004) and will not be 1992), such as 1P/Halley (West et al., 1991) and C/1995 O1
addressed here. Hale-Bopp. The poor spatial resolution when observing such
A second technique relies on the detection of thermal objects at these distances makes accounting for the coma’s
emission from the nucleus. The situation in this case is less contribution highly problematic. Once these long-active
favorable than for the reflected light because of the gener- comets finally do deactivate, the intrinsic faintness of the nu-
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 227

clear signals generally limits the observations to snapshots conveniently reformulated by Jewitt (1991) and, in the case
in one (R) or two (V, R) bands, often with large uncertainties of a spherical object, is given by
on the (V-R) color index.
Nevertheless, in a few cases multiple observations have pΦ(α)r 2n = 2.238 × 1022r2h∆210 0.4(m – m) (2)
been secured allowing the construction of a (sometimes par-
tial) light curve, which can be used to investigate the shape where m, p, α, and Φ(α) are respectively the apparent mag-
and rotational state of the nucleus. Despite these limitations, nitude, the geometric albedo, and the phase angle (Sun-
this approach has been pursued by several groups of ground- comet-observer angle) and phase function Φ(α) of the nu-
based observers and has produced valuable data on the physi- cleus in the same spectral band (e.g., V or R); m is the
cal properties of cometary nuclei. In addition, and quite re- magnitude of the Sun (V = –26.75, R = –27.09) in the same
cently, near-infrared spectra of a few weakly active nuclei spectral band; rh and ∆ are respectively the heliocentric and
have been obtained using large telescopes in an attempt to geocentric distances of the nucleus (both in AU); and rn is
detect spectral signatures (e.g., water ice and minerals). Cur- the radius of the nucleus (in meters). Observers often pro-
rently, only Centaurs (e.g., Chiron, Chariklo) present con- ceed in two steps, introducing first the absolute magnitude,
vincing cases of detection of water ice on their surface. H, of the nucleus (i.e., the magnitude at rh = ∆ = 1 AU, α = 0°)
An entirely different approach has been pioneered by
Lamy and co-workers (e.g., Lamy and Toth, 1995, Lamy et H = m – 5logrh∆ – αβ (3)
al., 1998a,b, 1999a, 2001b, 2002) and is based on the very
high spatial resolution offered by the Hubble Space Tele- where the phase function is given by
scope (HST). The basic rationale is that, while the nuclear
signal is preserved in the point spread function (PSF) of the –2.5log[Φ(α)] = αβ (4)
telescope, the signal from the coma, an extended source, is
diluted as the spatial resolution increases. The contrast be- and then incorporating the relationship between rn (in me-
tween the nucleus and the coma is maximized by observ- ters) and p
ing comets at their minimum geocentric distance. A model
for the surface brightness distribution of the nucleus plus
1.496 × 1011 0.2( m
coma is constructed and compared to the observed bright- rn = 10 − H) (5)
ness distribution to estimate the signal from the nucleus. The p
brightness distribution of the comet is modeled as
A linear phase coefficient β = 0.04 mag/deg is generally
B(ρ) = [knδ(ρ) + coma] ⊗ PSF (1) used, with an estimated uncertainty of ±0.02 mag/deg. In
fact, a value β = 0.06 mag/deg has been obtained for 2P/
where ρ is the projected distance from the nucleus, δ(ρ) is Encke (Fernández et al., 2000) and 48P/Johnson (Jewitt and
the Dirac delta function, ⊗ is the convolution operator, and Sheppard, 2003). For observations at small phase angles,
PSF is the point spread function of the telescope. The first the impact of the phase angle effect on the nuclear magni-
term is the contribution of the nucleus, i.e., the PSF scaled tude is small, but it becomes overwhelming at large phase
by the factor kn. The coma can be modeled by any func- angles (e.g., a correction of 2 mag to the nuclear magnitude
tion that provides a reasonable representation of the real and a factor 2.5 to the radius at α = 50°). Finally, once an
coma, e.g., the canonical kc/ρ inverse power law, where kc albedo is assumed (generally pV = pR = 0.04), or is indepen-
is a scaling factor, or a generalized kc/ρa, or a more complex dently determined, the radius rn of the nucleus can be calcu-
function containing radial and azimuthal variations such as lated. An uncertainty of ±0.017 on the albedo appears realis-
implemented for the asymmetric and structured comae of tic, at least for ecliptic comets (see section 4.3 below), and has
19P/Borrelly and Hale-Bopp (C/1995 O1). The scaling fac- an impact of ~20% on the value of the radius. In summary,
tor kn, the subpixel locations of the nucleus (xn,yn), and the for nuclei observed at small phase angles and whose physical
parameters of the coma model (e.g., kc, a) are determined properties are not too unusual (β = 0.04 ± 0.02 mag/deg and
individually on each image by minimizing the residuals be- p = 0.04 ± 0.017), the measurement of its magnitude offers a
tween the synthetic and the observed images. The fits are per- robust determination of its radius, at least of one of its cross-
formed either on the azimuthally averaged radial profiles, or sections in the case of single (i.e., “snapshot”) observations.
on X and Y profiles, or on the full image. The instrumental
magnitudes are calculated by integrating the scaled PSFs 2.3. Using the Thermal Emission
and are transformed to Johnson-Kron-Cousins magnitudes.
2.2.2. Interpretation of the observations. Once the 2.3.1. Observations. The asteroid community has been
magnitude, m, of the nucleus has been determined, the stan- using radiometry for over 30 years (e.g., Allen, 1971) to de-
dard technique introduced by Russell (1916) is used to re- rive robust sizes and albedos. The application of this method
trieve its physical properties. Russell’s original formula, de- to cometary nuclei began in 1984, i.e., before the 1P/Halley
vised for asteroids observed at large phase angles, has been apparition (Campins et al., 1987), and has been used in ear-
228 Comets II

nest since the mid-1990s with the advent of array-detectors Fth (λ) =
sensitive to radiation in the 10–20-µm range. (6)
∫∫
Φ
For datasets of outstanding quality — high signal and εth Bν[T(rh, pq, η, εth, θ, φ), λ]dφdcosθ r 2n π∆th2
multiple wavelengths — it is also possible to constrain vari-
ous fundamental parameters of the the nucleus, such as ther- where Φth is the phase function at thermal wavelengths, p
mal inertia and surface roughness (see Campins and Fer- is the geometric albedo at reflected wavelengths, Bν is the
nández, 2003). If multiepoch data are obtained, the thermal Planck function, εth is the emissivity at thermal wavelengths,
phase behavior of the nucleus may be deduced. If time series η is a factor to account for infrared beaming (see Spencer
of IR data are taken simultaneously with visible-wavelength et al., 1989), and T is the temperature. The temperature itself
photometry, the existence of large-scale albedo spots on the is a function of rh, p, η, εth, the surface cometographic co-
surface may be discovered. Observations at very long (milli- ordinates, θ and φ, and the phase integral q, which links the
meter or centimeter) wavelengths provide clues on the emis- geometric and Bond albedos. Buratti et al. (2004) derived
sivity of the bulk material in the nucleus (i.e., subsurface). q = 0.3 for 19P/Borrelly. Traditionally the largest sources
Unfortunately, the difficulties of observing cometary nu- of error in this modeling effort came from Φth and η. Φth
clei usually prevent one from obtaining such a robust data- was often parameterized as a function of phase angle, α,
set. The two main problems are related to the usual obser- such that –2.5 logΦth ∝ α, but recently the more sophisti-
vational paradigm: When the nucleus is close to Earth and cated approach of explicitly calculating the surface integral
bright, it is often shrouded in coma, but when it is far from of Planck emission over the Earth-facing hemisphere has
the Sun and less active, it is often too faint. Thus, tradition- become preferable (Harris, 1998; Lamy et al., 2002). The
ally the best nuclei to observe are those that are weakly ac- beaming parameter η, however, is still largely unconstrained
tive and/or large or nearby. Work by Campins et al. (1987), for comets and remains the largest uncertainty; we are only
Millis et al. (1988), and A’Hearn et al. (1989) are excellent beginning to understand the variety of values possible for
examples of successful observations of just such special near-Earth asteroids comparable in size to the cometary nu-
comets. clei (e.g., Delbo et al., 2003).
The techniques applied at visible wavelengths to deal For objects with low albedos, such as cometary nuclei,
with the effects of the coma can also be applied to the ther- rn can be determined to good accuracy from their thermal
mal IR images. Both cases require excellent spatial resolu- flux density, provided the observations are secured at low
tion, but a complication is that, for the ideal case of diffrac- phase angles. This is because the thermal emissivity is close
tion-limited observations where the width of the PSF is to 1, so the thermal emission does not depend strongly on
proportional to wavelength, the thermal radiation and re- the assumed value for εth. This is to be contrasted with the
flected light sample different scales of the inner coma. Thus, visible case, where the flux is proportional to the geometric
in this case when the dust opacity is constant with wave- albedo, which is very small and can, in principle, vary by a
length, or decreases with wavelength slower than λ–1, the large factor. Fortunately, the range of values measured for
nucleus-to-coma contrast ratio will generally be larger for the geometric albedo seems to be rather limited (see the pre-
the observations at visible wavelengths compared to those vious section), which means that accurate values for the nu-
made at thermal wavelengths. Since groundbased data in clear radius can be derived solely from the visible data as
the two wavelength regimes often have similar spatial reso- well. In section 2.7, we discuss the measurements of the
lutions owing to the effects of atmospheric seeing, the prob- albedo.
lem of sampling different spatial scales of the coma usually One important caveat to this formulation is that it as-
only applies to spacecraft data. Despite these difficulties, sumes the nucleus is spherical. Not only does this make rn
Jorda et al. (2000), Lamy et al. (2002), and Groussin et al. an “effective” radius instead of a true radius, but rn applies
(2003) successfully used the Infrared Space Observatory only to the Earth-facing cross section at the time the data
(ISO) to detect and characterize several nuclei in the 10-µm were taken. Observations over a rotation period are gener-
region, taking advantage of the much better sensitivity to ally needed to constrain the “mean” effective radius. It is,
thermal emission resulting from the absence of the warm of course, possible to implement the equations to handle a
terrestrial atmosphere. nucleus of ellipsoidal or even arbitrary shape, although fre-
While typical groundbased thermal measurements are quently the quality of the data does not warrant such an ac-
made in the 10-µm atmospheric window (and, less fre- tion. Early work by Brown (1985) demonstrated how ellip-
quently, in the 5- and 20-µm windows), the submillimeter, ticity of the nucleus can affect the measured fluxes. More
millimeter, and centimeter windows have been exploited to recently, Gutiérrez et al. (2001) have investigated how arbi-
detect the thermal radio continua of a few very bright nu- trary shapes and variegated surface-ice/surface-dust ratios
clei — namely Hale-Bopp (reviewed by Fernández, 2003) can affect the thermal behavior of nuclei.
and IRAS-Araki-Alcock (Altenhoff et al., 1983). The critical step for this method is to calculate a surface
2.3.2. Interpretation and analysis. Once the thermal temperature map T(θ,φ) of the nucleus for the time at which
continuum flux density Fth has been measured, it can be it was observed. This can be done using a thermal model,
interpreted via the equation the fundamental parameters of which are the rotation pe-
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 229

riod and the thermal inertia (the square root of the product is expected to detect comets out to ~5 AU from the Sun, so
of the conductivity, heat capacity, and bulk density). For the interpretation of radiometry must proceed with caution.
most datasets, one of two commonly used thermal models Enhancements to the thermal modeling can be made and
are usually employed. One, for slow-rotators (a.k.a. “stan- are justified when there are measurements of the nucleus’s
dard thermal model”), applies if the rotation is so slow, or thermal continuum at many wavelengths. At the very mini-
the thermal inertia is so low, that every point on the surface mum, the 10-µm vs. 20-µm color can be used to discrimi-
is in instantaneous equilibrium with the impinging solar ra- nate between slow-rotators and fast-rotators. A further tack
diation. The other, for rapid-rotators (a.k.a. “isothermal lati- is to recognize that comets have a significant near-surface
tude model”), applies if the rotation is so fast, or the thermal ice component (unlike the asteroids) that is sublimating
inertia is so high, that a surface element does not apprecia- away and thus probably affects their thermal behavior. The
bly cool as it spins away from local noon and out of sun- “mixed model” introduced by Lamy and co-workers (Lamy
light. This model also assumes that the rotation axis is per- et al., 2002; Groussin et al., 2003; Groussin and Lamy,
pendicular to the Sun-Earth-object plane. (For an axis that 2003a) employs a water-ice sublimation term when calcu-
points at the Sun, the two models predict the same tempera- lating the surface temperature map. The effect is to provide
ture map.) Note that the terms “slow-” and “rapid-rotator” a generally cooler nucleus than otherwise implied by the
are slightly misleading, in that the thermal inertia is usually standard slow-rotator model. The thermal inertia itself can
the physical quantity that determines the thermal behavior. be roughly constrained with this method. For example, very
Thus, two cometary nuclei with identical and long rotation low values of the thermal inertia, about one-fifth that of the
periods, but vastly different thermal inertias, may not nec- Moon, have been derived for Centaurs Chiron and Chariklo
essarily both be “slow-rotators.” by Groussin and Lamy (2003b). Naturally, even more de-
Furthermore, small bodies in the outer planets region, tailed models of nuclear structure and thermal behavior are
at ~10 AU or beyond, can behave like rapid-rotators even possible, and these are discussed in Prialnik et al. (2004).
if their rotational periods are long. This is because thermal
radiation scales as T 4 and when T is low enough, those bod- 2.4. Combining Reflected Light and
ies do not cool substantially during nighttime. Thermal Emission
In practice, there are few objects in the inner solar system
that behave thermally as rapid-rotators, so the slow-rotator If visible and thermal IR observations are performed
model is often employed as the default. Of the cometary simultaneously, then it is possible to solve independently
nuclei that have been studied, nearly all appear to behave as for the radius and the albedo of the nucleus using equa-
slow-rotators. The only possible (unconfirmed) exception so tions (2) and (6) as system with two unknowns, p and rn.
far is the very low activity Comet 107P/Wilson-Harrington This method has been implemented for a handful of nuclei
(Campins et al., 1995). Among the asteroids, one notable (see section 3.3). In practice, and as emphasized in the
rapid-rotator is (3200) Phaethon (Green et al., 1985), which above section, rn is determined by the thermal constraint
may be a dormant or extinct cometary nucleus. Whether or (i.e., equation (6)); consequently the visible constraint (i.e.,
not the thermal inertias of all highly evolved comets are low equation (2)) yields the albedo. An illustration of this prac-
remains to be seen. Campins and Fernández (2003) give tical implementation is given by Lamy et al. (2002) for the
some upper limits to the thermal inertias of a few nuclei, case of 22P/Kopff.
but, for the most part, these limits are roughly an order of
magnitude higher than the expected values. 2.5. Light Curves
The applicability of the slow- or rapid-rotator model can
be quantified by the parameter Θ, introduced by Spencer et The light curve (by which we mean the short-timescale
al. (1989), which is series of photometric measurements, not the orbit-timescale
study of activity as a function of rh) provides information on
Γ ω the shape and rotational period of a cometary nucleus. Only
Θ= (7)
εσ Tss
3 observations at visible (reflected light) and infrared (thermal
emission) wavelengths are presently capable of producing
where Γ is the thermal inertia, ω is the rotational angular such light curves. Very much like the case for asteroids, the
frequency, σ is the Stefan-Boltzmann constant, and Tss is the periodic temporal variation of the brightness is interpreted
temperature at the subsolar point. Ideal slow-rotators have in terms of the rotation of an elongated body. Light curves
Θ = 0; rapid-rotators, Θ = ∞. Since Θ depends so steeply of sufficient length have been obtained for only a few com-
on the subsolar temperature, cometary nuclei that mimic ets (e.g., 2P/Encke), and the interpretation is frequently dif-
slow-rotators near perihelion could conceivably act more ficult (e.g., multiple solutions for the rotational period may
like rapid-rotators at aphelion. Due to sensitivity limitations be found), but the situation has improved with recent data-
in the mid-IR, at the time of this writing there have been sets that show periods much more clearly (e.g., Lowry and
no detections of cometary nuclei at large heliocentric dis- Weissman, 2003; Jewitt and Sheppard, 2003). Samarasinha
tances, so currently the problem is moot. However, SIRTF et al. (2004) discuss these problems in some detail.
230 Comets II

One extra complication is the possibility that the nucleus example by the shape of the coma (Sekanina, 1987), the
has a nonuniform albedo, which would add a non-shape- amplitude of the light curve yields the a/b ratio. Together
related component to the temporal brightness variations. with the absolute magnitude, corresponding to either the
Indeed, spacecraft imaging of 19P/Borrelly revealed some minimum or maximum projected areas, one can obtain a
evidence of surface variations (Soderblom et al., 2002), solution for the spheroidal shape of the nucleus. Generally,
although they are difficult to separate from topography ef- ε is not known, so that only a minimum value of a/b can
fects because of the modest spatial resolution of the images; only be obtained, corresponding to ε = 90°. The situation
see Nelson et al. (2004) for a discussion of this problem. is even more difficult for “snapshot” observations, as the
The possibility of large-scale albedo features on the surface effective radius, rn,a, which represents the instantaneous pro-
of the nucleus can be ruled out if visible and thermal light jected area, will range between ab and b. For an axial ratio
curves are obtained simultaneously. Such light curves will of 2, rn,a = 0.707 ab , i.e., within 30% of the maximum
be in-phase for shape-dependent rotational modulation and value. The problem is, however, less serious than the above
out-of-phase for albedo-dependent modulation. Generally, simple analysis tends to imply because the temporal aspect
however, the subject is often disregarded simply because very much helps. As illustrated by the light curve of 19P/
datasets are rarely of sufficient quality to draw definite con- Borrelly (Fig. 8 of Lamy et al., 1998b), the fraction of time
clusions. during which the small cross-section is seen is compara-
The default case is to analyze the temporal variation in tively very short and may even be missed if the time reso-
terms of the varying apparent cross-section of a rotating, lution of the observations is not adequate. Consequently, a
elongated nucleus. All observations available so far are con- rotating spheroid displays a cross-section close to its maxi-
sistent with, and interpreted as, rotation of a prolate spher- mum most of the time. As discussed by Weissman and
oid (with semiaxes a and b = c) around one of the short axes. Lowry (2003), the integration over all possible (random)
In a few cases, independent constraints on b and c have been orientations and rotational phases shows that the average
obtained. The projected area of a spheroid in simple rotation projected area remains a large fraction κnπab of its maxi-
is given by mum value πab: κn = 0.924 for a/b = 1.5, κn = 0.892 for
a/b = 2, and κn = 0.866 for a/b = 3. For the effective radius,
S = πab2[(sin2φ/a2 + cos2φ/b2)sin2ε + cos2ε/b2]1/2 (8) rn,a, given by the instantaneous projected area, the scaling
varies as κ n . For a typical axial ratio a/b = 2, a snapshot
where φ is the rotation angle and ε is the angle between the observation will, on average, lead to rn,a = 0.945 ab , i.e.,
spin vector of the nucleus and the direction to the Earth. within 5.5% of the maximum value ab . Even more impor-
Figure 1 displays the ratio Smin/Smax (also expressed in mag- tant for questions such as the size distribution function is
nitude variation, ∆m) as a function of a/b and ε. If the ori- the effective radius, rn,v, that of the sphere having the same
entation of the spin axis is independently constrained, for volume (or mass) as the spheroid, via r 3n,v = ab2. The ratio
rn,v/rn,a remains close to 1 with value of 0.972 for a/b =1.5,
0.943 for a/b = 2, and 0.895 for a/b = 3. To summarize, the
radius calculated from an observed, apparent projected area
will give, on average, an excellent estimate of the effective
radius of the equivalent sphere. Note that the averaging with
respect to rotational phase is implicitly done when authors
average their data values that are too scarce to construct a
credible light curve.
A light curve does not strictly give access to a projected
area. In the visible, the bidirectional reflectance comes into
play but will not be a problem if the scattering properties
are homogeneous over the nuclear surface. In the thermal
infrared, it is the two-dimensional distribution of tempera-
ture over the surface that comes into play, and that is cer-
tainly not homogeneous. For example, Brown’s (1985) non-
spherical thermal model predicts that the amplitude of the
light curve will be larger in the infrared than in the visible,
an effect apparently observed on 10P/Tempel 2 (A’Hearn
et al., 1989). With the question of how to interpret the light
curve of cometary nuclei still in its infancy, interpretations
beyond the simple spheroidal model discussed above are not
Fig. 1. The minimum to maximum projected area (Smin/Smax) of warranted. Complex effects, such as shadowing and unillu-
rotating prolate ellipsoids with different axial ratios (values are minated areas, cannot yet be handled properly but have
marked near the curves) plotted vs. the aspect angle. The corre- already been noted [e.g., the skewness of the light curve of
sponding light curve amplitudes are also indicated (∆m). 9P/Tempel 1 (Lamy et al., 2001b)].
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 231

2.6. Radar Observations chord was measured, and, if real, it is impossible to tell if
this chord went through the nucleus, grazed the nucleus,
Studies of cometary nuclei using radar are discussed by or passed near by. The optical depth of the inner coma may
Harmon et al. (2004). For completeness, we provide here have been significant (i.e., approaching unity) for several
a brief outline of the method. Basically, one sends a burst tens of kilometers (cf. Weaver and Lamy, 1997). With some
of microwaves of known power towards a nucleus and reasonable assumptions about the dust outflow, the occulta-
measures the power of the returned echo. There have been tion constrained the (assumed-spherical) radius of the nu-
six such detections of nuclei, although the signal-to-noise cleus to be no larger than 48 km. With further restrictive
is better than 4 in only two cases, C/1983 H1 (IRAS-Araki- assumptions, the upper limit is ~30 km.
Alcock) and C/1996 B2 (Hyakutake). There are as yet no There are several other occultations by comets mentioned
delay-Doppler “images” of a cometary nucleus, as are now in the literature, but none of them have probed the nucleus.
being routinely created for close-approaching near-Earth
asteroids. The main reason is the scarcity of comets that can 2.8. Measuring the Albedo
overcome the ∆–4 dependence for detectability. In terms of
the properties of nuclei, the radar data have mostly been One must be careful to specify what is meant by the term
used to constrain the radar-albedo and density, via argu- “albedo” because many different definitions are used. In this
ments related to the bulk dielectric properties of cometary paper, we report values for the geometric albedo (p), which
nuclei and their response to microwaves. The radar albedos is defined as the zero-phase, disk-integrated reflectance
are apparently similar to the visible-wavelength albedos. relative to that produced by a “perfect” diffusing disk (cf.
The bulk densities range between 0.5 and 1.5 times that of Hanner et al., 1981). Sometimes the Bond albedo (A) is
water, values that are not unexpected. used instead of the geometric albedo; this is just the fraction
of incident light that is scattered in all directions and is
2.7. Occultations related to the geometric albedo by

Occultations are frequently used to constrain the shape A = pq (9)

and size of asteroids, and can provide a direct test of the
validity of other methods, such as radiometry (section 2.3). where q is the phase integral, which is given by (cf. Russell,
In principle, the same could be done for comets. An occul- 1916; Allen, 1976)
tation trace may also have wings, owing to nonnegligible
optical depth in the inner coma, and this could provide in-
formation on dusty gas hydrodynamics in the inner coma
∫
q = 2 Φ(α)sin(α )dα (10)

and the location of active regions on the surface. In prac- where Φ(α) is the disk-integrated, normalized phase func-
tice, this method is limited by the difficulty of locating a tion and α is the phase angle. Note that both albedos are
nucleus accurately within a surface brightness distribution functions of wavelength. In the energy balance equation for
that is dominated by coma for most astrometric observa- the surface of the nucleus, one must calculate the quantity
tions, and in finding suitable stars that are occulted. Even
a subarcsecond positional error perpendicular to the proper
motion can shift the path of the comet’s shadow on Earth by
∫ F (λ)A(λ)dλ (11)
hundreds or thousands of kilometers. Given that the nucleus
in question is typically on the order of 1–10 km across, the
∫ F (λ)dλ
difficulty of obtaining a successful observation becomes ap- which Clark et al. (1999) defines as the bolometric Bond
parent. Moreover, obtaining the ideal dataset with multiple albedo AB, and which is wavelength independent. However,
chords through the nucleus requires tight spatial sampling for A that varies only slightly with wavelength; e.g., for a
across the predicted path, which can be logistically diffi- gray object, the value at a particular wavelength will suffice
cult with limited labor resources and equipment. and A = AB.
Currently the most useful occultation event observed is Various complications arise when attempting to derive
one by the weakly active and large Centaur Chiron (Bus et al., photometric properties from disk-resolved imagery of the
1996). One chord through most of the nucleus and one pos- nucleus. So far, we have such data on Comets 1P/Halley and
sibly grazing chord were observed, and this constrained the 19P/Borrelly. For an unresolved image of a nucleus, we
radius to be at least 90 ± 7 km. Chiron’s ellipsoid is within work with a body that has a subsolar point, and the geomet-
10% of spherical, so this is thought to be a robust lower ric albedo is simply the true albedo at that point. In that case,
limit. Groundbased radiometric data (Campins et al., 1994; we also employ a phase-darkening function to describe the
Fernández et al., 2002a) currently imply a radius of ~80 km, photometric behavior from our (nonzero phase) vantage. For
while space (ISO) data give 71 ± 5 km (Groussin and Lamy, a resolved element of area on the surface of a nucleus, there
2003b), so the agreement is not really satisfactory. is likely no subsolar point, and we must account for sun-
Another occultation event, this one by C/1995 O1 Hale- light impinging on the element with some nonzero zenith
Bopp, was reported by Y. Fernández et al. (1999). Only one angle. Thus, an understanding of the scattering is crucial
232 Comets II

to disentangle albedo and scattering effects. In a few cases published, but a short note entitled Comet Nuclear Magni-
[e.g., asteroid Eros (Clark et al., 2002)], one has a full shape tudes, dated January 14, 1995 (hereafter denoted Sc) has
model of the object in question, and then one can use (1) the been widely circulated in the cometary community. Scotti ap-
observed disk-resolved photometry and (2) the known scat- plied a rudimentary technique to subtract the coma assum-
tering geometry as a function of position on the nucleus to ing a constant surface brightness inward from a thin annu-
derive fundamental scattering parameters. Most commonly, lus having a radius of a few times the radius of the seeing
the formulation presented by Hapke (1986) is used. disk [a more detailed description and an evaluation of this
The most straightforward, assumption-free way to ob- method are given by Tancredi et al. (2000)]. This is obvi-
tain the geometric albedo from resolved imaging of the ously an oversimplification, and it always leads to an over-
nucleus is to combine the projected area S known from re- estimation of the brightness of the nucleus by an amount
solved images with remote photometry of the unresolved that depends entirely on its activity. Scotti produced a table
nucleus, which gives pS as discussed in section 2.2. Then giving the absolute magnitude of 62 cometary nuclei from
the ratio unambiguously yields the geometric albedo p of which he calculated a radius, assuming an albedo of 0.03
the nucleus. In practice, this usually requires a good under- (they are reproduced here but scaled to an albedo of 0.04),
standing of the rotational state, shape, and phase function convincingly demonstrating that the bulk of them are very
of the nucleus, since in most cases the resolved imaging and small bodies with sizes of a few kilometers. These results
the groundbased data will have been obtained at different have further been very useful to estimate the exposure times
epochs. The resolved imaging must be matched to the re- for spacebased observations.
mote viewing, which may be at a different aspect angle, and 3.1.2. Lamy and Toth (1995), Lamy et al. (1996,
certainly one needs to match the rotational state and the 1998a,b, 1999a,b, 2000, 2001a,b, 2002, 2003), Jorda et al.
projected area. Application of this procedure to the nucleus (2000), Groussin et al. (2003, 2004), Toth et al. (2003). The
of 19P/Borrelly will be discussed in section 3.3.1 below. approach employed by this group (hereafter denoted La+),
Returning to disk-integrated (unresolved) data on a com- which is to use the high spatial resolution of the HST to
etary nucleus, the radiometric method (section 2.3) is cur- photometrically resolve the nucleus, has already been de-
rently the most common way to derive the visible and near- scribed in section 2.2.1. Except for the few cases of complex
IR geometric albedo. Whereas one usually only needs the comae, such as that of Hale-Bopp (C/1995 O1), the residuals
IR equation to obtain a good estimate of the nuclear radius between the observed and modeled images are usually very
(since almost all the incident energy is absorbed and then small, typically a few percent of the signal in the brightest
thermally reradiated), the full method — solving both equa- pixel. Figure 2 illustrates the solution obtained from the HST
tions for the two unknowns — is required in order to have observations of 19P/Borrelly (a spheroid), in comparison
a confident, robust albedo measurement. Simultaneity, or with the best in situ image obtained by the camera on the
an understanding of the rotation state, is also critical. Deep Space 1 spacecraft. Thirty-one nuclei have been de-
Another method involves deriving the radar albedo from tected during the HST observations, all active except for
radar echoes, and assuming that the reflectivity of the nu- 9P/Tempel 1, which was observed at rh = 4.48 AU. For 18
cleus at centimeter wavelengths is similar to that at visible
wavelengths. The existing radar data are discussed by Har-
mon et al. (2004). Generally, radar albedos seem to be as
dark as their visible counterparts, but the quality of the radar
data on cometary nuclei are not yet good enough to make
a robust comparison between albedos in the two wavelength
regimes.

3. PROPERTIES OF COMETARY NUCLEI

We now present a detailed discussion of the available

data on the physical properties of cometary nuclei: size,
shape, albedo, color, and rotational period. The bulk of these
data comes from six sources, which we briefly describe
below. Additional sources will be introduced when discuss-
ing individual comets.

3.1. Main Sources of the Data

3.1.1. Scotti (unpublished data, 1995). The largest Fig. 2. The prolate spheroid model of the nucleus of Comet 19P/
dataset obtained by a single observer with the same instru- Borrelly derived from the HST observations made in 1994 is veri-
ment (the 91-cm Spacewatch Schmidt telescope at Kitt Peak fied by the best in situ image taken by the Deep Space 1 spacecraft
equipped with a CCD camera) has unfortunately never been in 2001 (cf. Lamy et al., 1998b; Soderblom et al., 2002).
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 233

comets only snapshot observations were obtained (i.e., one 3.1.6. Tancredi et al. (2000). This group (hereafter de-
HST orbit per comet), while light curves were measured noted Ta+) has compiled a set of 3990 measurements of
for 13 nuclei (8 HST orbits per comet, except 6 for 19P/ “nuclear” magnitudes obtained from a variety of sources,
Borrelly and 11 for 67P/Churyumov-Gerasimenko). The mainly the Comet Light Curve Catalogue of Kamél (1990,
derived nuclear magnitudes were converted to standard R- 1992), the Minor Planet Center database (thus including the
band values, which were then used to derive sizes by adopt- results of Scotti presented above), the IAU Circulars, the
ing an albedo of pR = 0.04 and a phase coefficient of β = International Comet Quarterly, and various scientific arti-
0.04 mag deg –1. cles. The bulk of their analysis consisted of scrutinizing these
3.1.3. Licandro et al. (2000). This group (hereafter inhomogeneous data and making sense of them. They re-
denoted Li+) has used several groundbased telescopes to jected all magnitudes determined visually, performed various
observe 18 comets at large heliocentric distances to mini- corrections, and plotted the resulting heliocentric bright-
mize possible coma contributions. No attempt has been nesses. Their “best estimates” of the absolute visual mag-
made to subtract the contribution from the coma, although nitudes HN = V(1,1,0) generally corresponds to the faintest
seven comets were conspicuously active (six of them at rh > observed magnitudes and were used to derive sizes using
4 AU). The 11 others were deemed inactive on the basis of pV = 0.04 and a coefficient β = 0.04 mag deg–1 to correct
their stellar appearance. The nuclear sizes were derived from for phase angle. They have introduced four quality classes
the V magnitudes assuming pV = 0.04 and β = 0.04 mag (QC) that roughly quantify the uncertainties affecting the
deg–1. For reasons of consistency, we prefer using R mag- nuclear magnitudes, from ±0.3 mag (QC1) to ±1 mag (QC4).
nitudes in the discussion below and in the tables presented The respective numbers of nuclei are 9 for QC1, 18 for QC2,
later. Accordingly, we converted V magnitudes to R values 37 for QC3, and 41 for QC4 for a total of 105 nuclei. It is
assuming (V-R) = 0.5, the median value for the ecliptic readily seen that the bulk of the sizes belongs to the lowest
comets (Toth and Lamy, 2000), with the following excep- quality classes. An updated version of this catalog has been
tions: (1) 52P/Harrington-Abell, which was observed in the presented by G. Tancredi at the Asteroids, Comets, Meteors
R band; and (2) 49P/Ashbrook-Jackson, 74P/Smirnova- 2002 conference and has been kindly made available to us.
Chernykh, and 96P/Machholz 1, for which (V-R) was inde- Those results are included in Table 1, but we have no means
pendently determined. of assessing the quality of these improved determinations.
3.1.4. Lowry et al. (1999, 2003a,b), Lowry and Fitz-
simmons (2001), Lowry and Weissman (2003). This group 3.2. Sizes, Shapes, and Rotational Properties
(hereafter denoted Lo+) uses a method similar to that de-
scribed above, i.e., groundbased observations at large rh. Out In this section, we provide short summaries of the physi-
of 73 comets targeted, only 28 were deemed inactive on the cal properties of individual comets. First we treat the ECs,
basis of their stellar appearance, and the measured R mag- and then we discuss the NICs. Unless otherwise stated, rn
nitudes were converted to sizes using pR = 0.04 and β = is used as the generic notation for the radius of a cometary
0.035 mag deg –1. As most of the comets were observed at nucleus, while rn,v and rn,a refer to two “effective radii”: rn,v
small phase angles, the difference between using β = 0.035 refers to the radius of the sphere having the same volume
and β = 0.04 is usually small (e.g., a 2.3% increase in the as the observed object, and rn,a refers to the radius of the
radius for α = 10°), but will be applied for consistency. The disk having the same projected area as the observed object.
remaining 45 comets were either active or were not de- The albedo measurements are discussed separately in the
tected, so that only an upper limit on the size of the nucleus next section.
could be obtained. 3.2.1. Ecliptic comets (ECs). 2P/Encke: A robust ra-
3.1.5. Meech et al. (2004). This group (hereafter de- diometric measurement of the size is reported by Fernández
noted Me+) observed 16 JFCs and 1 HTC (109P/Swift- et al. (2000): 2.4 ± 0.3 km. This number is consistent with
Tuttle) with the Keck telescope using the method described an earlier radiometrically derived upper limit of 2.9 km by
above. They concluded that 11 JFCs, as well as 109P, were Campins (1988). Visible-wavelength estimates of the size
inactive based on their stellar appearance. Their V and R have frequently suffered from the spatially unresolved coma
magnitudes were converted to sizes using pV = pR = 0.04 that this comet displays at nearly every aphelion. Fernández
and β = 0.04 mag deg–1. This leads to two different values et al. (2000), updating a compilation by Sekanina (1976),
for the radius (except for 9P/Tempel 1), and we only com- review the “nuclear” magnitudes that have been published
piled those corresponding to the R magnitudes for reasons since the 1960s and find that the data having the least coma
of consistency. For 9P, we transformed the V to R magni- contamination are from HST in 1997 (published in that same
tudes using (V-R) = 0.5 and obtained rn = 3.04 km. The re- paper), by Garradd (1997) in 1997, and by Jewitt and Meech
maining five comets were active and only an upper limit to (1987) in 1986. Jewitt and Meech (1987) state that the maxi-
the size could be obtained. In a separate program, this group mum radius of the nucleus is 2.8 ≤ rn ≤ 6.4 km, assuming
used the Wide-Field Camera of the HST to search for five albedos between 0.02 and 0.10, which is consistent with the
NICs at geocentric distances ranging from 20 to 29 AU, but later radiometric observations. Some photographic photom-
none were detected and only upper limits could be placed etry was useful in constraining the absolute magnitude of
on the sizes of their nuclei. the nucleus, e.g., observations by Van Biesbroeck (1962) in
234 Comets II

1960 and by Roemer in 1973 (reported by Marsden, 1974) for the nucleus, assuming an aspect angle of ~90°, that are in
and 1974 (reported by Marsden and Roemer, 1978). Finally remarkable agreement: a = 3.8–3.9 km and b = 2.8–2.9 km.
Fernández et al. (2000) report an attempt to reconcile all Fernández et al. (2003) obtained simultaneous visible and
published light curves to derive a shape; the lower limit on near-infrared observations at rh = 2.55 AU outbound while
one of the axial ratios was found to be 2.6, indicating a very the comet was still quite active. Two different methods were
elongated nucleus. The rotational period was constrained used to correct for the contribution of the coma (=15%) in
in the 1980s by Jewitt and Meech (1987) and Luu and Jewitt their mid-infrared measurements and their interpretation
(1990a), using time series of CCD photometry. A period of using the standard thermal model leads to a radius of the
P = 15.08 h (or possibly 23 P = 22.62 h) satisfied all the data. maximum cross-section of the nucleus of 3.0 ± 0.2 km.
However, more recent data from 2001 and 2002 presented Combining this result with that of La+ gives pR = 0.048 ±
by Fernández et al. (2002c) and Lowry et al. (2003a,b) indi- 0.007, significantly different (but still within the respective
cate that the dominant periodicity may have changed in the uncertainties) from the value pR = 0.072 ± 0.016 derived by
intervening years (or was poorly measured in the past). Cur- Fernández et al. (2003). Their large albedo is probably a
rently, a period near P = 11.01 or 2P = 22.02 h (close to the consequence of their inability to properly account for the
above value of 22.62 h) fits the data best. Furthermore, the large coma contribution in their visible observations. Com-
dominant periodicities from the 1980s are not consistent bining the above albedo pR = 0.048 with the measurements
with the most recent data. The situation hints that the nu- of La+ and Weissman et al. (1999) leads to a spheroidal
cleus of 2P/Encke may perhaps be in a complex rotation solution with a = 3.5 km and b = 2.6 km and an effective
state (cf. Belton, 2000), although further investigations are radius rn,v = 2.9 km. From their partial light curve, La+
necessary before a definite conclusion can be drawn. extrapolated a rotational period in the range of ~25–33 h.
4P/Faye: Observed with the HST by La+ in October– Fernández et al. (2003) found that a longer period ~41 h
November 1991 and in February 2000. We favor the value (1.71 d) does not contradict their observations obtained at
rn = 1.8 km obtained in 2000 with the aberration-free HST. three different epochs.
Reexamination of the 1991 observations obtained with the 10P/Tempel 2: An early, in-depth investigation led
aberrated HST indicates that the signal from the nucleus was Sekanina (1987) to constrain the orientation of the rotation
overestimated. axis of the nucleus and its gross physical properties. 10P
6P/d’Arrest: A snapshot observation by Me+ at rh = was extensively observed by A’Hearn et al. (1989), who
5.4 AU of the inactive nucleus yields rn = 1.71 km. Lo+ first combined optical and infrared photometry, and by Jewitt
determined an upper limit of 2.1 km and later obtained a par- and Luu (1989), who performed CCD photometry from
tial light curve. They derived a mean effective radius of rn,v = aphelion (thus convincingly detecting a bare nucleus) to
1.6 ± 0.06 km (scaled to β = 0.04 mag deg –1) and a/b > perihelion. Their interpretations converge to a spheroidal
1.18 ± 0.08. The size determinations from Me+, Lo+, and nucleus with a = 8–8.15 km and b = c = 4–4.3 km with an
Ta+ (1.5 km) are in good agreement but are considerably albedo pR = 0.024 ± 0.005 and a rotational period of ~9 h.
smaller than previous estimates of 3.5 km by Campins and The effective radii are rn,a = 5.7–5.9 km and rn,v = 5.0–
Schleicher (1995) using IR photometry and of 2.7 km by 5.3 km. The revised values by Campins et al. (1995) remain
K. Meech (unpublished data). Determinations of the rota- in agreement with these results. Various snapshot observa-
tional period have been reported by Fay and Wisniewski tions are also in agreement with these results assuming the
(1978), 5.17 h; Lowry and Weissman (2003), 7.2 ± 0.12 h; above albedo of 0.024 except as noted: Mueller (1992), rn =
and Gutiérrez et al. (2003), 6.67 ± 0.03 h. The apparent dis- 5.9 km; Mueller and Ferrin (1996), rn = 5.2 km (p = 0.022);
crepancies have been thoroughfully analyzed by the latter La+, rn = 5.9 km; Me+, rn = 6.4 km. The value of Ta+
authors who concluded that, if all these measurements are scaled to pR = 0.024, i.e., rn = 3.7 km, is inconsistent with
correct, a change in the period has taken place or the nu- the above results.
cleus is in a complex rotational mode. We adopt 7.0 h as a 14P/Wolf: A snapshot observation by Lo+, when the
reasonable estimate for the present period of 6P. comet was apparently inactive at rh = 3.98 AU, yields rn =
7P/Pons-Winnecke: A snapshot observation by Lo+, 2.33 ± 0.12 km. The enormous scatter of the data points of
when the comet was apparently inactive at rh = 5.58 AU, Ta+ makes their estimate of rn = 1.3 km highly uncertain.
yields rn = 2.6 ± 0.1 km. 15P/Finlay, 16P/Brooks 2: The large scatter of the data
9P/Tempel 1: The two extreme cross-sections observed points of Ta+ makes their estimates highly uncertain.
by La+ give rn = 2.8 and 3.3 km. Converting the V magni- 17P/Holmes: A snapshot HST observation by La+
tude measured by Me+ to an R magnitude using an aver- yields rn = 1.71 km.
age (V-R) = 0.52 yields rn = 3.07 km, in excellent agreement 19P/Borrelly: A complete solution was first proposed
with the above range and with the upper limit of 3.2 ± by La+: a = 4.4 ± 0.3 km, b = 1.8 ± 0.15 km assuming an
0.1 km determined by Lo+ without any correction. We very albedo of 0.04 (see section 3.3.1 for a discussion of this
much doubt that the subsequent comatic correction intro- issue). The in situ observations of Deep Space 1 (Soderblom
duced by Lo+ and the resulting rn = 2.3 km are correct. As et al., 2002; Buratti et al., 2004) yield a = 4.0 ± 0.05 km
discussed above, comatic corrections of groundbased im- and b = 1.6 ± 0.04 km. The above determination gives rn,a =
ages remain highly problematic. The brightness obtained by 2.5 km and rn,v = 2.2 km. The snapshot results of Lo+ and
La+ and Weissman et al. (1999) lead to spheroidal solutions Weissman et al. (1999) are consistent with the above solu-
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 235

tion. The rotational periods P = 25.0 ± 0.5 h found by La+ with Earth but was at a large phase angle (~30°). The maxi-
and that obtained by Mueller and Samarasinha (2001), P = mum value of the infrared flux leads to rn = 10.6 ± 0.5 km
26 h, are in excellent agreement. and pV = 0.026. Their single minimum value is not consis-
21P/Giacobini-Zinner: A snapshot observation by tent with a light curve having P = 12.75 h (Delahodde et
Mueller (1992) at Rh = 3.75 AU gives rn = 2.1 km (using an al., 2001) and, in addition, brings the albedo down to an
albedo of 0.04) and a/b > 1.5. The heliocentric light curve unrealistic value of pV = 0.016. Visible photometry yields
of Ta+ indicates that the comet was still active at that dis- rn = 10.0 km (Jewitt and Meech 1988) with pR = 0.03 ± 0.01
tance and that their estimate rn = 1.0 km derived from obser- and rn = 11.4 km (Me+). The visible albedo pV = 0.026 and
vations beyond 4.5 AU is reasonable. A rotational period the color (V-R) = 0.45 leads to pR = 0.04, so that the above
of 9.5 ± 0.2 h has been reported by Leibowitz and Brosch values of rn need not be scaled. Assuming that (Me+) ob-
(1986). served the largest projected area πab, and that a/b = 1.5 [in
22P/Kopff: Combined visible and infrared photometry fact, a lower limit obtained by Delahodde et al. (2001)], we
(La+) leads to rn = 1.67 ± 0.18 km and pV = 0.042 ± 0.006 obtain a = 14.0 km, b = 9.3 km, and rn,v = 10.7 km, which
(pR = 0.047). The slightly different value of rn = 1.52 km, is our current best estimate. A detailed analysis of a large
reported by Jorda et al. (2000), resulted from an early, less- set of observations led Delahodde et al. (2001) to deter-
elaborate analysis of the same data. The visible light curve mine a rotational period of 12.75 ± 0.03 h, in good agree-
built from the eight HST observations spanning ~12 h had a ment with previous measurements.
small range of 0.14 ± 0.07 mag and could not constrain the 29P/Schwassmann-Wachmann 1: This is the largest EC
rotational state. The snapshot observation at rh = 5.11 AU by in our sample, but there is some confusion regarding the
Lo+, when scaled to pR = 0.047, gives rn = 1.65 ± 0.1 km, classification of this comet. With a Tisserand parameter TJ =
in remarkable agreement with the above results, as well as 2.983, it qualifies as an EC but its orbit also satisfies the
with the value estimated by Ta+ (rh = 1.8 km). A partial strict definition of Centaurs given by Jewitt and Kalas (1998):
light curve recently obtained by Lo+ at rh = 4.49 AU clearly q ≥ 5 AU and a ≤ 30 AU (corresponding to the orbits of Ju-
suggests a rotational period of 12.30 ± 0.8 h and an ampli- piter and Neptune respectively). Thus duality arises because
tude range of 0.55 ± 0.07 mag, corresponding to a minimum the criteria for the two classifications are not consistent, TJ
axial ratio of 1.66 ± 0.11 and a mean effective radius rn = for ECs and q and a for the Centaurs. The current perihe-
2.76 ± 0.12 km (scaled to pR = 0.047 and β = 0.04 mag deg–1). lion of 29P is less than 0.3 AU outside Jupiter’s aphelion,
As discussed by Lowry and Weissman (2003), their solu- and it could easily be perturbed into a fully crossing orbit in
tion is totally inconsistent with the above results (the pole- the near future. On the other hand, its albedo of 0.13 ± 0.04
on view assumed for the La+ observations must have re- (Cruikshank and Brown, 1983), if correct, is totally atypical
sulted in a near-maximum cross section assuming a nucleus of cometary nuclei (see section 3.3) while being common
in simple rotation) but is consistent with unpublished re- among Centaurs (Barucci et al., 2004). Various estimates
sults by K. Meech obtained at rh = 4.73 AU: rn = 2.8 km of its radius based on visible magnitudes range from 21 to
and Prot = 12.91 h. In an early study of 22P, Sekanina (1984) 52 km assuming an albedo of 0.04. Cruikshank and Brown
found P = 9.4 ± 1.3 h. At this stage, it is impossible to recon- (1983) combined thermal measurements at 20 µm and visi-
cile the two groups of observations without considering more ble photometry to obtain rn = 20.0 ± 2.5 km and pV = 0.13 ±
complex solutions for the rotational state and the shape of 0.04. They correctly noted that the size is controlled by the
the body. For the time being, we keep the self-consistent infrared measurements, while the albedo is controlled by the
solution of La+ for the size and albedo and the values of visible magnitude, which was estimated. Meech et al. (1993)
a/b and Prot from Lo+. argued that 29P is probably never totally inactive and at-
24P/Schaumasse: The large scatter in the data used by tempted to estimate the coma contribution by measuring the
Ta+ makes their estimate highly uncertain. total nucleus + coma signal in apertures of different sizes.
26P/Grigg-Skjellerup: A stellarlike nucleus was ob- They determined a minimum axial ratio of 2.6 and, assum-
served by Boehnhardt et al. (1999) and by Li+, and they ing pR = 0.04 and β = 0.04 mag deg–1, a rotationally aver-
derived radius values of 1.44 ± 0.05 and 1.57 km respec- aged radius of rn = 15.4 ± 0.2 km, a value that we presently
tively. However, a nondetection by Lowry et al. (1999) select. However, using an albedo of 0.13 reduces this value
places an upper limit on the radius of 1.2 ± 0.1 km. The to 8.6 ± 0.1 km. For the rotational state of 29P, we adopt
graph presented by Ta+ suggests an inactive nucleus be- the simple rotation with a period of 14.0 h (Meech et al.,
yond ~2 AU, and their estimated radius of 1.3 km seems 1993), consistent with the rough estimate of 10 h reported
reasonable. A spheroid with a ~ 2.2 km and b ~ 1 km (i.e., by Luu and Jewitt (1993). However, the former authors de-
a/b = 2.2) would be consistent with all the above results. termined a second period of 32.2 h, implying a complex
This solution corresponds to rn,v = 1.3 km. Radar observa- state of rotation.
tions yielded a lower limit rn > 0.4 km (Kamoun et al., 1982, 31P/Schwassmann-Wachmann 2: Observed as a star-
1999). like object at rh = 4.58 AU by Luu and Jewitt (1992), who
28P/Neujmin 1: This low-activity nucleus has been ex- derived a radius of 3.1 km, a minimum axial ratio of 1.6,
tensively studied and is the second largest EC in the sample. and a rotational period of 5.58 ± 0.03 h.
Campins et al. (1987) combined visible and infrared pho- 33P/Daniel: The value of Ta+ looks questionable be-
tometry when the comet made a relatively close encounter cause of the large scatter in the data.
236 Comets II

36P/Whipple: A snapshot observation of a starlike nu- this leads to rn = 0.78 km. The snapshot observation of Lo+
cleus at rh = 4.43 AU by Lo+ give rn = 2.28 ± 0.21 km, gives a much larger value of rn = 1.34 ± 0.55 km, but the
which is consistent with the value quoted by Ta+, rn = large error bar means that rn could be as small as 0.79–
2.3 km. 0.82 km if β = 0.06 mag deg–1 is applied, in agreement with
37P/Forbes: The stellarlike appearance at rh = 3.59 AU the above revised value. We conclude that rn = 0.8 km is
led Li+ to derive rn = 1.1 km, close to the value of 1.0 km probably the best estimate for the time-being.
estimated by Ta+. La+ obtained a slightly smaller value, 46P/Wirtanen: It was marginally detected on CCD
rn = 0.81 km. If the above authors observed different ex- frames by Boehnhardt et al. (1997) at rh = 4.6 AU, giving
treme cross-sections, the spheroidal solution leads to a = an upper limit of the radius of 0.8 km (assuming p = 0.04)
1.38 km, b = 0.8 km (not unrealistic since a/b = 1.73), and and a probable value of 0.69 km. The first unambiguous
rn,v = 0.96 km. detection of the nucleus was by La+, giving rn = 0.62 ±
39P/Oterma: The heliocentric light curve reported by 0.02 km (R band), a/b ≥ 1.2, and Prot = 6.0 ± 0.3 h. VLT
Ta+ does not allow a reliable derivation of the size. observations by Boehnhardt et al. (2002) gave rn = 0.56 ±
40P/Väisälä 1: Undetected by Lo+, thus giving an up- 0.04 km, a/b ≥ 1.4 ± 0.01, and a partial light curve in agree-
per limit rn < 3.6 ± 0.2 km. The estimate of rn = 1.5 km by ment with the above period. A slightly larger value of rn =
Ta+ is reasonable, although an error bar of ±1 km is war- 0.7 km is reported by both Meech et al. (2000) and Ta+,
ranted given the large scatter in the data. while upper limits are given by Lo+ and Me+. CCD pho-
41P/Tuttle-Giacobini-Krešák: The heliocentric light tometry of the already active comet suggested a possible
curve of Ta+ indicates that this is a very small nucleus; rn = period of 7.6 h (Meech et al., 1997).
0.7 km is probably a good estimate, but even this may only 47P/Ashbrook-Jackson: A partial light curve was ob-
be an upper limit. tained by La+ (2001), giving a mean radius rn = 2.8 km, a/b >
42P/Neujmin 3: There is too much scatter in the data 1.4, and Prot > 44.5 h. The nucleus appears inactive near
used by Ta+ to derive a reliable size of the nucleus. Krešák aphelion (stellar appearance), so that the determination of
et al. (1984) reported that this comet and 53P/Van Bies- Li+, rn = 3.1 km, and the estimate of Ta+, rn = 2.9 km, are
broeck are fragments from a parent comet that split in in agreement taking into account the fact that this nucleus
March 1845. is elongated.
43P/Wolf-Harrington: Two determinations have been 48P/Johnson: The nucleus was reported active at rh =
reported by Lo+ from observations at rh = 4.87 AU, rn = 3.36 AU by Lo+, thus only giving rn ≤ 3.5 km. Measure-
3.3 ± 0.7 km, and at rh = 4.46 AU, rn = 3.4 ± 0.2 km, when ments by Li+ at smaller rh were certainly contaminated by
the comet had a stellar appearance. At rh = 3.04 AU out- a coma, although they claimed a stellar appearance, and this
bound, the comet was very active, displaying both a coma would explain their large value of rn = 3.7 km. Several
and a tail, leading Li+ to impose rn << 3.1 km. On the fol- months of observations of a starlike nucleus at rh ~ 4 AU
lowing inbound branch, the comet was reported active at allowed Jewitt and Sheppard (2003) to secure a fairly com-
rh = 3.9 AU (Hainaut et al., 1996). The graph of Ta+ con- plete lightcurve and to derive a spheroidal solution with a =
vincingly shows a monotonic decrease of brightness as rh 3.5 and b = 2.6 km (yielding rn,v = 2.87 km) and a/b > 1.35
increases up to 4 AU, the faintest value yielding rn = 1.8 km. and Prot = 29.0 ± 0.04 h.
A spheroidal solution based on the two above extreme 49P/Arend-Rigaux: This is a nearly extinct nucleus that
cross-sections leads to a = 6.4 km, b = 1.8 km, and a/b = has been extensively studied by combined visible and infra-
3.6, which would be unusually large. Pending further ob- red photometry. Tokunaga and Hanner (1985) reported a
servations, we are inclined to think that the large values of size of rn = 4.8 ± 0.4 km and a geometric albedo of 0.05 ±
Lo+ are not correct and that rn = 1.8 km (Ta+) is a realis- 0.01 at 1.25 µm. Brooke and Knacke (1986) determined rn =
tic estimate. Finally, it must be noted that 43P has under- 5.1 ± 1.1 km and pV = 0.02 ± 0.01. Veeder et al. (1987)
gone major orbital changes in the recent past (e.g., q de- found the nucleus to be elongated with equivalent radii of
creased from 2.5 to 1.5 AU in 1936), and this could explain 5.1 and 3.8 km and pV = 0.03. The in-depth investigation by
surges of vigorous activity thereafter. Millis et al. (1988) resulted in a more accurate determina-
44P/Reinmuth 2: A snapshot observation by La+ gives tion of the size and shape: a = 6.5 km and b = 4 km (a/b =
rn = 1.61 km. The estimate of 1.5 km by Ta+ (but with con- 1.63), an albedo of pV = 0.028, and a rotational period of
siderable scatter in the data), and the upper limit of 3.1 km P = 13.47 h. The observational data have been reanalyzed
from Lo+, are consistent with that choice. by Campins et al. (1995) using new parameters for the ther-
45P/Honda-Mrkos-Pajdušáková: La+ obtained a mean mal model and they give an effective radius of 4.6 ± 0.2 km
value of rn = 0.34 ± 0.01 km from observations performed for a sphere having the maximum projected area πab and a
on two consecutive days, making this nucleus one of the geometric albedo of 0.04 ± 0.01. Keeping a/b = 1.63 from
smallest ever observed. However, they pointed out that the Millis et al. (1988), we obtained a = 5.9 km, b = 3.6 km, and
potentially large systematic error because of the large phase rn,v = 4.24 ± 0.2 km. From R-band CCD photometry, Lo+
angle (α = 90°) during the observations. In fact, if 45P/HMP reported two determinations of the radius, 3.8 ± 0.1 and
is as phase darkened as 2P/Encke and 48P/Johnson, then a 4.0 ± 0.11 km, assuming an albedo of 0.04. With the ex-
linear phase coefficient β = 0.06 mag deg–1 should be ap- ception of the value reported by Ta+ all the above results
plied instead of the standard value of 0.04 mag deg –1, and are consistent, the results of Millis et al. (1988) as corrected
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 237

by Campins et al. (1995) providing the most detailed de- 0.64 km, a/b > 1.3, and Prot > 18 h. At the time of the HST
scription. Thus we use rn,v = 4.24 km and pV = 0.04 ± 0.01. observations, rh = 2.96 AU, the comet was still very active,
Jewitt and Meech (1985) obtained a light curve from which the nucleus and the coma contributing equally to the sig-
they obtained two possible rotational periods, 9.58 ± 0.8 and nal in the peak pixel. The snapshot observation of Lo+ at
6.78 ± 0.08 h. rh = 4.4 AU, performed under nonphotometric conditions,
50P/Arend: A snapshot observation by La+ gave rn = gives rn = 0.92 ± 0.24 km. The low end, rn = 0.68 km, is
0.95 km. The revised estimate of Ta+, rn = 1.0 km (com- consistent with the result of La+. The comet may still have
pared to the original value of 3.0 km), is in good agreement been weakly active at 4.4 AU.
with the above result. 62P/Tsuchinshan 1: Certainly a very small nucleus (rn <
51P/Harrington: Lo+ give an upper limit of 1.9 km. 1 km) and (Ta+) estimated rn = 0.8 km, but the compiled
Although consistent with it, the value of rn = 1.4 km by Ta+ data in their plot have wide scatter, as in the case of 60P.
cannot be considered reliable because of the large scatter 63P/Wild 1: A snapshot observation by La+ gives rn =
in the data. Recent CCD images taken by Manteca (2001) 1.45 km. The nondetection by Lowry and Fitzsimmons (2001),
show that this comet has split again into two components. which results in an upper limit rn ≤ 0.6 km, is therefore puz-
A similar splitting was recorded at the 1994 apparition by zling. Invoking a highly elongated spheroid to reconcile the
Scotti (1994), who found a double nucleus on Spacewatch two observations would be rather artificial.
images. A detailed analysis of the astrometric data and of 64P/Swift-Gehrels: A starlike nucleus detected at rh =
the circumstances of the splitting is still in progress (Seka- 3.63 AU by Li+ gave rh = 1.6 ± 0.1 km, which is consistent
nina, 2001). with the upper limit rh ≤ 1.9 km obtained by Lo+ and with
52P/Harrington-Abell: Li+ obtained rn = 1.4 km from the estimate by Ta+ of rn = 1.7 km.
two images of a starlike nucleus at rh = 2.83 AU. The fainter 65P/Gunn: This comet is very active out to aphelion,
magnitude reported by Carlson (1990) corresponds to rn = so that only upper limits were obtained, rn << 11.7 km (Li+)
1.0 km, in close agreement with the value selected by Ta+, and rn ≤ 8.8 km (Lo+). The estimate proposed by Ta+ is
rn = 1.1 km. A spheroidal solution assuming that the above rn = 4.8 km.
observations correspond to extreme cross-sections yields a = 67P/Churyumov-Gerasimenko: A rotational light curve
2, b = 1 km (i.e., a/b = 2), and rn,v = 1.3 km. has been obtained by La+ giving a mean radius rn = 1.98 ±
53P/Van Biesbroeck: Me+ derived rn = 3.33 km from 0.02 km, a/b > 1.3, and Prot = 12.3 ± 0.27 h. This comet was
a snapshot observation at rh = 8.31 AU (i.e., close to aph- undetected by Lo+ at aphelion (5.72 AU), thus imposing
elion) in agreement with the result rn << 6.7 km of Li+. The rn ≤ 2.9 km. Observations at 4.87 and 4.97 AU by Mueller
comet is known to be active out to 6 AU, as illustrated by (1992) give rn = 2.8 ± 0.1 km (scaled to pR = 0.04) and a/b >
the very erratic heliocentric light curve of Ta+. Krešák et 1.7. The heliocentric light curve is well-behaved and shows
al. (1984) reported that this comet and 42P/Neujmin 3 are that the comet is inactive beyond 4.5 AU and the revised
fragments of a parent comet that split in March 1845. estimate rn = 2.0 km by Ta+ agrees with the result of La+.
54P/de Vico-Swift: Undetected by Lo+ at rh = 5.39 AU 68P/Klemola: The well-behaved heliocentric light
(aphelion), they obtained an upper limit of 2.1 km. curve produced by Ta+ suggests that their value rn = 2.2 km
56P/Slaughter-Burnham: A snapshot observation at is a good estimate.
rh = 7.42 AU by Me+ of the inactive nucleus gives rn = 69P/Taylor: This comet was found to be active at rh =
1.56 km. This is in good agreement with the estimate of 4.03 AU by Lo+, who obtained an upper limit of 3.4 km.
Ta+, rn = 1.5 km. 70P/Kojima: A partial rotational light curve was ob-
57P/du Toit-Neujmin-Delporte: Lo+ determined an tained by La+, giving a mean radius rn = 1.86 km, a/b >
upper limit of 1.1 km. The considerable scatter in the he- 1.1, and Prot > 22 h. The large scatter in the data at rh >
liocentric light curve of Ta+ makes their estimate of rn = 3.4 AU makes the estimate of Ta+, rn = 1.2 km, rather ar-
1.6 km unreliable. The comet has recently split: Two frag- bitrary.
ments were first discovered (cf. Marsden, 2002), followed 71P/Clark: A snapshot observation by La+ at rh =
by 18 more (Fernández et al., 2002b). A preliminary analy- 2.72 AU gives rn = 0.68 ± 0.07 km, which is consistent with
sis of this event has been reported by Sekanina (2002a,b). the nondetection at rh = 4.4 AU by Lo+ (rn ≤ 0.9 km). The
58P/Jackson-Neujmin: There is too much scatter in the observations by Me+ at aphelion (rh = 4.67 AU) yields rn =
light curve of Ta+ to estimate a size. 1.31 ± 0.04 km, similar to the value estimated by Ta+. A
59P/Kearns-Kwee: A snapshot observation by La+ spheroid with a = 2.13 km and b = 0.75 km could recon-
yields rn = 0.79 km. Such a small nucleus, active out to at cile the two determinations within the error bars, but has a
least 4.2 AU, would be very difficult to detect from the very large axis ratio, a/b ≥ 2.85, and further requires that
ground. La+ and Lo+ observed the smallest cross-section while
60P/Tsuchinshan 2: Certainly a very small nucleus Me+ observed the largest one. This nucleus certainly de-
(rn < 1 km) and Ta+ estimated rn = 0.8 km, but the com- serves further observations.
piled data in their plot have wide scatter. The nucleus may 73P/Schwassmann-Wachmann 3: The nucleus was re-
be as small as ~0.5 km. ported as split into two components by Schuller (1930), but
61P/Shajn-Schaldach: A partial rotational light curve there was no other independent report. In 1994, the comet
has been obtained by La+ giving a mean radius r n = was reported active at rh = 3.03 AU, and Boehnhardt et al.
238 Comets II

(1999) derived rn < 1.26 km. The principal nucleus further 0.02 km, a/b > 1.35, and an ill-defined period. A snapshot
split into at least three components in the autumn of 1995. observation at 4.95 AU by Me+ gives rn = 0.65 ± 0.03 km.
Undetected in 1998 by Lowry and Fitzsimmons (2001) at These two determinations are inconsistent but satisfy the
rh = 5.03 AU, they obtained an upper limit for the largest condition rn ≤ 0.9 km (Lo+). The unpublished value of
component of rn < 0.9 km. Fragment C was detected by the 3.1 km suggested by Meech is apparently unjustified.
HST at rh = 3.25 AU and Toth et al. (2003) derived rn = 87P/Bus: The light curve obtained by La+ at rh =
0.68 ± 0.04 km and a/b > 1.16. 2.45 AU gives a mean radius rn = 0.28 ± 0.01 km, a/b >
74P/Smirnova-Chernykh: A partial rotational light curve 2.20, and Prot = 25 h. Two upper limits have been reported,
was obtained by La+ giving a mean radius of rn = 2.23 ± rn ≤ 0.6 km at rh = 4.32 AU (undetected) by Lo+ and rn <
0.1 km, a/b > 1.14, and P ~ 20 h. At rh = 3.56 AU, the comet 3.42 km at rh = 4.77 AU (close to aphelion) by Me+ (a
was still very active, the nucleus and the coma contributing coma was present). It is probably impossible to detect this
equally to the signal in the peak pixel. This explains why Li+ nucleus from the ground.
(rh = 4.57 AU) and Lo+ (rh = 4.61 AU) obtained only up- 88P/Howell, 89P/Russell 2, 90P/Gehrels 1, 91P/Russell 3,
per limits, rn << 11.2 km and rn ≤ 7.1 ± 1.1 km, respectively. 94P/Russell 4: There is too much scatter in the data pre-
The value rn = 6 km estimated by Ta+ is totally arbitrary. sented by Ta+ to obtain reliable size estimates. 89P was
75P/Kohoutek: A nondetection by Lo+ gives rn ≤ found active at Rh = 3.04 AU by Lo+ leading to rn < 2.2 km,
1.5 km, while the estimate by Ta+ is rn = 1.8 km. and possibly rn ≤ 1.3 ± 0.3 km after removing the comatic
76P/West-Kohoutek-Ikemura: A partial rotational light contribution.
curve was obtained by La+ at rh = 3.09 AU giving a mean 92P/Sanguin: Two snapshot observations of a starlike
radius rn = 0.33 ± 0.03 km, a/b > 1.47, and Prot ~ 13 h. The nucleus, one at rh = 8.57 AU by Me+, the other at rh =
comet was still active, explaining the much larger value esti- 4.46 AU by Lo+, give rn = 1.19 km and rn = 1.7 ± 0.63 km
mated by Ta+. respectively. These values are consistent owing to the large
77P/Longmore: There is too much scatter in the data uncertainty in the latter value.
of Ta+ to obtain a reliable estimate. 97P/Metcalf-Brewington: A starlike nucleus (with pos-
78P/Gehrels 2: A snapshot observation of a starlike sibly a faint coma) detected at rh = 3.67 AU by Li+ gives
nucleus at rh = 5.46 AU Lo+ yields rn = 1.42 ± 0.12 km. The rn = 1.5 ± 0.16 km, which, strictly speaking, should be con-
heliocentric light curve of Ta+ displays a lot of scatter at sidered an upper limit. Observed at 4.76 AU inbound by
3.5 AU, suggesting that the comet is still active at that dis- Lo+, it was found inactive resulting in rn = 2.18 ± 0.41 km.
tance. An intermediate size of rn = 1.7 km is compatible with these
79P/du Toit-Hartley: A snapshot observation at rh = two determinations, taking into account the error bars.
4.74 AU by Lo+ revealed an inactive nucleus whose radius 98P/Takamizawa: Observed at rh = 3.78 AU by Li+ as
is rn = 1.4 ± 0.3 km. a trailed object, their determination of rn = 3.7 km cannot
81P/Wild 2: Observed while the nucleus was inactive be considered reliable. The heliocentric light curve of Ta+
at rh = 4.7 AU by Meech and Newburn (1998), they deter- suggests that this comet is weakly active; their radius rn =
mined rn = 2.0 ± 0.04 km and that the nucleus is fairly 2.4 km has now been revised to rn = 3 km.
spherical, or has a relatively long period. Still inactive at 99P/Kowal 1: There is too much scatter in the data
rh = 4.25 AU inbound, Lo+ obtained rn = 2.0 ± 0.3 km. The presented by Ta+ to obtain a reliable estimate.
comet was, however, found active at rh = 4.34 AU outbound, 100P/Hartley 1: Undetected by Lo+ at Rh = 3.94 AU,
so that Li+ put an upper limit rn << 5.7 km. Finally, Fernán- they derived an upper limit rn < 1.2 km.
dez (1999) obtained infrared images at 10.6 µm when the 101P/Chernykh: There is two much scatter in the data
comet was at rh = 1.85 AU, and therefore active. Although presented by Ta+ to obtain a reliable estimate. Luu and
the measured flux was probably dominated by coma, that Jewitt (1991) discovered that this comet has split.
author applied the standard thermal model for asteroids to 103P/Hartley 2: The thermal flux of the nucleus was
derive rn < 3.0 ± 0.6 km. A nearly spherical nucleus with measured at 11.5 µm using ISOCAM on ISO. The prelimi-
rn = 2 km is the most probable solution. This comet is the nary determination rn = 0.58 km (Jorda et al., 2000) has
target of the Stardust mission, which will fly by its nucleus now been revised to rn = 0.71 ± 0.13 km by Groussin et al.
in January 2004. (2003), which is consistent with the upper limits of Li+,
82P/Gehrels 3: A partial rotational light curve was ob- rn << 5.3 and of Lo+ rn ≤ 5.8 km.
tained by La+ at rh = 3.73 AU giving a mean radius rn = 104P/Kowal 2: A snapshot observation of a starlike nu-
0.73 ± 0.02 km, a/b > 1.6, and Prot ~ 50 h. The comet ap- cleus at rh = 3.94 AU by Lo+ gives rn = 1.0 ± 0.5 km.
pears to be active all along its orbit, so that Li+ could only 105P/Singer-Brewster: There is too much scatter in the
determine rn < 3.0 km. data presented by Ta+ to obtain a reliable estimate.
83P/Russell 1: A nondetection by Lo+ at rh = 3.01 AU 106P/Schuster: A snapshot observation by La+ gives
gives rn ≤ 0.5 km. rn = 0.94 ± 0.05 km, which is quite close to the value in the
84P/Giclas: A snapshot observation by La+ gives rn = revised catalog of Ta+, rn = 0.8 km.
0.90 ± 0.05 km. 107P/Wilson-Harrington: The identification of this
86P/Wild 3: A partial rotational light curve was obtained object as a comet remains problematic as discussed by
by La+ at rh = 2.32 AU giving a mean radius rn = 0.43 ± Weissman et al. (2003) and it was in fact first classified as
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 239

a near-Earth asteroid. It has a Tisserand parameter slightly 119P/Parker-Hartley: This comet was still very active
in excess of 3 (TJ = 3.084) but an orbit typical of ECs (a = at rh = 3.42 AU when observed by Lo+, who obtained an
2.643 AU, e = 0.621, i = 2.78°). In their dynamical analysis, upper limit rn < 7.4 ± 0.2 km and then refined that to rn <
Bottke et al. (2002) assign it only a 4% probability of be- 4.0 ± 0.6 km after estimating the comatic contribution. As
ing of cometary origin; they find the most probable source illustrated by the heliocentric light curve of Ta+, the comet
to be the outer main belt (65%). Its activity was observed is simply too active out to 4 AU to make a sensible esti-
on only one night, on two Palomar photographic plates mate of rn.
taken in 1949, and the object is trailed on both images; no 120P/Mueller 1: A starlike nucleus detected at rh =
activity was detected on plates taken three nights later. 3.08 AU by Lo+ gives rn = 1.5 km. The plot of Ta+ shows
Subsequent searches for cometary activity have all been considerable scatter of the magnitudes at that distance, in-
negative (e.g., Chamberlin et al., 1996). 107P was observed dicating that the comet could well be active.
simultaneously in the near and thermal infrared by Campins 121P/Shoemaker-Holt 2: A starlike nucleus detected at
et al. (1995). Using first the STM, they obtained rn = 1.3 ± rh = 5.03 AU by Lo+ gives rn = 1.62 ± 0.57 km.
0.16 km and pJ = 0.10 ± 0.02, a somewhat surprising value. 123P/West-Hartley, 124P/Mrkos, 125P/Spacewatch:
Thus, they favored the ILM solution, which gives rn = 2.0 ± There is too much scatter in the data presented by Ta+ to
0.25 km and pJ = 0.05 ± 0.01. Since the color is very neu- obtain reliable estimates.
tral, this value holds as well for the V and R bands. Visible 128P/Shoemaker-Holt 1: Two snapshot observations of
snapshot observations have been reported by Lo+ giving a starlike nucleus at rh = 4.99 AU by Lo+ give compatible
rn = 1.78 ± 0.03 km and Me+ giving rn = 1.96 ± 0.02 km. results, rn = 2.48 ± 0.1 km and rn = 2.12 ± 0.18 km, which
There also exists an unpublished value of rn = 2.0 km by are both consistent with the upper limit rn < 4.0 km when
K. Meech. The rotational state has been investigated by the comet was observed at rh = 3.66 AU by Lo+, when it
Osip et al. (1995), who found Prot = 6.1 ± 0.05 h and a/b ≥ was still active. We adopt an average value rn,v = 2.3 km.
1.2. If we scale the above Lo+ and Me+ values to pR = 0.05, 130P/McNaught-Hughes, 131P/Mueller 2, 132P/Helin-
we get rn = 1.59 ± 0.03 and rn = 1.75 ± 0.02, respectively. Roman-Alu 2, 134P/Kowal-Vavrová, 135P/Shoemaker-
A spheroidal solution with a = 1.9 km and b = 1.6 km with Levy 8, 136P/Mueller 3: There is too much scatter in the
pR = 0.05 is then compatible with all above results, imply- data presented by Ta+ to extract reliable estimates.
ing an obliquity of 90°, and that Campins et al. (1995) and 137P/Shoemaker-Levy 2: This comet was observed at
Me+ observed the largest cross-section while Lo+ observed rh = 4.24 AU by Li+, but various technical problems make
the smallest. We then obtain rn,v = 1.7 km. their determination rn = 4.5 km questionable. This is con-
110P/Hartley 3: A complete rotational light curve has firmed by the upper limit rn ≤ 3.4 km found by Lo+ when
been obtained by La+ giving a mean radius rn = 2.15 ± they observed the comet at rh = 2.29 AU, while it was still
0.05 km, a/b > 1.3, and Prot ~ 10 h. active. The heliocentric light curve of Ta+ indicates that the
111P/Helin-Roman-Crockett: This comet was undetec- magnitude at rh = 5 AU may provide a good estimate, rn =
ted by Lo+ at rh = 4.35 AU, thus imposing rn ≤ 1.5 km. NTT 2.9 km.
observations made at rh = 4.56 AU by Delahodde (2003) 138P/Shoemaker-Levy 7: There is too much scatter in
give a subkilometer radius of rn = 0.6 ± 0.3 km. the data presented by Ta+ to extract a reliable estimate.
112P/Urata-Niijima: A snapshot HST observation at 143P/Kowal-Mrkos: A starlike nucleus was observed by
rh = 2.30 AU by La+ gives rn = 0.90 ± 0.05 km. The esti- Jewitt et al. (2003) from rh = 3.4 to 4.0 AU and their almost
mate by Ta+ is 0.7 km, but the compiled data in their plot complete lightcurve clearly suggests a rotational period of
have wide scatter. 17.21 ± 0.1 h and an amplitude range of 0.45 ± 0.05 mag,
113P/Spitaler: This comet was undetected by Lo+ at corresponding to a minimum axial ratio of 1.49 ± 0.05.
rh = 4.22 AU, thus imposing rn ≤ 2.0 km. The estimate of Assuming an albedo of 0.04 and using the phase coefficient
Ta+, rn = 1.1 km, seems plausible. determined by these authors β = 0.043 ± 0.014 mag deg–1,
114P/Wiseman-Skiff: A snapshot HST observation at the spheroidal solution has semiaxes a = 7.0 and b = 4.7 km,
rH = 1.57 AU by La+ gives rn = 0.78 ± 0.04 km. yielding rn,v = 5.4 km. Note that the effective radius rn =
115P/Maury: Me+ observed a starlike nucleus at rh = 5.7 ± 0.6 km reported by the above authors was derived us-
5.34 AU and give rn = 1.11 km. ing a Bowell et al. (1989)-type phase curve having G = 0.15,
116P/Wild 4: The heliocentric light curve of Ta+ sug- which has an opposition effect of about 0.2 mag above the
gests that the comet could be inactive at rh = 4 AU. A ra- linear phase law.
dius of 3.5 km, recently revised to 3.0 km, is probably a 147P/Kushida-Muramatsu: The nucleus of this comet
good estimate, pending further observations. is the smallest of all the objects cataloged to date. From
117P/Helin-Roman-Alu: The value of Ta+, rn = 3.5 km, observations with the HST at rh = 2.83 AU over a 13-h time
comes from measurements at aphelion. It is unclear whether interval, La+ found a very small, rn = 0.21 ± 0.01 km,
the comet is inactive then. highly active nucleus with a/b > 1.53, and a possible rota-
118P/Shoemaker-Levy 4: A starlike nucleus detected tional period of 9.5 h. It is therefore not surprising that Lo+
at rh = 4.71 AU by Lo+ gives rn = 2.4 ± 0.2 km similar to could not detect the comet at rh = 4.11 AU, thus imposing
the value estimated by Ta+, but the compiled data in their rn ≤ 2.0 km.
plot have wide scatter. 152P/Helin-Lawrence: This comet is still active at aphe-
240 Comets II

lion (rh = 5.85 AU), and the smallest upper limit is pres- Jorda and Lecacheux (1992), ~69.6 h, Yoshida et al. (1993),
ently rn ≤ 1.74 km (Me+). 69.4 ± 0.24 h, and Boehnhardt and Birkle (1994), 67.08 h.
P/1993 W1 (Mueller 5), P/1994 A1 (Kushida), P/1994 J3 126P/IRAS: The thermal flux of the nucleus was meas-
(Shoemaker 4), P/1995 A1 (Jedicke), P/1996 A1 (Jedicke), ured at 11.5 µm using ISOCAM. The preliminary determi-
P/1997 C1 (Gehrels), P/1997 G1 (Montani), P/1997 V1 nation rn = 1.43 km (Jorda et al., 2000) has now been re-
(Larsen): There is too much scatter in the data presented fined to rn = 1.57 ± 0.14 km by Groussin et al. (2003).
by Tancredi et al. (2000) to extract a reliable estimate. P/1991 L3 (Levy): A stellar appearance at rh = 3.1 AU
3.2.2. Nearly isotropic comets (NICs). 1P/Halley: The led Fitzsimmons and Williams (1994) to consider that they
size and shape of its nucleus were determined from in situ observed a bare nucleus, shortly after it had ceased outgas-
imaging made by the Vega 1,2 and Giotto spacecrafts in sing. They determined rn = 5.8 ± 0.1 km, a/b > 1.3, and
1986 (Sagdeev et al., 1986a,b; Keller et al., 1986, 1987, Prot = 8.34 h.
1994; Keller, 1990; see also Keller et al., 2004). The nucleus C/1983 H1 (IRAS-Araki-Alcock): Extensive observa-
is an elongated, irregularly shaped body approximated by tions in the visible, infrared, radio, and radar wavelength
an ellipsoid with semiaxes (a × b × c) of 7.21 ± 0.15 × 3.7 ± ranges were performed when it passed near Earth on 11
0.1 × 3.7 ± 0.1 km (Giotto) and 7.65 ± 0.25 × 3.61 ± 0.25 × May 1983. The radar and radio observations of Altenhoff et
3.61 ± 0.25 km (Vega 1,2). It is in nonprincipal axis rota- al. (1983), Goldstein et al. (1984), Irvine et al. (1984), and
tion, and there was a long dispute over whether the nucleus Harmon et al. (1989) converge to a nonspherical nucleus
rotates in the “short-axis mode” (SAM) or “long-axis mode” with a radius is in the range 2.5–6.0 km (the a/b ratio could
(LAM) (Sagdeev et al., 1989; Peale and Lissauer, 1989; not be determined) and a rotation period is in the range 24–
Abergel and Bertaux, 1990; Belton, 1990; Belton et al., 72 h. From a study of the temporal variation of its asym-
1991; Samarasinha and A’Hearn, 1991). In the modes iden- metric coma, Watanabe (1987) and later Pittichová (1997)
tified as most likely, the long axis conducts a 3.7-d preces- estimated that the period lies in the range 18–170 h. From
sional motion around the space-fixed vector of the total ro- a synthesis of visible, infrared, and radar observations,
tational angular momentum, while the nucleus also rotates Sekanina (1988) derived a prolate spheroid nucleus with a =
around the long axis with a 7.3-d period. 8, b = c = 3.5 km, and a rotational period of 51.3 h. Infra-
8P/Tuttle: A single value rn = 7.8 km was reported by red observations and a simple thermal model, assuming a
Li+ when the comet was at rh = 6.29 AU and appeared in- constant temperature for the surface of the nucleus, were
active. used to derive that the radius was in the range of 3.6–5.0 km
55P/Tempel-Tuttle: Its effective radius of 1.8 km and (Feierberg et al., 1984; Hanner et al., 1985; Brown et al.,
a minimum value of 1.5 for the axial ratio were derived 1985). Groussin et al. (2004) reexamined the interpretation
from HST WFPC2 and ISO ISOCAM observations (La+). of all visible, infrared, and radio observations and using
Groundbased observers determined similar sizes, e.g., Hai- their thermal model, they derived an equivalent radius of
naut et al. (1998) and P. Weissman and B. Buratti (personal rn = 3.5 ± 0.5 km.
communication, 2003) in the visible and Fernández (1999) C/1983 J1 (Sugano-Saigusa-Fujikawa): Hanner et al.
in the midinfrared. There is still no data published for the (1987) obtained a value of 0.37 km for the average radius
rotational period of the nucleus. of the nucleus from infrared spectroscopic observations.
96P/Machholz 1: A starlike nucleus detected at rh = This result was a clear indication that cometary nuclei, in-
4.83 AU by Li+ gives rn = 3.5 km. There are unpublished cluding NICs, could be subkilometer-sized bodies.
data by K. Meech giving rh = 2.8 km, a/b > 1.4, and Prot = C/1995 O1 (Hale-Bopp): Weaver and Lamy (1997) and
6.38 h. A spheroid with a = 4.3 km and b = 2.8 km (a/b ~ Fernández (2003) reviewed all the data pertaining to the size
1.5) would be consistent with the two results above, yield- of the nucleus. The former review discusses all wavelengths,
ing rn,v = 3.2 km. while the latter focuses on infrared and radio observations.
109P/Swift-Tuttle: A mean effective radius of 11.8 km The dominant visible-wavelength dataset is from HST. The
was determined from groundbased CCD photometry (O’Ceal- spatial resolution and image quality were sufficient to ob-
laigh et al., 1995) at rh = 5.3 AU outbound in the presence tain photometric extractions of the nucleus, from which a
of a weak coma. Later, at rh ~ 5.8 AU outbound, the nucleus radius of ~35 km was derived (Weaver and Lamy, 1997).
had a stellar appearance and Boehnhardt et al. (1996) deter- The dominant radiometric datasets are from ISO (Jorda et
mined two comparable values of the radius, 12.2 and 12.5 ± al., 2000), the Very Large Array (VLA) (Fernández, 1999),
0.3 km at a time interval of 5 d. Meech et al. (2004) ob- the Owens Valley Radio Observatory (OVRO) (Qi, 1998),
served this comet at 14.5 AU and derived an effective ra- and the Institut de Radioastronomie Millimétrique (IRAM)
dius of 13.7 km. A radius of 15.0 ± 3.0 km was estimated (Altenhoff et al., 1999). Generally, the radio data suggest a
from groundbased IR photometry (Fomenkova et al., 1995). smaller nucleus than implied by the infrared data. A com-
An average radius of 13.0 km appears realistic. The rota- promise solution by Fernández (2003) was to argue that
tional period of the nucleus has been determined by Seka- (1) the subsurface layer sampled by the radio observations
nina (1981) from the recurrent pattern of coma jets on 1862 was cooler and/or less emissive than expected, and (2) there
photographs, Prot = 66.5 h, and on 1992 CCD images by was some excess dust not accounted for in the infrared pho-
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 241

tometry. This would shift the radii from the two wavelength 3.3. Albedo
regimes toward each other and leads to a radius of 30 ±
10 km, consistent with the HST results. The rotational pe- 3.3.1. Ecliptic comets (ECs). 2P/Encke: Using radiom-
riod of the nucleus was determined by two different meth- etry, Fernández et al. (2000) report 0.046 ± 0.023 for the
ods: 11.34 ± 0.02 h was derived by Licandro et al. (1998) V band.
and 11.35 ± 0.04 h by Jorda et al. (1999) (see Samarasinha 9P/Tempel 1: Using radiometry, Fernández et al. (2003)
et al., 2004). An extensive, groundbased CCD imaging ob- report 0.072 ± 0.016 for the R band. However, as discussed
servational campaign (Farnham et al., 1999) showed a sys- in section 3.2.1, this large value probably results from coma
tematic motion of the rotational pole of the nucleus, and contaminated visible magnitudes. The most likely value is
this was interpreted as resulting from precession due to pR = 0.048 ± 0.007.
complex rotation. However, Samarasinha (2000) showed 10P/Tempel 2: From radiometry of the nucleus, A’Hearn
that there are no effects due to precession in the observed et al. (1989) report an albedo of 0.022+0.004
–0.006 for a wavelength
coma morphology. of 4845 Å. Tokunaga et al. (1992) report a near-infrared
C/1996 B2 (Hyakutake): Optical, infrared, and radar (1.25 to 2.20 µm) albedo of 0.04–0.07, which is consistent
observations were performed during its close approach to with the reddening of the nucleus in this wavelength regime
Earth. Lisse et al. (1999) estimated a nuclear radius of 2.4 ± compared to the visible.
0.5 km from the infrared and optical data. Radar observa- 19P/Borrelly: Buratti et al. (2004) used disk-resolved
tions revealed a clear detection of the nucleus, but an ex- imaging of the nucleus obtained by the Miniature Integrated
tremely small radar albedo of 0.011 is required to be con- Camera and Spectrometer (MICAS) instrument on the Deep
sistent with the infrared data (Harmon et al., 1997, 2004). Space 1 (DS1) mission, and a scattering model based on
If the radar albedo is 0.04, the radius of the nucleus de- the Hapke (1986) formalism, to calculate a disk-integrated
rived from the radar detection drops to only ~1.3 km. Early geometric albedo of 0.029 ± 0.006. Table 3 of Buratti et al.
observations showed a fast rotation period of 6.30 ± 0.03 h, (2004) indicates that this is the pV value, but we think that
which was later refined by Schleicher and Osip (2002) to it in fact corresponds to the R band for two reasons. First,
6.273 ± 0.007 h. This NIC underwent a partial fragmenta- the DS1 images have an effective wavelength of 0.66 µm,
tion as large fragments (~10–20 m in diameter) were ob- and second, the albedo was derived from the absolute R
served traveling away from the nucleus with a velocity of magnitudes, R(1,1,α). Variations are, however, observed on
~10 m s –1 (Lecacheux et al., 1996; Desvoivres et al., 2000). the surface of the nucleus, and the two main types of ter-
C/1983 O1 (Cernis), C/1984 K1 (Shoemaker), C/1986 P1 rains, smooth and mottled, exhibit mean normal reflectances
(Wilson), C/1987 H1 (Shoemaker), C/1987 F1 (Torres), C/ of 0.03 and 0.022. The above albedo is lower than that
1988 B1 (Shoemaker), C/1997 T1 (Utsonomiya): Only up- assumed by La+ (0.04) but, as discussed by Buratti et al.
per limits are reported for the nuclear radii of these NICs (2004), the respective uncertainties in the HST and DS1
by Me+. An upper limit for the radius of C/1997 T1 is also measurements make the two results fully consistent. This
reported by Fernández (1999) from infrared measurements. justifies the superposition of the prolate spheroid model
C/1999 S4 (LINEAR): This comet underwent cata- derived from the HST observations and a DS1 image dis-
strophic fragmentation in July 2000. Lower limits for the played in Fig. 2.
size of the nucleus prior to disruption were derived indi- 22P/Kopff: Using radiometry, Lamy et al. (2002) report
rectly from the long-term monitoring of the water produc- 0.042 ± 0.006 for the V band.
tion rate: rn ≥ 0.375 km by Mäkinen et al. (2001), and rn ≥ 28P/Neujmin 1: As discussed in section 3.2.1, the maxi-
0.44 km by Farnham et al. (2001). mum value of the infrared flux measured by Campins et al.
C/2001 OG108 (LONEOS): First classified as an as- (1987) leads to pV = 0.026. This value and the color (V-
teroid of the Damocloid group, it developed a small amount R) = 0.45 leads to pR = 0.04, in good agreement with the
of cometary activity as it approached perihelion and was value pR = 0.03 ± 0.01 determined by Jewitt and Meech
subsequently reclassified as a comet. Simultaneous optical (1988).
and thermal observations by Abell et al. (2003) give an 29P/Schwassmann-Wachmann 1: Using radiometry,
effective radius of 8.9 ± 0.7 km and a visual albedo pV = Cruikshank and Brown (1983) report pV = 0.13 ± 0.04. As
0.03 ± 0.005. Their composite lightcurve indicates a simple emphasized in section 3.2, this value is controlled by the
rotation with a period of 57.19 ± 0.5 h and a minimum axial visible magnitude, which was estimated.
ration of 1.5. The spheroidal solution assuming a/b = 1.3 49P/Arend-Rigaux: The albedo has been constrained by
has a = 10.1 km and b = c = 7.9 km. many groups, all using groundbased radiometry. The results
Essentially all the best data on the sizes and shapes of of Millis et al. (1988), revised by Campins et al. (1994),
cometary nuclei are summarized in Tables 1, 2, and 3. The give pV = 0.04 ± 0.01. In the near-infrared (specifically J
column labeled rn,v displays what we consider to be the band), measurements by Tokunaga and Hanner (1985),
most reliable value of the effective radius, as defined in sec- 0.054 ± 0.010, and by Brooke and Knacke (1986), 0.03 ±
tion 3.2. An absence of value means that, in our opinion, a 0.01, are consistent with the value at visible wavelengths.
reliable determination does not yet exist. 107P/Wilson-Harrington: Using radiometry, Campins
242 Comets II

TABLE 1. Nuclei of the ecliptic comets (ECs).

Effective radius (km) a/b Prot

Comet La+ Lo+ Li+ Me+ Sc Others Ta+ rn,v (min) (h)
2P/Encke — 4.4 — — 3.2 2.4 3.1 4.5 2.4(1.3) 2.4 2.6 11.
4P/Faye 1.77 — — — 2.3 — 2.2(1.7) 1.77 1.25 —
6P/d’Arrest — 1.6 — 1.71 — 3.5 1.5 1.6 1.2 7.0
7P/Pons-Winnecke — 2.6 — — — — 1.5 2.6 — —
9P/Tempel 1 3.13 2.4 — 3.07 3.2 3.32 2.3(1.9) 3.1 1.40 41.0
10P/Tempel 2 4.63 — — 4.93 4.1 3.1 5.9 2.9 5.3 1.7 9.0
14P/Wolf — 2.33 — — 2.0 — 1.3 2.33 — —
15P/Finlay — — — — — — 0.9 — — —
16P/Brooks 2 — — — — — — 1.7 — — —
17P/Holmes 1.71 — — — — — 2.0(1.6) 1.71 — —
19P/Borrelly 2.4 1.9 — — — 2.4 2.50 3.0(2.2) 2.2 2.5 25.0
21P/Giacobini-Zinner — — — — — 1.9 1.0 1.0 1.5 9.5
22P/Kopff 1.67 1.8 — <2.9 — 2.46 1.8 1.67 1.7 12.30
24P/Schaumasse — — — — 1.1 — 0.8 — — —
26P/Grigg-Skjellerup — ≤1.5 1.5 — 1.9 1.44 1.3(1.2) 1.3 1.10 —
28P/Neujmin 1 — — — 11.44 — 10.22 10.6 9.1 10.7 1.50 12.75
29P/Schwassmann-Wachmann 1 — — — 15.4 — 20.0 — 15.4 2.6 14(32.3)
30P/Reinmuth 1 — ≤3.8 — — 3.4 — 1.3(1.0) — — —
31P/Schwassmann-Wachmann 2 — — — — 3.2 3.1 3.2 3.1 1.6 5.58
32P/Comas Solá — — — — 3.6 — — (2.1) — — —
33P/Daniel — — — — 1.1 — 0.9 — — —
36P/Whipple — 2.32 — — 2.8 — 2.3(1.9) 2.32 — —
37P/Forbes 0.81 — 1.1 — 2.0 — 1.0 0.96 — —
39P/Oterma — — — — — — 9.1(3.2) — — —
40P/Väisälä 1 — ≤3.6 — — 1.8 — 1.5 — — —
41P/Tuttle-Giacobini-Kresák — — — — — — 0.7 0.70 — —
42P/Neujmin 3 — — — — 1.0 — 0.6 — — —
43P/Wolf-Harrington — 3.4 <<3.1 — — — 1.8 1.8 — —
44P/Reinmuth 2 1.61 ≤3.0 — — 1.8 — 1.5 1.61 — —
45P/Honda-Mrkos-Pajdušáková 0.34 1.34 — — 1.1 — 0.5(0.3) 0.8 1.30 —
46P/Wirtanen 0.62 ≤2.6 — <1.66 0.56 0.7 0.7(0.6) 0.60 1.20 6.0
47P/Ashbrook-Jackson 2.8 ≤6.1 3.1 — 4.8 — 2.9(2.5) 2.8 1.4 >44
48P/Johnson — ≤3.5 3.7 — — 2.87 2.2 2.87 1.35 29.0
49P/Arend-Rigaux — 4.6 — — 3.9 4.8 5.1 3.2 4.24 1.63 13.47
50P/Arend 0.95 — — — — — 3.0(1.0) 0.95 — —
51P/Harrington — ≤1.9 — — 2.1 — 1.4(0.2) — — —
52P/Harrington-Abell — — 1.4 — 1.3 1.0 1.1 1.3 — —
53P/Van Biesbroeck — — <<6.7 3.33 3.9 — 3.8(3.3) 3.33 — —
54P/de Vico-Swift — ≤2.1 — — — — — — — —
56P/Slaughter-Burnham — — — 1.56 — — 1.5 1.56 — —
57P/du Toit-Neujmin-Delporte — ≤1.1 — — — — 1.6 — — —
58P/Jackson-Neujmin — — — — — — 0.6 — — —
59P/Kearns-Kwee 0.79 — — — 2.0 — 1.1 0.79 — —
60P/Tsuchinshan 2 — — — — — — 0.8 — — —
61P/Shajn-Schaldach 0.64 0.92 — — 1.0 — 1.1(1.0) 0.64 1.27 >18
62P/Tsuchinshan 1 — — — — — — 0.8 — — —
63P/Wild 1 1.45 ≤0.6 — — — — 1.5 1.45 — —
64P/Swift-Gehrels — ≤1.9 1.6 — — — 1.7(2.2) 1.6 — —
65P/Gunn — ≤8.8 <<11.7 — — — 4.8 — — —
67P/Churyumov-Gerasimenko 1.98 ≤2.9 — — — 2.8 2.5(2.0) 2.0 1.3 12.3
68P/Klemola — — — — — — 2.2 2.2 — —
69P/Taylor — ≤3.4 — — — — 2.9 — — —
70P/Kojima 1.86 — — — 1.3 — 1.2 1.86 1.10 >22
71P/Clark 0.68 ≤0.9 — 1.31 — — 1.3(0.8) 0.68 — —
72P/Denning-Fujikawa — — — — — — — (0.8) — — —
73P/Schwassmann-Wachmann 3 0.68* ≤0.9 — — — (1.3) <1.3 1.0 — 1.16* —
74P/Smirnova-Chernykh 2.23 ≤12.7 <<11.2 — — — 6.0 2.23 1.14 >20
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 243

TABLE 1. (continued).

Effective radius (km) a/b Prot

Comet La+ Lo+ Li+ Me+ Sc Others Ta+ rn,v (min) (h)
75P/Kohoutek — ≤1.5 — — 2.0 — 1.8 — — —
76P/West-Kohoutek-Ikemura 0.33 — — — 1.6 — 1.3 0.33 1.47 >13
77P/Longmore — — — — — — 2.4 — — —
78P/Gehrels 2 — 1.42 — — — — 2.1 1.42 — —
79P/du Toit-Hartley — 1.4 — — 1.9 — 1.2 1.4 — —
81P/Wild 2 — 2.0 <<5.7 — — 2.0 2.2(2.0) 2.0 — —
82P/Gehrels 3 0.73 — <3.0 — 2.1 — 2.0 0.73 1.6 >50
83P/Russell 1 — ≤0.5 — — — — — — — —
84P/Giclas 0.90 — — — 1.3 — 1.4(1.2) 0.90 — —
86P/Wild 3 0.43 ≤0.9 — 0.65 1.3 3.1 0.9 0.43 1.35 >11
87P/Bus 0.28 ≤0.6 — <3.42 2.0 — 1.3 0.28 2.20 >25
88P/Howell — — — — 1.9 — 1.1(1.0) — — —
89P/Russell 2 — ≤2.2 — — 1.2 — 1.1 — — —
90P/Gehrels 1 — — — — 3.4 — 2.8 — — —
91P/Russell 3 — — — — — — 1.3 — — —
92P/Sanguin — 1.73 — 1.19 — — — 1.19 — —
94P/Russell 4 — — — — — — 1.9 — — —
97P/Metcalf-Brewington — 2.2 1.5 — — — 1.3 1.7 — —
98P/Takamizawa — — 3.7 — 2.3 — 2.4(3.0) — — —
99P/Kowal 1 — — — — 4.4 — 4.8 — — —
100P/Hartley 1 — <1.2 — — — — 1.3 — — —
101P/Chernykh — — — — 2.4 — 2.2 — — —
103P/Hartley 2 0.8 ≤5.8 <<5.3 — 2.4 — 3.8 0.8 — —
104P/Kowal 2 — 1.0 — — — — — 1.0 — —
105P/Singer-Brewster — — — — 1.0 — 1.0(0.8) — — —
106P/Schuster 0.94 — — — — — 0.8 0.94 — —
107P/Wilson-Harrington — 1.77 — 1.96 — 2.0 — 1.7 1.2 6.10
108P/Ciffreo — — — — 1.4 — — (1.1) — — —
110P/Hartley 3 2.15 — — — 2.4 — 1.9 2.15 1.30 10
111P/Helin-Roman-Crockett — ≤1.5 — — 2.4 0.6 1.5 0.6 — —
112P/Urata-Niijima 0.90 — — — 0.9 — 0.7 0.90 — —
113P/Spitaler — ≤2.0 — — 1.0 — 1.1 1.10 — —
114P/Wiseman-Skiff 0.78 — — — — — — (0.8) 0.78 — —
115P/Maury — — — 1.11 — 0.8 1.11 — —
116P/Wild 4 — — — — — — 3.5(3.0) — — —
117P/Helin-Roman-Alu 1 — — — — 3.9 — 3.5) — — —
118P/Shoemaker-Levy 4 — 2.4 — — — — 1.7 2.4 — —
119P/Parker-Hartley — ≤4.0 — — — — 2.5(2.1) — — —
120P/Mueller 1 — 1.5 — — 1.9 — 0.8 1.5 — —
121P/Shoemaker-Holt 2 — 1.62 — — — — 2.6 1.62 — —
123P/West-Hartley — — — — — — 2.2(1.7) — — —
124P/Mrkos — — — — — — 1.6 — — —
125P/Spacewatch — — — — 1.0 — 0.8 0.80 — —
128P/Shoemaker-Holt 1 — 2.12 2.48 — — — — 2.0 2.3 — —
129P/Shoemaker-Levy 3 — — — — — — — (2.4) — — —
130P/McNaught-Hughes — — — — 1.8 — 1.7(1.5) — — —
131P/Mueller 2 — — — — — — 0.8 — — —
132P/Helin-Roman-Alu 2 — — — — — — 0.9 — — —
134P/Koval-Vávrová — — — — — — 1.4 — — —
135P/Shoemaker-Levy 8 — — — — 1.6 — 1.5(1.3) — — —
136P/Mueller 3 — — — — — — 1.9(1.5) — — —
137P/Shoemaker-Levy 2 — ≤3.4 4.5 — — — 2.9 2.90 — —
138P/Shoemaker-Levy 7 — — — — — — 0.8(1.0) — — —
139P/Väisälä-Oterma — ≤4.6 — — — — 2.6 — — —
140P/Bowell-Skiff — — — — — — — (2.3) — — —
141P/Machholz 2 — — — — — — — (1.0) — — —
143P/Kowal-Mrkos — — — — — 5.7 — (2.6) 5.4 1.5 17.2
244 Comets II

TABLE 1. (continued).

Effective radius (km) a/b Prot

Comet La+ Lo+ Li+ Me+ Sc Others Ta+ rn,v (min) (h)
144P/Kushida — — — — — — — (1.2) — — —
147P/Kushida-Muramatsu 0.21 ≤2.0 — — — — 2.3(1.9) 0.21 1.53 9.5
148P/Anderson-LINEAR — — — — — — — (2.1) — — —
152P/Helin-Lawrence — ≤6.0 — <1.74 — — 4.6 — — —
154P/Brewington — — — — — — 1.5 — — —
P/1993 W1 (Mueller 5) — — — — — — 2.1 — — —
P/1994 A1 (Kushida) — — — — — — 1.2 — — —
P/1994 J3 (Shoemaker 4) — — — — — — 3.3 — — —
P/1995 A1 (Jedicke) — — — — — — 3.0 — — —
P/1996 A1 (Jedicke) — — — — — — 5.0 — — —
P/1997 C1 (Gehrels) — — — — — — 2.3 — — —
P/1997 G1 (Montani) — — — — — — 2.5 — — —
P/1997 V1 (Larsen) — — — — — — 3.6 — — —
P/1998 S1 (LINEAR-Mueller) — — — — — — — (4.2) — — —
P/1999 D1 (Hermann) — — — — — — — (0.7) — — —
P/1999 RO28 (LONEOS) — — — — — — — (0.1) — — —
*Fragment C.
See text for the references. New radii given by Ta+ are in brackets.

TABLE 2. Nuclei of the nearly isotropic comets (NICs).

Effective radius (km) a/b Prot

Comet La+ Lo+ Li+ Me+ Sc Others rn,v (min) (h)
1P/Halley* — — — — — — 5.5 2.0 52.8; 177.6
8P/Tuttle — — 7.8 — — — 7.8 — —
55P/Tempel-Tuttle 1.80 — — — — 1.8 1.80 1.50 —
96P/Machholz 1 — — 3.5 — — 2.8 3.2 1.4 6.38
109P/Swift-Tuttle — — — 13.7 — 11.8–12.5 13.0 — 69.4
126P/IRAS 1.57 — — — — — 1.57 — —
P/1991 L3 (Levy) — — — — — 5.8 5.8 1.3 8.34
C/1983 H1 (IRAS-Araki-Alcock) — — — — — 3.5–3.7 3.5 — 51.0
C/1983 J1 (Sugano-Saigusa-Fujikawa) — — — — — 0.37 0.37 — —
C/1983 O1 (Cernis) — — — <10.5 — — — — —
C/1984 K1 (Shoemaker) — — — <6.4 30.6 — — — —
C/1984 U1 (Shoemaker) — — — <6.4 29.3 — — — —
C/1986 P1 (Wilson) — — — — 16.1 <6.0 — — —
C/1987 A1 (Levy) — — — <4.0 2.1 — — — —
C/1987 H1 (Shoemaker) — — — <4.0 26.7 — — — —
C/1987 F1 (Torres) — — — <5.9 — — — — —
C/1988 B1 (Shoemaker) — — — <6.1 16.1 — — — —
C/1988 C1 (Maury-Phinney) — — — <6.1 1.1 — — — —
C/1995 O1 (Hale-Bopp) 37 — — — — 30 37 2.6 11.34
C/1996 B2 (Hyakutake) — — — — — 2.4 2.4 — 6.27
C/1997 T1 (Utsonomiya) — — — — — <5.8 — — —
C/1999 S4 (LINEAR)† — — — — — 0.4 0.4 — —
C/2001 OG108 (LONEOS) — — — — — 8.9 8.9 1.3 57.19
* See Table 3. The two periods correspond to the SAM and LAM rotations.
† Nucleus size prior to breakup.

See text for the references.

 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 245

TABLE 3. Cometary nuclei with known shape and size.

a×b×c
Comet (km × km × km) 1 : a/b : a/c Notes*
1P/Halley 7.65 ± 0.25 × 3.61 ± 0.25 × 3.61 ± 0.25 1 : 2.13 : 2.13 [1]
7.21 ± 0.15 × 3.7 ± 0.1 × 3.7 ± 0.1 1 : 1.95 : 1.95 [2]
10P/Tempel 2 8×4×4 1 : 2.0, c = b [3]
8.2 × 4.9 × 3.5 1 : 1.67 : 2.34 [4]
19P/Borrelly 4.0 ± 0.1 × 1.60 ± 0.02 × 1.60 ± 0.02 1 : 2.5, c = b [5]
4.4 ± 0.15 × 1.80 ± 0.08 × 1.80 ± 0.08 1 : 2.4, c = b [6]
*Notes: [1] Vega 1, 2, TVS in situ imaging (Merényi et al., 1990); [2] Giotto HMC in situ imag-
ing (Keller et al., 1994); [3] groundbased CCD photometry (Jewitt and Luu, 1989); [4] ground-
based observations and modeling (Sekanina, 1989); [5] Deep Space 1 MICAS in situ imaging
(Buratti et al., 2004); [6] HST WFPC2 high-precision photometry (Lamy et al., 1998b).

et al. (1995) report pJ = 0.10 ± 0.02 using the STM and pJ = TABLE 4. Albedos of cometary nuclei.
0.05 ± 0.01 using the ILM, the latter value being favored.
3.3.2. Nearly isotropic comets (NICs). 1P/Halley: Re- Comet Geometric Albedo λ
solved imaging of the nucleus led to a value of 0.04+0.02–0.01 , Ecliptic Comets
irrespective of the spectral bands “VIS,” “RED,” or “NIR” 2P/Encke 0.046 ± 0.023 V
of the Vega 1,2 cameras (Sagdeev et al., 1986a). 9P/Tempel 1 0.05 ± 0.02 R
55P/Tempel-Tuttle: Using radiometry, Fernández (1999) 10P/Tempel 2 0.022+0.004
–0.006 4845
and Jorda et al. (2000) both arrived at similar values for the 10P/Tempel 2 0.04–0.07 JHK
R band: 0.06 ± 0.025 for the former, 0.045 for the latter. 19P/Borrelly 0.03
22P/Kopff 0.042 ± 0.006 V
109P/Swift-Tuttle: Fomenkova et al. (1995) used radi-
28P/Neujmin 1 0.026 V
ometry to estimate a nuclear size, from which the large-
28P/Neujmin 1 0.03 ± 0.01 R
heliocentric distance observations by O’Ceallaigh et al. 49P/Arend-Rigaux 0.04 ± 0.01 V
(1995) may be used to derive an approximate albedo of 49P/Arend-Rigaux 0.054 ± 0.010 J
about 0.02–0.04 in the R band. 49P/Arend-Rigaux 0.03 ± 0.01 J
C/1983 H1 (IRAS-Araki-Alcock): Extensive datasets at 107P/Wilson-Harrington 0.05 ± 0.01 J
many wavelengths allowed Sekanina (1988) to create a uni-
fied model of the properties of the nucleus. The implied Nearly Isotropic Comets
albedo in the V band is 0.02 ± 0.01. Groussin et al. (2004) 1P/Halley 0.04+0.02
–0.01 V, R, I
have reanalyzed these data and obtained a slightly larger 55P/Tempel-Tuttle 0.06 ± 0.025 R
value of 0.03 ± 0.01. 55P/Tempel-Tuttle 0.045 R
109P/Swift-Tuttle 0.02–0.04 R
C/1995 O1 (Hale-Bopp): While more data were ob-
C/1983 H1 IRAS-Araki-Alcock 0.03 ± 0.01 V
tained on this comet than any other, the albedo derivation
C/1995 O1 Hale-Bopp 0.04 ± 0.03
is problematic owing to the comet’s strong coma swamp- C/2001 OG108 (LONEOS) 0.03 ± 0.005 V
ing the nucleus during the whole apparition to date. Cam-
pins and Fernández (2003) combine the results of Jorda et λ = band or wavelength (in Å) to which albedo applies. References
are given in the text.
al. (2000) and Fernández (1999), who both used radiom-
etry and find a compromise (but very unconstrained) value
of 0.04 ± 0.03.
C/2001 OG108 (LONEOS): Using radiometry, Abell et and their interrelationships. Near-infrared spectroscopic
al. (2003) report 0.03 ± 0.005 for the V band. observations of cometary nuclei have been attempted in an
Table 4 summarizes these results on the albedo measure- effort to detect the spectral signals of water ice and silicates,
ments of cometary nuclei. as successfully performed on several KBOs and Centaurs
(e.g., Jewitt and Luu, 2001). Finally, we discuss the few
3.4. Colors thermal spectra obtained so far and their implications for
the surface temperature of cometary nuclei.
Colors by themselves do not provide much information 3.4.1. Broadband colors and reflectivity: The most
on the physical properties of cometary nuclei, but the dis- common color characterization comes from color indices,
tribution of colors compared to other solar system objects, e.g., (B-V), (V-R), (V-I), etc. As discussed in section 3.1.2,
or the correlation of colors with other parameters (e.g., size, magnitudes of nuclei observed at large heliocentric dis-
orbital parameters, … ), has the potential of offering inde- tances are very faint, and this often leads to large uncer-
pendent clues on the origin and evolution of these objects tainties in the indices. Continuum spectra of a few nuclei
246 Comets II

have been obtained, and they can be parameterized using 48P/Johnson: Note the large uncertainty of 0.3 on (V-R).
the normalized reflectivity gradient S' = dS/dλ/<S>, where 49P/Arend-Rigaux: The result of (V-R) = 0.47 ± 0.01,
S is the reflectivity (object flux density divided by the flux obtained by both filter photometry and spectrophotometry
density of the Sun at the same wavelength, λ) and <S> is on this inactive nucleus, appears to be extremely accurate
the mean value of the reflectivity in the wavelength range and reliable. Note the large uncertainty on the (R-I) reported
over which dS/dλ is computed (Luu and Jewitt, 1990b). The by Lowry et al. (2003a), 0.54 ± 0.14, which makes it com-
gradient, S', is used to express the percentage change in the patible with the result of Millis et al. (1988), (R-I) = 0.43 ±
strength of the continuum per 1000 Å (%/1000 Å). Broad- 0.02.
band color indices can also be converted to a normalized 86P/Wild 3: The surprising result of (V-R) = 0.12 ± 0.14
reflectivity gradient using the following relation (Luu and makes this nucleus a very blue object, although the error
Jewitt, 1990b) bar is quite large.
107P/Wilson-Harrington: We favor the spectrophoto-
2 + S'∆λ metric result (V-R) = 0.31 ± 0.03 of Chamberlin et al. (1996),
(V-R)n = (V-R) + 2.5 log (12)
2 − S'∆λ which is intermediate between the two available photomet-
ric results.
where (V-R)n and (V-R) are the color indices of the nu- There are only three NIC nuclei for which color informa-
cleus and the Sun respectively and ∆λ is the difference be- tion is available: 1P/Halley, 96P/Machholz 1, and C/2001
tween the effective wavelengths of the two filters. OG108 (LONEOS).
The quantity S' remains of interest as long as it is con- 1P/Halley: From in situ imaging by the Giotto HMC,
stant over a sufficiently large spectral interval. This is rarely Thomas and Keller (1989) determined a constant reflectivity
the case and different values in different spectral intervals gradient S' = 6 ± 3 per 1000 Å in the range 440–810 nm
must be introduced. Then the S' values become strictly leading to (B-V) = 0.72 ± 0.04, (V-R) = 0.41 ± 0.03, (V-I) =
equivalent to the color indices via the above equation. 0.80 ± 0.09, and (R-I) = 0.39 ± 0.06.
Table 5 is an updated version of Table 3 in Jewitt (2002), 96P/Machholz 1: The two available measurements are
summarizing all presently available data on the colors of not consistent at the 1σ level.
cometary nuclei. It incorporates recent results from Meech C/2001 OG108 (LONEOS): Measurements of (B-V),
et al. (2004), except for the nuclei of 22P/Kopff, 46P/Wir- (V-R), and (R-I) have been reported by Abell et al. (2003).
tanen, 87P/Bus, and P/1993 K2 (Helin-Lawrence), which 3.4.2. Visible and near-infrared spectra. In principle,
were active at the time of observations, from the compila- spectral analysis is the most effective way to characterize
tion of Hainaut and Delsanti (2002), and from Lowry and the surface properties of the cometary nuclei. First, it yields
Weissman (2003). We comment below on some of the re- high-accuracy color information as presented above, and
sults, starting with the ECs. second, it offers the possibility of detecting solid-state ab-
2P/Encke: Note the accurate (V-R) from spectropho- sorption bands, namely those of water ice and minerals.
tometry. A value (V-R) = 0.46 ± 0.02 is consistent with all With one exception, and contrary to the case for several
the data and their respective error bars. Centaurs and KBOs, this expectation has failed to materi-
6P/d’Arrest: (V-R) = 0.56 ± 0.02 is consistent with the alize, reinforcing for the time being the value of color in-
results of Jewitt (2002) and Meech et al. (2004), while the formation. In addition to the general difficulties of detecting
value reported by Lowry and Weissman (2003), (V-R) = cometary nuclei, spectral observations face the additional
0.33 ± 0.09, is well outside the above uncertainty. (R-I) = problem of very low signals per spectral element. This ex-
0.45 ± 0.04 from Jewitt (2002) is, however, consistent with plains the paucity of groundbased nuclear spectra, mostly
the results reported by Lowry and Weissman (2003), 0.33 ± restricted to (nearly) inactive nuclei, and the clear superi-
0.12. At the 2σ level, the two values of (B-V) agree, and ority of in situ spectral observations.
we adopt (B-V) = 0.85+0.2 –0.07 . 2P/Encke, 10P/Tempel 2, 21P/Giacobini-Zinner, 49P/
10P/Tempel 2: (V-R) = 0.56 ± 0.01 is consistent with Arend-Rigaux: Visible spectra obtained at large rh with a
the three measurements. spectral resolution of 10–20 Å are presented by Luu (1993).
14P/Wolf, 19P/Borrelly: Note the large uncertainties, No absorption features were detected, except for a down-
making these measurements of limited value. turn feature in the blue part of the spectrum of 21P, remi-
28P/Neujmin 1: There is an excellent agreement on the niscent of chondritic spectra.
(V-R) color of this large and inactive nucleus. Taking the 19P/Borrelly: The short-wavelength infrared imaging
average of all measurements leads to (V-R) = 0.47 ± 0.20, spectrometer (SWIR) onboard DS1 secured 45 scans spec-
making it similar to D-type asteroids (Campins et al., 1987; tra of the nucleus in the 1.3–2.6-µm range (Soderblom et al.,
Fitzsimmons et al., 1994) and most Trojans (Jewitt and Luu, 2002). They reveal a strong positive slope toward the red
1990). and a single absorption feature at ~2.39 µm, whose origin
45P/Honda-Mrkos-Pajdušáková: In addition to the re- is unknown (fits of various hydrocarbons were attempted,
sults included in Table 5, Lamy et al. (1999a) reported the but none were satisfactory).
first (U-B) index ever measured on a comet nucleus, (U-B) = 28P/Neujmin 1: Observations at large rh in the spectral
0.68 ± 0.04. range 0.9–2.4 µm by Campins et al. (2001) do not show a
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 247

TABLE 5. Colors of cometary nuclei.

Comet (B-V) (V-R) (R-I) Photometry* References

Solar colors 0.65 0.35 0.28

Ecliptic Comets
2P/Encke 0.78 ± 0.02 0.48 ± 0.02 — S LJ90
— 0.43 ± 0.05 — F J02
— 0.38 ± 0.06 — F J02
— 0.37 ± 0.09 — F HD02
6P/d’Arrest 0.78 ± 0.04 0.54 ± 0.04 0.45 ± 0.04 F J02
— 0.62 ± 0.08 — F M+02
1.08 ± 0.12 0.33 ± 0.09 0.33 ± 0.12 F LW03
10P/Tempel 2 — 0.53 ± 0.03 — F JM88
— 0.58 ± 0.03 — S JL89
— 0.56 ± 0.02 — F M+02
14P/Wolf — 0.02 ± 0.22 0.25 ± 0.35 F Lo+03
19P/Borrelly — 0.25 ± 0.78 — F Lo+03
21P/Giacobini-Zinner 0.80 ± 0.03 0.50 ± 0.02 — S L93
22P/Kopff 0.77 ± 0.05 0.50 ± 0.08 0.42 ± 0.03 F La+02
26P/Grigg-Skjellerup — 0.42 ± 0.10 — F B+99
28P/Neujmin 1 — 0.46 ± 0.04 — F Ca+87
— 0.45 ± 0.05 — F JM88
— 0.50 ± 0.04 — F JM88
— 0.45 ± 0.05 — F D+01
— 0.48 ± 0.06 — F M+02
45P/Honda-Mrkos-Pajdušáková 1.12 ± 0.03 0.44 ± 0.03 0.20 ± 0.03 F La+99
46P/Wirtanen — 0.45 ± 0.10 — F La+98a
48P/Johnson — 0.50 ± 0.30 — F Li+00
49P/Arend-Rigaux 0.77 ± 0.03 0.47 ± 0.01 0.43 ± 0.02 F M+88
— 0.47 ± 0.01 — S L93
— 0.40 ± 0.30 — F Li+00
— 0.49 ± 0.11 0.54 ± 0.14 F Lo+03
53P/Van Biesbroeck — 0.34 ± 0.08 — F M+02
73P/SW3 — 0.48 ± 0.17 — F B+99
86P/Wild 3 — 0.12 ± 0.14 — F M+02
107P/Wilson-Harrington — 0.31 ± 0.03 — S Ch+96
— 0.41 ± 0.02 — F M+02
0.61 ± 0.05 0.20 ± 0.04 — F LW03
0.75 ± 0.06 — — F LW03
143P/Kowal-Mrkos 0.84 ± 0.02 0.58 ± 0.02 0.55 ± 0.02 F J+03
0.80 ± 0.02 0.58 ± 0.02 0.57 ± 0.02 F J+03

Nearly Isotropic Comets

1P/Halley 0.72 ± 0.04 0.41 ± 0.03 0.39 ± 0.06 F/HMC TK89
96P/Machholz 1 — 0.43 ± 0.03 — F M+02
— 0.30 ± 0.05 — F Li+00
C/2001 OG108 (LONEOS) 0.76 ± 0.03 0.46 ± 0.02 0.44 ± 0.03 F A+03
*F = filter photometry, S = spectrophotometry; HMC = in situ measurements by the Giotto Halley Multicolour Camera.

References: A+03 (Abell et al., 2003); B+99 (Boehnhardt et al., 1999); Ca+87 (Campins et al., 1987); Ch+96 (Cham-
berlin et al., 1996); D+01 (Delahodde et al., 2001); HD02 (Hainaut and Delsanti, 2002); JM88 (Jewitt and Meech, 1988);
JL89 (Jewitt and Luu, 1989); J+03 (Jewitt et al., 2003); LJ90 (Luu and Jewitt, 1990a); L93 (Luu, 1993); La+98a (Lamy et
al., 1998a); La+02 (Lamy et al., 2002); Li+00 (Licandro et al., 2000); Lo+03 (Lowry et al., 2003a); LW03 (Lowry and
Weissman, 2003); M+88 (Millis et al., 1988); M+02 (Meech et al., 2004); TK (Thomas and Keller, 1989).
248 Comets II

water ice signature, a result consistent with earlier obser- parametric model, for instance that of Hapke (1993). Of
vations by Campins et al. (1987) and recent observations particular interest is the opposition effect, which is neglected
by Licandro et al. (2002). when using simple phase laws, such as the one introduced
82P/Gehrels 3: A featureless red spectrum in the range in section 3.2. In addition to the intrinsic difficulties of
0.4–0.98 µm, with a resolution of 30 Å, has been obtained observing cometary nuclei, the determination of the phase
by De Sanctis et al. (2000). This spectrum is very similar to function further requires observations at different phase
those of D-type asteroids. angles, each one having to be corrected for the effect of
90P/Gehrels 1: Observations at large rh in the spectral the rotation of the nucleus. Ideally, this requires determin-
range 0.9–2.4 µm by Delahodde et al. (2002) show the ab- ing the light curve at each phase angle, so that the mea-
sence of spectral signatures. surements may be phased to the same rotational position,
107P/Wilson-Harrington: A featureless spectrum in say the maxima of the light curves (Delahodde et al., 2001).
the range 0.38–0.62 µm with a resolution of 5 Å has been 2P/Encke: A detailed analysis of recent, original meas-
obtained by Chamberlin et al. (1996). urements and a large collection of historical data led Fer-
124P/Mrkos: Observed by Licandro et al. (2003) while nández et al. (2000) to derive β = 0.06 mag deg–1. This very
inactive at rh = 1.85 AU, its near-infrared (0.9–2.3 µm), low- steep phase function makes 2P/Encke one of the most
resolution spectrum is featureless and slightly redder than phase-darkened objects in the solar system and implies a
the Sun, resembling that of a D-type asteroid. very rough surface.
C/2001 OG108 (LONEOS): Observed by Abell et al. 9P/Tempel 1: Fernández et al. (2003) estimated a phase
(2003) while inactive, its near-infrared (0.7–2.5 µm) is fea- coefficient β = 0.07 mag deg –1 that is poorly constrained. It
tureless, slightly redder than the Sun, resembling that of a is indeed unlikely that such a steep phase function is correct.
D-type asteroid. 19P/Borrelly: Combining the disk-integrated magni-
3.4.3. Thermal spectrum — Surface temperatures. The tudes calculated from the DS1 images with the HST (Lamy
surface temperature of the nucleus has been measured for et al., 1998b) and groundbased measurements (Rauer et al.,
only two comets, 1P/Halley and 19P/Borrelly, thanks to in 1999), Soderblom et al. (2002) and Buratti et al. (2004)
situ observations. determined Φ(α) over a large range of phase angle, from
1P/Halley: The infrared radiation of its nucleus was 3° to 88°. The phase curve is very similar to that of the dark
measured at rh = 0.8 AU by the IKS spectrometer onboard C-type asteroid 253 Mathilde (Clark et al., 1999). Except
the Vega 1 spacecraft in two wavelengths bands, 7–10 and for a minor opposition effect restricted to α < 3°, this phase
9–14 µm (Combes et al., 1986). The temperature was ob- curve is well approximated by a constant linear phase co-
tained with two independent and different methods, and the efficient β = 0.04 mag deg –1 over the interval 3°–90°.
most probable maximum value lies in the range 360–400 K. 28P/Neujmin 1: Jewitt and Meech (1987) determined
The hottest region was not at the subsolar point, and the a phase coefficient β = 0.034 ± 0.012 mag deg –1. Delahodde
angular thermal lag was about 20° (Emerich et al., 1987). et al. (2001) obtained phase coverage extending from 0.8°
These results suggest that a large fraction of the nucleus to 19° and have been able to correct several data points for
surface of 1P/Halley is inactive and not cooled by sublimat- the effects of rotation. A linear phase coefficient β = 0.025 ±
ing ices or evolving gases. The surface may be a lag deposit 0.006 mag deg–1 applies down to α ~ 5°. At smaller phase
crust, or perhaps a radiation processed mantle. angles, the function steepens and a strong opposition ef-
19P/Borrelly: The spectra recorded by SWIR onboard fect appears at α < 1.5°. This effect, comparable to those
DS1 at rh = 1.36 AU (Soderblom et al., 2002) permitted a found on medium albedo pV ~ 0.15 M-type asteroids and
determination of the temperature at the two tips of the elon- icy satellites, is quite surprising for a cometary nuclei. As
gated nucleus: 300 K and 345 K. These high temperatures surface ice is excluded on such a low-activity nucleus, a
are consistent with the absence of water ice bands (cf. sec- high surface porosity could perhaps be invoked, but this
tion 3.4.2) and, as for 1P/Halley, suggest that a large fraction possible interpretation has not been investigated.
of the nuclear surface is inactive [only ~10% of its surface is 45P/Honda-Mrkos-Pajdušáková: As discussed in sec-
active according to Lamy et al. (1998b)]. tion 3.2, there is a distinct possibility that the HST and
groundbased observations can be reconciled by a steep
3.5. Phase Function phase function with β = 0.06 mag deg –1, similar to that of
2P/Encke and 48P/Johnson.
In the above sections, we have highlighted the impor- 48P/Johnson: Observations of a starlike nucleus at
tance of the phase function Φ(α) in the determination of the phase angles between 6° and 16° led Jewitt and Sheppard
size of cometary nuclei and emphasized that it remains a (2003) to derive β = 0.0592 mag deg –1.
nonnegligible source of uncertainty. Aside from this tech- 55P/Tempel-Tuttle: The combination of HST and
nical aspect of the data reduction, the phase function of an groundbased observations allowed Lamy et al. (2004) to ob-
atmosphereless body offers a powerful means for investigat- tain the phase function in the interval 3°–55° and to derive
ing the properties of its surface (e.g., roughness and single- a linear phase coefficient β = 0.041 mag deg–1, similar to
particle albedo). Typically, the phase angle data are fit to a those of 19P/Borrelly and asteroid Mathilde.
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 249

143P/Kowal-Mrkos: Observations of a starlike nucleus tion. These latter authors conclude that the “satellite” is
at phase angles between 5° and 12.7° led Jewitt et al. (2003) probably due to the residual signal when fitting an over-
to derive a linear phase coefficient β = 0.043 ± 0.0014 mag simplified elliptical coma model to the real, highly struc-
deg–1. tured coma of Hale-Bopp. Such artifacts have been found
in another analysis performed by Sekanina (1995), namely
3.6. Satellites of Cometary Nuclei that of Comet D/Shoemaker-Levy 9: Clumps of positive
residuals were identified as fragments, while clumps of
The detection of a satellite companion to a cometary identical but negative residuals were also present.
nucleus, and the determination of its orbit, would be of Adaptive optics observations with the ESO 3.6-m tele-
unique value as it would provide access to the mass of the scope in the near-infrared performed on 6 November 1997
primary. If the mass of the nucleus is known, and if the size possibly revealed the presence of a satellite: Marchis et al.
is independently derived, then the mean bulk density and (1999) discussed the pros and cons of this interpretation,
porosity can be calculated, providing insight into the inter- but did not reach a clear and firm conclusion. HST images
nal properties of the nucleus. taken on the same day, and on other days, with the Space
There are various processes leading to the formation of Telescope Imaging Spectrograph (STIS) do not reveal any
binary systems among small bodies. In the case of cometary obvious companion (Weaver et al., 1999) at the location and
nuclei, a companion could be primordial or could result magnitude expected if the groundbased detection were real.
from the capture of a large fragment ejected by the nucleus; If there is a satellite, then either it remained within 1 STIS
the capture of an external object appears unlikely. To be of pixel (0.05 arcsec) of the primary for more than three
value in the sense described above, a satellite must be suf- months, or the HST observers were unlucky and observed
ficiently large to allow its detection and should travel on a near the time of an orbital transit event (i.e., when the two
stable orbit for some time. However, the motion of such a objects appear to move across each other).
possibly active object around a rotating, nonspherical, and Possible additional evidence for a companion of Comet
active primary is extremely complex, and is in fact a major Hale-Bopp comes from the analysis of the complex mor-
concern for the Rosetta orbiter. We review below the few phology of its coma (jets and halos). Vasundhara and
cases where a companion may have been directly or indi- Chakraborty (1999) and Sekanina (1998b) have noted dif-
rectly detected. ficulties in explaining several coma features with a single
17P/1892 V1 (Holmes): In late 1892, this comet under- rotating nucleus, thereby suggesting that two nuclei are
went a major outburst (leading to its discovery), then faded involved, but the analysis of Samarasinha (2000) demon-
by 7–8 mag, and flared up again by 6 mag a couple of strates that the coma morphology is consistent with a single
months later. Whipple (1983, 1984) proposed that a satellite nucleus.
could produce this double burst: first a grazing encounter C/2001 A2 (LINEAR): The splitting of this comet was
on 4.6 November 1892 and a final impact on 16.3 Janu- accompanied by outbursts, and Sekanina (2002c) quoted the
ary 1893. Several details of this scenario explain the obser- rare, but possible, scenario of the flaring of the primary nu-
vations rather well. Whipple (1999) estimated the crushing cleus due to collision with a companion that had been cre-
strength (compressive strength, force/area) from the mo- ated by the fragmentation events (Whipple, 1984; Sekanina,
mentum transfer during the collision of the secondary with 1982). Sekanina (1997) had previously suggested that a part
the primary nucleus, and it ranges from 4.2 × 103 to 5.9 × of the mantle of the nucleus (icy-dust mantle) could be
105 dynes cm–2, corresponding to mean bulk densities of 0.2 lifted off the surface and then travel away from the primary
and 1.5 g cm–3 respectively. The idea of an hypothetical during a nontidal splitting. However, this is only specula-
satellite, however, remains highly speculative. tion, and there is no direct evidence of a satellite around
26P/Grigg-Skjellerup: During the Giotto flyby of this this comet.
comet in 1992, the in situ optical probe experiment (OPE) Concluding remarks: While the occurrence of satellites
recorded several “spikes.” One of them was interpreted by for both main-belt and near-Earth asteroids, Kuiper belt
McBride et al. (1997) as an object 10–100 m in radius objects, and Trojans is steadily growing (Merline et al.,
sporting a weak dust coma. However, it is not clear whether 2002), there is still no definite, observational evidence that
this object was in a bound orbit, or slowly traveling away binary cometary nuclei exist. Since detecting and charac-
after possibly separating from the nucleus. terizing cometary nuclei remains a huge challenge, the de-
C/1995 O1 (Hale-Bopp): From his analysis of HST tection of a smaller companion is probably beyond our
WFPC2 images taken in May–October 1996, Sekanina present and near-future capabilities. Do double craters and
(1998a) reported the detection of a companion that could crater chains (catenae) observed on planetary satellites
be bound. He estimated a mass ratio of =0.1, a semimajor (Melosh and Schenk, 1993; Melosh and Whitaker, 1994;
axis of = 180 km, and a period of 2–3 d for a primary Schenk et al., 1996) provide independent evidence of bi-
nucleus of radius =35 km. Our analysis of the same set of nary and multiple objects? Known double craters are plau-
images using a fully anisotropic coma model (Weaver and sibly created by the impact of two orbiting bodies and can
Lamy, 1997; Toth et al., 1999) does not support this detec- likely be explained with the currently known asteroidal
250 Comets II

sources, and do not require a cometary component, but that truncated at 12 km for better legibility of the histograms at
does not mean that a cometary component is ruled out. small sizes). These represent the largest datasets ever as-
Catenae are thought to be formed from tidally disrupted sembled. The histograms show several structures, which
cometary nuclei (an asteroidal origin is, however, not ruled most likely result from the limited statistics in the dataset.
out) but, in that case, the fragments are not orbiting one We note that there are not very many large cometary nu-
another; rather, the multiple objects are laid out in a line clei; only two EC and two NIC nuclei have radii larger than
along their common orbit. In the case of a cometary im- 10 km. The apparent roll-off in the number of small com-
pactor, fragmentation may have first taken place, leading to etary nuclei is very likely an observational selection effect
the creation of a trail of small bodies, very much like the (i.e., smaller nuclei are simply harder to detect). A similar
case of D/Shoemaker-Levy 9. effect is often encountered with flux-limited surveys, e.g.,
for the NEOs at magnitudes fainter than ~17, but additional
4. ANALYSIS AND INTERPRETATION mechanisms cannot be excluded (see below). Brandt et al.
(1996) advocated the idea of a large population of unde-
4.1. Size Distribution of Cometary Nuclei tected ECs having very small nuclei, but they presented no
observational evidence to support this hypothesis. For NICs,
Figures 3a and b present the distribution functions of the the above shortcomings are exacerbated by the small num-
effective radius rn,v of ECs and NICs respectively, as sum- ber of comets in the sample. However, if the Sun-grazing
marized in Tables 1 and 2 (the range of radius has been comets, which are probably the fragments of one or several
large nuclei, are considered as full members of this family,
then there is clear evidence of a large population of very
small, sub-100 m, cometary nuclei (Biesecker et al., 2002).
This clearly shows that under the right circumstances, e.g.,
coronagraphic observations of Sun-grazers, small objects
can be detected.
A more robust and physically enlightening way to view
size distributions is to introduce cumulative distribution
functions, which are less prone to artifacts. One can con-
sider the cumulative luminosity function (CLF) NL(<H),
where NL is the number of nuclei with absolute magnitude
brighter than H, and the cumulative size distribution (CSD)
NS(>rn), where NS is the number of nuclei larger than radius
rn. If these two distributions are represented by power laws

NL(<H) ∝ 10 qLH (13)

NS(>rn) ∝ r n–qS (14)

and if all objects have the same albedo, then qS = 5 qL (Weiss-

man and Lowry, 2003). Quite recently, several groups have
collected various datasets and studied the CLF and/or the
CSD of ecliptic comets; their results are summarized in
Table 6.
At stake here is the question of the origin of ECs. If they
are collisional fragments of TNOs (Stern, 1995; Farinella
and Davis, 1996), then the theoretical value qS = 2.5 for a
collisionally relaxed population (Dohnanyi, 1969) is ex-
pected. In reality, the question is probably more complex.
On the one hand, the model of Dohnanyi applies to a
population of self-similar bodies having the same strength
per unit mass. Several groups have attempted to relax this
assumption, with O’Brien and Greenberg (2003) present-
ing the most comprehensive results on steady-state size dis-
tributions for collisional populations. In the range of sizes
of interest for cometary nuclei, the size distribution of frag-
ments is wavy, and oscillates about the distribution of a pop-
Fig. 3. Distributions of the effective radius rn,v for (a) ecliptic ulation evolved under pure gravity scaling. The differential
comets, (b) nearly isotropic comets, and (c) ecliptic “cometary” size distribution of such a population is characterized by a
NEOs. Note that the largest nuclei are excluded to allow legibility power law with an exponent of –3.04. This translates into
of the histograms at small sizes. qS = 2.04 using our notation for the cumulative distribution.
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 251

TABLE 6. Power exponents of the cumulative luminosity function (CLF) and

of the cumulative size distribution (CSD) of the nuclei of ecliptic comets.

Reference CLF CSD

Fernández et al. (1999) 0.53 ± 0.05 2.65 ± 0.25
Lowry et al. (2003a) 0.32 ± 0.02 1.6 ± 0.1
Meech et al. (2004) — 2.5*
Weissman and Lowry (2003) 0.32 ± 0.01 1.59 ± 0.03
Weissman (personal communication, 2003) 0.36 ± 0.01 1.79 ± 0.05
This work 0.38 ± 0.06 1.9 ± 0.3
*From Monte Carlo simulations after truncation at small radii.

On the other hand, noncollisional fragmentation (i.e., and then explored the variation of PKS in the neighborhood
splitting) is frequent among comets (see Boehnhardt, 2004), of the value of qS determined by the M-estimate technique
and nuclei are progressively eroded by their repeated pas- (Fig. 5). The high value of PKS (0.953) for the nominal
sages through the inner part of the solar system, so that we value of qS returned by the M-estimate fit is encouraging,
are certainly not observing a primordial, collisionally re- as is the result that the distribution of PKS values is sym-
laxed population of TNO fragments. A crude calculation by
Weissman and Lowry (2003) indicates that a typical EC
loses ~400 m in radius at half its lifetime as an active ob-
ject. Samarasinha (2003) undertook a more comprehensive
study of this problem in which mass loss includes outgas-
sing and splitting events (rotational and tidal splitting). His
only example for a population of nuclei with an initial dif-
ferential size distribution having an exponent of –3 indeed
shows considerable leveling off after 1000 years. Mass loss
may therefore significantly distort the size distribution of
nuclei, particularly at the low end. While it is tempting to
introduce this kind of statistical correction to account for
mass shedding, this approach certainly does not reflect the
reality for any given comet, which could be at any stage of
its orbital evolution. But a case-by-case correction faces the
difficulty of the chaotic nature of the orbital evolution of
ecliptic comets.
Figure 4a presents the CSD of 65 ecliptic comets for
which we have reliable values of the effective radius rn,v
(Table 1). Above some critical radius (rc ~ 1.6 km), the CSD
appears to follow a single power law. Below rc, the distri-
bution levels off, a likely result of observational bias and
mass loss, as discussed above. The determination of the
power exponent qS, and of the value of rc, was performed
using three different techniques. We first used the least-
squares fit because it has been widely used for similar stud-
ies by various groups; we stress, however, that this method
is not applicable to CSDs because the data points are not
independent, which renders the standard χ2 statistic mean-
ingless. Next, we used a fit based on a maximum likelihood
parameter estimation, namely the M-estimate technique
based on the MEDFIT algorithm described by Press et al.
(1986) and implemented as the routine LADFIT in IDL.
This procedure returns the mean absolute deviation of the
data from the power law but does not return an uncertainty Fig. 4. Cumulative size distributions of the nuclei of (a) ecliptic
on the power exponent. Finally, we calculated the probabil- comets and (b) nearly isotropic comets are represented by the solid
ity PKS that the observed distribution for rn > rc and the circles while the open circles apply to the populations augmented
model distribution N(>rn) ∝ r n–qS are drawn from the same by the “cometary” NEOs. The two solid lines in (a) correspond
parent distribution using the Kolmogorov-Smirnov (K-S) to optimum power law fits according to the Kolmogorov-Smirnov
test. We found that the optimum cut-off value is rc = 1.6 km test, from the cutoff radius rc = 1.6 km up to the largest bodies.
252 Comets II

PKS value of 0.86. Although this result is consistent with

the previous one, given the uncertainties, we note that the
distribution of PKS values is not centered on the nominal
value of qS returned by the M-estimate fit.
In a second step, we also removed the next largest nu-
cleus, namely 28P/Neujmin 1, and obtained a nominal value
of qS = 2.4 , with PKS only reaching 0.62. Note also that
the distribution of PKS values is even more skewed away
from the nominal M-estimate value, which suggests that qS
is not very well-determined.
In summary, we conclude that qS could be as small as
~1.6 and as large as ~2.5, with a preferred value of ~2.0.
However, we will quote qS = 1.9 ± 0.3 because that is our
result for the CSD that includes all the ECs for which reli-
able data have been obtained.
Table 6 shows that our result is intermediate between
those of Lowry et al. [(2003a), qS = 1.6 ± 0.1] and Weissman
and Lowry [(2003), qS = 1.59 ± 0.03, recently revised to
qS = 1.79 ± 0.05 (P. Weissman, personal communication,
2003)], on the one hand, and J. Fernández et al. [(1999),
qS = 2.65 ± 0.25], on the other hand. Regarding the first
group of authors, we note that they incorrectly included 8P/
Tuttle, a quite large nucleus, in their dataset and that their
power exponent has been revised upward to be nearly com-
patible with our range (note also that their quoted uncer-
tainty is underestimated owing to their use of least-squares
fitting). Regarding the second group, i.e., J. Fernández et
al. (1999), we concur with Weissman and Lowry (2003) in
noting that their fitted slope covers only 12 comets over a
very small range of radius, namely a factor of only 1.6. J.
Fernández et al. (1999) have further limited their sample
to those nuclei having perihelion distances q < 2 AU, fear-
ing a possible bias, with nuclei with q > 2 AU being sys-
Fig. 5. The Kolmogorov-Smirnov probability as a function of the tematically larger than those with q < 2 AU. We have
exponent of the power law fitting the observed CSDs down to a examined this question in detail, and Fig. 6 shows that there
cut-off radius rc = 1.6 km; (a) corresponds to the distribution of is no evidence for a systematic trend of size of the nucleus
ECs as listed in Table 1, while (b) corresponds to the distribution with perihelion distance. While there is indeed a larger
of ECs + “cometary” NEOs as listed in Table 7. The circles apply number of small nuclei (rn < rc) with q < 2 AU than with
to the nominal case while the other symbols apply to two experi-
q > 2 AU, the two populations of larger nuclei (rn > rc) have
ments where 29P/Schwassmann-Wachmann 1 is removed (trian-
similar statistical properties (at least at the present level of
gles) and where 28P/Neujmin 1 is further removed (squares). The
open symbols correspond to the M-estimate (i.e., maximum like- accuracy), as already noted by Weissman and Lowry (2003).
lihood) solution while the solid symbols correspond to the least- This is thus irrelevant when fitting the size distribution of
squares fit solution. nuclei with rn > rc to a power law, and in fact has not been
considered by the other groups listed in Table 6.
The comparison with the result of Meech et al. [(2004),
metric about the nominal M-estimate value. In order to qS = 2.5] is not straightforward because it was obtained
define an uncertainty on qS, we adopted the criterion that from a Monte Carlo reconstruction of the CSD that attempts
PKS ≥ 0.5, which implies that qS = 1.9 ± 0.3 for a cut-off to remove various selection effects, i.e., to unbias the ob-
rc = 1.6 km (Table 6). served CSDs. From their Table 11, we estimate qS ~ 1.5,
As the largest comets are removed from the CSD, the but we wonder whether this observed CSD includes both
M-estimate technique tends to consider the remaining larg- the short-period and long-period comets, as it is the case
est nuclei as outliers, yielding steeper slopes. As a first test, for the histogram given in their Fig. 6. We note that these
we removed the largest nucleus in our database, namely authors truncated their original distribution (qS = 2.5), and
29P/Schwassmann-Wachmann 1 (the deletion of this comet that in fact their best-fit model is truncated below rn =
may also be justified on the basis that it is more properly 5.0 km. It will be interesting to see how their result evolves
classified as a Centaur, rather than an EC), and obtained a when their Monte Carlo simulation is applied to a larger
nominal value of qS = 2.1 from the M-estimate fit, with a dataset, such as ours.
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 253

than the ECs, thus significantly filling the 2–10-km radius

range, but flattening the CSD simply because they are more
of them at larger sizes; indeed, we found qS = 1.6 ± 0.2,
PKS reaching 0.85 when including these NEOs. The experi-
ment of removing 29P and 28P has also been performed,
and the results are illustrated in Fig. 5b. Because the new
CSD is better constrained, the impact of removing these
objects is much reduced compared to the case of ECs alone.
We further note that the new CSD better fits a power-law
function, thus reducing the differences between the M-es-
timate and K-S determinations of qS.
Table 8, adapted from Weissman and Lowry (2003), dis-
plays the power exponents qS and qL for various minor-body
populations in the solar system. The power exponent of the
CSD of KBOs is quite large, qS = 3.15–3.45, but strictly
applies to objects with rn > 20 km. It is not clear whether
this value extends down to smaller sizes to allow a mean-
ingful comparison with ECs. In fact, it has been suggested
that KBOs follow a broken power law with the larger ob-
jects (rn > 50 km), retaining their primordial size distribu-
tion with the above value of qS, while the smaller objects
represent collisional fragments having a shallower distribu-
Fig. 6. The effective radius rn,v of the cometary nuclei vs. helio- tion (e.g., Davis and Farinella, 1997), which could then be
centric distance for ecliptic comets (solid circles), for nearly iso- rather similar to that of the ECs. The power exponent of
tropic comets (open circles), and for “cometary” NEOs (open the CSD of Centaurs, qS = 2.7–3.0, is also larger than that
squares). of the ECs. However, the statistics are rather poor, and we
found that, from the data of nine Centaurs reported by
Barucci et al. (2004), it is very difficult to fit a power law
to the observed CSD: The exponent can take any value,
It is tempting to compare our result for the distribution from 3.1 down to 1.2, depending on the imposed cutoff at
of ECs, qS ~ 1.9 ± 0.3, with the general trend of the power small sizes.
law of a collisionally population evolved with pure gravity The CSD of ecliptic comets is beginning to look remark-
scaling, qS = 2.04 (O’Brien and Greenberg, 2003). On the ably similar to that of NEOs: Note the result of Stuart
one hand, it must be kept in mind that the simulated distri- (2001), qS = 1.96, which is essentially identical to our value.
bution is in fact wavy in the size interval of cometary nu- For the main-belt asteroids, size distributions are so well-
clei, so that different values of qS may hold in different size defined that changes in the power exponent can be recog-
intervals. On the other hand, our dataset has not yet been nized in different size regimes [see details in Jedicke and
corrected for bias effects and the statistics still remain lim- Metcalfe (1998)], and we have simply indicated the ranges.
ited, at essentially all sizes. We need far more measurements Near-Earth objects and main-belt asteroids are thought to
before we can conclusively determine the size distribution be collisionally dominated populations, yet they have power
of ECs. As a way of testing how the distribution could exponents significantly different from the canonical value
evolve, we decided to incorporate additional objects. Our of qS = 2.5 obtained by Dohnanyi (1969).
sample already includes highly evolved nuclei such as 28P/ A final comparison is that with the CSD of the fragments
Neujmin 1. We now go one step further and include the of Comet D/1999 S4 (LINEAR): From water production
population of asteroidal objects thought to be dormant or rates measured following its breakup, Mäkinen et al. (2001)
extinct comets, on the basis of their Tisserand parameters, found that the measurements could best be explained by a
or their association with meteor streams. The cometary ori- fragment size distribution having qS = 1.74, which is within
gin of these NEOs is still highly speculative, and many of the range we estimate for the ECs.
them may be bona fide asteroids coming from the outer The question of the size distribution of ECs at the lower
regions of the asteroidal belt, including the Hilda group and end, rc < 1.6 km, remains totally open. The possible influ-
Jupiter Trojans (Fernández et al., 2002). Selection effects ence of both observational and evolutionary biases has been
are also different from those of the ECs, and any future mentioned already, but a real depletion cannot be excluded.
unbiasing should reflect these differences. For the purpose Indeed, the depletion of small nuclei is supported by the
of the present exercise, we considered 21 “cometary” NEOs measurements of crater distributions on several airless bod-
that can be associated with ECs, and whose sizes have been ies of the solar system, where cratering from comets is be-
determined (Table 7), thus bringing the database to 86 ob- lieved to dominate, e.g., Europa (Chapman et al., 1997) and
jects. The “cometary” NEOs tend to be larger on average Ganymede and Callisto (Zahnle et al., 2001).
254 Comets II

TABLE 7. Physical properties of probable dormant or extinct comets.

Name TJ* rn pV Note Association References

Selected NEOs and possible dead comets based on TJ < 3 and low albedo (<0.05)
1580 Betulia 3.07 3.75 ± 0.15 0.034 ± 0.004 — EC Fe99
3552 Don Quixote 2.31 9.2 ± 0.4 0.045 ± 0.003 1983 SA EC Fe99
1983 VA 2.97 1.35 ± 0.05 0.07 ± 0.01 — EC Fe99
2000 EJ37 2.44 5.8 — — EC Fe+03
2000 OG44 2.74 3.87+0.50
–0.40 0.038 +0.018
–0.017 — EC Fe+01
2000 PG3 2.55 3.08+1.42
–0.95 0.021+0.031
–0.017 — EC Fe+01
2000 SB1 2.81 3.57+0.92
–0.62 0.019+0.015
–0.010 — EC Fe+01
2000 VU2 2.62 6.0 — — EC Fe+03
2000 YN30 2.64 1.4 — — EC Fe+03
2001 KX67 2.85 1.6 — — EC Fe+03
2001 NX17 2.79 9.3 — — EC Fe+03
2001 OB74 2.98 1.0 — — EC Fe+03
2001 QF6 2.28 2.6 — — EC Fe+03
2001 QL169 2.97 0.4 — — EC Fe+03
2001 QQ199 2.32 10.2 — — EC Fe+03
2001 RC12 2.69 1.6 — — EC Fe+03
2001 SJ262 2.98 0.16 — — EC Fe+03
2001 TX16 2.77 3.7 — — EC Fe+03
5335 Damocles 1.14 8.5 0.03 † NIC(HTC) Le+02
15504 1999 RG33 1.95 14.8 0.03 † NIC(HTC) Le+02
20461 1999 LD31 –1.54 6.8 0.03 † NIC(HTC) Le+02
1996 PW 1.72 6.5 0.03 † NIC(ERC) Le+02
1997 MD10 0.98 2.5 0.03 † NIC(HTC) Le+02
1998 WU24 1.40 3.9 0.03 † NIC(HTC) Le+02
1999 LE31 –1.31 9.05+4.04
–2.71 0.031 +0.030
–0.020 — NIC(HTC) Fe+01
1999 XS35 1.42 1.4 0.03 † NIC(HTC) Le+02
2000 AB229 0.78 6.2 0.03 † NIC(ERC) Le+02
2000 DG8 –0.62 8.64+2.26
–1.83 0.027 +0.022
–0.015 — NIC(HTC) Fe+01
2000 HE46 –1.51 3.55+1.10
–0.78 0.023+0.021
–0.013 — NIC(HTC) Fe+01

Selected NEOs associated with meteor stream

2101 Adonis 1.40 0.28‡ ? meteor stream EC Fe99
2212 Hephaistos 3.1 2.85 ? meteor stream EC Fe99
3200 Phaeton 4.51 2.35 ± 0.25 0.11 ± 0.02 meteor stream EC Fe99
*Tisserand parameter with respect to Jupiter.
† Radius derived from absolute magnitude (Le+02) using an albedo of 0.03.
‡ Averaged radius derived from the radar measurements made by Benner et al. (1997).

References: Fe99: from the list compiled by Fernández (1999); Fe+01: Fernández et al. (2001); Fe+03: Fernández et
al. (2003); Le+02: Levison et al. (2002).

TABLE 8. Power exponents of the CSD and CLF for various minor object populations.

Population CSD CLF References

KBOs (r > 20 km) 3.45 0.69 Gladman et al. (2001)
3.20 ± 0.10 0.64 ± 0.02 Larsen et al. (2001)
3.15 ± 0.10 0.63 ± 0.06 Trujillo et al. (2001)
Centaurs 2.70 ± 0.35 0.54 ± 0.07 Larsen et al. (2001)
3.0 0.6 Sheppard et al. (2000)
ECs 1.9 ± 0.3 0.38 ± 0.06 This work
ECs + “cometary” NEOs 1.6 ± 0.2 0.32 ± 0.04 This work
Near-Earth objects 1.75 ± 0.10 0.35 ± 0.02 Bottke et al. (2002)
1.96 0.39 Stuart (2001)
Main-belt asteroids 1.25–2.80 0.25–0.56 Jedicke and Metcalfe (1998)
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 255

Figure 4b displays the CSD of the 13 NIC nuclei whose measured so far have periods in a more restricted range,
effective radii, rn,v, have been determined (Table 2). Also 5–18 h, but this may result from observational bias.
plotted is the CSD of this population augmented by the 12 The results on rotational periods and axial ratios can be
asteroidal objects thought to be dormant or extinct NICs used to estimate lower limits on the density of the nuclei,
on the basis of their Tisserand parameters (Table 7). Owing assuming that they are strengthless (i.e., that cometesimals
to the poor statistics, we did not attempt to fit power laws
to the observed CSDs. We note, however, based on the
present dataset, the rather shallow CSD of the NICs and the
lack of small nuclei that NICs apparently share with ECs.

4.2. Shape and Rotation Period of

Cometary Nuclei

Figure 7 displays the distribution of the axial ratio a/b

of cometary nuclei. One should bear in mind that the bulk
of the values are, strictly speaking, lower limits. There is
not enough data for NICs to draw any conclusion. For ECs,
the histogram is highly skewed with a median value of ~1.5,
and there is a priori no reason to suspect that this property
is biased by the aspect angle. There are a few cases of
highly elongated nuclei with a/b > 2, the maximum value
being 2.6 at present.
Figure 8 displays the distribution of rotational periods.
One should bear in mind that most of them are not accu-
rately determined because of the scarcity of data points to
define the light curves. The range of 5–70 h is remarkably
similar to that of the periods of main-belt asteroids and
NEOs, excluding the monolithic fast rotators (e.g., Whiteley
et al., 2002). We further note that the bulk of the nuclei Fig. 8. Distribution of the rotational periods for cometary nuclei.

Fig. 7. Distribution of the lower limits of the axial ratio for com- Fig. 9. Rotational periods vs. axial ratio for the cometary nuclei
etary nuclei. The comet nucleus is assumed to be a prolate spher- assumed to be prolate spheroids. The solid lines show curves of
oid rotating around its axis of maximum moment of inertia for critical rotation for densities of 0.02, 0.06, 0.20, 0.60, 2.0 g cm–3
both ecliptic comets and nearly isotropic comets. (from top to bottom).
256 Comets II

are not physically bound) and that they are not rotating
faster than the centrifugal limit for breakup (Luu and Jewitt
1992; Meech, 1996). Figure 9 displays the relevant diagram,
where periods are plotted vs. axial ratios. Lines correspond-
ing to the critical rotational period for different bulk densi-
ties of the nucleus are also plotted. The figure suggests that
the fastest rotating nuclei are stable against centrifugal dis-
ruption, if their bulk densities exceed ~0.6 g cm–3 (see also
Weissman et al., 2004).

4.3. Albedos of Cometary Nuclei

One of the features evident in Table 4 is the very nar-

row range of albedos of cometary nuclei, namely 0.02 to
0.06. 29P/Schwassmann-Wachmann 1 stands as an excep-
tion with possibly p = 0.13 according to Cruikshank and
Brown (1983), suggesting that this object may indeed be
better classified as a Centaur. We further note that the low-
est values have been measured at 4845 Å. As most nuclei
have a red color, converting these values to the V band
slightly increases them. As an example, we find pV = 0.025
for 10P/Tempel 2 and pV = 0.030 for 49P/Arend-Rigaux.
The average value for the 13 nuclei listed in Table 4, ex-
cluding 29P, is pV = 0.038 ± 0.009 and pR = 0.042 ± 0.017,
assuming a typical normalized reflectivity gradient of S' =
10%/1000 Å. These values nicely bracket the canonical
albedo of 0.04, which is therefore fully justified. The range
of albedos is so narrow that looking for trends is almost
hopeless. This question has been recently investigated by
Campins and Fernández (2003), who concluded that there
is no trend with perihelion distance and a slight trend of
decreasing albedo with increasing nuclear radius, the cor-
relation being significant only at the 2σ level.

4.4. Colors of Cometary Nuclei Fig. 10. The distributions of the (B-V), (V-R), and (R-I) color
indices of the ecliptic comets, excluding 19P/Borrelly. The average
Figure 10 displays the distributions of the (B-V), (V-R), values of the color indices are displayed and the color indices of
and (R-I) color indices, excluding 19P/Borrelly for which the Sun are indicated.
the uncertainty is too large, which can be compared to the
solar indices (B-V) = 0.65, (V-R) = 0.35, and (R-I) =
0.28. The mean values of the indices <(B-V)> = 0.82, <(V- 5. SUMMARY, OPEN ISSUES,
R)> = 0.41, and <(R-I)> = 0.38 confirm the well-known AND FUTURE DIRECTIONS
result that cometary nuclei are statistically redder than the
Sun. Their colors are, however, very diverse, as already 5.1. Current Status
discussed for a smaller sample (Luu, 1993), from slightly
blue to very red. Even if we exclude 14P/Wolf and 86P/ Remarkable progress has been made during the past
Wild 3, for which the uncertainty in (V-R) is very large, decade in measuring the sizes of cometary nuclei, but it is
there are two comets, 43P/Wolf-Harrington and 107P/Wil- also clear that this field is still in its infancy. Reliable data
son-Harrington, that have a well-determined (V-R) = 0.31 ± exist for only 65 comets, so any conclusions regarding the
0.03, significantly less than that of the Sun. The reddest distribution of sizes is necessarily tentative and subject to
nucleus in the present sample is that of 143P/Kowal-Mrkos, future revision. Measurements are needed for substantially
with (V-R) = 0.58, still less red than the average (V-R) = more comets, at least doubling or tripling the current num-
0.61 of KBOs (Jewitt, 2002). ber, before confidence can be gained in the conclusions
As pointed out in section 4.4, colors by themselves do regarding the size distribution. Our current best estimate,
not reveal much about the physical properties, but the dis- qS = 1.9 ± 0.3, is conspicuously different from that of the
tribution of colors compared to other solar system objects KBO and Centaur populations, but is similar to that of the
may provide information on their interrelationships. This NEOs. This value also corresponds to that of a collisionally
topic is discussed in Jewitt (2004). evolved population with pure gravity scaling, but we reem-
 Lamy et al.: Sizes, Shapes, Albedos, and Colors of Cometary Nuclei 257

phasize that O’Brien and Greenberg (2003) showed that this aged 2P/Encke on the other)? Continual loss of the surface
distribution is in fact wavy in the size range relevant to ECs. layers through repeated passages through the inner solar
The situation for cometary albedos is even worse, in the system obviously affects the size, and probably the shape
sense that reliable values are available for only about a and color, of cometary nuclei. How do we account for this
dozen objects. Nevertheless, we are struck by the relatively in estimating the primordial distribution of physical prop-
small range in the albedo (0.04 ± 0.02), which suggests that erties? Some combination of improved modeling and ob-
the surfaces of cometary nuclei are exceptionally dark, con- servations of nuclei will help, but it is not yet clear that these
trary to the early expectations for these “icy” bodies. issues can ever be resolved satisfactorily.
Measuring accurate shapes of cometary nuclei is some- Splitting events obviously affect the size and shape of
times possible but requires intensive observing campaigns, cometary nuclei, but how do we estimate their effect on the
generally extending over several days. Furthermore, the as- distribution functions? Perhaps better data on the splitting
pect angle of the rotational axis usually varies with time, so rates of nuclei, coupled with a better understanding of the
that observations at widely separated places in the comet’s physical mechanism(s) for splitting events, will help to re-
orbit are desirable to obtain a clear picture of the comet’s solve these issues, but that remains to be seen.
rotational properties and true shape. Although there are Of course, one of the most interesting avenues for future
some examples of highly elongated cometary nuclei, with exploration is the relationship between cometary nuclei and
the major axis being up to 2.6 times larger than the minor the other minor bodies in the solar system. Can we use the
axis, most cometary nuclei seem to differ from spherical size distribution of cometary nuclei to conclude that they
bodies by ~50%. However, we must keep in mind that the are a collisionally evolved population? In particular, can the
axial ratio values are often lower limits. Fortunately, con- size distribution and the shapes of cometary nuclei be used
clusions regarding the size distribution of cometary nuclei to conclude that they are collisional fragments of the TNOs?
are not strongly affected by uncertainties in the shapes. If the Centaurs are TNOs on the road to becoming ecliptic
It is also difficult to obtain reliable color data on com- comets, then perhaps Centaurs and these comets share com-
etary nuclei. While the color of the nucleus itself does not mon physical properties. If not, can the differences be ex-
provide unique information on the physical properties, color plained by evolutionary effects? Although cometary nuclei
data are useful for comet-to-comet comparisons, which may generally contain much more ice than do asteroids, perhaps
suggest differences in surface properties, particularly when “evolved” comets share many common characteristics with
in making comparisons with other minor bodies in the solar asteroids. In addition, at least some asteroids, and many com-
system (e.g., Centaurs, TNOs, and asteroids). The colors of etary nuclei, are thought to have porous, “rubble-pile” physi-
cometary nuclei are diverse, with some being highly red- cal structures (Davis et al., 1985; Weissman, 1986). Does
dened compared to solar color, some being neutral, and a this point to commonalities in their formation mechanism?
few having a slightly blue color. It seems clear that remote observations with 2–3-m tele-
scopes will continue to play a critical role in measuring the
5.2. Outstanding Issues and physical properties of cometary nuclei as a population. We
Future Investigations can certainly hope to make as much progress during the
next decade as we have witnessed in the previous one, and
An important, unresolved issue concerns the interpreta- we can look forward to many new advances in our under-
tion of disk-integrated thermal measurements, which, in standing of the physical properties of cometary nuclei in the
principle, provide robust determinations of sizes and albe- future. During its remaining lifetime, and subject to ap-
dos. The so-called standard thermal model for asteroids is proval of the relevant programs, HST can essentially com-
often used to interpret cometary thermal data, although its plete a survey of the bulk of the known population of ECs
applicability to objects having a mixture of dust and ice is and provide unique, accurate color data. Large groundbased
questionable. telescopes (e.g., Keck and the Very Large Telescope) will
A totally open issue is the nature of the size distribution also contribute by detecting nuclei at large heliocentric dis-
of cometary nuclei at the small end of the spectrum. Does tances, where they are presumed inactive. With its unsur-
the relatively steep power law derived from the intermedi- passed sensitivity, SIRTF will be capable of detecting the
ate-sized objects extend indefinitely to smaller sizes? Or is nuclei of a large fraction of the ECs in the midinfrared, thus
the size distribution truncated at some value that depends providing albedo-independent determinations of their size.
on the physical formation mechanism (e.g., gravitational Herschel will also be able to provide albedo-independent
instability within the solar nebula) or destruction mecha- size determinations, but for larger, more distant nuclei in
nism (e.g., total disruption)? the submillimeter wavelength range. Finally, the Atacama
What is the bias in ecliptic comet discoveries and how Large Millimetre Array (ALMA) will be able to detect a
does that affect the current distribution of sizes? Why do significant number of nuclei at 1.3 mm. Combining ALMA
we observe so few large (rn > 5 km) cometary nuclei? and SIRTF data should provide robust information on the
How does evolution affect the physical properties of com- long-wavelength emissivity and internal thermal properties
etary nuclei? Is there really a continuum of surface prop- of cometary nuclei.
erties that is dependent on the activity level and physical Future spacecraft encounters will undoubtedly shed fur-
evolution (e.g., with a youthful Chiron at one end and an ther light on the nature of cometary nuclei, and will even
258 Comets II

start to address the diversity issue in a serious way as more N. Samarasinha for their constructive remarks. P.L.L. and I.T. ac-
and more objects come under intense scrutiny. While we knowledge the support of the French Programme National de Plan-
very much regret the loss of the CONTOUR mission, which étologie, jointly funded by CNRS and CNES, and the bilateral
would have flown by 2P/Encke and 73P/Schwassmann- French-Hungarian cooperation program. I.T. further acknowledges
the support of the Université de Provence and of the Hungarian
Wachmann 3, we now look forward to the flybys of 81P/
State Research Foundation for Sciences (OTKA) through Grant
Wild 2 (Stardust mission) and 9P/Tempel 1 (Deep Impact
No. T025049. H.A.W. acknowledges financial support by NASA
mission), the latter also probing the interior of the nucleus. through Grants HST-GO-8699.01-A and HST-GO-8876.01-A
Space investigations of cometary nuclei will culminate with from the Space Telescope Science Institute (STScI), which is op-
the Rosetta mission, whose orbiter will accompany the erated by the Association of Universities for Research in Astron-
nucleus of 67P/Churyumov-Gerasimenko from a heliocen- omy, Inc., under NASA contract NAS5-26555. This work is partly
tric distance of 3.6 AU to perihelion at 1.3 AU and observe based on observations made with the NASA/ESA Hubble Space
it at all spatial scales down to a few millimeters, thus al- Telescope and obtained at the STScI.
lowing an unprecedented view of how the activity starts and
evolves. The Rosetta lander will perform a broad range of
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 Harmon et al.: Radar Studies of Comet Nuclei and Grain Comae 265

Radar Studies of Comet Nuclei and Grain Comae

John K. Harmon and Michael C. Nolan
Arecibo Observatory

Steven J. Ostro
Jet Propulsion Laboratory, California Institute of Technology

Donald B. Campbell
Cornell University

A close-approaching comet can show detectable echoes from its nucleus, or from large coma
grains, or both. Nine comets have been detected since 1980 with the Arecibo and Goldstone
radars; this includes six nucleus detections and five grain-coma detections. The nucleus radar
cross sections span a large range of values consistent with a factor-of-10 range of nucleus sizes.
Comparisons with independent size estimates for these comets support this size range and give
radar albedos of 0.04–0.1, which is about half the typical asteroid radar albedo. The albedos
correspond to nucleus surface densities ~0.5–1.5 g/cm3. Coma echo models based on simple
grain ejection theories can explain the radar cross sections using reasonable grain size distri-
butions that include a substantial population of centimeter-sized grains; in one case there is
evidence for a cutoff in the size distribution consistent with a gravity-limited maximum lift-
able grain size. The models indicate that some comets emit large grains at rates (~106 g/s) that
are comparable with their gas and dust production rates. The primary goal of cometary radar is
to obtain delay-Doppler images of a nucleus. Eleven short-period comets are potentially de-
tectable over the next two decades, a few of which may be suitable for imaging. These could
be supplemented by chance close apparitions of new comets.

1. INTRODUCTION as a surprise result from the 1983 observations of C/IRAS-

Araki-Alcock (Campbell et al., 1983; Goldstein et al., 1984)
When the comet radar chapter by Kamoun et al. (1982a) and has since been seen for four other comets. The impli-
was written for the first Comets book (Wilkening, 1982), cation is that large-grain emission by comets is common
only one comet, 2P/Encke, had been detected by radar. and can account for a significant fraction of the total nucleus
Since then, eight more comet detections have been made mass loss. This is in line with a growing body of evidence
with the Arecibo and Goldstone radars (Table 1). While few from other observations (spacecraft encounters, infrared
in number, owing to the rarity of close comet approaches, dust trails, submillimeter continuum, antitails, etc.) that
these detections have been sufficient to establish comets as large grains are an important component of the cometary
interesting and diverse radar targets. particulate population.
The Encke detection of 1980 (Kamoun et al., 1982a,b; Here we review the various cometary radar findings to
Kamoun, 1983) showed a narrow Doppler spike consistent date, discuss their implications in the context of other ob-
with backscatter from a solid rotating nucleus a few kilo- servations, and survey prospects for future work. Although
meters in size. Subsequent nucleus detections of other com- covering much of the same ground as an earlier review
ets have been similar in character, but show differences in article by these same authors (Harmon et al., 1999), the
radar cross section consistent with an order-of-magnitude material presented here has been substantially reorganized
range of nucleus sizes. In principle, delay-Doppler radar and updated.
imaging can determine the size, shape, rotation, and radar
albedo of a nucleus unambiguously, as is being done for 2. RADAR MEASUREMENTS
an increasing number of asteroids. Since no delay-Doppler AND DETECTABILITY
detection has yet been made for a comet, radar data have
mainly been used to estimate or constrain nucleus param- All comet radar detections to date have come from Dop-
eters from comparisons with other types of observations. pler-only observations with the Arecibo S-band (wavelength
For example, comparisons of nucleus radar cross sections λ = 12.6 cm), Goldstone S-band (12.9 cm), or Goldstone X-
with independent size estimates have placed useful bounds band (3.5 cm) radar systems. Here we summarize the types
on nucleus radar albedos and surface densities. of measurements made using Doppler-only observations.
In addition to the nucleus echo, some comets also show Discussion of delay-Doppler measurements is deferred to
an echo component from large coma grains. This first came section 5.1.

265
266 Comets II

TABLE 1. Comet radar detections.

Comet Radar* Epoch (m/d/y) ∆ (AU)† References

2P/Encke AS 11/2–11/8/1980 0.32 [1,2]
26P/Grigg-Skjellerup AS 5/20–6/2/1982 0.33 [2,3]
C/IRAS-Araki-Alcock (1983 H1) GS 5/11.94/1983 0.033 [4]
GX 5/14.08/1983 0.072 [4]
AS 5/11.92/1983 0.033 [5,6]
C/Sugano-Saigusa-Fujikawa (1983 J1) AS 6/10–6/12/1983 0.076 [5,7]
1P/Halley AS 11/24–12/2/1985 0.63 [8]
C/Hyakutake (1996 B2) GX 3/24–3/25/1996 0.10 [9,10]
C/1998 K5 (LINEAR) AS 6/14.25/1998 0.196 [11]
C/2001 A2 (LINEAR) AS 7/7–7/9/2001 0.26 [12]
C/2002 O6 (SWAN) AS 8/8–8/9/2002 0.26 [13]
*AS = Arecibo S-band (λ = 12.6 cm); GS = Goldstone S-band (λ = 12.9 cm); GX = Goldstone
X-band (λ = 3.54 cm).
† Distance from Earth at time of observation.

References: [1] Kamoun et al. (1982b); [2] Kamoun (1983); [3] Kamoun et al. (1999); [4] Gold-
stein et al. (1984); [5] Campbell et al. (1983); [6] Harmon et al. (1989); [7] Harmon et al. (1999);
[8] Campbell et al. (1989); [9] Ostro et al. (1996); [10] Harmon et al. (1997); [11] Harmon et
al. (1999); [12] Nolan et al. (2001); [13] this paper.

2.1. Doppler Spectrum The Doppler spreading of the nucleus spectrum repre-
sents the line-of-sight (radial) velocity spread from the
A Doppler-only observation involves transmission of an apparent rotation of the nucleus. The Doppler frequency for
unmodulated (monochromatic) wave and reception of the radial velocity Vr and radar wavelength λ is f = 2Vr /λ. The
Doppler-broadened echo. One computes the power spec- Doppler bandwidth of a spherical nucleus is then given by
trum of the received signal, within which a detectable echo
would appear as a statistically significant spike or bump 8πR sin φ 29.1 R(km) sin φ
B= = (Hz) (1)
sticking up out of the background noise. The echo can λp λ(cm) p(days)
appear as a narrow (few Hz wide) spike from the nucleus,
or a broad (tens to hundreds of Hz) component from the where R is the nucleus radius, φ is the angle between the
grain coma. Two comets, C/IRAS-Araki-Alcock and C/Hya- apparent rotation axis and the line of sight, and p is the
kutake, showed echoes from both nucleus and coma. The apparent rotation period. For strong detections (e.g., Figs. 3
spectra for these comets are shown in Figs. 1 and 2. and 4), bandwidth B is easily determined from the well-

Fig. 1. Doppler spectra (OC and SC polarizations) for C/IRAS- Fig. 2. Doppler spectra (OC and SC polarizations) for C/
Araki-Alcock showing the narrowband nucleus echo and broad- Hyakutake showing both nucleus and coma echoes. A model fit to
band coma echo. The spectrum is truncated so that only the bottom the coma echo is also shown (dashed line). The spectrum is from
2% of the nucleus echo is showing. The spectrum is from Arecibo Goldstone X-band observations on March 24, 1996 (Harmon et
S-band observations on May 11, 1983 (Harmon et al., 1989). al., 1997).
 Harmon et al.: Radar Studies of Comet Nuclei and Grain Comae 267

Fig. 3. Doppler spectra (OC and SC polarizations) for the nu- Fig. 4. Doppler spectra (OC and SC polarizations) for the nu-
cleus of C/IRAS-Araki-Alcock, from Arecibo S-band observations cleus of C/Sugano-Saigusa-Fujikawa, from Arecibo S-band obser-
on May 11, 1983 (Harmon et al., 1989). vations on June 11, 1983 (Harmon et al., 1999).

defined edges of the nucleus spectrum. The shape of the 2.3. Polarization
nucleus spectrum is determined by the nucleus shape and
orientation as well as by the intrinsic angular scattering law Echo polarization provides additional information on the
of the surface. target and its scattering properties. All comet radar observa-
The Doppler spreading of the coma echo represents the tions have followed the standard practice of transmitting a
collective sum of the radial velocities of all the large grains circularly polarized wave and receiving in both (orthogonal)
within the radar beam. The coma spectrum shape is deter- senses of circular polarization. These polarization senses on
mined by the velocities, sizes, and spatial distribution of the receive are referred to as OC (for “opposite circular”; also
grains, as well as by the cutoff effect of the radar beam. called the “polarized” or “expected” sense) and SC (for
For the spectra presented here the mean (absolute) Dop- “same circular”; also called the “depolarized” or “unex-
pler frequency of the nucleus has been subtracted off, so pected” sense). Separate echo spectra are computed for each
that zero Doppler defines the nucleus center frequency. polarization (see Figs. 1–4), from which one can compute
However, the absolute Doppler offset of the nucleus is of OC and SC cross sections σoc and σsc. A circular polariza-
intrinsic interest for refining estimates of a comet’s orbital tion ratio is then defined as µc = σsc/σoc.
elements. Comet Doppler offsets or refined orbits based on The OC echo is the stronger of the two (µc < 1) for most
them have appeared in several reports (Ostro et al., 1991b, solar system targets, being the expected sense for specular
1996; Yeomans et al., 1992; Giorgini, 2002). reflection, while the weaker SC echo is normally attributed
to depolarization by wavelength-scale roughness or multiple
2.2. Radar Cross Section and Albedo scattering. For scattering by particle clouds one expects µc <
1 when single scattering dominates, with µc << 1 for parti-
The most fundamental radar parameter measured from cles in the Rayleigh size regime a < λ/2π. When multiple
the echo is the radar cross section σ. Integrating under the scattering predominates, as for Saturn’s rings, one can get
echo Doppler spectrum to get the echo power Pr , σ is then µc ~ 1.
calculated from the radar equation
2.4. Detectability
(4π)3 ∆4 Pr
σ= (2)
Pt G 2 λ2 The strength of the radar detection is given by the de-
tectability D, which is the ratio of the echo power to the
where ∆ is the comet distance, Pt is the transmitted power, rms statistical fluctuation in the noise power. This is given
and G = 4πAe/λ2 is the beam gain of the radar antenna of by the radiometer equation D = (S/N) t∆f , where S/N is
effective area Ae. If the size of the nucleus is known or the ratio of the signal and noise spectral densities, t is the
estimated, then σ can be normalized to give a geometric integration time, and ∆f is the frequency resolution. Com-
radar albedo bining this with the radar equation (2), and assuming the
spectrum is optimally smoothed (matched filtered), gives
σ
σ= (3)
Ap PtG2λ2t1/2 ησ
D= (4)
(4π)3∆4kTsB1/2
where Ap is the apparent projected area of the nucleus. This
albedo is useful for estimating surface density (see sec- where k is Boltzmann’s constant, Ts is system temperature,
tion 3.2.2). and η is a factor (≈1) that depends on the shape of the echo
268 Comets II

TABLE 2. Nucleus echo parameters.

Comet λ (cm) σoc (km2) µc B (Hz) [m/s]*

Encke 12.6 1.1 ± 0.7 6 [0.38]
GS 12.6 0.5 ± 0.13 <0.3 <0.5 [<0.03]
IAA 12.6 2.14 ± 0.4 0.105 ± 0.005 3.5 [0.221]
12.9 2.25† 3.1 [0.20]
3.5 4.44† 0.25† 20.3 [0.36]
SSF 12.6 0.034 ± 0.008 0.23 ± 0.03 2.5 [0.158]
Hyakutake 3.5 0.13 ± 0.03 0.49 ± 0.10 12 [0.21]
1998 K5 12.6 0.031 ± 0.015 <0.5 <1.5 [<0.09]
*Full (limb-to-limb) Doppler bandwidth in Hz, also expressed as a velocity
λB/2 in m/s (in brackets).
† From Goldstein et al. (1984), which gives no error estimate.

spectrum. Substituting the current system parameters for the 0.37 km) based on its infrared core flux (Hanner et al.,
upgraded Arecibo S-band radar in equation (4) and using 1987). Although there is no independent size estimate for
equation (1) gives C/1998 K5, its extremely low absolute magnitude (Mars-
den, 1998) suggests that it, too, was very small.
1.0σ(km 2 )t1/2 (hours) Most size estimates for the three comets with intermedi-
D≈ ≥ ate radar cross sections (Encke, Grigg-Skjellerup, Hyaku-
∆4 (AU)B1/2 (Hz)
(5) take) do, in fact, fall between those of IAA and SSF. For
2.1σR 3/2(km )p1/2 (days) t1/2 (hours) Encke, the infrared results of Campins (1988) give R <
∆4 (AU) 2.9 km and the red-visible photometry of Luu and Jewitt
(1990) gives 2.2 < R < 4.9 km. The most recent size esti-
For the Goldstone X-band radar one substitutes 0.12 for the mate for Encke is the infrared-based value R = 2.4 km of
2.1 factor. Equation (5) is useful for evaluating future comet Fernández et al. (2000). For Grigg-Skjellerup, Boehnhardt
radar opportunities (section 5.2). et al. (1999) and Licandro et al. (2000) give radius esti-
mates of 1.4–1.5 km based on the comet’s visual magnitude
3. NUCLEUS at large heliocentric distance. Size estimates for Hyakutake
vary. The most sensitive radio continuum nondetection gave
Six comets have yielded radar detections of their nuclei an upper limit for R of 1.05 km (Altenhoff et al., 1999).
(Table 2). The strongest and best-resolved nucleus spec- Infrared estimates are larger, with R = 2.1–2.4 km (Sarme-
tra are those for C/IRAS-Araki-Alcock (henceforth abbre- canic et al., 1997; Fernández et al., 1996; Lisse et al., 1999).
viated IAA) and C/Sugano-Saigusa-Fujikawa (abbreviated One can use equation (1) to estimate the rotation period
SSF), which are shown in Figs. 3 and 4 respectively. Addi- from the Doppler bandwidth B if both R and φ are known,
tional nucleus spectra have been published elsewhere, viz. or place an upper limit on the period if only R is known.
Kamoun et al. (1982a,b) (P/Encke); Goldstein et al. (1984) Sekanina (1988) showed that the radar bandwidth and coma
(IAA); Kamoun et al. (1999) (P/Grigg-Skjellerup); Har- jet structure of IAA were consistent with a relatively slow
mon et al. (1997) (C/Hyakutake); Harmon et al. (1999) (C/ rotation period of 2.14 d. For SSF, combining the measured
1998 K5). B = 2.5 Hz with R = 0.37 km gives a relatively fast rotation
with p < 8.3 h. The estimated bandwidth for Encke (Kamoun
3.1. Size, Rotation, and Albedo et al., 1982b) gives p < 22 h assuming R = 2.4 km. This up-
per limit encompasses all of Encke’s observed periodicities,
3.1.1. Size and rotation. The observed nucleus cross which span the range 7–22 h (Samarasinha et al., 2004),
sections span two orders of magnitude, from the 2–4 km2 and includes the recently claimed dominant period of 11 h
of IAA down to the 0.03 km2 of SSF and C/1998 K5. This (Fernández et al., 2002). The estimated Hyakutake band-
implies, assuming albedos are equal, that the nucleus sizes width (Harmon et al., 1997) gives p < 20 h assuming R =
vary by about a factor of 10 for the radar-detected sample. 1.2 km, which is consistent with the Hyakutake rotation
This is supported by independent size estimates. Sekanina period estimate of 6.25 h (Schleicher et al., 1998). The
(1988) combined radar data with radio continuum (Altenhoff Grigg-Skjellerup spectrum was unresolved (Kamoun et al.,
et al., 1983) and infrared (Hanner et al., 1985) results to 1999) and hence yielded no useful constraint on rotation.
deduce that IAA had a large (Halley-size) nucleus meas- The echo from 1998 K5 was too weak to readily separate
uring 16 × 7 × 7 km and showing an effective radius of true bandwidth from ephemeris drift, so no rotation con-
4.4 km at the epoch of the S-band radar observations. Comet straint is available for that comet. None of the radar-derived
SSF, on the other hand, was deduced to be a tiny object (R = rotation period upper limits violate the 3.3-h critical period
 Harmon et al.: Radar Studies of Comet Nuclei and Grain Comae 269

TABLE 3. Nucleus radar albedo estimates. Clearly, the size and radar albedo of the Hyakutake nucleus
remain controversial.
Comet Albedo* R (km) References The fact that nucleus radar and optical albedos are low
Encke >0.04 <2.9 [1] and have about the same values is interesting but probably
0.02–0.08 2.2–4.9 [2] not significant. While it is true that optical and radar albedo
0.06 2.4 [3] both depend on composition and density, there are impor-
GS 0.08 1.5 [4,5] tant differences. First, optical albedo can be dominated by
IAA† 0.04, 0.07 4.4, 4.9 [6,7] a thin surface layer, whereas the radar can respond to re-
SSF 0.10 0.37 [8] flections from meters below the surface. Second, composi-
Hyakutake 0.01–0.015 2.1–2.4 [9,10,11]
tional differences are likely to be much more important in
>0.06 <1.05 [12]
the optical than in the radio. For example, a carbonaceous
*Total radar cross section divided by πR2, where R is the tabulated or organic composition could give a surface that is ex-
radius. No entry is given for C/1998 K5, for which no radius tremely dark optically, but which may not have distinctive
estimate is available. radio dielectric properties.
† The first and second entries for the albedo and radius correspond

to the S-band and X-band observations respectively.

3.2. Surface Properties
References for radius estimate: [1] Campins (1988); [2] Luu and
Jewitt (1990); [3] Fernández et al. (2000); [4] Boehnhardt et al. 3.2.1. Roughness. The resolved nucleus spectra of IAA
(1999); [5] Licandro et al. (2000); [6] Sekanina (1988); [7] Alten- (Fig. 3) and SSF (Fig. 4) are broad (relative to the total
hoff et al. (1983); [8] Hanner et al. (1987); [9] Sarmecanic et al. bandwidth B) rather than sharply peaked, which is sugges-
(1997); [10] Fernández et al. (1996); [11] Lisse et al. (1999); tive of high-angle scattering from very rugged surface re-
[12] Altenhoff et al. (1999). lief. The polarization ratios can give some idea of the scale
of this relief and its comet-to-comet variation. The relatively
low S-band µc for IAA is consistent with highly specular
scattering from meter-scale or larger structure, although the
for breakup of a spherical nucleus with 1 g/cm3 density higher X-band µc points to an extra component of smaller
(Samarasinha et al., 2004). rubble. Comet SSF shows a higher S-band µc than IAA,
3.1.2. Albedo. Nucleus radar albedos and the radius indicating roughness that is concentrated more toward deci-
values R assumed in their calculation are listed in Table 3. meter scales. The highest µc is the 0.5 measured for Hyaku-
Here we give the total albedo (σoc + σsc )/πR2, adding an take at X-band, which suggests a surface that may be nearly
assumed 15% SC component for those comets (Encke and saturated with pebble-sized rubble. Hyakutake was an un-
Grigg-Skjellerup) with OC-only detections. The IAA albedo usually active comet for its size, and its surface texture may
estimates are 0.04 at S-band and 0.07 at X-band, based on be related to that activity. For example, there could be an
the nucleus projected area estimates of Sekanina (1988) accumulation of surface debris from ejecta fallback (Kührt
at the respective epochs of the S-band and X-band obser- et al., 1997). Ice sublimation could also produce surface
vations. The recent radius estimates of 2.4 km for Encke
(Fernández et al., 2000) and 1.5 km for Grigg-Skjellerup
(Boehnhardt et al., 1999; Licandro et al., 2000) give albe-
dos of 0.06 and 0.08 respectively. The highest s is the 0.10
value estimated for SSF from the Hanner et al. (1987) in-
frared size. This high albedo is consistent with the sugges-
tion by Hanner et al. (based on an apparently high thermal
inertia and unusually low dust production) that the surface
of the SSF nucleus is more highly compacted than normal.
For Hyakutake, the R < 1.05 km upper limit from the ra-
dio continuum nondetection (Altenhoff et al., 1999) gives
s > 0.055, whereas the larger infrared-based sizes give very
low (~0.01) albedos. Such a low radar albedo would imply
a very lightly packed nucleus, as suggested by Schleicher
and Osip (2002). The alternative is that Hyakutake had a
“normal” radar albedo similar to those of the other com-
ets, in which case the infrared size estimates must have been
biased high. The most likely source of such a bias would
be a dust contribution to the infrared flux (Lisse et al., Fig. 5. Distribution of main-belt (squares) and near-Earth
1999). Harmon et al. (1997) estimated the Hyakutake size (crosses) asteroids in radar albedo and circular polarization ratio
to be R = 1–1.5 km using IAA’s S-band albedo, which they (Benner, 2002). Also shown for comparison is the range of values
considered to be the most reliable radar albedo available. for comet nuclei (dashed rectangle).
270 Comets II

structure (Colwell et al., 1990). This might explain the

roughness for a comet such as SSF, which was very inactive
in terms of dust production but very active in the amount of
gas it produced for its size.
Comet nucleus polarization ratios (µc = 0.1–0.5) are simi-
lar to those for many near-Earth and main-belt asteroids
(Ostro et al., 2002; Benner, 2002; Magri et al., 1999, 2001),
as can be seen from the comparison in Fig. 5. This suggests
that comets are similar to asteroids in the scale of their
surface relief. However, no comets have yet shown the very
low depolarization (µc ~ 0.05) seen for a few main-belt
asteroids or the high depolarization (µc ~ 1) seen for a few
near-Earth objects.
Comet nuclei also resemble asteroids in their spectral
shape. It is customary with asteroids to fit the Doppler spec-
trum with the function Fig. 6. Bulk density d of the nucleus surface vs. radar albedo s
S(f) ∝ [1 – (2f/B)2]n/2 (6) for dry snow (solid curve) and a silicate soil (dashed curve). A
backscatter gain g = 3/2 was assumed. Various albedo estimates
which corresponds to the echo spectral shape for a sphere from Table 3 are also shown (vertical dotted lines).
with a scattering law of the form
σo(θ) ∝ cosnθ (7)
function of s for snow and soil surfaces assuming g = 3/2
where σo(θ) is the specific cross section as a function of (n = 1, assuming geometric optics). Here we have used the
incidence angle θ. Using this model, Harmon et al. (1989) expression
found the IAA nucleus followed a uniformly bright (n = 1)
or possibly even limb-brightened (n < 1) scattering law
0.526 (ε − 1.00) (ε ≤ 1.95)
based on the sharp edges of its spectrum, arguing that this d≈ (10)
was evidence for scattering from a chaotic surface with 0.347 (ε − 0.51) (ε > 1.95)
super-wavelength-scale roughness elements giving both
specular reflection and shadowing. The SSF spectra more for the case of dry snow (Hallikainen et al., 1986) and
closely followed a Lambert law (n = 2), the cosine-law fits
giving n values of 1.4, 2.2, and 2.8 for the three different
ε −1
days. If the scattering is assumed predominantly specular d ≈ 3.9 (11)
(low µc), then the roughness can be estimated from geo- ε+2
metric optics (Mitchell et al., 1995). In that case the rms
slope θr of the surface roughness is related to n by for a soil of silicate powder (Campbell and Ulrichs, 1969).
From Fig. 6 we see that an IAA-like albedo corresponds to
θr = tan−1 2/n (8) a surface with the consistency of a dense (0.5 g/cm3) ter-
restrial snowpack or very fluffy (0.9 g/cm3) soil. A higher
This suggests that comets such as IAA and SSF have rms albedo such as that of Comet SSF gives densities closer to
surface slopes ~50°. This is consistent with the rough to- that of solid ice or a moderately packed soil. The overall
pography seen in spacecraft images of Comets Halley and range of albedo estimates indicates that comet nuclei have
Borrelly (Weissman et al., 2004). surface densities in the range 0.5–1.5 g/cm3. (This density
3.2.2. Density. If the nucleus surface layer is thick and would apply to surface layers down to the penetration depth
homogeneous, then one can estimate its bulk density from of the radar wave, which is of the order of 10 wavelengths
the radar albedo. If the nucleus radar scattering is predomi- or so for packed soils.) It is interesting to note that this sur-
nantly specular, then ρo ≈ s/g, where ρo is the square of face density range is identical to the most recent estimates
the Fresnel reflection coefficient at normal incidence and for the overall bulk density of comet nuclei (Skorov and
g is the backscatter gain. For a cosnθ scattering law in the Rickman, 1999; Ball et al., 2001; Weissman et al., 2004),
geometric optics approximation, one has g = (n + 2)/(n + 1). although this does not necessarily imply that nucleus sur-
Once ρo is estimated, the dielectric constant ε is given by faces and interiors have the same structure.
A comparison of albedos indicates that the surfaces of
(1 + ρ1/2
o )
2 comet nuclei are less dense than asteroid surfaces. Most
ε= (9)
(1 − ρ1/2
o )
2 main-belt asteroids (Magri et al., 1999) and near-Earth
asteroids (Ostro et al., 1991a, 2002; Magri et al., 2001;
This can then be used to estimate the bulk density d using Benner et al., 1997) have higher radar albedos than com-
some suitable expression for d(ε). In Fig. 6 we plot d as a ets, as can be seen from the comparison in Fig. 5. This al-
 Harmon et al.: Radar Studies of Comet Nuclei and Grain Comae 271

bedo difference should translate directly into a difference 4. GRAIN COMA

in reflectivity ρo (and density), since the similarity between
comet and asteroid scattering implies similar backscatter A grain coma echo has been detected from five comets.
gains. The near-Earth asteroid 433 Eros is the only aster- Two of these, IAA (Fig. 1) and Hyakutake (Fig. 2), gave
oid with both a known radar cross section and known mass nucleus detections as well. The three comets giving only
(and hence known bulk density). Putting the measured to- coma detections were Halley (Fig. 7), C/2001 A2 (Fig. 8),
tal radar albedo of 0.32 of Eros (Magri et al., 2001) into and C/2002 O6 (Fig. 9). The estimated radar parameters for
equations (9) and (11) gives a surface density of 3.0 g/cm3, all the coma detections are listed in Table 4.
which is close to the bulk density of 2.7 g/cm3 estimated One can deduce some basic properties of the large-grain
from the NEAR Shoemaker spacecraft flyby (Veverka et al., population from rather simple arguments and models, as
2000) and 3× larger than the comet nucleus bulk densities discussed below.
quoted above; this suggests that the nucleus surface den-
sity differences between comets and asteroids inferred from 4.1. Grain Populations and Radar Scattering
albedo comparisons may reflect differences in total bulk
densities for these objects. Another implication of the low Some basic constraints on the large-grain population can
comet albedos is that one should expect any extinct comet be established by simply assuming the grains have a power-
nuclei masquerading as asteroids to also have low albedos. law size distribution n(a) ∝ a–α with minimum and maxi-
The asteroids with properties (including low radar albedo)
closest to the middle of the domain of comet properties are
the 7-km-diameter near-Earth object 1999 JM8 (Benner et
al., 2002), for which a cometary origin cannot be excluded
(Bottke et al., 2002), and the 0.5-kilometer-diameter object
3757 (1982 XB), which does not have a comet-like orbit.

Fig. 8. Doppler spectrum (OC and SC polarizations) for C/2001

A2 (LINEAR) from Arecibo S-band observations on July 7, 2001.

Fig. 7. Doppler spectrum (OC polarization) for P/Halley from

a five-day average of Arecibo S-band observations between No-
vember 24 and December 2, 1985. The frequency resolution is Fig. 9. Doppler spectrum (OC and SC polarizations) for C/2002
1.95 Hz. Smoothing to a resolution of 62 Hz increases the OC O6 (SWAN) from Arecibo S-band observations on August 8 and 9,
detection to nine standard deviations. From Campbell et al. (1989). 2002.
272 Comets II

TABLE 4. Grain-coma echo parameters. scattering grains will have a total radar cross section

Comet λ (cm) σoc (km2) µc Bh (Hz) [m/s]* am

IAA 12.6 0.80 ± 0.16 0.014 ± 0.003 72 [4.54]

σ=π ∫ ao
n(a)Q b (a)a2 da (13)
12.9 0.8† 90 [5.81]
Halley 12.6 32 ± 10 0.52 ± 0.26 42 [2.65] The corresponding total mass of this population is
Hyakutake 3.5 1.33 ± 0.28 0.31 ± 0.12 1180 [20.9]
2001 A2 12.6 4.4 ± 1.3 0.28 ± 0.03 170 [10.7]
4 am
2002 O6 12.6 1.1 ± 0.3 0.32 ± 0.08 230 [14.5]
*Full Doppler bandwidth at half-max. in Hz, also expressed as a
M=
3
πdg ∫ao
n(a)a 3da (14)

velocity λBh/2 in m/s (in brackets).

† From Goldstein et al. (1984), which gives no error estimate.
where dg is grain density. In the Rayleigh approximation
(a << λ/2π)
Qb(a) = CRa4 (15)
mum grain radii of ao and am respectively. The size cutoff where
am not only is useful for assessing the effective size of the
radar-scattering grains, but also can have some physical 4
2π ε−12
significance. We start with a discussion of the optical depth CR = (16)
of the grain coma, which is important for establishing the λ ε+2
dominance of single scattering and for determining the radar
visibility of the nucleus through the coma (section 4.1.1). Then, from equations (13)–(15), a grain coma with radar
We then discuss how am is constrained by radar cross sec- cross section σ has a total mass
tion and total grain mass (section 4.1.2) and coma echo
polarization (section 4.1.3). 4−α
4dg 7−α ao
4.1.1. Optical depth. The maximum optical depth to M≈σ 1− −3
am (17)
backscatter for a line of sight passing through the center of 3CR 4−α am
the grain coma is given by τ = σ/(4πRRc), where σ is the
coma radar cross section, R is the nucleus radius, and Rc is This am –3 dependence shows the extreme sensitivity of the

the grain coma radius. (Here we assumed that the grain mass M to maximum grain size in the Rayleigh regime, a
number density in the cloud falls as 1/r2 and that Rc >> R.) result of the rapidly decreasing Rayleigh backscatter effi-
This result implies that τ ~ 10 –4 or less. This can also be ciency with smaller grain size. Using this equation, Harmon
used as an upper limit on the ratio of multiple to single et al. (1989) and Campbell et al. (1989) showed that mak-
scattering. Another useful quantity is the ratio of the absorp- ing am < 0.5 mm resulted in a total mass in grains exceed-
tion and backscatter cross sections, which in the Rayleigh ing the nucleus mass for both IAA and Halley, from which
approximation (Bohren and Huffman, 1983) is given by they concluded that the effective grain size must have been
at least a few millimeters.
4.1.3. Polarization and maximum grain size. The coma
σa (ε + 2)ε tanδ 7−α echo from Comet IAA was only ~1% depolarized (µc =
≈
σ (ε − 1)2 4−α 0.014), which is the smallest depolarization ever measured
(12) for a solar system radar echo. This is consistent with a phys-
4−α −3
a am ically real cutoff am not much larger than λ/2π. [It is shown
1− o in Harmon et al. (1989) that µc for irregular grains increases
am λ / 2π
dramatically from ~10–2 or less to >0.1 as radius approaches
λ/2π, although the transition size can be larger for low-
where ε and tanδ are the dielectric constant and loss tan- density grains.] Combining this with the lower bounds on
gent of the grains respectively. Assuming reasonable grain am from the total mass (section 4.1.2) and mass-loss rate
parameters and setting am at the Rayleigh transition (λ/2π) (section 4.2.3) points to a sharp size cutoff at a few centi-
gives σa/σ ~ 0.1. (The ratio does not increase for am > λ/ meters. As pointed out by Harmon et al. (1989), this would
2π.) Combining this with the backscatter optical depth given be consistent with the gravitational cutoff in simple gas-drag
above indicates that the absorption optical depth in front theories of particle ejection (section 4.2.1). However, since
of the nucleus is negligible unless am is smaller than ~0.1(λ/ this apparent cutoff is close to the Rayleigh polarization
2π), which is unlikely from mass and mass-loss arguments threshhold, one would expect to see coma echoes from other
(see below). Hence, the nucleus radar detections have prob- comets with µc much higher than for IAA, owing to a less
ably suffered negligible obscuration by the coma. massive nucleus or more explosive activity. Although both
4.1.2. Size distribution and total mass. A spherical grain Halley and Hyakutake showed hints of nonnegligible coma
of radius a has a radar cross section of πa2Qb(a), where Qb depolarization, the only firm detection of significant coma
is the backscatter efficiency. Then, a population of single- depolarization is from the recent detection of C/2001 A2
 Harmon et al.: Radar Studies of Comet Nuclei and Grain Comae 273

(Nolan et al., 2001). Since the nucleus of this comet had be higher for fluffy grains (Keller and Markiewicz, 1991).
split prior to the radar observations (Sekanina et al., 2002), The velocity Vg is often taken to be the thermal expansion
it is possible that the depolarization was from boulder-sized velocity at the surface multiplied by some correction fac-
debris left over from the splitting or produced in violent tor to allow for expansion effects; this factor is ≈9/4 in
activity of small, freshly exposed subnuclei. Finson and Probstein (1968). Nonradial or asymmetric ex-
pansion can also give Vt different from the canonical model
4.2. Grain Ejection and Echo Modeling (Crifo, 1995).
Using these equations, Harmon et al. (1989) argued that
Further analysis of the coma echo requires modeling the the IAA coma echo was consistent with the simple gas drag
grain ejection process and estimating the mass-loss rates model. Taking am = 3 cm as a reasonable cutoff size (based
required to sustain the observed grain coma. A good start- on the mass and polarization arguments above) requires a
ing point is to assume that the grain emission process is a gas flux Z of ~1 × 10 –5 g/cm2 s, a reasonable value when
continuous one in which grains are ejected as free (un- compared with the 5 × 10–5 g/cm2 s sublimation rate for
bound) particles in the comet orbit frame. That the grains clean ice at 1 AU. This also gives reasonable grain veloci-
are predominantly unbound is consistent with the lack of a ties (8 m/s for a = 1 cm) and a good match to the Doppler
clear symmetric component about the nucleus echo in the spread in the coma spectrum model (see next section).
coma spectra for IAA and Hyakutake (Figs. 1 and 2). While Hyakutake did not fit so neatly into this picture, its much
it is expected that some grains will be injected into circum- broader spectrum requiring higher grain velocities (40 m/s
nuclear orbits (Richter and Keller, 1995; Fulle, 1997), Fulle for a = 1 cm) than for IAA despite its smaller nucleus
estimates that only about 1% of the ejected grains will do (Harmon et al., 1997). This implied a much higher effec-
so; this would not be enough to accumulate a significant tive gas flux (~4 × 10 –4 g/cm2 s), or much fluffier grains,
bound population, especially if the grains are undergoing or both. Since Hyakutake’s nominal surface active fraction
evaporation or disintegration. is about 1.0 assuming Z = 5 × 10–5 g/cm2 s, then the effec-
4.2.1. Gas drag models. For grain ejection we adopt tive Z must have been much higher than this in the discrete
the canonical model first formulated by Whipple (1951) and active regions that were observed to dominate the emission
refined by others. Assuming a uniform radial outflow of gas (Schleicher et al., 1998). Grain fluffiness could also boost
with thermal expansion velocity Vg, one can write a differ- the ejection velocity by lowering grain density and raising
ential equation for the outward drag velocity V of the grains the drag coefficient.
(Wallis, 1982; Gombosi et al., 1986) 4.2.2. Doppler spectrum modeling. The shape of the
Doppler spectrum contains information on the grain velocity
dV 1 ZR2 GMg Mn vectors and spatial distribution. Although the grain coma
MgV = CD π a2 (Vg − V)2 − (18)
dr 2 Vg r 2 r2 cannot be uniquely characterized from its spectrum, some
useful results have been obtained by treating the forward
where CD is the drag coefficient, Z is the surface gas mass problem of comparing the observed spectrum with model
flux, R is nucleus radius, G is the gravitational constant, spectra computed from trial input parameters. If one starts
and Mg and Mn are grain and nucleus mass respectively. with the gas-drag model (section 4.2.1) and ignores radia-
Then, assuming that the grain and nucleus are spheres of tion pressure, then it is fairly straightforward to compute a
density dg and dn, that Vg is constant with radial distance r, Doppler spectrum by assuming a production size distribu-
and that V << Vg, integrating equation (18) gives a terminal tion and summing over discrete grain emission times and
grain velocity directions (Harmon et al., 1989). Once the nucleus and grain
properties are assumed, then the remaining free parameters
Vt(a) = Cva–1/2 (1 – a/am)1/2 (19)
in the model are the ejection geometry and Z (or am).
where Model spectra have been computed for the coma echoes
from IAA (Harmon et al., 1989) and Hyakutake (Harmon
1/2 et al., 1997). The shape and offset of the IAA coma spec-
3CDVg ZR
Cv = (20) trum could be well modeled (Fig. 10) by invoking a sun-
4d g
ward grain emission fan with centroid aimed below the
comet orbit plane in a direction consistent with the orien-
is a velocity scale factor, and tation of the infrared and visual dust fans. No doubt this
was aided by the fact that IAA was a slow rotator with an
9CDVg Z unusually stable sunward fan (Sekanina, 1988). The model
am = (21)
32π GRdnd g shown in Fig. 10 has Z = 1.2 × 10–5 g/cm2 s and am = 3 cm,
which is consistent with the observed echo polarization and
is a maximum grain size in the gravitational correction fac- gives plausible nucleus mass-loss rates and gas fluxes. A
tor (1 – a/am)1/2. [Equations (20) and (21) are equivalent model spectrum for Hyakutake is shown overplotted in
to equation (4) of Jewitt and Matthews (1999) and equa- Fig. 2. Here a much higher Z of 4 × 10 –4 g/cm2 s [Vt
tion (72) of Gombosi et al. (1986) respectively.] One has (1 cm) = 40 m/s] was required to reproduce the large Dop-
CD = 2 for a solid sphere, although the drag coefficient can pler spread (see discussion in previous section). Since the
274 Comets II

as equation (14) of Harmon et al. (1999), although the cal-

culations in that paper were based on the correct original
equation.] For a < λ/2π one gets a Rayleigh approxima-
tion for M by using the following analytic solution for the
integral
−α
I = CR B(1/2, 15/2 – α)a15/2
m
(26)
where B is the beta function. Implicit in equation (24) is
the assumption that the velocity scale factor Cv is a func-
tion of am. If, on the other hand, one has an independent
estimate of Cv (say, from the width of the Doppler spec-
trum), then one could treat it (and am) as a constant, to give
the modified expression
Fig. 10. Model coma spectrum (dashed line) overplotted on the
OC coma echo for C/IRAS-Araki-Alcock. The data spectrum 4−α
8Cv dg ao
(solid line) has been smoothed to 10-Hz resolution. See text for M(a max ) = σ 1−
details.
3 amax (27)
4 − α [(4 − α)π hI ]−1
amax

dust emission for this fast rotator was more complicated where amax (<am) can be taken as some other (nongravita-
than for IAA, no attempt was made to arrive at a single tional) cutoff size that replaces am as the upper integration
consistent model for the grain emission geometry. limit in equation (25).
4.2.3. Mass-loss rates. If one assumes that the grain In Fig. 11 we show results of mass-loss rate calculations
coma is replenished by continuous particle ejection, then for three comets. Here we have used equation (24) to calcu-
the coma radar cross section can be used to estimate the late M(am) for IAA and Halley, and equation (27) to calcu-
mass-loss rate in large grains. We assume the grains have a late M(amax) for Hyakutake [assuming Vt (1 cm) = 40 m/s].
production-rate size distribution n(a) ∝ a–α. The mass-loss Mie theory was used to calculate Qb assuming the grains
rate M is given by to be spherical snowballs with density dg = 0.5 g/cm3 (re-
am fractive index = 1.4). We took the production rate size dis-
4
M=
3
π dg ∫
ao
n(a )a3da (22) tribution to be an n(a) ∝ a–3.5 power law between ao = 1 µm
and the cutoff size. The α = 3.5 power law was chosen not
The total radar cross section of the grains in the radar beam only because it conforms to size distributions measured for
is Halley (McDonnell et al., 1986) and Hyakutake (Fulle et
am
al., 1997), but also because it has the convenient property
σ=π ∫
ao
n(a)L(a )Q b (a)a2 da (23) of giving an M that is determined primarily by the larger
(radar-reflecting) grains and that is relatively insensitive to
where L(a) is the mean lifetime of a grain of radius a within the precise value of α. The Rayleigh regime (am < λ/2π) in
the beam. If the grains are ejected isotropically and remain Fig. 11 shows the M(am) ∝ am–3 behavior expected from
intact as they traverse the beam, then the mean lifetime is substitution of equation (26) in equation (24). It is this
the mean beam transit time πh/2Vt(a), where h is the half- strong Rayleigh size dependence that requires the presence
width of the cylinder defined by the radar beam at the of large (greater than millimeter-sized) grains in order to
comet. Then, combining equations (19)–(23) gives explain the radar cross sections for reasonable mass-loss
rates; for example, taking am = 1 mm implies an M that
8Rdg 8 1/2 would have a typical comet nucleus losing most of its mass
M(a m ) = σ π Gd n during a single perihelion passage. The M curves flatten out
3 3
at the larger sizes (am > λ/2π), corresponding to large-grain
4−α
(24)
a production rates in the range 3 × 105–1 × 10 6 g/s.
1− o a9/2 − α [(4 − α)π hI ]−1 4.2.4. Comparisons with other mass-loss rate estimates.
m
am
By comparing the radar-derived production rates with other
measurements sensitive to smaller dust particles, we can get
where some idea of the relative importance of the large grains
to the overall particulate population of the coma. Infrared
am a5/2 − α Q b (a ) measurements for IAA (Hanner et al., 1985) gave dust
I = ∫
ao (1 − a/a m )1/2
da (25)
production rates of 1–2 × 105 g/s. This is a bit smaller than
the rates shown in Fig. 11 and would be consistent with an
This is the same as equation (B9) of Harmon et al. (1989). overall production size distribution spectral index α = 3.8.
[An incorrectly rewritten version of this equation appeared Clearly, large grains contributed a substantial fraction of the
 Harmon et al.: Radar Studies of Comet Nuclei and Grain Comae 275

7000-km Goldstone beam. This is supported by the photo-

metric data of Schleicher and Osip (2002), which show a
slow falloff in CN, C2, and dust with increasing aperture
size that is consistent with fragmentation or evaporation of
grains from that comet. Further support comes from Harris
et al. (1997), who argued that evaporation of large icy grains
produced Hyakutake’s spherical gas coma and accounted
for 23% of the comet’s total gas production. This would
give 1 × 106 g/s in secondary gas from grains, so the total
large-grain mass lost to disintegration could have been sig-
nificantly higher than this if the volatile fraction was low.
It is clear that the total mass contained in large grains is
high enough that grain fragmentation could be an important
secondary source of coma gas in the typical active comet.
Finally, it is worthwhile comparing the radar M values
Fig. 11. Mass-loss rate M vs. maximum grain radius am for Com- with those estimated from millimeter-wave continuum ob-
ets Halley (solid), IRAS-Araki-Alcock (dashed), and Hyakutake servations, which are also sensitive to large grains (Jewitt
(dot-dashed). These were computed using the measured radar cross and Luu, 1992). An equivalent continuum equation for M
sections and assuming the grains to be 0.5 g/cm3 snowballs with can be written by replacing σ in equations (24) or (27) with
an a–3.5 production size distribution. Also shown are M curves Sλ2∆2/2kT and replacing Qb in equation (25) with Qa, where
computed on the basis of the measured radio continuum fluxes
S is the continuum flux density, T is grain temperature, and
for Halley and Hyakutake (lighter curves).
Qa is the grain absorption efficiency. This has been used to
compute M curves (Fig. 11) from the 3.5-mm continuum
detection of Halley (Altenhoff et al., 1986) and the 1.1-mm
mass loss for IAA. Comparison of the Halley curve in continuum detection of Hyakutake (Jewitt and Matthews,
Fig. 11 with the dust production rate of 2 × 106 g/s from 1997). [We have not included a curve for IAA, as the 1.3-
infrared measurements indicates large grains constituted a cm continuum detection by Altenhoff et al. (1983) appears
slightly smaller fraction of the mass loss for this comet, to have been dominated by thermal emission from the nu-
although Giotto dust detector results (McDonnell et al., cleus, as was also argued by Harmon et al. (1989).] Note
1986) suggest that Halley’s large-grain production should that these curves do not show the same extreme sensitivity
have dominated the mass loss with M = 5 × 106 g/s at the to am in the Rayleigh regime as the radar curves, which
time of the Arecibo observations. The dust production rate reflects the different behaviors of Qa and Qb. The compari-
of 5 × 106 g/s estimated for Hyakutake (Fulle et al., 1997) son with radar is uncertain because of the sensitivity of the
exceeds by several times the radar-derived rate for am > continuum curves to assumed grain properties such as po-
1 cm (Fig. 11), suggesting that large grains were important rosity and electrical conductivity, although the sensitivity
but not dominant for this comet. to the assumed conductivity becomes less important as the
Since the radar-derived mass-loss rates assume that the larger grains become optically thick. For the curves in
grains remain intact as they traverse the radar beam, the M Fig. 11 we assume the grains to be dirty snowballs with
curves in Fig. 11 are actually lower limits and hence may 0.5 g/cm3 density and 0.01 imaginary part refractive index.
underestimate the relative contribution of large grains to the The radar beam was 4× and 6× larger than the continuum
total particulate mass loss. Grain evaporation and disintegra- beam for Halley and Hyakutake respectively, so any grain
tion are, in fact, believed to be important processes (Hanner, evaporation would also affect the comparison. Note that
1981; Combi, 1994). It has been estimated that (at 1 AU) the continuum curves are significantly higher than the ra-
ejected dirty-ice grains with radii of 1 mm and 1 cm only dar curves for am larger than 1 cm. Including grain evapo-
travel 100 km and 2000 km respectively before evaporat- ration would reduce some of this discrepancy. A possible
ing (Hanner, 1981; Harris et al., 1997). This may explain way to remove the remaining discrepancy is to invoke
why the Arecibo and Goldstone S-band coma echoes for fluffier grains (which would also help to explain the high
IAA gave the same radar cross section despite the fact that grain velocities inferred from the Hyakutake coma spectrum,
the Goldstone beam was 3× wider than the 2200 km sub- as mentioned in section 4.2.1). This is because increasing
tended by the Arecibo beam at the comet, although icy the grain porosity raises the absorption per unit mass (or
grains from IAA were not detected in the infrared obser- opacity κ) as it lowers the backscatter per unit mass, the
vations of Hanner et al. (1985). For Halley, Campbell et combined effect being to bring the radio and radar curves
al. (1989) also suggested that ignoring grain evaporation closer together (Harmon et al., 1997). This implies that
might account for the apparent discrepancy between the κ(1 mm) would have to be higher than the κ(1 mm) = 2–
radar and Giotto grain production rates. Similarly, many of 3 cm2/g that characterizes the curves in Fig. 11. In fact,
the large grains from Hyakutake may have evaporated or Altenhoff et al. (1999) assumed “fluffy dust” with κ(1 mm) =
disintegrated before traversing a substantial fraction of the 75 cm2/g to estimate Hyakutake’s dust production from their
276 Comets II

radio continuum observations. This accounted for the very rings, has significant potential for direct plane-of-sky im-
large discrepancy that they noted between their production aging of the grain comae of close-approaching comets (de
rates and those inferred by Jewitt and Matthews (1997) us- Pater et al., 1994). The VLA resolution is too coarse for nu-
ing a much lower κ(1 mm) = 0.5 cm2/g value typical of in- cleus imaging, but bistatic radar observations with the Very
terstellar dust. Long Baseline Array (VLBA) would be suitable, with reso-
lutions at S- and X-bands of 3 mas and 0.8 mas respectively.
5. FUTURE WORK
5.2. Short-Period Comet Opportunities
5.1. Radar Imaging: Delay-Doppler and
Interferometric Radar observations in the coming years will include a
mix of short-period and new comets. The short-period com-
The highest priority of future cometary radar is to ob- ets include the ecliptic comets (and their Jupiter-family
tain images of the nucleus and/or coma echoes. Imaging subset), with a putative Kuiper belt origin, and the Halley-
could provide data on nucleus size, shape, rotation, and type comets, most of which probably come from the Oort
surface features, as well as the size of the grain coma and cloud (Levison, 1997). The “new” comets include both
its position relative to the nucleus. It can also be used to dynamically new objects and newly discovered long-period
more accurately determine the nucleus albedo and scatter- comets. Although new comets such as IAA may well offer
ing law. Imaging can be done using either the delay-Dop- the best radar opportunities, the short-period comets hold
pler method or an interferometer. some intrinsic interest. They are the most likely targets for
Delay-Doppler combines pulsed or coded transmission spacecraft missions, for which groundbased radar can pro-
with spectral analysis in order to resolve the echo into cells vide both mission support and a complementary dataset.
in delay-Doppler space. The detectability in a given delay- Also, though relatively inactive compared to some new
Doppler cell is roughly given by D/(Nd ND) , where D is comets, they are thought to play an important role in the
the Doppler-only detectability from equation (4) and Nd and interplanetary dust budget and are the source of meteor
ND are the number of delay and Doppler bins, respectively, streams and infrared dust trails; hence, echoes from their
across the target. Any comet nucleus passing within about large-grain comae are of interest. There are several good
0.1 AU should provide a good delay-Doppler imaging op- short-period comet radar opportunities over the next decade
portunity for Arecibo (Harmon et al., 1999), although crude or so. These are listed in Table 5. Below we discuss some
imaging or delay-profiling suitable for size estimation may of the more interesting apparitions. (We include the Encke
be feasible at larger distances. A delay-Doppler image could apparition of 2003 in this discussion and Table 5, even
provide direct information on a nucleus and also be used though the observations planned for that apparition will have
to construct a three-dimensional model of the rotating ob- been done by the time this book goes to press.) The quoted
ject, in a similar manner to work done on near-Earth aster- detectabilities are computed from equation (5) assuming a
oids (Ostro et al., 1995; Hudson and Ostro, 1995). If the 1-h integration time, a nucleus albedo of 0.05, and (unless
radar images have adequate orientational coverage and an otherwise noted) a rotation period of 0.5 d. The D values
adequate time span, then the modeling can decipher the also assume |sinφ| = 1, and therefore represent lower limits.
nucleus spin state. This would be of particular interest for 5.2.1. 2P/Encke. Although one of the most intensely
slow rotators because of their tendency for non-principle- studied of all comets, Encke’s nucleus properties remain
axis rotation (Ostro et al., 2001; Samarasinha and A’Hearn, uncertain. Observations in 2003 should give D ~ 60 at Are-
1991; Hudson and Ostro, 1995; Samarasinha et al., 2004). cibo and ~3 at Goldstone. This may allow some crude delay-
Also, any absolute range measurement would provide even Doppler imaging and a direct size estimate. While not a very
more accurate orbit astrometry than could be derived from active comet, Encke is known to produce centimeter-sized
Doppler alone. For the grain-coma echo, the extra informa- grains and to be the source of the Taurid meteors and an
tion provided by a delay-resolved echo would remove some infrared dust trail (Epifani et al., 2001; Reach et al., 2000).
of the ambiguity encountered in coma-echo modeling us- The large grains may give a weak coma detection.
ing Doppler spectra alone. However, coma delay-Doppler 5.2.2. 73P/Schwassmann-Wachmann 3. This comet
images would pose their own special interpretation prob- makes a very close pass in 2006 and offers a nominally
lems, as the mapping problem is unlike that for a rigid ro- excellent, if unpredictable, radar opportunity. This comet
tating body. Furthermore, unlike the nucleus echo, a coma split into three main pieces during its 1995 apparition, those
echo is likely to be “overspread” (product of delay depth pieces reappearing at the 2001 apparition. If each piece has
and Doppler bandwidth >1), which would require a spe- one-third the mass of a R = 1 km parent body (Boehnhardt
cial observing strategy as discussed by Harmon (2002). et al., 1999), its detectability should be ~1000 at Arecibo
Interferometric imaging offers an alternative to delay- (~60 at Goldstone), making this a good imaging opportu-
Doppler imaging. The Very Large Array (VLA) can poten- nity. Detectable coma echoes are also likely.
tially image coma echoes from Goldstone 3.5-cm transmis- 5.2.3. 8P/Tuttle. This little-studied object is the only
sions with a synthesized beam as small as 0.24 arcsec. This Halley-type comet in this sample and thus the only one
bistatic method, which has been applied successfully to a likely to have an Oort cloud origin. The only known radius
few asteroids as well as Mercury, Venus, Mars, and Saturn’s estimate is R = 7.3 km from optical magnitude measure-
 Harmon et al.: Radar Studies of Comet Nuclei and Grain Comae 277

TABLE 5. Future radar opportunities for short-period et al., 2002). There is a nominally excellent opportunity in
comets (passing within 0.5 AU through year 2020). 2018, although the comet’s large nongravitational accelera-
tion (Jorda and Rickman, 1995) makes the distance predic-
Comet Date (m/d/y)* ∆ (AU)† tion uncertain. Comet 9P/Tempel 1, the target of the Deep
2P/Encke 11/17/2003 0.261 Impact mission, approaches within 0.71 AU in early May
73P/Schwassmann-Wachmann 3 5/12/2006 0.051–0.076‡ 2005, two months before the spacecraft encounter. Taking
8P/Tuttle 1/2/2008 0.252 R = 3 km (Lamy et al., 2001) and p = 41 h (Meech et al.,
6P/d’Arrest 8/10/2008 0.353 [0.375] 2002) gives an Arecibo detectability of only D = 3. Still,
103P/Hartley 2 10/21/2010 0.120 an Arecibo attempt at a nucleus detection at closest ap-
45P/Honda-Mrkos-Pajdušáková 8/15/2011 0.060§ [0.220]
proach is probably warranted. An attempt might also be
2P/Encke 10/17/2013 0.478
made to look for echoes from debris ejected in the July 4,
P/2000 G1 (LINEAR) 3/22/2016 0.032 [0.105]
45P/Honda-Mrkos-Pajdušáková 2/11/2017 0.087 2005, impact experiment, although Tempel 1 will be even
41P/Tuttle-Giacobini-Kresak 3/27/2017 0.136 [0.190] more distant (0.89 AU) at that time. Finally, the Stardust
21P/Giacobini-Zinner 9/11/2018 0.380 mission target, 81P/Wild 2, is not observable from Arecibo
64P/Swift-Gehrels 10/28/2018 0.444 at less than 1.5 AU for the next two decades.
46P/Wirtanen 12/16/2018 0.075
*Date of closest approach. 6. SUMMARY
† Distance from Earth at closest approach (with closest distance

for Arecibo observations, if different, in brackets). Earth-based radar has proven to be an important tool for
‡ Range of distances for fragments B, C, and E. studying close-approaching comets. The various nucleus
§ Just below Goldstone horizon at this distance. detections show comet nuclei to be rough objects with rela-
tively low surface densities. They have also established a
factor-of-10 nucleus size range for this limited sample,
ments by Licandro et al. (2000) at large heliocentric dis- based on the observed range of radar cross sections. A large
tances. This would place it in the Halley size class, so a fraction of the radar-detected comets have been found to
radar-based size estimate would be of considerable inter- show broadband echoes from large coma grains. This has
est. If Tuttle is really this large, it would give D ~ 300 at provided some of the strongest evidence yet for the preva-
Arecibo (~17 at Goldstone). This comet is the parent of the lence of large-grain emission by comets. With radar-derived
Ursid meteor stream (Jenniskens et al., 2002), so there is productions rates ~106 g/s, large (approximately centime-
the potential for a coma echo. ter-sized) grains must constitute a significant fraction of the
5.2.4. 6P/d’Arrest. This second 2008 apparition is less total mass loss for some comets.
favorable than that of Tuttle, owing to the larger ∆ and The full potential of cometary radar will not be realized
southerly declinations. Using R = 2.7 km (Lisse et al., 1999) until radar imaging of a comet is achieved. Delay-Doppler
and the oft-quoted short rotation period of 5.2 h (itself of imaging holds the potential for accurately determining
intrinsic interest) gives D ~ 5 for Arecibo. This comet shows nucleus properties such as size, shape, spin state, albedo,
an antitail (Fulle, 1990) and must therefore produce some and scattering law. An imaged or delay-resolved coma echo
large grains. would also be of considerable interest. A few of the upcom-
5.2.5. 103P/Hartley 2. The small ∆ of this comet in ing short-period comet apparitions may afford opportunities
2010 offers a good radar opportunity despite its apparent for at least crude nucleus imaging. Favorable imaging op-
small size. Using R = 0.56 km (Jorda et al., 2000) gives a portunities from new-comet apparitions are also anticipated.
D ~ 150 at Arecibo and ~9 at Goldstone. This comet is fairly
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and 654 Zelinda. Icarus, 118, 105–131. Wilkening L. L., ed. (1982) Comets. Univ. of Arizona, Tucson.
Nolan M. C., Howell E. S., Harmon J. K., Campbell D. B., Margot 766 pp.
J.-L., and Giorgini J. D. (2001) Arecibo radar observations of Yeomans D. K., Chodas P. W., Keesey M. S., Ostro S. J., Chan-
C/2001A2(B) (LINEAR) (abstract). Bull. Am. Astron. Soc., 33, dler J. F., and Shapiro I. I. (1992) Asteroid and comet orbits
1120–1121. using radar data. Astron. J., 103, 303–317.
280 Comets II
 Samarasinha et al.: Rotation of Cometary Nuclei 281

Rotation of Cometary Nuclei

Nalin H. Samarasinha
National Optical Astronomy Observatory

Béatrice E. A. Mueller
National Optical Astronomy Observatory

Michael J. S. Belton
Belton Space Exploration Initiatives, LLC

Laurent Jorda
Laboratoire d’Astrophysique de Marseille

The current understanding of cometary rotation is reviewed from both theoretical and ob-
servational perspectives. Rigid-body dynamics for principal axis and non-principal-axis rota-
tors are described in terms of an observer’s point of view. Mechanisms for spin-state changes,
corresponding timescales, and spin evolution due to outgassing torques are discussed. Differ-
ent observational techniques and their pros and cons are presented together with the current
status of cometary spin parameters for a variety of comets. The importance of rotation as an
effective probe of the interior of the nucleus is highlighted. Finally, suggestions for future re-
search aimed at presently unresolved problems are made.

1. INTRODUCTION space missions to comets; for example, it allows the mis-

sion planners to assess the orientation of the nucleus dur-
Since the publication of the first Comets volume (Wil- ing a flyby.
kening, 1982), our understanding of the rotation of comet- In the next section, we will discuss basic dynamical as-
ary nuclei has evolved significantly, first due to research pects of cometary rotation, while section 3 deals with ob-
kindled by the apparently contradictory observations of servational techniques and the current status of cometary
Comet 1P/Halley, and more recently due to numerical mod- spin parameters. Section 4 addresses interpretations of ob-
eling of cometary spin complemented by a slowly but servations and some of the current challenges. The final sec-
steadily increasing database on cometary spin parameters. tion discusses suggestions for future research.
Subsequent review papers by Belton (1991), Jewitt (1999),
Jorda and Licandro (2003), and Jorda and Gutiérrez (2002) 2. ROTATIONAL DYNAMICS
highlight many of these advances. In this chapter, we dis-
cuss our current understanding of cometary rotation and the 2.1. Rigid-Body Dynamics
challenges we face in the near future.
Knowledge of the correct rotational state of a cometary The prediction from the icy conglomerate model of the
nucleus is essential for the accurate interpretation of obser- nucleus (Whipple, 1950) and the subsequent spacecraft
vations of the coma and for the determination of nuclear images of Comets 1P/Halley (e.g., Keller et al., 1986; Sag-
activity and its distribution on the surface. The spin state, deev et al., 1986) and 19P/Borrelly (e.g., Soderblom et al.,
orbital motion, and activity of a comet are linked to each 2002) are consistent with a single solid body representing
other. Accurate knowledge of each of these aspects is there- the nucleus. Therefore, in order to explain the rotational
fore required in order to properly understand the others, as dynamics of the nucleus, to the first approximation, we con-
well as to determine how they will evolve. As we will elab- sider it as a rigid body. Chapters in this book on splitting
orate later, ensemble properties of spin parameters — even events (Boehnhardt, 2004), nuclear density estimates (Weiss-
the spin rates alone — can be effectively used to understand man et al., 2004), and formation scenarios (Weidenschilling,
the gross internal structure of cometary nuclei. This has di- 2004) are suggestive of a weak subsurface structure made up
rect implications for understanding the formation of com- of individual cometesimals, and the question of any effects
ets in the solar nebula as well as for devising effective mi- of non-rigid-body behavior are still on the table.
tigation strategies for threats posed by cometary nuclei We use the terms “rotational state” and “spin state” inter-
among the near-Earth-object (NEO) population. In addition, changeably, and they are meant to represent the entire rota-
a priori knowledge of the spin state is necessary for effec- tional state. Similarly, “rotational parameters” and “spin
tive planning and maximization of the science return from parameters” are used interchangeably. However, the term

281
282 Comets II

Fig. 1. (a) Component rotations for short-axis modes (SAM) and

long-axis modes (LAM). Component rotations are depicted in
relation to the long axis. (b) Characteristics of different spin states
as the energy of rotation for a given rotational angular momen-
tum increases from the least-energetic state (rotation around the
2
short axis, M = I ) to the most energetic state (rotation around
2E 2 s
the long axis, M 2E
= Il). Behavior of the component periods Pφ and
Pψ are indicated for spin states near principal-axis states. For SAM
states, the amplitude of the oscillatory motion of the long axis,
Aψ (as well as the nodding amplitude of the long axis, Aθ), in-
creases as the spin state becomes more energetic. For LAM states,
the mean value of the angle θ (as well as the amplitude of the
nodding motion of the long axis, Aθ) decreases as the kinetic
energy of the rotational state increases.

“spin vector” specifically refers to the instantaneous angular ertia around the three principal axes satisfy the condition
velocity vector. Is ≥ Ii ≥ Il. Spin states with kinetic energies in between are
The most stable rotational state of a rigid body is de- characterized by two independent periods. These spin states
fined by the least-energetic state for a given rotational an- are known as non-principal-axis (NPA) states (also called
gular momentum (this does not mean that the rotational complex rotational states, or tumbling motion, with the latter
angular momentum is fixed, but for each given rotational term primarily used by the asteroid community). It should
angular momentum of the rigid body, there is a correspond- be stressed that, unlike for PA states, the spin vector and
ing lowest-energy spin state). This lowest-energy spin state M are not parallel to each other for NPA states. A nucleus
is represented by a simple rotation around the short princi- having a spin state other than the PA rotation around the
pal axis of the nucleus occurring at a constant angular ve- short axis is in an excited rotational state.
locity. (Note that in this chapter, unless specified otherwise, Figure 1 shows the basic characteristics of different rigid
long, intermediate, and short axes, denoted by l, i, and s body rotational states. The short-axis-mode (SAM) and
respectively, refer to the mutually orthogonal principal axes long-axis-mode (LAM) states (Julian, 1987) differ from
of the nucleus as determined by the inertia ellipsoid. De- each other depending on whether the short or the long axis
pending on the shape and the internal density distribution, “encircles” the rotational angular momentum vector, M,
these axes may have offsets from the physical axes defined which is fixed in the inertial frame. The SAM states are less
by an ellipsoidal fit to the physical shape.) For this spin energetic than the LAM states. The component periods can
state, the rotational angular momentum, M, and the rota- be defined in terms of Euler angles θ, φ, and ψ (Fig. 2).
2
tional kinetic energy, E, are given by M 2E
= Is, where Is is Most cometary nuclei are elongated (i.e., closer to prolates
the moment of inertia around the short axis. Since the nu- than oblates), as implicated by large lightcurve amplitudes
cleus is only rotating around the short axis, this is called a and spacecraft images. From an observational point of view,
principal-axis (PA) spin state. Other PA spin states include component rotations defined in terms of the long axis are
the dynamically unstable rotation around the intermediate easier to discern than those defined with respect to the short
2
axis (e.g., Landau and Lifshitz, 1976) corresponding to M 2E
= axis. Therefore, following Belton (1991), Belton et al. (1991),
Ii and that around the long axis, which characterizes the and Samarasinha and A’Hearn (1991), we adopt the system
of Euler angles where θ defines the angle between M and
2
most energetic rotational state at M 2E
= Il. Moments of in-
 Samarasinha et al.: Rotation of Cometary Nuclei 283

the long axis, ψ defines the rotation around the long axis tional angular momentum vector, which requires two pa-
itself, and φ defines the precession of the long axis around rameters; and the reference values for the Euler angles φ
M as depicted in Fig. 2. [Many textbooks (e.g., Landau and and ψ at a given time.
Lifshitz, 1976) use a different system of Euler angles appro- The rate of change of M of the rigid body in an inertial
priate for flattened objects such as Earth, as opposed to frame (with the origin at the center of mass) is given by
elongated objects; see Jorda and Licandro (2003) for a
comparison between the two systems.] In Fig. 1, Pθ refers
dM
to the period of the nodding/nutation motion of the long =N (1)
axis, Pψ to the period of oscillation (in the case of SAM) dt inertial
or rotation (in the case of LAM) of the long axis around
itself, and Pφ to the mean period of precession of the long where N is the external torque on the body. Since the rate
axis around M (for an asymmetric rotator, the rate of change of change of M in the inertial and in the body frames are
of φ is periodic with Pψ/2 and therefore we consider the related by
time-averaged mean value for Pφ). The period Pθ is equal
to Pψ for SAM or exactly Pψ/2 for LAM, leaving only two
dM dM
independent periods Pφ and Pψ. In general, Pφ ≠ Pψ and there- = +Ω×M (2)
fore for a random NPA spin state, even approximately the dt inertial dt body
same orientations of the rotator in the inertial frame are rare.
Principal-axis spin states can be uniquely defined with
dM
three independent parameters and one initial condition: the +Ω × M=N (3)
period of rotation; the direction of the rotational angular dt body
momentum vector, which requires two parameters; and the
direction for the reference longitude of the nucleus at a where Ω is the angular velocity. By dropping the “body”
given time. For NPA spin states, six independent parameters subscript and expressing M in terms of moment of inertia,
and two initial conditions are necessary: e.g., Pφ; Pψ; ratio we have
of moments of inertia Il/Is and Ii/Is; direction of the rota-
d(IΩ)
+ Ω × (IΩ) = N (4)
dt

where I is the moment-of-inertia tensor. Since the moment

of inertia is constant for a rigid body, we derive Euler’s
equations of motion (e.g., Landau and Lifshitz, 1976)

IlWl = (Ii – Is)ΩiΩs + Nl (5)

IiWi = (Is – Il)ΩsΩl + Ni (6)

and

IsWs = (Il – Ii)ΩlΩi + Ns (7)

The subscripts denote the components along the three prin-

cipal axes. If α jk represents the direction cosine between the
body frame axis j and the inertial frame axis k, then the
transformation between the two frames is governed by the
following nine scalar equations (Julian, 1990)

alk = Ωsαik – Ωiαsk (8)

aik = Ωlαsk – Ωsαlk (9)

Fig. 2. Euler angles θ, φ, and ψ. The axes X, Y, and Z form a
righthanded orthogonal coordinate system in the inertial frame. and
Principal axes l, i, and s respectively form the righthanded body
frame coordinate system. The rotational angular momentum vec- ask = Ωiαlk – Ωlαik (10)
tor, M, coincides with the Z axis and is fixed in the inertial frame
in the absence of external torques. where k = X, Y, and Z. The rotational motion of the nucleus
284 Comets II

in the inertial frame can be followed by simultaneously In order to derive the reaction torque, the reaction force
solving equations (5)–(10). For a force-free motion, com- needs to be evaluated. The reaction force, dFi,dS, due to the
ponent torques are zero and one obtains an analytical solu- gas species, i, sublimating from an elemental surface area,
tion in terms of Jacobian elliptic functions (Landau and dS, can be expressed as
Lifshitz, 1976). When there are nonzero torques, in general
one cannot derive an analytical solution and should resort dFi,dS = –αmiZivdS (11)
to numerical integration of Euler’s equations (also see sec-
tion 2.3). For further details on rigid-body rotation in a com- where α is a momentum transfer efficiency, mi is the mo-
etary context, the reader is referred to Samarasinha and lecular weight of the gas species, Zi is the sublimation rate
A’Hearn (1991), Belton (1991), and Jorda and Licandro for the gas species in molecules per unit surface area, and
(2003). v is the outflow velocity of the gas species at the surface.
The net reaction force F can be determined by integrating
2.2. Mechanisms for Changing the Spin States over the entire nuclear surface and then summing up for
all sublimating gas species, i.e.,
The spin state of a cometary nucleus will evolve with
time due to various reasons. Fortunately, for many comets,
the timescales for such changes are sufficiently large (i.e.,
many orbital periods) and little or no measurable changes
F=− ∑ ∫
gas species
surface
αm i Z i vdS (12)

in the rotational parameters occur from one orbit to another

(Schleicher and Bus, 1991; Mueller and Ferrin, 1996). F can be evaluated using simplified assumptions: e.g.,
Protocomets have undergone multiple collisions while water is the dominant gas species, outgassing occurs pri-
being scattered to the Oort cloud from the giant-planet re- marily from the sunlit surface, and the outgassing velocity
gion (Stern and Weissman, 2001) or while in the Kuiper belt is normal to the surface. It should be stressed that the
(Stern, 1995; Davis and Farinella, 1997). In addition, many momentum transfer efficiency, which is on the order of one,
present-day Kuiper belt comets could be breakup fragments depends on many factors including the degree of collima-
due to collisional events (Farinella and Davis, 1996). There- tion of outgassing, the relationship used to compute the
fore, it is unlikely that the spin states of most dynamically outflow velocity v in equation (11), and the amount of back
new comets from the Oort cloud and especially those from pressure on the nucleus — which in turn will be based on
the Kuiper belt are of primordial origin. the near-nucleus coma environment and the gas and dust
In general, a sufficiently large collision or any of the production rates, among others (Skorov and Rickman, 1999,
other mechanisms described below could result in an ex- and references therein; Rodionov et al., 2002). This non-
cited spin state. The stresses and strains associated with the gravitational force alters the orbital motion of the comet,
NPA rotation of an excited nucleus would result in a loss making long-term orbital predictions a difficult task. For
of mechanical energy. Consequently, in the absence of any further details on the nongravitational force and its effect
further excitation events, the spin state will damp toward on the orbital motion, see Yeomans et al. (2004).
the stable, least-energetic state (e.g., Burns and Safronov, The net torque, N, on the nucleus due to outgassing
1973; Efroimsky, 2001, and references therein). Therefore, forces can be expressed as
whether the current spin state of a cometary nucleus is ex-
cited or not will depend on the timescale for the relevant
excitation mechanism and the damping timescale, as well
as on when and how long the excitation mechanism was
N=− ∑ ∫
gas species
surface
αm i Z i (r × v)dS (13)

active. For extensive discussions on timescales, see Jewitt

(1999) and Jorda and Licandro (2003). where r is the radial vector from the center of mass to the
2.2.1. Torques due to outgassing. Outgassing of vola- elemental surface area dS.
tiles from the nucleus causes a reaction force on the nucleus. The component torques Nl, Ni, and Ns along the princi-
In addition to changing the orbital motion of a comet, it pal axes can be used to numerically solve Euler’s equations
generates a net torque on the nucleus resulting in changes of motion described in section 2.1. This outgassing torque
of the nuclear spin state (Whipple, 1950, 1982). This is the may alter the spin state of the nucleus in two ways: an in-
2
primary mechanism for altering the spin states of comets. crease (or decrease) of M2E
for the spin state and a change
The outgassing torque on a nucleus alters a PA spin state in M. A change in M can manifest itself either as a change
of the lowest energy. It produces a change in the spin period in its magnitude and/or its direction. (In the literature, a
and in the direction of the angular momentum vector with a change in the direction of M is routinely called precession,
timescale that can be as short as a single orbit (e.g., Samara- which is a forced motion of M and therefore is entirely dif-
sinha et al., 1986; Jewitt, 1992). It can also trigger excited ferent from the free precession of the rigid-body motion de-
spin states with a timescale that is not fully understood at scribed in section 2.1.) Specific model calculations were
the moment, but could be on the order of several orbits for carried out by different investigators to assess the changes
small, very active comets (Jorda and Gutiérrez, 2002). in the spin state due to outgassing torques (e.g., Wilhelm,
 Samarasinha et al.: Rotation of Cometary Nuclei 285

1987; Peale and Lissauer, 1989; Julian, 1990; Samarasinha 2.2.5. Other mechanisms. There are a few other mech-
and Belton, 1995; Szegö et al., 2001; Jorda and Gutiérrez, anisms proposed in the literature for altering spin states.
2002). The reader’s attention is also drawn to section 2.3 These include shrinkage of a porous cometary nucleus
where we discuss long-term spin evolution. (Watanabe, 1992b) as a spin-up mechanism and angular
2.2.2. Changes to the moment of inertia due to mass loss momentum drain due to preferential escape of particles
and splitting events. Another mechanism for altering spin from equatorial regions (Wallis, 1984) as a mechanism for
states is via changes to the moment of inertia of the nucleus nucleus spin-down. The ice-skater model by Watanabe was
(cf. equation (4)). There are two primary mechanisms for proposed to explain the observed rapid spin-up of Comet
changing the moment of inertia tensor: (1) mass loss of Levy (C/1990 K1).
volatiles and dust associated with regular nuclear outgas- In addition, the Yarkovsky effect (or specifically, the so-
sing and (2) splitting events of the nucleus (Boehnhardt, called YORP effect due to the resultant torque) could alter
2004). For cometary nuclei, the timescale for changing the spin states (Rubincam, 2000). Changes of the angular mo-
spin state due to sublimation-caused mass loss, τ massloss, is mentum are caused by the thermal lag between absorption
much larger than that due to outgassing torques, τ torque. This of sunlight and its reradiation as thermal radiation for ir-
justifies the adoption of Euler’s equations of motion for regularly shaped objects. The timescale, τYarkovsky, for spin-
monitoring the spin-state evolution rather than the more state changes due to this effect is much larger than for other
general Liouville’s equation, which allows for changes in mechanisms (Jorda and Gutiérrez, 2002). However, τYarkovsky
the moment of inertia. In general, τ massloss is at least a few becomes smaller for subkilometer nuclei since the Yarkov-
tens of orbits for most comets (Jewitt, 1999; Jorda and sky force (and consequently τYarkovsky as well) has a radius-
Licandro, 2003). squared dependence (Rubincam, 2000).
The timescale for changes in the spin state associated
with splitting events, τsplitting, is uncertain because such 2.3. Long-Term Evolution of Spin States
events themselves are stochastic in nature. Chen and Jewitt
(1994) estimated a lower limit to the splitting timescale of While any of the above mechanisms can alter the spin
100 yr per comet. Assuming few splitting events are re- state of a nucleus, as discussed earlier, many are stochastic
quired to appreciably alter the moment-of-inertia tensor and in nature or have large timescales. Therefore, the outgas-
hence produce an observationally detectable change in the sing torque is the primary mechanism of spin-state alter-
spin state (cf. Watanabe, 1992a), the value of τsplitting for ation (also Fig. 2 of Jewitt, 1999) for which the monitoring
most comets is likely to be larger than 100 yr. of the long-term spin evolution is feasible. After the ini-
2.2.3. Collisions with another object. Another stochas- tial prediction by Whipple (1950) that outgassing can alter
tic mechanism that is capable of altering the spin states is cometary spin, Whipple and Sekanina (1979) presented a
collision of the cometary nucleus with another solar sys- model where the spin evolution caused by outgassing can
tem object of sufficient momentum — typically an asteroid be evaluated. Unfortunately, that model adopts an oblate
(e.g., Sekanina, 1987a; Samarasinha and A’Hearn, 1991). nucleus (whereas observations suggest elongated shapes)
Comets that have low orbital inclinations to the ecliptic and only the forced-precession of the nucleus is considered
(e.g., Jupiter-family comets) are more likely than high-in- (i.e., no excitation of the nucleus is allowed), therefore limit-
clination comets to undergo frequent collisions with another ing its applicability. In the context of understanding Comet
solar system object. In other words, the timescale, τcollision, 1P/Halley’s spin state, Wilhelm (1987), Julian (1988, 1990),
for spin-state change depends strongly on the orbit of the and Peale and Lissauer (1989) carried out numerical moni-
comet. Even for such low-inclination comets, τcollision is toring of the spin state in order to study changes due to out-
expected to be larger than that for the mechanisms described gassing torques. All of them found that outgassing torques
earlier (cf. Farinella et al., 1998; also D. Durda, personal can cause changes in the spin state in a single orbit. Nu-
communication, 2002). merical studies by Samarasinha and Belton (1995) cover-
2.2.4. Tidal torques. Tidal torques primarily due to the ing multiple orbits demonstrate that Halley-like nuclei can
Sun or Jupiter could also alter cometary spin states. The be excited due to the multiorbit cumulative effects of the
differential gravitational potential experienced by different outgassing torques. Small, highly active nuclei with local-
parts of the nucleus causes a net torque on the nucleus. It ized outgassing are prime candidates for excitation. For ex-
could arise either due to the tidal deformation of the nucleus ample, Comet 46P/Wirtanen may undergo observable spin-
or due to the shape of the nucleus. To correctly evaluate state changes during a single orbit (Samarasinha et al., 1996;
the timescale for spin-state change due to tidal torques, τ tidal, Jorda and Licandro, 2003). Monitoring of such objects pro-
the torques need to be integrated over many orbits prop- vide a golden opportunity to accurately assess the nongravi-
erly accounting for rotational and orbital cancellations. This tational forces and torques due to outgassing.
in effect would prolong the timescale. However, the spin Many early studies used prolate or near-prolate shapes
state could be significantly altered for a sufficiently close to investigate the spin evolution due to outgassing torques.
encounter with a planet, i.e., within few planetary radii Recent work by Jorda and Gutiérrez (2002) (also Gutiérrez
(Scheeres et al., 2000). Such close encounters are more et al., 2002) shows that nuclei with irregular shapes and
likely for Jupiter-family comets, but are still rare. three unequal moments of inertia are more difficult to ex-
286 Comets II

cite than prolates. Numerical studies by N. H. Samarasinha term “sidereal” may not be the most suitable. However, the
(unpublished data, 1995) using triaxial shapes show the analogous periods of rotation (i.e., independent of the Sun-
same tendency. It should be stressed that the process of comet-Earth geometry and any changes in it) can be defined
excitation is not forbidden for complex-shaped nuclei, but in terms of the periods associated with the Euler angles (see
only that it is not as efficient as that for prolates. In addition, section 2.1).
as one may expect, fast rotators are much more difficult to There are two primary observational techniques to de-
excite than slow rotators. We note that sometimes in the rive rotational periods: (1) rotational lightcurve observa-
literature, the timescale for spin-state changes due to outgas- tions consisting of a time series of photometric variations
sing torques, τtorque, and the excitation timescale, τ excitation, are and (2) periodic variability of the coma structure when the
used interchangeably. In light of the above results, τ torque nucleus is active. In general, the former provides more pre-
should be considered only as a lower limit to τexcitation. Recent cise periods, and this is especially true in the case of NPA
numerical calculations for Comet 46P/Wirtanen by Jorda rotators. The periods derived directly from lightcurve ob-
and Gutiérrez (2002), which still need to be confirmed and servations correspond to “synodic” periods rather than to
generalized to other comets, suggest that τexcitation for objects “sidereal” periods. The rotational lightcurves themselves
with unequal moments of inertia could be at least one order can be categorized into two categories: lightcurves of bare
of magnitude larger than that for a prolate body. nuclei, and lightcurves that represent changes in nuclear
Multiorbit, long-term numerical monitoring of spin states activity. The “synodic” periods from the latter category of
by Samarasinha (1997, 2003) indicate that in the majority lightcurves depend on the changes in the Sun-comet orien-
of the cases (especially when a dominant active region is tation during the observing window and therefore the term
present), the rotational angular momentum vector of the “synodic” has the classical definition. This period is also
spin state evolves toward the orbital direction of the peak known as the “solar day.” On the other hand, the “synodic”
outgassing or that directly opposite to it. This occurs since periods from the lightcurves of bare nuclei depend addi-
such a configuration will present the least net torque in the tionally on the changes in the Earth-comet orientation dur-
inertial frame when averaged over an orbit. Analytical treat- ing the observing window. Therefore, in this case, the term
ment of the problem by Neishtadt et al. (2002) confirmed “synodic” has the same meaning as that used by the aster-
this as a main evolutionary path whereby they also explore oid community (in contrast to its classical definition). The
other paths. If indeed this evolutionary scenario is accurate, changes in the Sun-comet-Earth geometry can also affect
one may find many evolved comets with their rotational the period determinations based on the variability of coma
angular momentum vectors directed toward or near the structures. In principle, model fittings (including knowledge
orbital plane. Unfortunately, the current database is not of the rotational angular momentum vector) are required for
sufficiently large enough to make a robust assessment. the derivation of “sidereal” periods. In this chapter, unless
specified otherwise, rotational periods based on observa-
3. OBSERVATIONAL tions refer to “synodic” periods.
TECHNIQUES AND DATA Depending on the spin parameters and/or the Sun-comet-
Earth geometry, cometary activity can cause a component
To derive the rotational state of a cometary nucleus, the period of a NPA spin state to become masked [cf. 1P/Halley
main parameters to be determined are the rotational peri- (Belton et al., 1991)]. The reader should be alert to this
od(s) and the direction of M. The axial ratio(s), especially possibility.
important for the NPA rotators, are a byproduct of the rel- 3.1.1. Rotational lightcurves. The ideal rotational
evant observations, namely lightcurve observations. For lightcurve requires the nucleus to be entirely inactive, but
example, under the assumption of Lambertian scattering, a scenario where the flux within the photometric aperture
for a PA rotator, the lightcurve amplitude of a bare nucleus is dominated by the scattered solar light from the nucleus
will provide a lower limit to the ratio between long and (rather than from the coma) can still provide reliable results.
intermediate physical axes (see also Lamy et al., 2004). Rotational lightcurves of the nucleus are therefore observed
Below is a summary of the observational techniques; the at large heliocentric distances when the comet is relatively
reader is also referred to Belton (1991) for additional details. dim. This makes lightcurve observations of bare nuclei
challenging, requiring relatively large telescopes and a sig-
3.1. Rotational Periods nificant amount of observing time.
If the spatial resolution is adequate, even when the nu-
For a PA rotator, one of the fundamental parameters of cleus is active, the coma contamination can be effectively
rotation is given by the sidereal rotational period (i.e., the subtracted to derive the flux contribution from the nucleus.
time required to make a complete cycle of rotation around For successful coma subtraction, the spatial resolution
the fixed axis of rotation as seen by an inertial observer — should be such that the flux in the central pixel is domi-
in this case distant stars). The sidereal period is indepen- nated by the scattered solar light from the nucleus. This
dent of the Sun-comet-Earth geometry or any changes in it. technique has been routinely applied for Hubble Space
For a NPA spin state, since not all the component rotations Telescope (HST) observations by Lamy and colleagues to
occur with respect to axes fixed in an inertial frame, the estimate the nuclear sizes of comets (see Lamy et al., 2004).
 Samarasinha et al.: Rotation of Cometary Nuclei 287

Fig. 3. (a) Lightcurve data for Comet 28P/Neujmin 1 in the R filter as a function of time. The magnitudes are normalized for helio-
centric and geocentric distances of 1 AU each and a phase angle of 0°. Time is expressed in terms of Julian days (JD). (b) Fourier
power spectrum corresponding to the data. (c) Power spectrum, after application of the clean algorithm. (d) Rotationally phased lightcurve
data for the rotation period of 12.6 h.

Such multiple observations of the same comet in a time Dworetsky, 1983; Fernández et al., 2000), least-squares fit
series will yield estimates of rotational periods (e.g., Lamy of a sine curve (e.g., Lamy et al., 1998a), and wavelet analy-
et al., 1998a). sis (Foster, 1996). The Fourier technique is often coupled
As mentioned earlier, if the nuclear activity is highly with a subsequent application of a clean algorithm (e.g.,
modulated by the rotation (e.g., the turning on and off of Roberts et al., 1987) to “clean” the Fourier spectrum from
jets in response to insolation), even a lightcurve constructed aliases and spurious periods introduced by uneven sampling
by a series of photometric measurements, where the flux and observational gaps. During this process, most of the har-
is dominated by the variable coma, can be effectively used monics get cleaned out too. In general, the clean algorithm
to probe the nuclear rotation. For example, lightcurves in would yield accurate periods, but one should be alert to the
dust and in emission species for Comet 1P/Halley were used possibility of it occasionally cleaning out the correct peri-
to derive rotational signatures of the nucleus (Millis and od(s) (cf. Foster, 1995).
Schleicher, 1986; Schleicher et al., 1990). Figure 3 shows a rotational lightcurve of the nucleus of
Extraction of periods from the lightcurves can be Comet 28P/Neujmin 1 taken on April 27–30, 2002 (Mueller
achieved through different techniques. Among these are et al., 2002a). Application of WindowClean (Belton and
Fourier analysis (e.g., Deeming, 1975; Belton et al., 1991), Gandhi, 1988), a clean algorithm, to the output from the
phase dispersion minimization (e.g., Stellingwerf, 1978; Fourier analysis (dirty spectrum), identifies the dominant
Millis and Schleicher, 1986), string length minimization (e.g., signature corresponding to the lightcurve data. In interpret-
288 Comets II

rate of the feature. The features themselves may require

image enhancement, and because of the unintended artifacts
introduced, some enhancement techniques are preferred
over others for this purpose (Larson and Slaughter, 1991;
Schleicher and Farnham, 2004). It should be pointed out
that this technique could be considered as a more reliable
modification of the Halo (also known as the Zero Date)
method (Whipple, 1978; Sekanina, 1981a). The latter has
a tendency to produce spurious results (Whipple, 1982;
A’Hearn, 1988) since it uses the coma (or feature) diam-
eter and an assumed expansion rate in the calculations.
3.1.3. Other techniques. Radar observations can yield
estimates for rotation periods based on the Doppler band-
width. However, the values of the nuclear radius and the
angle between the instantaneous spin vector and the line
of sight must be known to derive a unique value (see Har-
mon et al., 2004). In addition, similar to asteroid 4179 Tou-
tatis, sufficient radar image coverage in the observing geom-
etry and time domains could yield the solution for the entire
spin state (Hudson and Ostro, 1995). However, this has yet
Fig. 4. These 11-µm images of Comet Hale-Bopp (C/1995 O1) to be carried out in the case of a comet. Due to the ∆–4
cover an entire rotational cycle (adapted from Lisse et al., 1999). dependence for the radar signal, where ∆ is the geocentric
The images are enhanced and the brightness scale is nonlinear. distance, only comets that will have close approaches to
The nucleus is at the center of each panel. The rotational phase Earth can be probed via radar techniques.
(in white) increases from left to right and from top to bottom. In principle, the curvature of jet features and their evo-
Notice the outward movement of coma features during the rota-
lution could also be used to determine the rotation period
tion cycle.
as well as the spin axis (e.g., Larson and Minton, 1972;
Sekanina and Larson, 1986, and references therein). But
due to the multiparameter nature of the problem and the
many unknowns associated with this quasinumerical ap-
ing the dominant frequency, f, in the cleaned spectrum, it proach, the results are often not accurate. Despite this un-
is assumed that the rotational signature is due to the shape reliability, the solutions based on the curvature of jets could
rather than due to an albedo feature on the surface. Hence serve as useful but crude estimates in some cases. At this
the corresponding synodic rotational period, P, and the fre- point, it should be emphasized that determinations based
quency f are related by on jet curvatures assume outgassing is confined to a local-
ized active region on the surface of the nucleus. There is a
2
P= (14) competing school of thought that argues that coma struc-
f tures are not due to localized outgassing but are caused by
hydrodynamical effects due to topographical variations on
When interpreting lightcurve signatures, one has to be alert a uniformly outgassing surface (Crifo et al., 2004, and ref-
to the possibility of spurious signatures introduced due to erences therein). If topography rather than localized out-
temporal seeing variations (Licandro et al., 2000). gassing is indeed primarily responsible for coma structures,
3.1.2. Repetitive coma structures. Repetitive structures then adoption of jet curvature as a tool to determine rota-
in cometary comae can also be used to determine rotation tion periods needs to be reassessed.
periods. Figure 4 shows the repetitive coma morphology for
Comet Hale-Bopp (C/1995 O1) while it was near perihelion. 3.2. Observational Manifestation of
Care should be taken to confirm that the repetitive structure Non-Principal-Axis Rotational Periods
is indeed due to the rotation and corresponds to successive
rotation cycles. Temporal monitoring of the evolution of fea- Clearly, the PA spin states will show a single period (and
tures over a rotation cycle [e.g., similar to the 11-µm im- perhaps its harmonics) in the lightcurve, which can be
ages of Comet Hale-Bopp (C/1995 O1) from Lisse et al. readily used to deduce the rotation period of the nucleus
(1999), which cover an entire rotational cycle; see Fig. 4] using equation (14). On the other hand, as discussed in
and a consistency check for the outflow velocity derived section 2.1, the NPA states have two independent periods,
using two adjacent repetitive features are two such checks. Pφ and Pψ. How exactly do these periods manifest them-
Multiple images taken at different times showing the out- selves in the lightcurve? In the following discussion, what
ward movement of the same repetitive feature may yield one directly derives from the periodic signatures in the
the rotation period as well as an estimate for the expansion lightcurves correspond to “synodic” periods. However, if
 Samarasinha et al.: Rotation of Cometary Nuclei 289

Fig. 5. (a) A simulated bare-nucleus lightcurve for a 5.6 × 3.1 × 2.5-km ellipsoidal NPA rotator. Pφ and Pψ are 9.168 h and 6.754 h
respectively. A random 5% noise is added to the lightcurve data. Consecutive data points are connected only to guide the eye. (b) Fourier
power spectrum. (c) Cleaned Fourier spectrum. The primary signatures are present at 1/Pφ, 2/Pφ, and (2/Pφ + 2/Pψ). The very low sig-
nature between 1/Pφ and 2/Pφ, which was not fully cleaned out, is a daily alias of 1/Pφ.

the changes in the Sun-comet-Earth geometries during the be present in the lightcurve, or instead of 2/Pφ, 1/Pφ might
observing windows are sufficiently small, quick identifica- be present. This depends on (1) the orientation of the Earth
tions with periods Pφ and Pψ are possible. (observer) with respect to the direction of M, (2) the ori-
Analysis of bare-nucleus model lightcurves with elon- entation of the Earth with respect to the cone swept out by
gated but triaxial ellipsoidal shapes for a limited number the long axis (due to the precessional motion in the case of
of SAM and LAM states indicate that for most cases the a LAM state), (3) the nuclear shape, (4) observational time
major signatures of the Fourier spectrum are at 2/Pφ and coverage, and (5) the quality of the data. In addition, the
(2/Pφ + 2/Pψ) and multiples of these periods (Kaasalainen, relative strengths of the major signatures also depend on
2001; Mueller et al., 2002b). [Kaasalainen (2001) used the similar factors. Clearly, a detailed investigation of the pa-
same set of Euler angles as described above for LAM states, rameter space is warranted, and such efforts are currently
but he prefers the system of Euler angles used in Landau underway.
and Lifshitz (1976) for SAM states because of certain sym- If the nucleus is close to axial symmetry, for example, in
metry considerations.] Figure 5 shows a simulated light- the case of a near-prolate, a bare-nucleus lightcurve might
curve for a NPA rotator, as well as the dominant signatures not indicate any signature related to Pψ. An observer may
present in the lightcurve. However, for specific scenarios, identify the lightcurve period with the rotation period of a
the situation is much more complex. For example, our cur- PA rotator, whereas it really relates to the precession of the
rent understanding based on limited exploration of the pa- long axis. Repeated lightcurve observations of the same ob-
rameter space suggests that both rotation periods might not ject at different observing geometries or coma morphologies
290 Comets II

may provide evidence that prior determinations are in fact spin axis (Soderblom et al., 2002). Farnham and Cochran
in error. (2002) and Schleicher et al. (2003) monitored the position
angle of this jet at different times using groundbased im-
3.3. Direction of the Rotational aging. This enabled them to determine the direction of the
Angular Momentum spin axis by finding the common direction of the intersec-
tion for all the position angles. The solution (both sets of
To specify the spin state of a comet, the direction of the authors derive values within one degree of each other) is
rotational angular momentum must be known. In the case consistent with a restricted set of solutions obtained by
of a PA rotator, this means determining the spin-axis direc- Samarasinha and Mueller (2002) using the position angle
tion. Similar to the case of determining rotation period(s), of this polar jet and the nucleus lightcurve amplitude. It is
the relevant techniques are primarily based on rotational not clear whether strong active regions near poles are a
lightcurves or coma morphology. common occurrence among evolved comets. However, if
3.3.1. Rotational lightcurves. The brightness and am- multiple position-angle determinations would yield consis-
plitude of a rotational lightcurve depends on (1) the rota- tent results for the spin-axis direction, determinations of the
tional phase, (2) the nuclear shape and size, (3) the aspect spin axis based on position angles might prove to be a use-
angle, and (4) the scattering effects (including the solar ful technique. Again, cross-checking results obtained from
phase angle). In particular, the lightcurve amplitude strongly different techniques is advised. This technique is not ca-
depends on the nuclear shape and the aspect angle. Using pable of determining the sense of rotation. The curvatures
these properties, multi-epoch lightcurve observations can be of jet structures due to rotation are useful for that purpose.
used to derive spin vectors, and this is indeed the case for Again, this discussion is based on the assumption that
a number of asteroids. The magnitude-amplitude method an active region rather than the topography of the nucleus
(Magnusson et al., 1989, and references therein) which uses is responsible for the coma structure. At this time, it is not
both the magnitude and the amplitude, enables calculation of clear what the implications are for the latter hypothesis
axial ratios and the spin pole. This process assumes that the (Crifo et al., 2004) since detailed simulations are yet to be
variations in the lightcurve amplitude are primarily due to carried out.
the viewing geometry. Since the cometary lightcurve obser-
vations could be contaminated with an unknown low-level 3.4. Individual Comets
coma, it introduces an additional complexity to the prob-
lem. Therefore, care should be taken in the interpretation At present, the entire spin state of a cometary nucleus
of the results based on the magnitude-amplitude method. On is known only in the case of three comets, 1P/Halley (Belton
the other hand, the epoch method (Magnusson et al., 1989, et al., 1991; Samarasinha and A’Hearn, 1991), 19P/Bor-
and references therein) is less sensitive to this issue since relly (Farnham and Cochran, 2002; Mueller and Samara-
it relies on a specific but accurately determined “feature” sinha, 2002; Schleicher et al., 2003; Boice et al., 2003), and
(or a phase) in the lightcurve. However, to our knowledge, Hyakutake (C/1996 B2) (Schleicher and Woodney, 2003).
there are no cometary spin-axis determinations based en- However, even in the case of 1P/Halley, some controversy
tirely on lightcurve observations, but we hope with the in- exists (Szegö, 1995). For 19 other comets, reasonably good
creasing multi-epoch observations this will soon be realized. estimates of spin periodicities are available (Table 1). For
3.3.2. Coma morphology. In a modification of his ear- some of these comets, information on the rotational angu-
lier model (Sekanina, 1979), which aimed at explaining fan- lar momentum vector is available but sometimes the sense
shaped comae, Sekanina (1987b) proposed that such features of rotation is not known. For other comets only periodicities
seen in many comets are due to ejecta from a high-latitude are known. Comets 19P/Borrelly and 1P/Halley are unique
active region. In particular, if the active region is in the sun- in that they both were the subjects of successful space mis-
light over the entire rotation cycle, the fan is bounded by the sion encounters. In both cases, different, but critical, im-
boundary of the cone swept out due to the rotation of the aging data for the determination of the spin state were ac-
nucleus. In many instances, due to projection effects, the fan quired. Hyakutake (C/1996 B2) is unique because of its
can manifest itself as two bright jets at the boundary of the close perigee during its 1996 apparition and the concomi-
cone. Therefore, the bisector of the fan (when the active re- tant rapid change and the wide range of viewing geometry.
gion is constantly in sunlight) would yield the projected Hale-Bopp (C/1995 O1) was special because of its highly
spin-axis direction. Sekanina has applied his fan model to structured coma. In addition, its intrinsic brightness yielded
several comets, but there is no definite confirmation regard- an extended apparition that allowed a wide range of observ-
ing the reliability of this technique (Belton, 1991). While ing geometries. The fact that information on the spin state
this technique will work in some cases, such as in the case of most other comets is limited underscores the observa-
of Comet 19P/Borrelly (e.g., Farnham and Cochran, 2002; tional and interpretational difficulties that must be faced in
Schleicher et al., 2003), there are counterexamples that re- spin determinations as discussed elsewhere in section 3.
quire caution (e.g., Sekanina and Boehnhardt, 1999; Samara- 3.4.1. Comets for which the spin state is approximately
sinha et al., 1999). determined.
Deep Space 1 images of Comet 19P/Borrelly indicate the 1P/Halley: The spin state of this comet has been the
presence of a strong sunward jet essentially parallel to the subject of many investigations with conflicting results. The
 Samarasinha et al.: Rotation of Cometary Nuclei 291

TABLE 1. Information on spin states of specific comets.

Pφ Pψ θ Ptotal M (J2000) Long Axis (J2000) Epoch

Comet Spin Mode (day) (day) (deg) (day) α (deg) δ (deg) α (deg) δ (deg) (JD-2440000)
Comets for which the spin state is approximately determined
1P/Halley Excited (LAM) 3.69* 7.1* 66 2.84* 7 –60 314 –7 6498.806
19P/Borrelly Unexcited 1.08 ‡ 90 1.08 214 –6 300 –10 12175.438
C/Hyakutake (1996 B2) Unexcited 0.2618* ‡ 90 0.2618* 205 –1

Comets for which partial knowledge of the spin state is available

2P/Encke Excited? ? ? ? ? 205† 3†
10P/Tempel 2 Unexcited 0.372 ‡ 90 0.372 148† 55†
109P/Swift-Tuttle Unexcited 2.77* ‡ 90 2.77* 128 –72
I-A-A (C/1983 H1) Unexcited 2.14* ‡ 90 2.14* 256 –15
Hale-Bopp (C/1995 O1) Unexcited 0.4712 ‡ 90 0.4712 ? ?

Comets for which only periodicities associated with rotation are presently known
6P/d’Arrest ? 0.30?
9P/Tempel 1 ? 1.75
21P/Giacobini-Zinner ? 0.79
22P/Kopff ? 0.54
28P/Neujmin 1 Unexcited 0.53 ‡ 90 0.53
29P/S-W 1 Excited? 0.58? 1.35?
31P/S-W 2 ? 0.242
46P/Wirtanen ? 0.32?
48P/Johnson Unexcited 1.208 ‡ 90 1.208
49P/Arend-Rigaux Unexcited 0.561 ‡ 90 0.561
95P/Chiron Unexcited 0.2466 ‡ 90 0.2466
96P/Machholz 1 ? 0.266?
107P/Wilson-Harrington Unexcited 0.25 ‡ 90 0.25
133P/Elst-Pizarro Unexcited 0.1446 ‡ 90 0.1446
143P/Kowal-Mrkos Unexcited 0.72 ‡ 90 0.72
Levy (C/1990 K1) ? 0.708
Levy (C/1991 L3) ? 0.348
*Sidereal period.
† Sense of M not known.
‡ P approaches its unknown minimum value with zero A and A as the energy of the spin state approaches the minimum (cf. section 2).
ψ ψ θ

LAM spin state listed in Table 1 (Belton et al., 1991) pro- d period (Sagdeev et al., 1989). However, other interpreta-
vides a satisfactory explanation of time variations in all tions yield results that are related to a 7.4-d periodicity and
major groundbased datasets as well as a viable interpreta- in which a 2.2-d period is absent (Belton, 1990; Samara-
tion of spacecraft encounter data; however, disagreements sinha and A’Hearn, 1991). That several interpretations of
on the spin state still persists. In this model, which is also the spacecraft imaging data are possible is primarily due
consistent with independent investigations by Samarasinha to uncertainties introduced by the defocused state of the
and A’Hearn (1991), the long axis of the nucleus precesses Vega 1 camera (Dimarellis et al., 1989; Belton, 1990) and
around the rotational angular momentum vector once every the particular shape of the nucleus. There were subsequent
3.69 d at an angle of 66°. At the same time, the long axis attempts at correcting the defocused Vega 1 images (Szegö,
executes a rotation about itself once every 7.1 d. This ful- 1995), but there is no consesus among different groups of
fills the observational requirement that the aspect of the researchers on the effectiveness of the results.
nucleus return to roughly the same position every 7.4 d as To discriminate between the various possible spin states,
seen by the Sun (Schleicher et al., 1990). Prior to the space- Belton et al. (1991) used Earth-based observations of light-
craft encounters in 1986, the investigations of Sekanina and curve periodicities, most importantly the extensive photo-
Larson (1986) and others suggested a nucleus in a PA spin metric observations of Millis and Schleicher (1986), and the
state with a period near 2 d. Images from three distinct periodic appearances of CN jet structures documented by
viewing geometries and timings during the encounters of Hoban et al. (1988). Important assumptions in this work
the Vega 1, Vega 2, and Giotto spacecraft allow for several are that (1) for the several months around the 1986 appari-
possible spin states depending on the interpretation of the tion, cometary activity originated primarily from several
images. One such interpretation, strongly advocated by the active areas that were stable in their location on the nucleus;
Vega investigators, yields a spin state with a dominant 2.2- (2) dynamical effects of jet torques are negligible to the first
292 Comets II

order; and (3) the rotational motion can be approximated erence direction for the orientation of the long axis. At the
by that of a freely precessing symmetric top. The latter time of the spacecraft encounter, the small end of the long
assumption is based on the near-prolate symmetry of the axis nearest to the spacecraft was directed at RA = 300° and
nucleus that is suggested by published shape models (Sag- Dec = –10° (Soderblom et al., 2004).
deev et al., 1989; Merényi et al., 1990). Because the shape Hyakutake (C/1996 B2): As with Comets 1P/Halley
model by Merényi et al. (1990) is based on the spin state and 19/Borrelly, this long-period comet displays well-de-
deduced by Sagdeev et al. (1989), it will require modifica- fined jet structures whose projected geometry varied mark-
tion, presumably minor, if it is to be consistent with the spin edly during its apparition. Observations of these features,
state reported in Table 1. together with periodicities derived from photometric light-
The Sagdeev et al. (1989) spin state, later improved by curves, allow the comet’s spin state to be specified with con-
Szegö and his colleagues (Szegö, 1995), is based on an siderable accuracy (Schleicher and Osip, 2002; Schleicher
interpretation of the spacecraft data in terms of an asym- and Woodney, 2003). The comet is in its lowest-energy PA
metric top. The Sagdeev et al. (1989) model yields a nucleus spin state. A reference direction for the orientation of the
in the SAM mode characterized by a 2.2-d precession of long axis of the nucleus is not available since there are no
the long axis around the rotational angular momentum vec- data on the shape of the nucleus. However, in this case, a
tor. The long axis nods with an amplitude of about 14° and reference direction could be defined relative to one of the
a period of 7.4 d. The nucleus must also oscillate back and active areas found by Schleicher and Woodney (2003).
forth around its long axis with the same period of 7.4 d. 3.4.2. Comets for which partial knowledge of the spin
However, both the Sagdeev et al. (1989) model as well as state is available.
the more recent Szegö (1995) model have internal inconsis- 2P/Encke: Numerous groundbased photometric obser-
tencies (the component periods and moments of inertia are vations of this active comet show that several harmonically
dynamically in conflict with the quoted nodding ampli- related periodicities occur in its lightcurve. Interpreted as
tudes), and the 2.2-d periodicity that shows up strongly in nucleus rotation periods these are P1 = 22.4 h (Jewitt and
model lightcurves (Szegö et al., 2001) is not convincingly Meech, 1987), P2 = 15.08 h (Luu and Jewitt, 1990), P3 =
seen in any Earth-based observational data (Belton, 1990; 11.05 h, and P4 = 7.3 h (Fernández et al., 2002). These
Schleicher et al., 1990). In addition, the observational re- synodic periods appear to be related in the ratios 2P1 ≈ 3P2 ≈
quirement that the geometrical aspect of the nucleus as seen 4P3 ≈ 6P4. The 15.08-h period, which is based on observa-
by the Sun return to essentially the same position every tions taken when the nucleus was near aphelion and was
7.4 d (Schleicher et al., 1990) is not satisfied. presumed to be essentially inactive, has usually been taken
19P/Borrelly: HST and Earth-based observations have as the rotation period (e.g., Belton, 1991; Jewitt, 1999; Jorda
established a period of 26 h (Lamy et al., 1998a; Mueller and Gutiérrez, 2002). However, a recent assessment (Meech
and Samarasinha, 2002). The direction of the spin axis has et al., 2001) has shown that the presumption of inactivity
been determined by observations of the coma morphology. at aphelion is incorrect. This throws into doubt the assump-
Images returned from the Deep Space 1 mission showed a tion that the 15.08-h period directly reflects the changing
strong linear dust jet emanating from the nucleus that was geometry of the nucleus as viewed by the observer. The
stable in its projected orientation and morphology during array of harmonically related periods is reminiscent of the
the several days approach to the encounter. The location of case of 1P/Halley, in which the similarly numerous periodici-
the base of this feature near the waist of the elongated nu- ties from sets of groundbased photometric time series show
cleus was consistent with it being parallel to the axis of the a similar character. In that case the various periodicities all
maximum moment of inertia (however, the relation of this relate to a basic 7.4-d period (Belton, 1990). Whether or not
jet to the near-nucleus coma morphology is yet to be fully a periodicity exists that would similarly unite the 2P/Encke
understood). The dust jet is therefore interpreted as defin- observations is unclear. Also, the question of whether an
ing the rotation axis of the nucleus (Soderblom et al., 2002). excited spin state is implied for 2P/Encke is also unclear.
This requires that the nucleus be essentially in PA rotation. Belton (2000) claimed the presence of a second periodicity
Groundbased observations show the evolution of the pro- in the early lightcurve datasets at P5 = 2.76 h that appeared
jected geometry of this jet and thus allow an independent to be unrelated harmonically from those noted above, sup-
determination of the direction of the spin axis (Farnham porting the idea of complex spin for this comet. However,
and Cochran, 2002; Schleicher et al., 2003). On the long- the discovery of a dominant role for P3 by Fernández et al.
est timescales, covering many apparitions, both Farnham (2002) suggests that the periodicity by Belton (2000) is in
and Cochran (2002) and Schleicher et al. (2003) find that fact harmonically related to the above series, i.e., P3 ≈ 4P5.
the spin axis slowly precesses by 5°–10° per century. The If the analogy to 1P/Halley is accepted, then a period near
interpretation of these phenomena is that the comet is spin- 45 h may play a similar role for 2P/Encke as the 7.4-d pe-
ning close to its lowest-energy PA spin state with the rota- riod does for 1P/Halley. Clearly further work is required to
tional angular momentum slowly evolving under torques understand the spin state of 2P/Encke.
due to cometary activity. The sense of rotation (defined by 2P/Encke is one of those comets, like 19P/Borrelly dis-
the righthanded rule) is such that the spin axis is in the di- cussed above, that displays a diffuse sunward fan structure
rection of the strong jet seen by the Deep Space 1 mission in its coma. Sekanina (1988a,b) has investigated the evo-
(Boice et al., 2003). The spacecraft images provide a ref- lution of the geometry of this structure in 2P/Encke under
 Samarasinha et al.: Rotation of Cometary Nuclei 293

the assumption, recently born out for the sunward jet and (Samarasinha, 2000). However, there is currently no de-
fan structure seen in 19P/Borrelly, that the axis of symme- tailed spin state/activity model combination that can suc-
try of the fan is roughly coincident with the projection of cessfully explain all the morphological structures of Hale-
the comet’s rotation vector. Note that this assumption is not Bopp (C/1995 O1) seen during the entire apparition. This
the same as the one that he used in his earlier study (Seka- again highlights the inherent difficulties associated with
nina, 1979) of four comets. The revised assumption of Seka- deriving accurate spin-axis directions based on coma mor-
nina (1987b, 1988a) is in fact essentially the same as that phology. The large size of the nucleus of this long-period
successfully used in the recent work on fan structures in comet makes it likely that it rotates near or at its state of
19P/Borrelly by many investigators. This work should pro- lowest energy.
vide a reliable estimate of the direction of a comet’s rota- 3.4.3. Comets for which only periodicities associated
tional angular momentum vector (even if the spin state is with rotation are presently known.
complex). Festou and Barale (2000) derived the direction 6P/d’Arrest: Early investigations that produced con-
of the angular momentum given in Table 1, which is in flicting results for this comet are reviewed in Belton (1991).
excellent agreement with that from Sekanina (1988a). The Based on recent observations, Lowry and Weissman (2003)
work of Sekanina (1988a,b) also provides evidence that the quote a rotation period of 7.20 h (see Table 1). Independent
spin of 2P/Encke has precessed slowly in the past at rates observations by Gutiérrez et al. (2003) yield a rotation
of approximately 1° per orbit. The sense of spin is unknown. period of 6.67 h, highlighting the difficulties associated with
10P/Tempel 2: Early thermal and visible investigations determination of spin parameters for this comet.
(A’Hearn et al., 1989; Jewitt and Luu, 1989; Sekanina, 9P/Tempel 1: This comet is the target of NASA’s Deep
1991) yielded a spin period of 8.932 h. This period is con- Impact mission and a worldwide observational campaign
firmed by Mueller and Ferrin (1996), who also found evi- has been organized to determine its rotational and photo-
dence for a small secular change in the spin period over an metric properties (Meech et al., 2000; McLaughlin et al.,
orbital timescale. Sekanina (1987b) has applied his assump- 2000). Variations in the nucleus brightness observed from
tion that the symmetry of the comet’s sunward-oriented fan the HST loosely suggest a rotational periodicity in the range
reflects the projected direction of the spin vector to this of 25–33 h (Lamy et al., 2001). In a preliminary interpre-
comet to yield the direction of the spin vector. The sense of tation of data collected in the worldwide campaign, light-
spin is not determined and the spin pole direction is consis- curve variations suggest a spin period near 42 h (Meech et
tent with it having been stable for many orbits. al., 2002).
109P/Swift-Tuttle: A spin period near 2.8 d has been 21P/Giacobini-Zinner: Leibowitz and Brosch (1986)
derived from studies of repetitive spiral dust jets (Sekanina, found evidence for a periodicity in this comet’s lightcurve
1981b; Yoshida et al., 1993; Boehnhardt and Birkle, 1994; at 9.5 h. Belton (1990) suggested that the spin period was
Jorda et al., 1994; McDavid and Boice, 1995). Table 1 lists near 19 h based on these observations.
the period given by Sekanina (1981b). The spin is prograde 22P/Kopff: Lamy et al. (2002) find no evidence for
and appears to be unexcited. Sekanina (1981b) and Jorda periodicities in the nucleus lightcurve of this comet and sug-
et al. (1994) derived somewhat disparate directions for the gest that the nucleus may be near spherical (although a pole-
spin axis. We give the pole by Sekanina (1981b) in Table 1. on situation cannot be discounted). However, Meech (1996)
Jorda et al. (1994) attribute the difference (nearly 50°) be- shows a double-peaked lightcurve with a rotation period
tween the two directions to precession of the spin pole over of 12.91 h (listed in Table 1), while Lowry and Weissman
the orbital period. However, the difference may simply be (2003) derive a rotation period of 12.3 h.
a reflection of the uncertainties in the calculations. 28P/Neujmin 1: A’Hearn (1988) reviewed the thermal
IRAS-Araki-Alcock (C/1983 H1): In a synthesis of avail- and visible observations of this comet and suggested a pe-
able observations, including radar, Sekanina (1988c) has de- riod of 12.67 h. Delahodde et al. (2001) and Mueller et al.
rived the spin state of the comet as it passed close to the (2002a) derived similar results.
Earth in 1983. He finds prograde rotation with a sidereal 29P/Schwassmann-Wachmann 1: Meech et al. (1993)
period of 2.14 d. The spin axis direction was found as indi- found evidence for three periodicities in the lightcurve of
cated in Table 1. This long-period comet is not expected to this comet, one harmonically related to the other two. They
have excited spin and no evidence to the contrary was found. proposed that the spin state is excited with 14.0 and 32.3 h
A reference direction for the long axis is not available. as the underlying periods.
Hale-Bopp (C/1995 O1): Jorda and Gutiérrez (2002) 31P/Schwassmann-Wachmann 2: Luu and Jewitt (1992)
have provided a detailed review of the observational mate- found periodicity in the lightcurve of this comet and pro-
rial available on this comet and its interpretation. Numer- pose a spin period of 5.58 h.
ous determinations of periodicities are in rough agreement 46P/Wirtanen: Lamy et al. (1998b) suggest a perio-
and yield a firm estimate of the spin period (e.g., Farnham dicity near 6 h. Meech et al. (1997) find evidence for a perio-
et al., 1998; Licandro et al., 1998). The direction of the dicity at 7.6 h, which is included in Table 1. The lightcurve,
angular momentum vector is poorly determined and the which has been the subject of an extensive international
characteristically similar morphology around perihelion, campaign, is of low amplitude and a clear characterization
which lasted nearly three months (despite huge changes in of any periodicity has not been obtained. Independent ob-
the viewing geometry), is understood to be due to wide jets servations by Boehnhardt et al. (2002) are consistent with
294 Comets II

the above periodicity but again the S/N for the data is poor. 9P/Tempel 1), all inferences on the bulk density as well as
The relatively high activity that is observed in this comet on the structure of cometary nuclei have to be based on
relative to the estimated size of its nucleus has led to the remote observations. Rotational studies provide one of the
proposal that the nucleus is most likely in an excited spin best probes, if not the best, for exploring the structural prop-
state (Samarasinha et al., 1996). However, this work is erties of the nucleus.
based on the assumption that the nucleus is a near-prolate
body. Jorda and Gutiérrez (2002) have shown that for an 4.1. Spin Rate as a Probe of the Bulk Density
asymmetric body, the nucleus may remain in a PA spin state
during more than 10 orbits. Assuming a spherical PA rotator, the balance of forces
48P/Johnson: Jewitt and Sheppard (2003) derive a ro- (per unit area) at the surface of a nucleus is given by (cf.
tation period of 29.00 h for this comet. Samarasinha, 2001)
49P/Arend-Rigaux: Millis et al. (1988) have shown that
the thermal and visible lightcurves for this comet are in 2π 2ρR2N cos 2 λ 2
phase as expected for the signature of the nucleus. They find pgas + ≤ π Gρ2 R2N + σ (15)
a dominant periodicity at 6.73 h and propose a spin period P2 3
of 13.47 h. The relatively low activity of this nucleus sug-
gests a low-energy PA spin state for this comet. where pgas is the interior gas pressure, ρ is the bulk density,
95P/Chiron: Chiron is a Centaur with cometary ac- RN is the nuclear radius, λ is the latitude, P is the rotation
tivity. Bus et al. (1989) find a precise synodic period of period, G is the gravitational constant, and σ is the tensile
5.9180 h for this object. strength. In the absence of any interior gas pressure, the
96P/Machholz 1: Meech (1996) gives a rotation period tensile strength at zero latitude (corresponding to the regime
of 6.38 h. of highest centrifugal force) can be expressed by
107P/Wilson-Harrington: Osip et al. (1995) find evi-
dence for a period of 6.1 h.
2π 2ρR2N 2
133P/Elst-Pizarro: This object, which shares many char- σ≥ − π Gρ2 R2N (16)
acteristics with 107P/Wilson-Harrington (e.g., Jewitt, 2004), P2 3
has a rotation period of 3.471 h (Hsieh et al., 2003).
143P/Kowal-Mrkos: Jewitt et al. (2003) derive a rota- For a strengthless spherical body, the critical rotation pe-
tion period of 17.2 h for this comet. riod, Pcritical, below which the nucleus will rotationally break
Levy (C/1990 K1): Jewitt (1999) reviewed the discor- up can be derived by equating the self-gravity and rotation
dant results on the spin period by Schleicher et al. (1991) terms. Pcritical is given by
and Feldman et al. (1992) and concluded that outgassing
torques could have been responsible for spin-up. The two
3π 3.3 h
spin-period determinations were 18.9 and 17.0 h respec- Pcritical = = (17)
tively and were separated approximately by 21 d. Table 1 Gρ ρ
shows the later period determination.
Levy (C/1991 L3): Fitzsimmons and Williams (1994) where ρ must be expressed in g cm–3. Therefore, the fast-
find a synodic spin period of 8.34 h for this comet. No other est rotation period among comets can be effectively used
information on the spin state is available. to probe the bulk density of the nucleus. In the case of a
Additional information on individual comets can also be prolate nucleus, for the PA state of lowest energy, the high-
found in Meech (1996) and Lamy et al. (2004). est centrifugal force corresponds to the ends of the long
axis. Therefore, for a prolate, the above equation can be
4. INTERPRETATION OF modified to represent the conditions relevant to the ends of
OBSERVATIONS the long axis (Jewitt and Meech, 1988; Luu and Jewitt,
1992), which can be approximated as follows (Pravec and
In this section we will discuss the interpretation of rota- Harris, 2000)
tional parameters, which highlights some of the challenges
we face in the process. As mentioned in the introduction to
3.3 h a
this chapter and elsewhere in this book, determination of Pcritical ≈ (18)
the nuclear structure is one of the most important goals of ρ b
cometary science. It is critical for understanding the for-
mation as well as the evolution of comets. Understanding where 2a is the length of the long axis and 2b is the length
the nuclear structure requires the determination of the bulk of the symmetry axis. Therefore, a plot of a/b vs. P could
density and porosity (both at macro and micro levels) as be used to determine a lower limit to the bulk density. Fig-
well as material properties. In the absence of a spacecraft ures 8 in both Lamy et al. (2004) and Weissman et al. (2004)
(preferably orbiting) with suitable instruments (i.e., at least show the current status of observations. Based on these fig-
until the rendezvous phase of the Rosetta spacecraft and to ures, a lower limit to the nucleus bulk density near 0.4 g cm–3
a lesser degree with the Deep Impact mission encounter of can be inferred. However, unlike for asteroids and NEOs
 Samarasinha et al.: Rotation of Cometary Nuclei 295

(e.g., Whiteley et al., 2002; Pravec et al., 2003), the number the damping timescales require reevaluation. For such nu-
of comets with reliable rotational data is much smaller. This clei, the energy loss due to internal mechanical friction is
makes robust density determinations difficult, emphasizing much more efficient and the damping timescales must be
the necessity for additional data on cometary rotation. smaller than the currently accepted values.
Currently, except for a few objects [e.g., 2001 OE84 The importance in knowing accurate damping timescales
(Pravec and Kušnirák, 2001) and 2002 TD60 (Pravec et al., was further emphasized when Jewitt (1999) pointed out that
2002)], the vast majority of asteroids larger than about most, if not all, short-period comets must be in excited spin
200 m have rotation periods greater than 2.2 h. This clear states based on a comparison of damping and excitation
demarcation for rotation periods suggests that most kilo- timescales, where the latter was set equal to τtorque (see his
meter-sized and larger asteroids are loosely bound aggre- Fig. 2). However, observations point to only a few, if any,
gates (rubble piles). On the other hand, there are many small excited short-period cometary nuclei (see Table 1). How can
asteroids (<200 m) that rotate much faster with periods as this be resolved? Are we overestimating the damping time-
small as a few minutes (Whiteley et al., 2002). These bodies, scale, underestimating the excitation timescale, or are our
known as monoliths, must have a nonzero tensile strength rotational lightcurve data not accurate enough (i.e., not
to withstand rotational breakup. This strength, while larger enough S/N) to pick up multiple periodicities? Based on
than the current estimates for the large-scale tensile strength what was discussed so far in this chapter, all these effects
of cometary nuclei, which is of the order of 102 dyn cm–2 may contribute to this apparent conflict between theory and
(Asphaug and Benz, 1996; Weissman et al., 2004), may still observations.
be relatively small (e.g., on the order of 10 5 dyn cm–2 for a
100-m object with a 100-s rotation period). This highlights 5. FUTURE DIRECTIONS
the effectiveness of the spin rate as a probe of the interior
structure. The following are a few tasks that, in our opinion, could
be carried out within the coming decade in order to better
4.2. Damping Timescale and Internal Structure understand the cometary rotation and by extension the na-
ture of cometary nuclei:
A nucleus in an excited rotational state will lose energy 1. Well-sampled nuclear lightcurve observations at mul-
because of internal friction and will eventually end up in tiple orbital phases and other relevant observations aimed at
the least-energy spin state. The damping timescale, τdamp, precise determination of spin parameters of as many comets
for this process is given by (e.g., Burns and Safronov, 1973) as possible.
2. Simulations of model lightcurves for different sce-
narios aimed at understanding how to accurately interpret
K1 µQ
τ damp = (19) lightcurve periodicities.
ρR2N Ω 3 3. Modeling aimed at understanding how collisional
effects (e.g., in the Kuiper belt) and evolutionary effects
where K1 is a nondimensional scaling coefficient, while µ (e.g., due to outgassing) might affect cometary spin.
and Q represent the rigidity and the quality factor of the 4. Accurate determination of the excitation and the
cometary material. ρ, RN, and Ω stand for density, radius, damping timescales for cometary nuclei via theoretical
and angular velocity of the nucleus. Efroimsky (2001 and means and estimation of structural parameters for cometary
references therein) argued that the coefficient K1 must be analogs using experimental techniques.
nearly two orders of magnitudes smaller than what was sug- 5. Placing greater emphasis on experiments that focus
gested by Burns and Safronov (1973). On the other hand, on determining structural and physical properties of comet-
as pointed out by Paolicchi et al. (2003), there is complete ary nuclei aboard future cometary missions.
agreement among all the authors on the functional depen-
dency of the damping timescale on µ, Q, ρ, RN, and Ω. In Acknowledgments. We thank K. Mighell for help with the
a recent revisitation of the problem, Burns and colleagues conversion of image formats across different platforms, D. Schlei-
(Sharma et al., 2001) conclude that their initial assessment cher for relevant discussions, and C. Lisse for providing Fig. 4.
for τdamp is reasonable. However, the issue is not yet fully We also thank K. Szegö and an anonymous reviewer for their help-
ful comments. N.H.S. and B.E.A.M. thank the NASA Planetary
resolved and it is important to understand the value of K1, in
Astronomy Program.
particular, its dependence on the axial ratios and on the de-
gree of excitation. In addition, τdamp has a large uncertainty
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300 Comets II
 Boehnhardt: Split Comets 301

Split Comets
H. Boehnhardt
Max-Planck-Institut für Astronomie Heidelberg

More than 40 split comets have been observed over the past 150 years. Two of the split
comets have disappeared completely; another one was destroyed during its impact on Jupiter.
The analysis of the postsplitting dynamics of fragments suggests that nucleus splitting can oc-
cur at large heliocentric distances (certainly beyond 50 AU) for long-period and new comets
and all along the orbit for short-period comets. Various models for split comets have been pro-
posed, but only in one peculiar case, the break-up of Comet D/1993 F2 (Shoemaker-Levy 9)
around Jupiter, has a splitting mechanism been fully understood: The nucleus of D/1993 F2
was disrupted by tidal forces. The fragments of split comets seem to be subkilometer in size.
It is, however, not clear whether they are cometesimals that formed during the early formation
history of the planetary system or are pieces from a heavily processed surface crust of the parent
body. The two basic types of comet splitting (few fragments and many fragments) may require
different model interpretations. Disappearing comets may represent rare cases of complete
nucleus dissolution as suggested by the prototype case, Comet C/1999 S4 (LINEAR). At least
one large family of split comets exists — the Kreutz group— but other smaller clusters of comets
with common parent bodies are very likely. Comet splitting seems to be an efficient process of
mass loss of the nucleus and thus can play an important role in the evolution of comets toward
their terminal state. The secondary nuclei behave as comets of their own (with activity, coma,
and tail) exhibiting a wide range of lifetimes. However, at present it is now known whether the
fragments’ terminal state is “completely dissolved” or “exhausted and inactive.”

1. THE PHENOMENON 1.1. Types of Split Comets

Split comets appear as multiple comets with two or more Two types of split comets are known from observations:
components arising from the same parent and initially Type A: The split comet has a few (usually two) com-
moving in very similar orbits. When active, the components ponents. The primary fragment is the one that remains “per-
usually display well-defined individual comae and tails that manent”; the secondary can be minor, short-lived, or per-
can overlap each other when the ensemble is close (see sistent for a longer time (years to centuries). The primary
Fig. 1). Most of the components of a split comet “disap- is considered to be identical to the original nucleus (the
pear” sooner or later; i.e., within time spans of hours to parent body), while the secondary represents a smaller piece
years the components become too faint to be detected even that is broken off the nucleus (typically 10–100 m in size).
by the largest telescopes, and only one main component Type A splitting events can recur in the same object. Known
“survives” for a longer period of time. Activity outbursts cases are the comets listed in section 8 (with the exception
and the appearance of coma arclets can be associated with of the ones mentioned as Type B below).
comet splitting events. However, the ultimate proof of comet Type B: The split comet has many (more than 10) com-
splitting is provided through the detection of at least one ponents that could arise from a single or a short sequence
secondary component (also called a fragment or compan- of fragmentation events. The fragments are short-lived (pos-
ion) to the primary nucleus. sibly of small size), and no primary component can be iden-
The scientific interest in split comets reaches beyond the tified. Tertiary fragmentation of secondaries is occasionally
obvious questions “Why do comets split?” and “What is the observed. Type B events are believed to represent cases of
sequence of events?” and focuses on the understanding of dissolution and/or disruption of the comet and the parent
the internal structure and chemistry of the cometary nucleus body may become completely destroyed. Known cases are
as well as its overall evolution with time. The answers ob- Comet D/1993 F2 (Shoemaker-Levy 9) and Comet C/1999
tained from split comets may even provide information on S4 (LINEAR).
the formation scenario of the solar system (for instance, the In summary, observations and modeling results provide
size distribution of the cometesimals, the original ice chem- evidence for at least 42 split comets producing several hun-
istry, and even the “birth place” of cometary nuclei). dred (>400) fragments in more than 100 splitting events.

301
302 Comets II

and names [like Comets C/1965 S1 (Ikeya-Seki) and C/

1882 R1 (Great September Comet)] and are only linked a
posteriori to a common parent body.

2. DYNAMICS OF COMET SPLITTING

As discussed in Marsden and Sekanina (1971), simple

backward integration of the orbits of the fragments of split
comets does not yield unique and well-defined “collision”
points of their orbits that could be considered the places
where the fragmentations of the nuclei happened. Moreover,
this approach does not provide a sensible description of the
dynamical aspects of the splitting event itself.

2.1. Dynamical Models for Comet Splitting

Sekanina (1977, 1978, 1979, 1982) has developed a five-

parameter model to approximate the dynamics of the mo-
tion of the fragments of split comets. He and colleagues
applied this model to more than 30 split comets. A similar
approach was used by Meech et al. (1995) for Comet C/
1986 P1 (Wilson). The parameters are used to constrain the
fragmentation event dynamically through the time Ts when
the splitting happened, the radial Vr, transverse Vt and nor-
mal Vn components of the separation velocity of the second-
ary fragment relative to the primary one, and the decelera-
tion parameter Γ of the secondary relative to the primary
component. Vr points in the direction of the radius vector
of the comet, positive along the radius vector; Vt is perpen-
dicular to the radius vector of the comet in the orbital plane,
positive in the direction of the velocity vector of the comet;
Fig. 1. Three components of split Comet 73P/Schwassmann- Vn is perpendicular to the orbital plane of the comet, posi-
Wachmann 3 are detected in mid-December 1995 shortly after the tive toward the direction of the angular momentum. The
splitting event of the nucleus. Each fragment has its own coma and deceleration Γ is a result of the momentum transfer between
tail that overlap. Component C (to the east) is the primary fragment, the two fragments due to their different outgassing rates and
companions B (middle) and A (to the west) are secondary fragments. masses. It is measured in radial direction only; the two other
Fragment B is considered persistent, since it survived the subse-
components of the deceleration are set to zero. Γ is assumed
quent perihelion passage in January 2001. Fragment A was not
found upon the next return of the comet. The images are taken in
to vary with solar distance r proportional to 1/r2.
the visible R-band filter (upper three panels; NTT + EMMI) and in The model implies a single-step, two-body fragmentation
the mid-IR N band (bottom panel; 3.6-m + TIMMI). Courtesy of of the nucleus. Its parameters (or subsets of them) are de-
the European Southern Observatory (ESO). termined by nonlinear least-squares fits of astrometric posi-
tions of the fragments. As such, the quality of the parameter
solution depends very much on the accuracy, the number,
and the measured arc of astrometric positions of the frag-
1.2. Designation of Fragments ments. Moreover, at least in the case of more than two frag-
ments, a variety of splitting sequences of the fragments are
In general, the fragments are denoted with the designa- possible and need to be analyzed (Sekanina, 1999; Weaver
tion and name of the parent comet [given by the Interna- et al., 2001), and for events that produce many fragments
tional Astronomical Union (IAU)], followed by upper-case like C/1999 S4 (LINEAR) a complete and unique solution
letters beginning with the letter A for the component that becomes impossible. Also, different numerical solutions are
passes perihelion first. This fragment is supposed to be the possible even for a two-fragment case by considering vari-
primary component. However, cases of misidentified pri- ous subsets of fit parameters, and the selection of the most
maries exist (for instance, 73P/Schwassmann-Wachmann 3A plausible one requires a critical discussion of the physical
and C, the latter being the primary; see also Fig. 1). Indi- meaning of the solutions.
ces for tertiary components that split from already denoted Desvoivres et al. (1999) have introduced a description
fragments were introduced, such as in the case of D/1993 F2 of the dynamics of split comets that is based on a physical
(Shoemaker-Levy 9) components P1, etc. Widely separated outgassing model for the components. As in Sekanina’s
components may even receive different IAU designations approach, this model implies a single-step two-body frag-
 Boehnhardt: Split Comets 303

mentation scenario of the nucleus, and the many model 2.2. Results from the Dynamical
parameters — including the size and bulk density of the Modeling of Comet Splitting
fragments — are determined through a numerical fit of the
motion of the fragments involving plausibility consider- The results discussed below are primarily based on the
ations on some of the fit parameters. The authors applied work by Sekanina and collaborators over the past 25 years
their model to three splitting events observed in Comet C/ (Sekanina, 1977, 1978, 1979, 1982, 1988, 1991, 1995b, 1997a,
1996 B2 (Hyakutake) in 1996 and could indeed demonstrate 1998, 1999, 2001, 2002c; Sekanina and Marsden, 1982; Seka-
that outgassing of the fragments together with the initial nina and Yeomans, 1985; Sekanina and Chodas, 2002a–d;
momentum from the splitting event provide a suitable de- Sekanina et al., 1996, 2002; Marsden and Sekanina, personal
scription of the dynamics of the companions. communication). Figure 2 contains plots that illustrate the
Neither model implies a particular physical process that results and conclusions on the dynamical modeling of split
causes the splitting of comets, and in each model only the comets. The underlying database contains 33 comets pro-
separation dynamics of the fragments after breakup (and ducing a total of 97 fragments in 64 splitting events (9 dy-
when at larger distance from each other) is described. They namically new comets with 22 components in 13 events, 13
were successfully applied to split comets with fragments of long-period comets with 37 components in 24 events, and 11
small (a few arcseconds to a few degrees) mutual distances. short-period comets with 38 components in 28 events).

Fig. 2. Results from the dynamical modeling of comet-splitting events. (a) Solar distance vs. splitting time to perihelion (negative/
positive before/after perihelion). (b) Location of splitting events: Projected out-of-ecliptic distance vs. projected in-ecliptic distance
(c) Histogram distribution of relative deceleration of companions. (d) Histogram distribution of endurances of companions. (e) Endurance
vs. deceleration of companions. (f) Separation velocity of the companions vs. solar distance at time of splitting. Symbols and colors
used in the plots are as follows: short-period comets — squares (plots) and black (histograms); long-period comets — diamonds (plots)
and gray (histograms); dynamically new comets — triangles (plots) and white (histograms). In (e) the three groups of companions
(“persistent”, “short-lived”, “minor”) are indicated between dotted vertical lines. The broken line in this panel shows the best fit de-
scribed by equation (2) in section 2.2. The broken line in (f) represents the relationship obtained by Sekanina (1982) and described in
section 2.2.
304 Comets II

TABLE 1. Mean values for the deceleration, endurance, and separation velocity of fragments.

New Comets Long-Period Comets Short-Period Comets

Deceleration (10 –5 solar units) 86 ± 134 41 ± 43 49 ± 59
Number of fragments 13 24 25
Endurance (days) 52 ± 31 514 ± 653 161 ± 128
Number of fragments 13 26 25
Separation velocity (m/s) 1.3 ± 1.3 2.0 ± 1.9 2.7 ± 2.3
Number of fragments 7 12 16

2.2.1. Primary and “higher-order” fragments. The of the latter comets may be parts of a more evolved surface
identification of the primary fragment of a splitting event crust, i.e., they contain more dust of higher bulk density and
is made purely on dynamical grounds: The primary is the less sublimating ices that can contribute to the nongravita-
companion that passes perihelion first and thus shows the tional forces on the body. The breakup products of the two
smallest nongravitational force of the breakup products. For other groups may contain more volatile ices since their sur-
many cases one can assume that it carries the vast majority faces have experienced little loss by thermal heating dur-
of mass of the original nucleus. “Secondaries” are believed ing the much rarer perihelion passages. The mean decelera-
to represent lighter pieces from the splitting event since they tion of fragments from new comets (Table 1) is about twice
show higher nongravitational forces than the primaries. as high as for those of long- and short-period comets (all
Tertiary fragments are produced when secondaries disinte- with large error bars).
grate further, and so on for even higher-order fragments. 2.2.5. Endurance E of the fragments. The lifetimes of
The presence of multiple companions requires a careful split components differ by a large amount, even for the same
analysis of the observations in order to definitively estab- comet. This indicates that the fragments have different reser-
lish the sequence of nucleus splitting events that generated voirs of outgassing material and they must be of different
the fragments. size and mass after all. Sekanina (1977, 1982) has intro-
2.2.2. Splitting time Ts. The plot “splitting time” vs. duced the so-called endurance parameter E of a fragment
“solar distance” in Fig. 2 shows a clustering of splitting as a measure for the persistence of fragments. The endur-
events close to perihelion, a trend that may have consider- ance E has been defined as the time interval from the split-
able observational bias since these events happen closer to ting event (given by Ts) to its final observation (at time Tf),
the observers on Earth. The comet splitting is about equally normalized by the inverse-square law to a distance of 1 AU
likely before and after perihelion. The behavior of short- from the Sun. In other words, the endurance measures a
period, long-period, and dynamically new comets seems to minimum sublimation lifetime of a companion. In terms of
be similar. A few early breakups (i.e., long before perihelion orbital parameters, E (in days) can be written as
passage) of long-period and dynamically new comets are
known. The results for Ts suggest that at least short-period E = 1.015 * Asf /[a * (1 – e2)]1/2 (1)
comets seem to split all along their orbits.
2.2.3. Splitting location. The solar distances, where where Asf is the length of the heliocentric arc of the orbit
comet splitting happens, peak within about 2 AU. However, (in degrees) that the fragment passed through between Ts
there are several cases where comets split at larger distances, and Tf, a is the semimajor axis, and e is the eccentricity of
even beyond 50 AU (not plotted in Fig. 2; see also sec- the cometary orbit. Obviously, the endurance values of split
tion 3.1). While the splitting locations of short-period com- comets are lower limits only, since Tf may be rather con-
ets are naturally close to the ecliptic, such a bias does not strained by the visibility of the objects and telescope capa-
exist for new and long-period comets that can split at large bilities.
distance in and out of the orbital plane of the planets. In- The measured endurances E cover three orders of mag-
dications exist (Sekanina, 1982, 1997a, 1999) that comets nitude from a few to several thousand days. In Fig. 2 the
may split all along the orbit even at large heliocentric dis- endurance E is plotted vs. the deceleration Γ for about 50
tances (>5 AU) up to aphelion of long-period comets (Seka- companions seen in split comets. Here, “companion” means
nina and Chodas, 2002a, 2002b; Sekanina et al., 2002). secondary fragments, the decelerations of which were mea-
2.2.4. Deceleration parameter Γ. The deceleration pa- sured relative to the primary ones. The latter are to be con-
rameter Γ ranges from 10–5 to almost 10 –2 × solar gravity. sidered the more persistent products since their lifetimes are
The coarse histogram distribution in Fig. 2 suggests that at least as long as (and in most cases much longer than)
long-period and new comets tend to produce fragments those of the secondary ones. The conclusion of Sekanina
subject to decelerations Γ of 10 –4 –10 –3 × solar gravity, (1982) that the endurance E scales with the deceleration Γ
while the fragments of short-period comets show on the of the secondary fragments is still valid. However, the larger
average smaller Γ values. This trend suggests that fragments dataset available now suggests a steeper exponent for Γ
 Boehnhardt: Split Comets 305

(correlation coefficient 0.7) times for perihelion passage and despite the failure to iden-
tify the location and time of the splitting along the orbit
E (in days) = 690 (±180) * Γ–0.77 (±0.07) (2) from simple numerical backward integration of their orbits
(Marsden and Sekanina, 1971). Such evidence, i.e., from
Based upon an anticipated clustering in the endurance similarity of orbital elements, exists for several possible
vs. deceleration plot of companions, Sekanina (1982) has pairs of split comets: C/1988 F1 (Levy) and C/1988 J1
introduced a classification scheme for the fragments of split (Shoemaker-Holt) (Bardwell, 1988); C/1988 A1 (Liller) and
comets, i.e., persistent (Γ < 10 –4 solar gravity), short-lived C/1996 Q1 (Tabur) (Jahn, 1996); C/2002 C1 (Ikeya-Zhang)
(10–4 < Γ < 10–3 solar gravity), and minor components (Γ > and C/1661 C1 (Green, 2002); C/2002 A1 (LINEAR) and
10–3 solar gravity). In the larger dataset now available (see C/2002 A2 (LINEAR) (Sekanina et al., 2003), C/2002 Q2
Fig. 2) the original clustering is less obvious. Nevertheless, (LINEAR) and C/2002 Q3 (LINEAR) (Adams, 2002).
the “minor components” are distinguished from the merg- Backward integration of the orbits of periodic Comets 42P/
ing groups of “short-lived” and “persistent” objects. Among Neujmin 3 and 53P/Van Biesbroeck suggests a good agree-
the latter, a few fragments with very long lifetimes (E > ment of their orbits before 1850 when a very close encoun-
1000 d) have been observed. The mean values for the endur- ter with Jupiter may have occurred (Carusi et al., 1985).
ances of the three dynamical classes of comets (Table 1) Tancredi et al. (2000) have addressed the question of
suggest that new comets are on the average less persistent as families of split pairs and families among short-period com-
long- and short-period comets, although the mean devia- ets through a statistical approach. The authors analyzed the
tions of the mean endurance values are large. dynamical taxonomy of Jupiter-family comets and near-
2.2.6. Separation velocities. The relative speed of the Earth asteroids (NEAs) using clustering of Lyapunov indi-
fragments shortly after the fragmentation event amounts cators derived from the orbital elements of the objects. A
from 0.1 to 15 m/s with the majority between 0.3 and 4 m/s. splitting hypothesis for the Jupiter-family comets, i.e., to
In many cases the velocity components are ill-defined originate from a “giant” 50-km nucleus (comparable in size
through the available observations, if measurable at all. In to a small Kuiper belt object), is not very likely. Moreover,
Fig. 2 only cases are plotted for which all three components they found that the contribution of split comets to the popu-
of the separation velocity are estimated, thus the total am- lation of near-Earth asteroids is small, if at all significant.
plitude Vtotal can be calculated. It is unclear whether trends The clustering of the Lyapunov indicators of Comets 42P/
with solar distance r exist as suggested by Sekanina (1982) Neujmin 3 and 53P/van Biesbroeck with those of Comets
based on a smaller dataset: Dynamically new comets (and 14P/Wolf and 121P/Shoemaker-Holt 2 is not only support-
less likely long-period comets as well) may follow approxi- ing a splitting scenario for the former pair of comets, but
mately Sekanina’s (1982) data fit of Vtotal ~ 0.7 * r –0.57, may even suggest the involvement of further candidates, i.e.,
while a similar behavior is not obvious for the short-period the latter two comets.
comets. Instead, for the latter, a random scatter of Vtotal In order to model the dynamics of splitting events over
independent of r is found. Therefore, on the average, a more than one orbital revolution, Sekanina and Chodas
slightly larger separation velocity (see Table 1) may be in- (2002a,b) have integrated planetary and nonrelativistic per-
dicative of a different fragmentation mechanism or of higher turbations in the original approach of Sekanina (1982) (see
tensile strength of the nuclei as compared to the long-pe- section 2.1). The authors used their enhanced model to link
riod and dynamically new comets (which may be less major Sun-grazing comets as fragments of parent bodies
evolved due to rarer passages close to the Sun). (fitting Vr, Vt, Vn, but neglecting the deceleration param-
eter Γ): Comets C/1965 S1 (Ikeya-Seki) and C/1882 R1
3. SPLIT PAIRS, FAMILIES, AND (Great September Comet) were produced by a common par-
COMET EVOLUTION ent that split in 1106 shortly after perihelion passage [this
was already suggested by Marsden (1967)]. Moreover, the
The dynamical modeling described in section 2 is pref- motion of Comet C/1970 K1 (White-Ortiz-Olelli) is con-
erably applied to cases where evidence for the comet split- sistent with a scenario in which the parent was an unknown
ting comes from the observations of the fragments that third fragment of the 1106 splitting event, and the separa-
appear close in time and space. In fact, most of the frag- tion of C/1970 K1 (White-Ortiz-Olelli) occurred in the eigh-
ments are observed within the same — narrow — field of teenth century at a large heliocentric distance of about
view of the telescopes used. Linking “wider and older” pairs 150 AU. C/1880 C1 (Great Southern Comet) split off C/
and clusters of split comets is a more difficult task. 1843 D1 (Great March Comet) at 2.5–3 AU after perihe-
lion passage in the eleventh century [also previously sug-
3.1. Pairs and Families of Split Comets gested by Marsden (1989), with breakup in the fifteenth
century only). As a by-product, but most interesting for link-
Similarity of the dynamical (semimajor axis, eccentric- ing orbits of fragments over longer time intervals, Sekanina
ity) and geometrical (inclination, ascending node, argument and Chodas (2002a) summarize the orbit perturbations of
of perihelion) orbital elements of comets suggests a com- Sun-grazing comets that split since the last perihelion pas-
mon origin of the respective nuclei despite very different sage with nonzero separation velocity.
306 Comets II

3.2. Kreutz Group and Solar and Heliospheric would argue for the existence of break-up families among
Observatory (SOHO) Comets the current population of comets. And indeed some indica-
tions are found (see sections 3.1 and 3.2). The Lyapunov
The Kreutz group comets (also called Sun-grazers) are indicator cluster analysis by Tancredi et al. (2000) suggests
comets that approach the Sun to a perihelion distance <2.5 that break-up families are not very abundant among Jupiter-
solar radii. The number of discovered Sun-grazer comets family comets. This could imply that the production of long
has increased tremendously with the advent of corona- persistent fragments by short-period comets is low and/or
graphic observations from satellites, e.g., SOLWIND, So- that the decay rate of the break-up products is fast compared
lar Maximum Mission (SMM), and in particular the Solar to the typical dissipation timescale for the Lyapunov indi-
and Heliospheric Observatory (SOHO), which has detected cators of these class of comets (on the order of several hun-
several hundred new objects (Sekanina, 2000b). Two main dreds of years).
families (I and II, with a further division into two subgroups From simple estimates on the mass loss due to recurrent
for family II) are identified through statistical methods [clus- nucleus splitting events it becomes clear that fragmentation
tering of orbital elements (Marsden, 1967, 1989; Sekanina, may be an efficient destruction process for comets. For in-
2002a)]. There also exists a non-Kreutz near-Sun comet stance, from the current catalogue of about 160 short-period
group among the SOHO comets that is characterized by comets, 10 objects are known to have split, three of them
similar orbital elements (Meyer and Marsden, 2002). Prac- repeatedly (16P/Brooks 2, 51P/Harrington, 141P/Mach-
tically all smaller Sun-grazers (i.e., most of the so-called holz 2); one object (3D/Biela) disappeared completely after
“SOHO” comets) do not survive perihelion passage (Seka- nucleus splitting. The observational baseline for this class
nina, 2000a,b), but the larger (i.e., brighter) ones in the of comets is on the order of 200 years, and it must be as-
Kreutz group do. sumed that some other splitting events escaped detection.
Nucleus splitting of the Kreutz group and SOHO com- Thus, the numerical splitting rate of ~3% per century and
ets suggests the following: (1) some larger objects (Mars- object may only represent a lower limit for short-period
den, 1967, 1989; Sekanina, 2002a,b) are among the list of comets. This rough order-of-magnitude result is consistent
split comets (see Appendix); (2) there are tremdendous with the splitting rate estimate of at least 1 event per cen-
similarities in the orbital elements of these comets and their tury and comet published by Chen and Jewitt (1994) based
subgroups (Marsden, 1967, 1989; Meyer and Marsden, on observations of break-up events of comets in general.
2002); and (3) the SOHO comets show a significant tem- Weissman (1980) reports splitting rates of 1%, 4%, and 10%
poral clumping since more than 15 pairs of comets were for short-period, long-period, and dynamically new com-
observed that appeared within less than 0.5 d in similar ets based on a sample of 25 objects (of which 7 are at least
orbits within the field of view of the SOHO coronagraph. questionable candidates).
A dynamical analysis of the latter (Sekanina, 2000b) indi- Over its mean lifetime in the inner planetary system, a
cates that the pairs originate from fragmentation events all short-period comet may experience about 1000 splitting
along the orbit, i.e., not necessarily close to the Sun, but events. If the average mass loss in these events corresponds
more or less at any point along the orbit, even near aph- to a 50-m fragment, the total mass loss by nucleus split-
elion. The dissolution of the smaller SOHO comets close ting can amount to 500–1000-m equivalent radius over the
to the Sun happens before reaching perihelion and it is fre- lifetime of a comet, i.e., it is on the order of the typical size
quently indicated through an activity flare at ~3 solar radii of the nuclei of short-period comets. Therefore, nucleus
with a subsequent drop in brightness. Sekanina attributes splitting may represent an important mass loss factor in the
the disappearance of these comets to an “erosion” effect of life of a comet and should be considered carefully in the
the nuclei due to the strong heating of the Sun. scenarios for the evolution and “end state” of comet nuclei.
Sekanina (2000b) has introduced a scenario for the for-
mation of this group of comets involving a parent nucleus
that split into two major fragments, possibly through tidal 4. SECONDARY EFFECTS: OUTBURSTS
forces or at least tidally triggered, during perihelion very AND COMA ARCLETS
close to the Sun. After the break-up the two major fragments
evolved into slightly different orbits, but continued to split The main effect of comet splitting is the appearance of
along their paths around the Sun, generating a cascade of one or more companions of a primary component (Type A).
tertiary components of very different size that form the In a very few cases, many more fragments appear (quasi-)
group and subgroups of Kreutz comets. simultaneously and without clear indication of a primary
component among them (Type B). Unfortunately, in gen-
3.3. Nucleus Splitting and the eral the existence of primary and secondary components
Evolution of Comets becomes detectable in direct images only long (typically
weeks) after the time when the splitting actually occurred.
The role of nucleus splitting in the evolution of comets Activity outbursts and arclets in the coma of a comet can
is widely unexplored. Multiplicity and persistence of frag- indicate the occurrence of a nucleus break-up event at or
ments and recurrence of the splitting phenomenon in comets shortly after the time when the comet splits.
 Boehnhardt: Split Comets 307

Fig. 3. Pre- and post-break-up visual lightcurve of Comet 73P/Schwassmann-Wachmann 3. The lightcurve of the total brightness
estimates in the visual wavelength range over four apparitions of the comet from 1979 to 2001. Nucleus splitting happened around
perihelion 1995 and shortly thereafter. Even one apparition, i.e., 4–6 years later, the brightness of the comet (component C) is still 2–
3 mag above normal level before break-up. The observations obtained during the 1979, 1990, 1995–1996, and 2001 perihelion pas-
sages are marked by symbols. Least-squares fits to the various apparition lightcurves are indicated by lines. In the legend, numbers
next to the symbols and lines denote the year of the comet apparition, “in” stands for inbound, “out” for outbound, “all” for all data
of the apparition, “fit” for least-squares fit.

4.1. Activity Outbursts sequent perihelion passage the comet remains 2–3 mag
brighter than before splitting.
Outbursts in the visual lightcurve of comets can indicate The outbursts identified in the visual and most of the
splitting events. There are prominent cases that demonstrate broadband brightness estimates and measurements of com-
the temporal relationship between nucleus splitting and ets indicate a higher dust content in the coma. Most of this
activity outbursts with amplitudes of 3 mag and more: C/ dust in the visible is of micrometer size (McDonald et al.,
1975 V1 (West), 73P/Schwassmann-Wachmann 3, and C/ 1987). Most of the outbursts to which nucleus break-ups can
1999 S4 (LINEAR) as described by Sekanina (1982), Seka- be associated (Sekanina, 1982; Sekanina et al., 1996, 2002)
nina et al. (1996), and Green (2000). Smaller lightcurve peak several days after the estimated dates of these events,
peaks and nucleus break-ups are associated with Comets suggesting that additional dust is released during or — more
C/1899 E1 (Swift), C/1914 S1 (Campbell), C/1943 X1 likely — after the splitting of the comet. The early phases
(Whipple-Fedtke), C/1969 T1 (Tago-Sato-Kosaka), and C/ of the dust expansion after break-up events are documented
1975 V1 (West) (see Sekanina, 1982); C/1986 P1 (Wilson) for C/1999 S4 (LINEAR) by Schulz and Stüwe (2002) and
(see Meech et al., 1995); and 73P/Schwassmann-Wachmann 3, Kidger (2002). Outbursts in the gas production, although in
C/1996 J1 (Evans-Drinkwater), and C/2001 A2 (LINEAR) smaller and short-term events difficult to observe, are also re-
(Sekanina, 1998; Sekanina et al., 1996, 2002). The rise ported for split comets, e.g., 73P/Schwassmann-Wachmann 3
times of these outbursts, if measurable, last for a few (2– (Crovisier et al., 1996) and C/1999 S4 (LINEAR) (Mäkinen
20) days. The durations of the activity outbursts have a very et al., 2001; Farnham et al., 2001). For C/1999 S4 (LIN-
wide range, from a few days to months or maybe even EAR) the published measurements show a rapid decay of
years. Figure 3 shows the lightcurve of 73P/Schwassmann- the gas and dust production of the comet in late July 2000.
Wachmann 3 during the past four apparitions observed: The This in turn suggests that the reservoir of sublimating ice
lightcurves in 1979 and 1990, plus most of the preperihelion in this comet was exhausted rapidly after the complete dis-
phase in 1995, define the (rather repetitive) normal activ- ruption of the nucleus.
ity level before break-up of the comet in autumn 1995. The However, the relationship between outbursts in the light-
postperihelion lightcurve in 1995–1996 is about 5 mag (fac- curve on one side and splitting events on the other is not
tor of 100) brighter than normal due to the break-up events “one-to-one”: Not all splitting events are accompanied by
around perihelion and thereafter, and even during the sub- noticeable outbursts (e.g., fragment E in 73P/Schwassmann-
308 Comets II

Fig. 4. Coma arclets of fragments of Comet C/2001 A2 (LINEAR). These broadband R-filter exposures of the comet show three
coma arclets observed during the break-up episodes of the comet. In the left image (taken on 18 May 2001) two arclets are seen, one
(to the left) between companions B and C (both not directly visible in the image) and another one (to the right) close to fragment A.
The former arclets seem to be associated with the splitting of component C from B on 10 May 2001, while for the latter case no
companion of fragment A is reported. The right image (taken on 13 July 2001) shows another very wide arclet around component B.
Apart from the main component no further fragments could be identified. However, the straight tail-like extension away from the Sun
may represent dust released by the invisible fragment(s) that might have split off fragment B a few days before the image was taken.
The images are taken with the New Technology Telescope (NTT) and the Very Large Telescope (VLT) of the European Southern
Observatory (ESO), respectively. North is up and east to the left; field of view is 2.5 × 1.9 arcmin2 in the left and 1.0 × 1.2 arcmin2 in
the right panel. Image courtesy of E. Jehin et al., ESO Chile.

Wachmann 3) and not all outbursts indicate splitting events be exposed to sunlight for the first time since the forma-
that produce detectable companions (e.g., the 10-mag out- tion of the comet. The measurements of lightcurves for indi-
burst of Comet 52P/Harrington-Abell observed from July vidual components usually suffer from the overlap of the
1998 to February 1999). Outbursts of smaller amplitude (1– comae shortly after the splitting event such that the meas-
3 mag) may also occur as episodes of enhanced activity of ured magnitudes are contaminated by light from the neigh-
the comet without obvious splitting of the nucleus (see boring coma(e).
Prialnik et al., 2004; Meech et al., 2004). Activity outbursts
of splitting events start around the estimated time of the 4.2. Coma Arclets
nucleus break-up and they usually reach peak brightness a
short time (order of days) thereafter. However, it is not clear Coma arclets, also called “coma wings” because of their
whether brightness outbursts are associated with the actual bird-shaped appearance, have been seen in three comets
cause of the break-up or are more a consequence of the shortly after splitting events that produced short-lived com-
nucleus splitting. panions of the primary nuclei, i.e., in Comets C/1996 B2
The visual and broadband filter lightcurves of compan- (Hyakutake) (Harris et al., 1997; Rodionov et al., 1998),
ions in split comets show a systematic decay in brightness C/1999 S4 (LINEAR) (Farnham et al., 2001), and C/2001
and intrinsic short-term variability of the fragments (Seka- A2 (LINEAR) (Jehin et al., 2002). They show up easily
nina, 1982, 1998; Sekanina et al., 1996, 1998). Both phe- when some simple structure enhancement (like wavelet or
nomena seem to be due to outgassing behavior of fresh adaptive Laplace filtering or radial renormalization) is ap-
material from the interior of the original nucleus that may plied to the flat-fielded images. Figure 4 shows examples
 Boehnhardt: Split Comets 309

of arclets observed during break-up of Comet C/2001 A2 5. PHYSICO-CHEMICAL PROPERTIES

(LINEAR). OF SPLIT COMETS AND
The arclet structure appears to be located in between two THEIR FRAGMENTS
split companions. The observed arcs are almost perpendicu-
lar to the connecting line of the fragments, rather symmet- The observations of split comets, and in particular the
ric on both sides and preferably — but not exclusively — measurements of the fragments of Comet C/1999 S4 (LIN-
with tailward curvature. The observed arclets extended over EAR) (Weaver et al., 2001), suggest that “solid” second-
1000 to 10,000 km on both sides and intersected the con- ary bodies are produced by fragmentation of a primary
necting line of the fragments at a few 100 to a few 1000 km nucleus. If one assumes that the fragments are the original
projected distance. They appeared soon (within 10 d) after building blocks of cometary nuclei, the break-up of Comet
the fragmentation event of the nucleus and faded away C/1999 S4 (LINEAR) provides indications of the typical
within 3–5 d after first appearance. From narrow and broad- size distribution of cometesimals, at least for the (yet un-
band imaging in the visible and near-IR (Harris et al., 1997), known) region of the planetary disk where its nucleus was
it is clear that the coma arclets are made of gas (OH, CN, formed. The former assumption, however, can be ques-
and C2 gas was identified). Dust does not participate in their tioned, at least for comets coming from the Kuiper belt re-
formation. Nevertheless, arclets are also detectable in broad- gion [such as the short-period comets (Farinella and Davis,
band images taken in visible wavelengths if their gas con- 1996)] if one considers the collision environment of the belt
tent is large enough and covered by the filter bandpasses. that may have created the population of comet-size bodies
Thus far, coma arclets have only been reported in split com- through collisional break-ups of larger objects over the life-
ets close to quadrature position and at distances close to time of the solar system. The impact energy induced in a
Earth. The importance of both conditions on the visibility Kuiper belt body through long-term bombardment is of an
of the phenomenon is presently unclear. amount that could potentially modify the constitution of the
Three physical interpretations of the coma arclets are whole body or at least a major part of it.
published. Harris et al. (1997) proposed an arc model in- Size estimates of nuclei before or during the fragmenta-
volving gas release from the primary nucleus plus an ex- tion episode exist only for two comets, 73P/Schwassmann-
tended source located on the connecting line toward the Wachmann 3 [radius 1.1 km (Boehnhardt et al., 1999)] and
secondary component. The extended source is claimed to C/1996 B2 (Hyakutake) [radius 2.4 km (Lisse et al., 1999)].
be a train of boulders produced during the splitting event Photometric measurements of fragment sizes are published
and emitted in the same direction as the major secondary for C/1999 S4 (LINEAR) [50–100 m for 4% albedo (Weaver
fragment. No shock wave of gas is predicted in this model, et al., 2001)]; a few more size estimates of fragments or
but the main contribution to the arclets should come from upper limits were derived from the dynamical models of
the gas released by the boulder train. Indeed, in the case of the splitting event (Sekanina, 1982; Sekanina et al., 1996;
Comet C/1996 B2 (Hyakutake) a straight spike of diffuse Desvoivres et al., 1999; Boehnhardt et al., 2002), from the
light, typical for dust streamers, was seen along the con- brightness evolution of Sun-grazer and SOHO comets
necting line of the two fragments at the time when the [50 km to 5 m (Sekanina, 2000b, 2002a,b)] and from the
arclets occurred. A similar phenomenon was found for one break-up of Comet D/1993 F2 (Shoemaker-Levy 9) (Seka-
of several arclets observed in Comet C/2001 (LINEAR), nina, 1995a; Asphaug and Benz, 1996). Lower limits of the
although in this particular case no fragment could be de- fragment’s sizes were also derived from the explosion blan-
tected (Jehin et al., 2002). Rodionov et al. (1998) model kets produced during the impacts of the split Comet D/
the arclets of Comet C/1996 B2 (Hyakutake) through a two- 1993 F2 (Shoemaker-Levy 9) on Jupiter (see, e.g., Ortiz et
source (the two fragments) outflow of rarefied supersonic al., 1995). Mass estimates of the fragments are provided
gases that produce shock waves in the region between the by the authors assuming a bulk density for the nucleus
two components. The shock waves are best visible edge- material. A size distribution function N(R) for the fragments
on (i.e., close to quadrature geometry of the comet). This of C/1999 S4 (LINEAR) was derived by Mäkinen et al.
model involves activity on the night side of the primary (2001): N(R) ~ R–2.7 (R for the radius of the fragment).
nucleus — otherwise no shock front is formed. Farnham However, the overall size or mass budget of split comets
et al. (2001) interpret the arclets seen in Comet C/1999 S4 (before and after break-up) remains unknown since it was
(LINEAR) before the major break-up of the nucleus in July not yet measured for individual objects.
2001 as a dust jet from an active region close to the equa- As mentioned in section 2, some of the fragments of split
tor of a fast rotating nucleus. According to this scenario, comets are “persistent” and endure for several years. It
the rotation axis should point toward the Sun. This scenario seems likely that independent and long-lived cometary
certainly has some difficulties in explaining the many arclets nuclei may evolve. Other fragments have very short life-
of gaseous origin seen in the other two comets. times of only a few days to weeks. The fragments of C/
Even though the physical nature of coma arclets in split 1999 S4 (LINEAR) survived intact after the nucleus disrup-
comets is not yet clearly understood, there is no doubt that tion for about 2–3 weeks (see Fig. 5). Thereafter, they dis-
they can be considered as early tracers of nucleus break- appeared quickly — and “collectively” — within a few
up events. days. Exactly what happens to the short- and long-lived
310 Comets II

of comet nuclei (such as internal structure, nucleus/surface

stratification, material types, tensile and shear strengths,
size, and rotation) used in these models are not at all or not
very well known, and (2) the available observations do not
constrain well the actual event sequence and the physical
properties of the parent and daughter components of split
comets. Not surprisingly, only for one split comet, D/1993
F2 (Shoemaker-Levy 9), do modelers seem to agree on the
fragmentation scenario (i.e., tidal splitting close to Jupiter),
although with significant differences in the details of inter-
pretation and conclusion.

6.1. Scenarios

6.1.1. Tidal splitting. Tidal splitting of a body (comet

Fig. 5. Many short-lived fragments of Comet C/1999 S4 (LIN- nucleus) in the neighborhood of a large mass (a planet or
EAR). This R-filter image taken in early August 2000 at the ESO the Sun) is induced when the differential gravitational “pull”
VLT shows at least 16 short-lived fragments that were produced of the large mass throughout the small body exceeds the
in the break-up of the nucleus between 21 and 24 July 2000. The forces of self-gravity and material strength (tensile and/or
fragments are embedded in a diffuse coma of which a long dust- shear) of the latter. A simplified condition for tidal disrup-
tail streamer extends away from the Sun. Image processing is used
tion of spherical bodies was published by Whipple (1963)
to increase the contrast of the fragments on the diffuse coma back-
ground. North is up and east to the left; field of view is 3.4 ×
2.5 arcmin2. Image courtesy of European Southern Observatory σ < GMoρR2/∆3 (3)
(ESO).
The parameter σ is the tensile strength of the material, G
is the gravitational constant, Mo is the mass of the large
body, ρ and R are the bulk density and radius of the sphere,
fragments when they disappear is not known: Do they dis- and ∆ is the distance between the two bodies. A rigorous
solve into even smaller pieces, or do they become inactive? theoretical treatment of the problem for spheres and biaxial
From the 10 split comets (4 short-period and 6 long- ellipsoids can be found in Davidsson (1999, 2001).
period) that are classified taxonomically, 7 comets [16P/ The models predict that the break-up should start from
Brooks 2, 69P/Taylor, 101P/Chernykh, 108P/Ciffreo, C/ the center of the nucleus and that it should affect the body
1975 V1 (West), C/1986 P1 (Wilson) (see A’Hearn et al., as a whole. The products of tidal splitting should be larger
1995), and C/1999 S4 (LINEAR) (see Mumma et al., 2001)] pieces in the center of the nucleus and smaller ones toward
belong to the group of carbon-depleted objects, and 3 com- the surface of the body. This latter prediction, however, may
ets [C/1988 A1 (Liller) (see A’Hearn et al., 1995), C/ depend on the internal structure of the nucleus as well.
1996 B2 (Hyakutake) (Schleicher and Osip, 2002), and C/ Obviously, this scenario works only in the neighborhood
2001 A2 (LINEAR) (see Jehin et al., 2002)] appear to be of heavy bodies. Tidal forces, even if not causing the nu-
“typical” in their carbon content. A link between this taxo- cleus splitting, can be responsible for major cracks in the
nomic parameter and the splitting behavior of the nucleus body that weaken its structural strength such that it may split
is not obvious. The chemical composition of fragments is later as the result of another process (e.g., thermal or rota-
known even less, and not even a single fragment has mea- tional splitting).
sured production rates of gas and/or dust. Bockelée-Morvan 6.1.2. Rotational splitting. Splitting of a rotating nu-
et al. (2001) have inferred from gas production rates of the cleus happens when the centrifugal force exceeds self-grav-
coma of C/1999 S4 (LINEAR) before and after the fatal ity and material strength inside the body. A simplified
splitting in July 2001 that the nucleus of this comet may expression for the condition of disruption of a rotating
have had a rather homogeneous chemistry. This conclusion sphere is given by Sekanina (1982)
would support the (unproven) scenario that this nucleus may
have contained cometesimals that were formed in the same σ < 2π2ρR2/P2 = 1/2ρV2rot (4)
region of the planetary formation disk.
with σ, ρ, and R as explained above; P is the rotation pe-
6. FRAGMENTATION MECHANISMS riod and Vrot is the rotation velocity at the equator of the
sphere. A comprehensive theoretical model for centrifugal
Several fragmentation mechanisms are used to explain forces in rotating spheres and biaxial ellipsoids is presented
the splitting of cometary nuclei. Thus far, the success of by Davidsson (1999, 2001). The acceleration of the rota-
these scenarios in the understanding of these events is lim- tion speed of the nucleus can be caused by reaction forces
ited, presumably since (1) the most important parameters due to outgassing (see Jorda and Gutiérrez, 2002).
 Boehnhardt: Split Comets 311

The prediction of the model is that “dense” nuclei with passage. However, a crust of porous material held together
nonnegligible material strength should break up from the by cohesive forces can withstand internal gas pressure up
body center, while strengthless nuclei should loosen frag- to the tensile strength estimated for cometary nuclei (see
ments from the surface. The properties of the fragmenta- section 6.2).
tion products are case dependent, i.e., larger pieces in the Two different scenarios for comet break-up by internal
center and smaller fragments at the surface for the case of gas pressure have been proposed: (1) an explosive blow-off
“dense” nuclei or — more likely — only smaller pieces for of localized surface areas (possibly covered by an imperme-
strengthless bodies. Rotational splitting depends mainly on able crust) as described by Whipple (1978), Brin and Mendis
the rotation motion of the nucleus and can happen at any (1979), and Brin (1980); or (2) a complete disruption of the
distance from the Sun. Due to changes of the rotational state nucleus as suggested by Samarasinha (2001). The latter case
of the nucleus by reaction forces from comet activity and imposes additional “requirements” on the internal structure
modification of the properties of surface material by the of the nucleus and its surface: It should allow gas diffusion
mass loss of the nucleus when active, the occurrence of throughout the whole body via a system of connecting voids
rotational splitting may in principle happen randomly along in the nucleus, and before splitting, the surface does not out-
the orbit, but clearly with a preference for solar distances gas enough to efficiently reduce the gas pressure inside the
where the comet is active. nucleus. Since both scenarios are based on comet activity,
6.1.3. Splitting by thermal stress. Due to their variable they are restricted to orbit arcs not far from the Sun, even
distances to the Sun, comet nuclei are exposed to diffusion though sublimation of supervolatile ices such as CO and N2
of heat waves penetrating into their interior during orbital can occur up to ~50 AU solar distance (Delsemme, 1982).
revolutions. Thus thermal stress is induced in the body and, Prialnik and Bar-Nun (1992) have proposed crystallization
if the material strength is exceeded, nucleus splitting may of amorphous ice to explain the outburst activity of Comet
occur. Tauber and Kührt (1987) have considered both ho- 1P/Halley at 14 AU outbound. This scenario could also po-
mogeneous bodies (water ice) and nuclei with material in- tentially work to produce internal gas pressure that may
homogeneities (water ice with inclusions of CO2 and sili- cause the fragmentation of cometary nuclei.
cates). In both cases cracks due to thermal stress can form 6.1.5. Impact-induced comet splitting. During their or-
on the surface and, subsequently, minor pieces could split bital revolution around the Sun, comet nuclei can experi-
from the comet. Shestakova and Tambostseva (1997) and ence (hypervelocity) impacts by other solar system bodies
Tambostseva and Shestakova (1999) have presented model such as asteroids. Since comets are small, such an impact,
calculations for comet splitting by thermal stress. A number if it happens, will most likely destroy the whole nucleus,
of cases are distinguishable depending on nucleus size and even if the impactor is a small (subkilometer-sized) body
solar distance: Break-up may occur for larger bodies due itself. Toth (2001) considered asteroid impacts for the dis-
to compression stress, splitting of subkilometer-sized bod- ruption of Comet C/1999 S4 (LINEAR). Impact probabili-
ies due to radial stress may happen closer than 40 AU from ties and the range of impact energies due to meter-sized im-
the Sun, and thermal splitting in general should be effi- pactors from the asteroid belt on short-period comets are
cient — provided that tensile strength of the body material estimated by Beech and Gauer (2002).
is low — when the object is closer than 5 AU to the Sun. A “modification” of this scenario is comet splitting by
The fragmentation products should depend on the cause. impacts of larger boulders produced by the comet itself.
The extend to which the body is affected by thermal stress Such pieces may exist, and it is feasible that they can travel
splitting depends on the depth of the heat wave penetration “aside” the comet in its orbit around the Sun. Impact may
and thus also on the size of the nucleus: Smaller bodies occur at intersection points of their orbits, e.g., near aph-
(subkilometer-sized) can split as a whole, while the break- elion for boulders produced near perihelion. As for most
up of surface fragments is more likely for larger bodies. of the other scenarios described in this section, no detailed
Thermal stress splitting clearly is a scenario that may be analysis and prediction of observable effects are available.
able to produce fragments even at larger distances (several
10 AU) from the Sun. 6.2. Observational Facts and Constraints
6.1.4. Splitting by internal gas pressure. High gas
pressure in the nucleus can be caused by sublimation of sub- 6.2.1. Comet D/1993 F2 (Shoemaker-Levy-9). Comet
surface pockets of supervolatile ices (e.g., CO) when the D/1993 F2 (Shoemaker-Levy 9) broke up in 1992 during a
comet approaches the Sun and the heat wave from the in- close approach with Jupiter (<20,000 km above the cloud
creasing solar illumination reaches the depths of these ice level of the giant planet) (Fig. 6). Modelers (Sekanina, 1994;
pockets. If the gas pressure cannot be released through Asphaug and Benz, 1996; and references contained therein)
surface activity, the tensile strength of the nucleus material of this event agree that the tidal forces of Jupiter have
can be exceeded and fragmentation of the comet occurs. caused the cracking of the nucleus structure of this comet.
Kührt and Keller (1994) present models for crust forma- However, according to Sekanina (1994) the separation of
tion and the buildup of vapor pressure underneath. They the fragments started only 3 h after the time of closest ap-
conclude that a purely gravitationally bound crust is un- proach to Jupiter, i.e., after the tidal forces reached maxi-
stable and will be blown off the nucleus during perihelion mum amplitude. Apparently, the largest fragments traveled
312 Comets II

excludes all activity driven models as the fragmentation

mechanism.
6.2.2. Tensile strength. Thus far, the tensile strength of
a cometary nucleus is less constrained by actual observa-
tions and modeling of splitting events than by comets that
do not split. The large size of Comet C/1995 O1 (Hale-
Bopp) together with its fast rotation of 11.5 h puts a lower
limit of 104 –105 dyn/cm2 on the tensile strength of its
nucleus (assuming a bulk density of 0.5–1 g/cm3). Assum-
ing a similar tensile strength for the nuclei of comets for
which reliable size and rotation period estimates exist, it is
clear that these comets are — at present — “safe” against
Fig. 6. Tidally disrupted chain of fragments in Comet D/1993 F2 rotational break-up. On the other hand, if rotational break-
(Shoemaker-Levy 9). This R-filter exposure taken on 5 May 1994 up is involved in the splitting of short-period comets, a simi-
at the Calar Alto 3.5-m telescope shows fragments F to W of the lar range for the tensile strength as for Comet Hale-Bopp
broken comet. The fragments’ chain extends diagonally across the would follow from the observed separation velocities of the
image. Each fragment is surrounded by its own coma while their
fragments (see section 2.2). Unless one assumes a special
diffuse and wider dust tails overlap, causing a brighter background
nature for the bodies of split comets, it is obvious from the
above the image diagonal. North is up and east to the left; field
of view is 4.3 × 2.5 arcmin2. Image courtesy of K. Birkle, Max- existence of fragments that the nuclei of split comets are
Planck-Institut für Astronomie, Heidelberg. not strengthless and they have an intrinsic substructure or
at least nonuniform tensile strength.

7. RELATED PHENOMENA: DISAPPEARING

in the middle of the “chain” of the known 23 Shoemaker- COMETS AND DUST-TAIL STRIAE
Levy 9 components, as inferred from the size estimates and
the impact explosions at Jupiter in July 1994. This picture 7.1. Disappearing Comets
would be in agreement with the tidal break-up model, which
expects larger fragments to be created in the center of the Comets can disappear in front of the “eyes” of the ob-
splitting body, while lighter and smaller ones, i.e., the frag- servers without obvious indication of a dramatic nucleus
ments at the leading and trailing end of the Shoemaker- fragmentation event: C/1988 P1 (Machholz), Comets C/
Levy 9 chain, arose closer to the surface. Similar signatures 1996 Q1 (Tabur), C/2000 W1 (Utsunomiya-Jones) (see
are also seen in some peculiar crater chains at the surface Fig. 7), C/2002 O4 (Hönig), and C/2002 O6 (SWAN) are
of the jovian moons Callisto and Ganymede (Schenk et al., some of the more recent cases. Leftovers of these disap-
1996). The crater chains in the icy crust of these satellites pearing comets are diffuse and fading comae and so-called
are believed to be caused by impacts of narrow ensembles “truncated” dust tails in which the synchrones are only
of fragments from tidally split comets after close encoun- populated to a certain start time at the nucleus and no
ters with Jupiter. In Comet Shoemaker-Levy 9, tertiary split- “younger” grains are found in the dust tails. Two scenarios
ting occurred in some of the fragments, in all cases for should be mentioned that could explain the observations:
unknown reasons (and certainly not due to tidal forces), but (1) the complete disintegration of the nucleus similar to
clearly suggesting that the split components may have had Comet C/1999 S4 (LINEAR) (see below) and (2) an
intrinsic substructure (Sekanina, 1995a). evolved, very crusty nucleus with one or only a few active
Tidal splitting at Jupiter or the Sun is claimed to be in- regions that become “suddenly” dormant due to shadow-
volved in the break-up of Comets 16P/Brooks 2 (Sekanina ing from solar illumination when the comet moves along
and Yeomans, 1985) and the Sun-grazer Comets C/1882 R1 its orbit. Both scenarios imply that disappearing comets are
(Great September Comet), C/1963 R1 (Pereyra) and C/ to be considered within the terminal phase of cometary
1965 S1 (Ikeya-Seki) (Sekanina, 1997a). The break-up evolution. It may be noteworthy that gas jets, perpendicu-
mechanisms of all other split comets remain unknown, even lar and symmetric to the Sun-comet line and without coun-
though one may favor rotational break-up for the short- terparts in the dust, were observed in Comet C/1996 Q1
period comets because of the range of observed separation (Tabur) before disappearance of the comet (Schulz, 2000).
velocities and their independence from the heliocentric dis- These jets very much resemble the arclets seen during split-
tance of the splitting event. Comet C/1999 S4 (LINEAR) ting events in other comets (see section 4.2). Since C/
has certainly experienced a nucleus splitting of a somewhat 1996 Q1 (Tabur) together with Comet C/1988 A1 (Liller)
unique nature, since its nucleus disrupted in many pieces is most likely a product of a splitting event during an ear-
that disappeared after a lifetime of a few weeks (see also lier apparition (Jahn, 1996), it is feasible that the former
section 7.1). Nucleus splitting at very large heliocentric comet has experienced further splitting events that may have
distances [beyond ~100 AU as suggested for Comet C/1970 culminated in an — unobserved — complete dissolution of
K1 (White-Ortiz-Olelli) (Sekanina and Chodas, 2002b)] the nucleus during its last return to the Sun. The disappear-
 Boehnhardt: Split Comets 313

ruption. The new interpretation, proposed by Z. Sekanina

and H. Boehnhardt at the Cometary Dust Workshop 2000
held in Canterbury, implies much earlier separation times
of the parent fragments from the main nucleus, i.e., the
boulders are produced by the cometary nucleus far away
from the Sun and drift slowly away from the primary nu-
cleus (hence no need for a high β) to the distance where,
during approach of the comet to the Sun, the secondary
fragmentation occurs in the region of the dust tail. This
secondary disintegration is a process of short duration (on
the order of one day or less) that may affect a boulder as a
whole, i.e., it may become completely dissolved. An inter-
esting candidate mechanism for the fragmentation of boul-
ders is gas and dust emission activity when boulders
approach the Sun. The proposed striae fragmentation hy-

Fig. 7. Comet C/2000 W1 (Utsunomiya-Jones), which disap-

peared in early 2001. This R-filter image, taken on 19 February
2001 at the 3.5-m Telescopio Nazionale Galileo (TNG) at the
Roque de los Muchachos Observatory in La Palma, shows only a
very weak and diffuse dust cloud without central condensation at
the position of the comet (center and uppermost part of the im-
age). North is up and east to the left; field of view is 3.0 ×
2.6 arcmin2. Image courtesy of J. L. Ortiz, Instituto Astrofisico de
Andalucia, Granada.

ance together with the later perihelion passage of C/1996

Q1 (Tabur) to C/1988 A1 (Liller) also supports the inter-
pretation of C/1996 Q1 being the fragment of C/1988 A1.
After some smaller splitting events before perihelion,
Comet C/1999 S4 (LINEAR) broke apart completely in the
second half of July 2000 close to perihelion (see Fig. 5).
More than 20 fragments, but no “dominant” primary frag-
ment, were observed (Weaver et al., 2001). About three
weeks after the disruptive splitting event the fragments
could not be detected, and it is assumed they disappeared,
more or less collectively, either by further fragmentation or
by becoming undetectable due to exhaustion of sublima-
tion activity. The rapid decay of water gas production after
break-up (Mäkinen et al., 2001) supports the scenario that
this comet disappeared completely in a diffusing and fading
cloud of previous dust release. This splitting comet can be
considered the prototype (since best studied) of a disappear-
ing comet.

7.2. Dust-Tail Striae and Comet Splitting Fig. 8. Striated dust tail of Comet C/1995 O1 (Hale-Bopp). In
March and April 1996 the diffuse dust tail (right part of the image)
The origin of striae in the dust tail of some bright com- of Comet C/1995 O1 (Hale-Bopp) contained many striae. In the
image the striae are best visible as narrow straight bands to the
ets, e.g., C/1975 V1 (West) and C/1995 O1 (Hale-Bopp)
outer edge of the dust tail. The striae are not coinciding with dust
(see Fig. 8), suggest secondary fragmentation of house-sized
synchrones pointing toward the nucleus in the coma (lower left,
boulders (Sekanina and Farrell, 1980). The previous two- overexposed), which indicates that the striae dust is not released
step model scenario introduced by Sekanina and Farrell directly from the nucleus. The prominent structured ion tail points
(1980) involved relatively large pieces with very high so- away from the direction of the Sun. North is up and east to the
lar radiation pressure parameter β (>0.1) as “parents” of left; field of view is 3.0 × 4.5 deg2. Image courtesy of K. Birkle,
striae that split off the cometary nucleus weeks before dis- Max-Planck-Institut für Astronomie, Heidelberg.
314 Comets II

TABLE A1. List of split comets, likely split pairs, and families of split comets.

Tidally split comets

C/1882 R1 (Great September Comet)* 16P/Brooks 2 (1889 + 1995)*
C/1963 R1 (Pereyra)* C/1965 S1 (Ikeya-Seki)*
D/1993 F2 (Shoemaker-Levy 9)†

Comets split for unknown reasons

3D/Biela (1840) C/1860 D1 (Liais)
C/1888 D1 (Sawerthal) C/1889 O1 (Davidson)
D/1896 R2 (Giacobini) C/1899 E1 (Swift)
C/1906 E1 (Kopff) C/1914 S1 (Campbell)
C/1915 C1 (Mellish) 69P/Taylor (1915)
C/1942 X1 (Whipple-Fedtke) C/1947 X1 (Southern Comet)
C/1955 O1 (Honda) C/1956 F1 (Wirtanen)
C/1968 U1 (Wild) C/1969 O1 (Kohoutek)
C/1969 T1 (Tago-Sato-Kosaka) C/1975 V1 (West)
79P/du-Toit-Hartley (1982) 108P/Ciffreo (1985)
C/1986 P1 (Wilson) 101P/Chernykh (1991)
C/1994 G1 (Takamizawa-Levy) 141P/Machholz 2 (1987 + 1989)
51P/Harrington (1994 + 2001) 73P/Schwassmann-Wachmann 3 (1995/1996 + 2001)
C/1996 B2 (Hyakutake) C/1996 J1 (Evans-Drinkwater)
C/1999 S4 (LINEAR) C/2001 A2 (LINEAR)
57P/du-Toit-Neujmin-Delporte (2002)

Likely split pairs

C/1988 F1 (Levy) and C/1988 J1 (Shoemaker-Holt)
C/1988 A1 (Liller) and C/1996 Q1 (Tabur)
C/2002 C1 (Ikeya-Zhang) and C/1661 C1
C/2002 A1 (LINEAR) and C/2002 A2 (LINEAR)
C/2002 Q2 (LINEAR) and C/2002 Q3 (LINEAR)

Likely split families

42P/Neujmin 3 and 53P/Van Biesbroeck and 14P/Wolf‡ and 121P/Shoemaker-Holt 2‡
C/1965 S1 (Ikeya-Seki) and C/1882 R1 (Great September Comet) and C/1970 K1 (White-Ortiz-Olelli)
C/1880 C1 (Great Southern Comet) and C/1843 D1 (Great March Comet)
Kreutz group and SOHO comets
*Likely scenario.
† The only secure case of a tidally split comet.
‡ Uncertain member.

pothesis somehow implies that striae should predominantly reported for both comets are to be considered uncertain for
appear in comets before reaching perihelion. the time being, we do not include 26P/Grigg-Skjellerup and
C/1995 O1 (Hale-Bopp) in the list below. Based on the clus-
8. APPENDIX: LIST OF SPLIT COMETS tering of dust impacts during the Giotto encounter, the ex-
istence of fragmenting boulder-sized pieces in the coma of
Here we compile a list of split comets, likely pairs, and Comet 1P/Halley (see Boehnhardt, 2002, and references
families of split comets as reported in the literature therein) is also the subject of speculation.
(Table A1). For periodic comets the year of the splitting
event is given in parenthesis. Comet C/1995 O1 (Hale- Acknowledgments. I wish to thank Drs. Z. Sekanina (Jet Pro-
Bopp) is not listed as split comet below even though indi- pulsion Laboratory, Pasadena) and B. Marsden (Center for Astro-
cations exist that this comet may have displayed double or physics, Cambridge) for the provision of partially unpublished re-
multiple nuclei (Sekanina, 1997b; Marchis et al., 1999) and sults on comet fragmentation. Images of split comets presented in
this paper are collected at the Cerro La Silla and Cerro Paranal Ob-
several companion comae (Boehnhardt et al., 2003). It is
servatories of the European Southern Observatory (ESO), at the
also noted that McBride et al. (1997) favor the existence
Calar Alto Observatory of the Max-Planck-Institut für Astronomie,
of a major boulder in the coma of Comet 26P/Grigg-Skjel- and at the Telescope Nazionale Galileo of the Roque de los Mu-
lerup from the Giotto flyby measurements at the comet. The chachos Observatory in La Palma. I am particularly grateful to
detection of fragments (several hundred meters in size) Dr. K. Birkle (Max-Planck-Institut für Astronomie Heidelberg), to
around this comet is not confirmed by other observations Dr. E. Jehin (European Southern Observatory, Santiago de Chile)
(Boehnhardt et al., 1999). Since the fragmentation products and collaborators, and to Dr. J.-L. Ortiz (Instituto Astrofisico de
 Boehnhardt: Split Comets 315

Andalucia, Granada) and collaborators for the provision of unpub- Farinella P. and Davis D. R. (1996) Short-period comets: Primor-
lished image material. Last, but not least, I wish to thank Dr. D. dial bodies or collisional fragments? Science, 273, 938–941.
Andersen (Max-Planck-Institut für Astronomie, Heidelberg) for a Farnham T. L., Schleicher D. G., Woodney L. M., Birch P. V.,
critical review of the manuscript. Eberhardy C. A., and Levy L. (2001) Imaging and photometry
of Comet C/1999 S4 (LINEAR) before perihelion and after
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(LINEAR). Earth Moon Planets, 90, 195–203. Sekanina Z., Boehnhardt H., Käufl H. U., and Birkle K. (1996)
Sekanina Z. (1977) Relative motions of fragments of the split com- Relationship between outbursts and nuclear splitting of Comet
ets. I. A new approach. Icarus, 30, 574–594. 73P/Schwassmann-Wachmann 3. JPL Cometary Sciences
Sekanina Z. (1978) Relative motions of fragments of the split com- Group Preprint Series 183, pp. 1–20.
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extensively observed comets. Icarus, 33, 173–185. ary fragmentation of Comet Shoemaker-Levy 9 and the rami-
Sekanina Z. (1979) Relative motions of fragments of the split com- fications for the progenitor’s break-up in July 1992. Planet.
ets. III. A test of splitting and comets with suspected multiple Space Sci., 46, 21–45.
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Sekanina Z. (1982) The problem of split comets in review. In Thomas D. (2002) Recurring outbursts and nuclear fragmenta-
Comets (L. L. Wilkening, ed.), pp. 251–287. Univ. of Arizona, tion of Comet C/2001 A2 (LINEAR). Astrophys. J., 572, 679–
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Sekanina Z. (1988) Comet Wilson (1986l). IAU Circular No. 4557. Sekanina Z., Chodas P. W., Tichy M., Tichy J., and Kocer M.
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Sekanina Z. (1994) Tidal disruption and the appearance of periodic Shestakova L. I. and Tambovtseva L. V. (1997) The thermal de-
Comet Shoemaker-Levy 9. Astron. Astrophys., 289, 607–636. struction of solids near the Sun. Earth Moon Planets, 76, 19–45.
Sekanina Z. (1995a) Evidence on sizes and fragmentation of the Tambovtseva L. V. and Shestakova L. I. (1999) Cometary splitting
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Sekanina Z. (1995b) Comet C/1994 G1 (Takamizawa-Levy). IAU onomy of comets and asteroids based on the Lyapunov indi-
Circular No. 6161. cators. Astron. Astrophys., 356, 339–346.
Sekanina Z. (1997a) The problem of split comets revisited. Astron. Toth I. (2001) Impact-triggered breakup of Comet C/1999 S4
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Sekanina Z. (1997b) Detection of a satellite orbiting the nucleus other small bodies with its orbit. Astron. Astrophys., 368, L25–
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(C/1996 J1). Astron. Astrophys., 339, L25–L28. Weaver H. A. and 20 colleagues (2001) HST and VLT investiga-
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 Meech and Svoren: Physical and Chemical Evolution of Cometary Nuclei 317

Using Cometary Activity to Trace the Physical and

Chemical Evolution of Cometary Nuclei
K. J. Meech
Institute for Astronomy at the University of Hawai‘i

J. Svoren
Astronomical Institute of the Slovak Academy of Sciences

Historically, minor bodies are classified as comets based on observations of “activity,” which
refers to the appearance of dust and gas around the nucleus. While cometary activity has been
observed for centuries, at ever-increasing heliocentric distances, our understanding of the mecha-
nisms for producing cometary activity and its heliocentric dependence has only recently been
developed to the level of sophistication needed to make detailed comparison with the observa-
tions. A thorough understanding of cometary activity is closely coupled with knowledge about
the formation of comets, thermal models of cometary nuclei, and chemistry in the coma. This
chapter summarizes the specific chemical and physical changes that a comet nucleus under-
goes, concentrating on the active phases. The specific drivers of activity are discussed, as well
as the means of measuring the activity in comets. Finally, some historical and modern examples
of specific types of cometary activity are discussed and are used to make inferences about both
primordial differences between comet dynamical classes and evolutionary, or aging, effects.

1. INTRODUCTION of the timescales for the physical evolution of comet nu-

clei, changes in shape, spin period, and eventual disappear-
What controls the activity of comet nuclei? Comets ex- ance of activity as comets either evolve into asteroidal-like
hibit a wide range of physical characteristics. Some of these objects or experience complete disintegration is presented
characteristics can be attributed to the systematic physical in Jewitt (2004). In this chapter a brief review of comet for-
differences among different dynamical and evolutionary mation, including the physical and chemical processes oc-
groups. We must try to distinguish whether these differences curring in the precursor comet material, is presented in the
are the products of aging or evolutionary process, or context of, and to set the stage for, distinguishing between
whether they reflect the primordial differences among the evolution and primordial differences among comets. This
groups. “Aging” of cometary nuclei refers to the effects is followed by a thorough discussion of the mechanisms of
since the time of formation that have altered the nucleus, comet activity and the means by which activity is measured.
either chemically or physically, and that may cause a change Finally, specific observations of cometary activity are pre-
in the type or level of activity. Some of the signs of aging in sented and inferences drawn about implications for pri-
comets include (1) the production of comae and tails consist- mordial composition and evolution of different dynamical
ing of escaping gas and dust, which creates debris occupy- classes of comets. The ultimate goal of understanding the
ing the orbits of the distintegrating comets; (2) nongravita- chemical and physical evolution of cometary nuclei is to
tional effects in the comet’s motion, produced by jet effects assess the extent to which comets represent the unaltered
of the escaping matter on a rotating nucleus; (3) outbursts source material from their regions of formation in the so-
(or sudden brightness changes) and splitting of cometary lar nebula, and thus to use comets as tracers of solar sys-
nuclei, possibly leading to total disruption; (4) changes in tem formation processes.
the volatile composition of the escaping gases and internal
physical nucleus properties, in particular in the upper layers 1.1. Source Regions and Formation
of the nucleus; (5) the progressive changes of the cometary
absolute brightness, including the temporary diminishing of Although discussed in detail elsewhere in this volume
cometary activity; (6) the change of the physical appearance (e.g., Duncan et al., 2004; Dones et al., 2004), it is impor-
of comets to objects indistinguishable from asteroids mov- tant to the understanding of the activity in comets to briefly
ing in cometary orbits (extinction of cometary nucleus); and summarize some of the essential elements of the formation
(7) the total disappearance of the comet nuclei. and dynamical evolution of comets. As the presolar nebula
A thorough discussion of the mechanisms, dynamics, collapsed, solid particles settled to the midplane. They may
and changes in activity caused by comet splitting are cov- have undergone processing (e.g., shock-induced sublima-
ered in Boehnhardt (2004) and Jewitt (2004) and will not tion and volatile recondensation) of their icy mantles as they
be discussed in detail here. Likewise, a detailed discussion fell (Lunine and Gautier, 2004). Dynamical evidence sug-

317
318 Comets II

gests that the short-period (SP) comets must have had a low- zula and Johnson, 1991). This will create both nonvolatile
inclination source in the transneptunian region (Duncan et material and highly reactive radicals, which will then po-
al., 1988, 2004), whereas the long-period (LP), Halley-type tentially be incorporated into the comets. There is also com-
(HT), and dynamically new (DN) comets perturbed inward plex thermal and chemical processing that can occur (see
from the Oort cloud may have formed at smaller heliocen- Wooden et al., 2004, for a complete discussion). However,
tric distances. While most of the Oort cloud comets prob- a fundamental question remains as to how much of this
ably formed beyond 20 AU, all the giant planets injected precursor material survives the formation process (Mumma
comets into the Oort cloud (Fernández and Ip, 1981; Dones et al., 1993). The water contained in comets is likely to have
et al., 2004). Recent dynamical work has shown that per- two sources: H2O ice that survived disk infall, and that
haps as much as one-third of the scattered-disk transnep- which formed in the disk (see Irvine and Lunine, 2004, for
tunian population may eventually end up in the Oort cloud a discussion).
(Fernández and Brunini, 2003). Thus, the source regions of 1.2.2. Accretion phase. Water-ice formed by low-pres-
the different dynamical classes of comets are not clear-cut, sure vapor deposition, conditions expected in the solar neb-
and there may be some SP, HT, and LP comets that may ula as interstellar grains were falling in toward the midplane,
have had the same source region in the Kuiper belt and scat- will have one of three forms: two crystalline polymorphs
tered disk, but would have followed different dynamical (hexagonal, Ih, and cubic, Ic), and both a low- and high-
paths (see the discussion in Duncan et al., 2004). density amorphous form, Ial and Iah respectively. When H2O
ice condenses at temperatures below 100 K, it condenses
1.2. Evolution of Comets in the amorphous form because it lacks the energy to form
a regular crystalline structure; below 20 K, this is likely to
Almost every observable property of comets is connected be Iah ice. As the H2O ice condenses, it has the ability to
with their progressive disintegration. All processes that trap gases as high as 3.3–3.5 times the amount of the ice
physically and chemically alter a cometary nucleus can be (Laufer et al., 1987).
regarded as aging. The aging processes in comets, imply- The mechanism for amorphous ice trapping is that gas
ing their limited physical lifetimes, are of fundamental sig- enters an open pore during condensation and is held in place
nificance for the evolutionary history of the whole cometary by van der Waals forces. The pore is subsequently covered
population. Due to accompanying nongravitational effects and the gases are trapped. The amount of gas that can be
and dynamical chaos, it is impossible to extrapolate the mo- trapped is a very strong function of the condensation tem-
tion of individual comets far beyond the time span covered perature: H2 and D2 can only be efficiently trapped below
by observations. The aging processes, accelerating with de- 20 K, Ne only below 24 K, and many other light gases may
creasing distance from the Sun, are too slow and irregular be trapped only up to 100 K. More gases can be trapped at
to become detectable during a single apparition (Kresák, lower temperatures because the molecules will have longer
1987). When a SP comet is followed over a number of re- residence times and are more likely to have their pores
turns, some changes may be observable. The lifetimes of sealed before they can escape. The gases that have stronger
individual active comets are very short compared with the van der Waals attraction (polarizability) will be preferen-
history of the solar system, and a replenishment with pre- tially enriched. The temperature also affects the size of the
viously inactive objects is necessary to maintain the present free channels in the ice, and hence the atoms that can per-
state. All these arguments point to the fact that the evolu- meate the ice.
tion of comets is best studied on a statistical basis. If a large amount of volatiles are present as the water is
The aging or evolutionary effects that a comet nucleus condensing at low temperatures, and after the maximum
will experience can be divided into four primary areas: the amount of gas is trapped in the pores, it is possible to have
precometary phase, where the interstellar material is altered some surface freezing of the more volatile species (Notesco
prior to incorporation into the nucleus; the accretion phase et al., 2003).
during nucleus formation; the cold storage phase, the phase This accretion phase will have significant implications
where the comet is stored for long periods at large distances for the observed activity in comets as described below. In
from the Sun; and the active phase (Meech, 1999). particular, Oort cloud comets and LP comets will have
1.2.1. Presolar nebula. The precursor cometary mate- predominantly formed in the vicinity of the giant planets
rial, interstellar grains, is stored in cold quiescent molecu- where nebular temperatures may have been between 60 and
lar clouds (T = 10 K, n = 103 cm–3) and in warm, dense 100 K and will be expected to consist mostly of ice Ial.
protostellar regions (T = 100 K, n = 106 cm–3). A complete Kuiper belt objects (KBOs) formed and have remained pre-
discussion of ice and grains in the precometary phase is dominantly at temperatures below 30–50 K. Formation in
presented in Irvine and Lunine (2004) and Wooden et al. these different temperature regimes can have profound
(2004). The mantles of interstellar grains undergo signifi- implications for the chemical composition of the comets.
cant processing in the molecular clouds from bombardment 1.2.3. Cold storage phase. Comets may be stored for
by cosmic rays. The ions lose energy by ionization of the billions of years in the Oort cloud or the distant outer solar
target material and breaking chemical bonds in the target, system before passing close to the Sun and entering the
and they can also cause sputtering from the surface (Straz- active phase. During this time galactic-cosmic-ray irradia-
 Meech and Svoren: Physical and Chemical Evolution of Cometary Nuclei 319

Fig. 1. Diagram showing the sequence of aging processes in the upper layers of a comet nucleus from (a) the pristine state, consist-
ing of primordial planetesimals (enlargement shown on left), (b) to the alterations it undergoes while stored in the Oort cloud includ-
ing a possible crystalline core caused by radioactive heating from 26Al to (c) the changes in the surface during the active phase and
(d) near the end of its evolution as a dust mantle builds up.

tion can create a thin, stable cohesive crust that will have In addition to the radiation damage to the surface, up to
some tensile strength to a depth of 10 g cm–2 (Strazzula and 20% of the Oort cloud comets will have been heated to at
Johnson, 1991). In addition, radicals will form in the up- least 30 K to a depth of 20–60 m from the passage of lumi-
per few meters of the comet surface, causing chemical al- nous stars, and most comets may have been heated as high
teration (to ~300 g cm–2). Finally, the upper layers will be as 45 K to a depth of 1 m from stochastic supernovae events
depleted in volatile material (to ~100 g cm–2). Of course (Stern and Shull, 1988). This heating may result in volatile
there may be similar irradiation processing of the precomet- depletion in the upper layers. Likewise, gardening from
ary grains from the higher radiation environment from the interstellar grain impacts will also alter the upper few centi-
young Sun, but these may sublimate from the grains dur- meters of the surface (Stern, 1986).
ing infall, and would be too large to be trapped in the con- While collisions themselves in the Oort cloud are prob-
densed amorphous H2O ice. Figure 1 summarizes the stages ably very rare, recent work indicates that many of the ob-
of evolution that a comet may undergo. jects ejected into the Oort cloud were probably heavily
320 Comets II

collisionally processed during their ejection (see Stern and comets has been observed for a long time. This is discussed
Weissman, 2001, and references therein). The space den- at length in the chapter by Dones et al. (2004) in the context
sity of objects in the region of the Kuiper belt is much of the “fading problem” first noted by Oort (1950).
greater, and as a result, collisional models show that small
objects in this region should have heavily damaged interi- 2. TYPES OF ACTIVITY
ors, and a significant percentage of the surfaces of the larger
objects should be heavily cratered (Durda and Stern, 2000). It is clear from recent studies of low-temperature vola-
Objects at smaller heliocentric distances, such as the Cen- tiles and from comet observations that the gases that are
taurs and SP comets, will not have a significant collisional released from the comet in addition to water are trapped
history different from their source regions over the age of within the H2O ice, and not just frozen among the H2O-ice
the solar system. The net effect of the different collisional crystals (Bar-Nun and Laufer, 2003; Prialnik et al., 2004).
regimes for the LP and SP comets should manifest itself as Table 1 shows the temperatures at which various volatile
differences in crater density on their surfaces, devolatiliza- processes may occur for pure ices that can lead to activity.
tion in the upper layers, and possibly surface chemistry. The table also indicates approximate heliocentric distances
Evolution of meteorites provides evidence of an early at which these equilibrium surface temperatures are reached
heat source in the solar system, and it is likely that the ra- for dark isothermal bodies (neglecting cooling caused by
dionuclide 26Al was responsible for radiogenic heating of sublimation). It should be noted that the sublimation tem-
large bodies. Models that investigate the role that 26Al plays perature or distance at which this is reached is not a single
in the evolution of cometary interiors showed that because number. Rather, the sublimation will occur over a wide
there is evidence for amorphous ice in comets, their interi- range of temperatures, but at different rates. For example,
ors cannot have been heated above 137 K (Prialnik et al., while the peak for the amorphous to crystalline ice phase
1987). The heating from 26Al would occur during the pe- transition occurs near 137 K, it will start slowly at much
riod of cometesimal formation early in the solar system’s lower temperatures, and while ice Ih sublimates at 180 K,
history and would raise temperatures to between 20 and this process will start at much lower temperatures.
120 K, depending on the nucleus size (the larger nuclei
would be less efficient at cooling). Whereas it would be 2.1. Sublimation of Pure Ices
expected that a pure ice nucleus would either be all crys-
talline or all amorphous (depending on size), the effect of The primary driver for activity close to the Sun is sub-
refractory material would be to quench the conversion, leav- limation, the transitions between the solid and vapor state.
ing a crystalline core with an amorphous mantle. This is a combination of surface and subsurface phenom-
The situation regarding heating in KBOs may be some- ena, since there can be sublimation from subsurface pore
what different because of their larger sizes. When consid- walls (see Prialnik et al., 2004). The temperature at which
ering combined models of accretion and thermal evolution
and the effect of radiogenic heating, it was found that very
small bodies were relatively unaffected, the largest KBOs TABLE 1. Temperature regimes for onset of comet activity.
would still contain significant amorphous material, while
the intermediate sizes would be the most heavily processed T (K) Process r (AU)
(Merk and Prialnik, 2003). In the bodies that were thermally 5 H2 sublimation >3000
altered, highly volatile species would be lost, and there 22 N2 sublimation 160
could be crystallization and even melting in the interiors. 25 CO sublimation 120
1.2.4. Active phase of comets. During the active phase, 31 CH4 sublimation 80
when the comet passes within the inner solar system and 35–80 Ice Iah anneals 60–10
experiences significant solar insolation, there is consider- 38–68 Iah converts to Ial 55–15
able evolution of the interior and surface of the comet. The 44 C2H6 sublimation 40
upper few meters of the surface of a comet making its way 57 C2H2, H2S sublimation 24
64 H2CO sublimation 20
into the inner solar system for the first time will be depleted
78 NH3 sublimation 14
in volatile material by sublimation, even at large heliocen-
80 CO2 sublimation, Ial anneals 13
tric distances, and may have highly volatile radicals created 91 CH3CN sublimation 9
due to the chemical processing from galactic cosmic rays. 95 HCN sublimation 8
Just below this layer, which will be removed during the first 99 CH3OH sublimation 8
passage, will be a layer of “pristine” amorphous ice. 70–120 Ice Ial anneals 18–
On the first passage through the inner solar system, the 90–160 Ice Ial → Ic phase change 11–
solar insolation will cause the crystallization of the amor- 160 Ice Ic → Ih phase change
phous ice from the surface inward at much lower tempera- 180 Ice Ih sublimation
tures than would be expected for H2O ice sublimation. The Water-ice information from Laufer et al. (1987), sublimation infor-
differences in the active phases of Oort clouds comets on mation from Yamamoto (1985) and Handbook of Chemistry and
their first perihelion passage in comparison with periodic Physics (Lide, 2003).
 Meech and Svoren: Physical and Chemical Evolution of Cometary Nuclei 321

this process begins depends on the latent heat of sublima- value of q = 0.3 and p = 0.03 and thus AB = 0.009 from Deep
tion and the equilibrium surface temperature of the nucleus. Space 1 observations of 19P/Borrelly. Also, L is the solar
The latter depends on many factors such as heliocentric dis- luminosity, r the heliocentric distance, ε the surface emis-
tance, albedo, surface emissivity, rotation rate, and pole direc- sivity, P the saturation vapor pressure for molecule µ (in
tion, as well as surface properties that affect heat transport this case water), mµ the mass of the water molecule, k the
below the surface. Boltzmann constant, and H the latent heat of sublimation.
The simple energy balance equation has been used for A figure produced by Delsemme (1982), who computed
many years to estimate the “turn on” of comets assuming the gas production rates for sublimation of pure volatiles,
that the activity is caused by sublimation of various pure led to the unfortunate interpretation that activity on a pre-
volatiles from the surface dominantly H2O-ice nucleus cannot be sustained beyond
r = 3 AU. In the original figure, ro was the distance at which
only 2.5% of the solar flux was used for vaporization of
(1 − AB)L mµ
= εσT4 + Pµ Hµ (1) volatiles, and it represented the turnover in the curve on the
4πr2 2πkT log-log plot. New calculations of these production rates are
shown in Fig. 2 using data from Prialnik et al. (2004) for the
Here, AB = pq is the Bond albedo, p is the geometric albedo, sublimation vapor pressures and latent heats. In these simple
and q is the phase integral. Buratti et al. (2004) derive a models, the pole is assumed to be perpendicular to the orbit,

Fig. 2. (a) Log-log plot of production rates of molecules as a function of log(r) for an isothermal nucleus of albedo AB = 0.04 for
CO, CH4, C2H2, C2H6, CO2, NH3, CH3OH, and H2O [after Delsemme (1982); see section 2]. Data for the computation of sublimation
vapor pressures and latent heats of sublimation from Prialnik et al. (2004). (b) Same as (a), but for a nucleus with albedo AB = 0.7.
(c) Total mass loss vs. r for AB = 0.04 for a RN = 10-km nucleus. (d) Total mass loss vs. r for AB = 0.04 for a RN = 100-km nucleus.
322 Comets II

and there is no variation with temperature as a function of surface of the nucleus as far out as 5–6 AU, CO2 can lift
distance from the subsolar point over the surface. off optically significant grains near 16–19 AU, whereas CO
Delsemme (1982) used a much higher albedo (pv ~ 0.7) fluxes are sufficiently high throughout the region of the
for the nucleus and an emissivity that was much lower (ε ~ Kuiper belt to entrain optically significant amounts of dust.
0.65) than is currently commonly accepted, but these were This equation assumes spherical nonporous grains; more
the best assumptions available at the time. The effect of the realistic shapes and porosities are even more readily lifted
albedo on the production rate is shown in Figs. 2a and 2b. off the nucleus because of their larger surface area per unit
While there is a distinct slope change in the log-log plots mass. Surface brightness profile comparisons of comet nuclei
between about r = 4–6 AU for H2O production, it is impor- in comparison to stars can place very strong limits on the pres-
tant to note that the production does not drop to zero beyond ence of dust coma, down to production limits of 10–2 kg s–1
this distance. Therefore, claims cannot be made that a nu- (see section 3).
cleus is bare based solely upon a heliocentric distance that Although low nucleus albedos have been commonly
is greather than 3 AU. This is more easily seen in Fig. 2c, accepted since the time of the 1P/Halley encounter, some
which is a plot of log(Q) vs. r. people have continued to naively ignore the consequences
Clearly there is some level of water leaving the nucleus of these low albedos, and have not adjusted their thinking
out to large distances. The issue is whether the gas flux is about the distances at which H2O-ice sublimation can cre-
sufficient to drag dust into an observable coma. Figures 2c ate a significant coma. It should be noted that OH has been
and 2d show the molecular loss rate converted into a total detected in Comets 1P/Halley (r ~ 4.9 AU; log Q[OH] ~ 29)
mass loss (kg s–1) for gas (or dust if one assumes a dust gas and C/1995 O1 (Hale-Bopp) (r = 5.13 AU; log Q [OH] =
mass ratio = 1). Depending on the dust-to-gas mass ratio 27.19) out to distances of r ~ 5 AU using narrowband pho-
and the grain sizes (and hence minimum grain size that can tometry in the near-UV (Schleicher et al., 1997, 1998).
be lifted off the nucleus), this translates to the potential for
significant observable dust coma at large r, and for large 2.2. Clathrate Sublimation
nuclei, this might translate into an observable coma.
The critical grain size, acrit, that can be lifted off the Early models attempting to explain the presence of highly
nucleus may be approximated by estimating the drag force, volatile compounds with orders-of-magnitude differences
Fdrag, on the grain as the product of the momentum per in vapor pressure appearing nearly simultaneously in the
molecule, µmHvth, and the number of collisions per unit cometary comae invoked the idea that these compounds
time. Here, vth is assumed to be the mean thermal speed of were trapped as clathrate hydrates (Delsemme and Swings,
the gas. The collisions per unit time is computed as the vol- 1952). A clathrate hydrate is a crystalline framework of
ume swept out by the grain in time t, πa2vtht multiplied by water molecules that incorporates guest molecules in the
the gas number density, N(r), and substituting this into the voids. The water molecules do not specifically interact with
equation of motion the guest molecules trapped within the clathrate-hydrates,
and the latter will be released as the water sublimates. Clath-
rate formation in impure ices is unlikely; laboratory experi-
d2r GMmg
mg =− + Fdrag (2) ments demonstrate that clathrate formation for many species
dt2 r2 is impossible at low temperatures and pressures, and their
presence is not necessary to explain the presence of spe-
where M and mg are the nucleus and grain masses respec- cies other than water (Jenniskens and Blake, 1996). In ad-
tively, G is the gravitational constant, and N(r) is given by dition, the abundances of the observed species are far too
high to be trapped in this manner. There are two types of
2 clathrate hydrates, and the size of the guest molecule de-
Q RN
N(r) = (3) termines which forms. The H-bonded water molecules in
4πRNvth r
2
the clathrate hydrate type I are geometrically organized into
cells with two small cages and six large ones. The type II
The critical radius is then clathrate has cells with 16 small and 8 large ones, the latter
being 10% bigger than the counterparts for the type I clath-
rate (Lunine and Stevenson, 1985). Clathrate type I can trap
9µmHQvth
acrit = (4) in the ratio of 1/7 and clathrate type II can trap in the ratio
64π2ρgρNR3NG of 1/17 to water.

where µ is the atomic weight of the gas in question, mH the 2.3. Amorphous Ice Crystallization and Annealing
mass of hydrogen, Q (molec s–1) is the gas production rate,
ρg and ρN are the grain and nucleus densities, and RN is the The high-density amorphous ice form undergoes a transi-
nucleus radius. For example, there is sufficient gas flux from tion to the low-density form in the temperature regime of
water sublimation to lift small (~0.01–0.1 µm) grains off the 38–68 K (Jenniskens and Blake, 1994). When amorphous
 Meech and Svoren: Physical and Chemical Evolution of Cometary Nuclei 323

H2O ice is heated, trapped gases are released at low levels or the changing orbital geometry (heliocentric and geocen-
between 35 and 120 K in response to the restructuring of the tric distances and phase dependence on brightness), or di-
ices, a process called annealing. rect spectroscopic observation of gas phase species. In this
It is important to note that the trapped gases do not come section we will focus on the dust observations.
out in proportion to their abundances. Van der Waals forces The evolving brightness of a comet is controlled by many
influence the residence time and contribute to enrichment complex factors, yet is often parameterized by a simple for-
of various species at different temperatures. Once trapped, mula (see equation (5)). This parameterization works only
the temperature at which release occurs is independent of as well as the user understands all the assumptions going
composition. Beginning near 90 K, gases are released as the into the formula. Unfortunately, this methodology is often
ice undergoes an exothermic amorphous to crystalline phase used indiscriminately, leading to misconceptions about
transition. The rate of transformation varies exponentially comet brightnesses, brightness predictions, and what meas-
with temperature, and the release of gases will peak and urements to make. Therefore, it is important to go into some
diminish as the trapped molecules are released (for a thin detail about the limitations inherent in reporting comet
layer, as seen in the laboratory). In real comets, the gas brightnesses.
release will occur over a range of distances between about
8 and 20 AU as the heat penetrates to deeper layers. Thus, 3.1. Total Brightness
in contrast to sublimation, which releases water and trapped
gases in the clathrate hydrate at the same time, comets can The traditional formula for expressing the brightness of
release volatiles at different (lower) temperatures than from a comet, m1, as a function of r may be written as (Marsden
the sublimation of water. and Roemer, 1982)
The only realistic way to produce significant activity at
very large distances (e.g., beyond distances where the ice m1 = H1 + 2.5nlogr + 2.5klog∆ + φ (5)
anneals or at the distances of the amorphous-to-crystalline
ice transition) is if there were highly volatile material that and a similar formula for the brightness of a nucleus, m2, as
froze out on the surfaces of the cometesimals (Notesco et
al., 2003; Bar-Nun and Laufer, 2003). However, we know m2 = H2 + 5logr + 5log∆ + φ (6)
that either there was not a significant amount of these di-
rectly frozen gases incorporated into comets, or that evo- H1 and H2 is the absolute magnitude at r = ∆ = 1 AU and
lutionary effects have released these volatiles, because the φ = 0, and n and k are a measure of the sensitivity of the
SP and the few HT and LP comets that have been studied magnitude variation to r and ∆. These values are not nec-
in detail do not show significant release of different volatiles essarily constant as a comet evolves from one apparition to
at different times that cannot be accounted for by models another. Most studies assume that k = 2, and n = 4 is fre-
of amorphous ice crystallization (Prialnik et al., 2004). A quently assumed if little data is available. The term φ had
spectacular example of this was seen with the radio obser- either incorporated a phase function or an aperture correc-
vations of C/1995 O1 (Hale-Bopp) (Biver et al., 1997). Vola- tion. Historically, this formula has been extremely useful
tiles with orders-of-magnitudes differences in volatilities for predicting the brightness of comets and for comparing
(e.g., CO, CH3OH, H2S, H2CO, HCN, CS, CH3CN, and the behavior of comets; however, given our current detailed
HNC) were seen to increase in abundance at somewhat simi- understanding of the physics of comets and thermal mod-
lar rates, beginning as far out as r = 7 AU. This is not likely els, this is not a very accurate estimator of comet activity,
to be caused by subsurface sublimation in response to solar and can often make very bad predictions. In particular, the
insolation, and is more likely controlled by the amorphous value of n has ranged between 2 and 8 for various comets.
to crystalline H2O-ice phase changes. There are several reasons why using the formula above for
an active comet is often a poor predictor of brightness and
3. MEASURING ACTIVITY activity level.
3.1.1. Heliocentric distance range. First, as was seen
The easiest way to observe that a comet has become in the previous section, the brightness of a comet varies as
active, i.e., that there is a flow of gas and entrained dust r –2 modulated by any nucleus rotational signature at large
grains that are populating the coma, is to observe the coma distances when there is no outgassing. Close to the Sun,
or tail that is produced from the activity. However, the pres- when all the solar energy is going into gas production, the
ence of a coma or tail does not necessarily imply either that brightness change as a function of distance behaves as r –2.
(1) activity from sublimation is continuing (since large grains Therefore, the value of n that might be determined from
may take a long time to move a way from the nucleus) or observations is a strong function of the range of r over which
(2) that the activity was caused by sublimation (since a col- this parameter is determined. The formula may produce a
lision could produce a temporary coma). A definitive test reasonable brightness estimate within the same range of
of activity can be made by observing a change in bright- distances that the exponents were determined, and fail com-
ness that cannot be accounted for by rotational modulation pletely elsewhere.
324 Comets II

Fig. 3. Broadband B and V Kron-Cousins filter system (from Mauna Kea) superimposed on the spectrum of Comet 8P/Tuttle [8P/
Tuttle spectrum, created by S. Larson and J. Johnson, courtesy of S. Larson; line identifications from A’Hearn and Festou (1990)].

3.1.2. Dust vs. gas. Second, the gas production is more have been made, and the relative fluxes of gas and dust that
strongly dependent upon r than is the dust. Depending on are measured by that filter. Figures 3 and 4 show a spec-
the size of the dust particles and the size distribution and trum of an active comet, 8P/Tuttle, upon which the typical
the interaction of the dust with both gravity and solar radia- broadband filters used by observers are superimposed. As
tion, the dust may remain in the vicinity of the nucleus for discussed in Schleicher and Farnham (2004), it is nearly
quite some time (Fulle, 2004). Thus, n will be smaller for impossible to separate the contributions of gas and dust in
dusty comets. an active comet when using broadband filters. The B and
3.1.3. Filter selection. Because of this difference in V bands are heavily contaminated by gas emission (CN, C3,
behavior of the dust and gas, the variation of n with r will C2, and NH2), and there is a small amount of contamination
also depend on the filter through which the observations from [OI] and NH2 in the R-band. In addition, there is some
 Meech and Svoren: Physical and Chemical Evolution of Cometary Nuclei 325

Fig. 4. Broadband R and I Kron-Cousins filter system (from Mauna Kea) superimposed on the spectrum of Comet 8P/Tuttle [8P/
Tuttle spectrum, created by S. Larson and J. Johnson, courtesy of S. Larson; line identifications from A’Hearn and Festou (1990)].

contamination from H2O+ between 6950 and 7080 Å in the nation in R or I is minimal; the contamination by NH2 drops
R-band (Schleicher and Farnham, 2004). The I-band, on rapidly with distance from the nucleus since it is short-lived;
the other hand, is relatively free of most gas emissions, but but weak CN bands in the near-IR can be a problem for
is not a commonly reported filter for comet observations (in low dust/gas comets at larger projected distances. There-
part because the effective wavelength of this bandpass de- fore, measurements done through different aperture sizes
pends on the red response of the detector used, and in part at different times will be subject to additional systematic
because the sky brightness is much greater in this bandpass). effects. A good correlation of Qgas and visual magnitude has
The amount of gas contamination in the broadband filters been shown for a selection of comets between r = 0.6 and
also varies with distance from the nucleus as well as the 2.8 AU (A’Hearn and Millis, 1980; Jorda et al., 1991),
dust-to-gas ratio. For instance, in dusty comets, contami- which would seem to contradict this statement. However,
326 Comets II

over the range in r where the correlation was observed, scattered light as seen from Earth for comparison with real
water sublimation is in a linear regime and behaves as r –2. comet images. Dust dynamical model development, modern
Further, the visual region spectrum is dominated by CN and usage, and limitations are discussed in detail in Fulle (2004).
C2, so for this range of r it is not surprising that there is a While there are numerous assumptions inherent in this
good correlation. type of modeling, it can be very useful for making infer-
Long-lived or lingering dust also implies that gas pro- ences about important parameters related to activity, such
vides a better measure of the ongoing production rate, while as the approximate turn-on and turn-off distances (mean-
dust measurements are often more of an abundance value ing the distances at which there is measurable brightening
rather than a production-rate value. Typical gas species due to the presence of a dust coma). The model parameter
“live” on the order of hours or days before photodissocia- that produces the biggest change in the appearance of the
tion, while larger-sized dust grains may have been emitted coma and tail is the production rate, which means that this
weeks or months earlier. Thus, for production-rate-activity is usually the best constrained of the parameters. However,
measurements, filters that record the maximum of the light to use this type of method to determine comet grain prop-
emitted by gas species (e.g., C2 or NH2) are good selections. erties and estimates of the activity level in comets, the tech-
3.1.4. Phase function. The term φ in equations (5) and nique must be used in conjunction with as much other
(6) is more complex for an active comet than for a solid information as possible, and careful attention to the particu-
surface. The observed brightness from the coma is the sum lar details of each comet (Farnham, 1996).
of the contributions of all the volume elements along the 3.2.2. Activity without coma? Traditionally, the visible
light of sight, and this contribution of the scattering from all appearance of coma around the nucleus has been the indi-
the dust per unit volume is the volume-scattering function. cation that a comet is exhibiting activity, and conversely the
This volume-scattering function, ψ, as a function of wave- lack of a coma was taken to mean that the observations were
length, λ, particle size, a, and scattering angle, θ, is defined as of a bare nucleus. However, it is possible that a comet could
be either weakly active, such that the coma was not apparent
a2 in the observations, or that the grains did not travel far from
∫
ψ(λ,θ) = n(a)πa2Qsca(a,λ)φ(a,λ,θ)da
a1
(7) the nucleus and the coma was contained within the extent
of the seeing disk, or stellar profile. An excellent example
of this is Comet 2P/Encke, whose orbit constrains it to travel
where Qsca is the scattering efficiency and φ is the phase between q = 0.34 AU at perihelion and Q = 4.10 AU at
angle (Grün and Jessberger, 1990). As discussed in detail aphelion. Thus, for its entire orbit it is well within the region
in Kolokolova et al. (2004), analytical methods (Mie theory) where H2O ice sublimates and can produce significant coma.
and laboratory measurements have been used to determine Observations of Comet 2P/Encke to determine the ro-
scattering efficiencies and phase functions for a wide vari- tation period described the nucleus as stellar (Jewitt and
ety of grain compositions, sizes and structures that likely Meech, 1987). Subsequent observations of the comet typi-
represent realistic cometary grains. As seen in equation (7), cally described the comet as low-activity, or a bare nucleus.
converting this to a realistic coma brightness behavior as a However, there were difficulties in reconciling the differ-
function of phase angle will depend on the possibly chang- ent rotation periods found by different observing teams. The
ing particle size distribution and scattering properties. Kolo- various rotational datasets were found to be inconsistent
kolova et al. (2004) summarized that data for many bright unless one assumed that there was a contribution from activ-
comets and showed that the brightness behavior has a small ity in the datasets (Sekanina 1991). In a database of obser-
backscattering peak, a strong forward-scattering surge at vations extending 16 years, from 1985 to 2001, broadband
large phase angles, and in between is somewhat flat. In a images of the comet showed definitive coma only for dis-
very active comet, most of the light is produced by reflec- tances r < 2 AU. However, as shown in Fig. 5, there was
tion from dust in the coma, which means that phase varia- clear evidence for activity near aphelion based on reported
tions of the nucleus are inconsequential. brightness variations (Meech et al., 2001). Near aphelion
there are excursions in brightness up to 2.5 mag, or a fac-
3.2. Presence of Coma as an tor of 10 in brightness, that are beyond any brightness in-
Indicator of Activity crease from rotation, or an assumed phase function of β =
0.04 mag deg–1.
3.2.1. Dust coma models. Dynamical models of the 3.2.3. Coma detection limits. When there is little or no
dust coma as a function of time can yield information about coma, the dust-dynamical models described in section 3
the onset and cessation of activity, the relative grain size cannot be used to determine the onset of activity. However,
distribution, velocity distribution, and the dust production there is still a way to place limits on the amount of activity
rate as a function of grain size and time. This dynamical that might be present. The technique relies on a detailed
technique is a method of computing the surface brightness comparison of the surface brightness profile of the comet
of a comet’s tail by evaluating the motions of model dust and field stars. One technique makes a comparison between
particles ejected from the nucleus under the influence of seeing-convolved models of nuclei plus varying amounts
solar radiation pressure and gravity, and then adding up their of coma (Luu and Jewitt, 1992). In this type of approach,
 Meech and Svoren: Physical and Chemical Evolution of Cometary Nuclei 327

the grain velocity, and r is in AU and ∆ in m. It should be

noted that if one assumes a Bobrovnikoff relation for the
terminal grain velocities, vgr = vbob = (µ/µH2O)0.5600 r –0.5
(Bobrovnikoff, 1954), and recalls that φ = ∆φ'/206265, where
φ' is the angular size of the aperture (arcsec), for a given
observed flux the dust production will vary as

Qp ∝ r1.5∆1 (9)

which shows that the most sensitive limits are placed for
those objects closest to the Earth and Sun. The total dust
production, Q (kg s–1), is obtained from Qp by multiplying
by the grain mass, mgr = 4/3πagr 3 ρ, assuming spherical par-

ticles. The dust limit results will also depend on the assumed
grain size distribution. Far larger mass loss rates are possible
for millimeter- or centimeter-sized particles, which would
never be detected. Much of the mass is probably hidden in
particles never observed, and values derived from optical
measurements are always lower limits to the total mass in
grains.

4. OBSERVATIONS OF ACTIVITY
Fig. 5. Reduced R-band brightness (r = ∆ = 1) of 2P/Encke from
September 1985 through April 2001 as a function of r. Filled AND EVOLUTION
squares represent preperihelion and open triangles postperihelion
data. The solid horizontal line is an estimate of the brightness of In the previous sections, the changes that a comet nu-
the average cross section of the bare nucleus and the dashed lines cleus undergoes as it evolves were described, as well as the
show the range of brightness variations due to rotation. Data are techniques used to measure observable changes in a comet
from Meech et al. (2001). as it evolves or ages. In this section we will examine some
of the large cometary datasets used to examine at the activ-
ity in comets from the point of view of aging.
It is important to be able to distinguish the effects of
however, the most sensitive constraints on the amount of aging from primordial differences among the comets since
scattered light from the coma dust are found in the profile the wide range of formation distances should imply signifi-
wings, far from the core of the image. However, it is far cantly different volatiles and abundances of trapped gases,
from the core where the precise determination and removal as well as differences in collisional histories. The following
of the night sky brightness is the most critical, and this lim- characteristics might be observable as changes in activity
its the sensitivity to mass loss rates >0.1 kg s–1 for objects level as a consequence of evolution and can also help char-
inside ~2 AU. Typical mass loss rates for low-activity com- acterize the physical mechanisms of the activity: (1) activity
ets near perihelion range between 5 < Q < 102 kg s–1. at large r from the onset of amorphous ice crystallization or
Techniques that utilize the central part of the surface sublimation of frozen volatiles, which would decrease post-
brightness profile (where the signal-to-noise is highest) and perihelion; (2) secular fading of the comet as a dust mantle
the sky background (not as critical) can yield mass loss lim- is built up, or because of loss of surface volatiles; (3) more
its that are 1–2 orders of magnitude more sensitive at the uniform activity in new comets, with larger surface areas
same r (Meech and Weaver, 1995). In this technique, an available for sublimation; (4) higher frequency of jets and
azimuthally averaged surface brightness profile of the star outbursts for older mantled comets; (5) differences in pro-
(or normalized average of several stars) is subtracted from duction rates of gases as a function of r for different species
an untrailed comet image profile. For an object with no and dynamical classes of comets; (6) primordial and evolu-
coma, the subtraction should yield a value of zero with an tionary differences in nucleus size distributions; and (7) peri-
associated error. The 3σ value of this error can be used as helion brightness asymmetries induced by thermal lags in
the limiting maximum flux contributed from scattered coma older devolatilized surfaces.
light. This flux is given by
4.1. Activity at Large r: Dynamical
F = S πagr
2 p Q φ/2r 2∆2v
v p gr (8) Class Comparisons

where S is the solar flux through the bandpass (W m–2), agr 4.1.1. Historical development. Oort’s deduction (Oort
(m) the grain radius, pv the grain albedo, Qp (s–1) the produc- 1950) of the existence of a large reservoir of comets with
tion rate, φ the projected size of the aperture (m), vgr (m s–1) aphelia between 5 × 104–1.5 × 105 AU was based upon a
328 Comets II

small sample of comets for which original (e.g., prior to passage was found (Whipple, 1978). Whipple suggested that
the effects of planetary perturbations) orbits were well de- the difference was caused by the loss of a frosting of super-
termined. In order to reconcile the observed distribution of volatile materials during the first passage near the Sun. This
1/a, where a is the semimajor axis of the orbit, Oort made was later explained to be due to an observational selection
the assumption that the new comets perturbed from the Oort of discoveries (Svoren, 1982).
cloud must subsequently fade after their first passage and Several additional older studies that analyzed the light
no longer be observable. The cause was attributed to a loss curves of comets also did not find differences with respect
of highly volatile ices (see Dones et al., 2004, for a more to absolute brightness, change in brightness vs. r, asymmet-
in-depth discussion). Later work reexamining the distribu- ric light curves, and dust-to-gas ratio or dust tail morpholo-
tion of original semimajor axes by selecting only those gies among the different dynamical groups (Roemer, 1962;
comets with perihelia q > 3 AU, where the nongravitational Kresák, 1977; Svoren, 1986; Donn, 1977). Svoren (1986)
effects were negligible, found a smaller size for the inferred calculated photometric parameters for the sample of 67 LP
Oort cloud (Marsden and Sekanina, 1973). comets on the basis of photometric observations beyond
This led to the suggestion that close stellar passages were 2.5 AU. For both old and new comets it was found that the
probably insufficient to bring comets into the inner solar photometric exponent decreases to the value n = 2, i.e., a
system directly from the Oort cloud; rather, they would have nonactive stage, at r > 7 AU. The observations at those dis-
diffused inward slowly and may have already had perihelia tances require large telescopes, so until recently the ability
near the region of the outer planets (Weissman, 1986, 1990). to obtain a large dataset has been limited.
Consequently, these new comets may have lost any highly A’Hearn et al. (1995), in a large survey of cometary pro-
volatile materials prior to ever reaching a region of observa- duction rates, found that DN comets have r-dependencies
bility, and that there would be no reason to expect significant that are much less steep inbound than on their outbound
differences in activity levels between new and old comets. legs (they are also much less steep inbound than any other
An analysis of the orbits for 200 comets in order to de- dynamical class).
termine their original orbits (Marsden et al., 1978) was used Rickman et al. (1991) conducted a statistical analysis of
to infer that, in fact, the DN comets do fade after their first a complete sample of SP cometary nongravitational param-
close solar passage. Marsden et al. (1978) divided the com- eters (through 1990). They found that the nongravitational
ets into two accuracy classes depending on the mean error parameter correlated well with the perihelion asymmetry of
of 1/a, the time span of the observations determining the the gas production over a wide range of r, showing a trend
orbit, and the number of planets whose perturbations were for SP comet nuclei to be less dust-covered with increasing
taken into account. They found a significant difference in perihelion distance. It was also found that the largest values
the number of DN vs. LP comets between the accuracy of the nongravitational parameters were exclusively asso-
classes. In the class where the orbits were the most accu- ciated with comets that had recently undergone large reduc-
rately known, as many as 55% of the comets were new (1/ tions of perihelion distance. They concluded that such dy-
aorig < 100 in units of 10–6 AU), whereas in the other class namically young comets have nucleus surfaces that were
the fraction was only 21%. If a comet fades substantially more free-sublimating than those of older comets.
after its first passage through the inner solar system, it will A summary of analyses based on larger samples of com-
subsequently be observed over a smaller portion of this orbit ets to search for statistical differences in the activity levels
and will have a less-secure orbit and be more likely to be between SP and Oort cloud comets is shown in Table 2.
included in the second group. 4.1.2. Production rate correlations. In a 20-year study
Delsemme (1985) suggested on the basis of the light of a sample of 85 comets, including 39 Jupiter-family (JF)
curves of 11 comets that the DN comets are not substan- comets, 8 HT comets, 8 DN comets, and 27 LP comets, pro-
tially different from the SP comets, claiming that the activ- duction rates were computed for C2, C3, OH, NH, and CN
ity for all of them is controlled by water sublimation and in order to look for trends in composition with origin and
that most likely the DN comets had spent several orbits evolution (A’Hearn et al., 1995). While overall they found
slowly diffusing into the inner solar system. Delsemme that most comets were similar in chemical composition,
evaluated the nature of the activity by comparing the light there was a group of JF comets that were depleted in the
curves of the comets to water vaporization curves and de- carbon chain molecules (C2 and C3). A’Hearn et al. argue
termining values of ro. Although the dataset was largely that this is attributable to a primordial rather than an evo-
uniformly obtained by two individual observers, the range lutionary difference. If this were an evolutionary difference
of r for the observations was limited, and in most of the there should be a correlation with dynamical age among
cases the value of ro was determined by extrapolation. None other comet classes, which was not seen. They suggest that
of the comets were observed at large distances where H2O- some process in the solar nebula may have preferentially
ice sublimation would not be significant. With the excep- produced or destroyed the carbon chain molecules at the
tion of three comets in the sample, none of the comets were distance of the Edgeworth-Kuiper belt, the source region
observed beyond r > 2.5 AU. for the JF comets.
Using the same dataset, a statistically significant system- A’Hearn et al. estimated the fractional areas active in
atic difference between the medians of the photometric ex- their comet sample by comparing the production rates of
ponents (see section 3) for the DN comets after perihelion OH to estimates of the icy surface area needed. They found
 Meech and Svoren: Physical and Chemical Evolution of Cometary Nuclei 329

TABLE 2. Search for activity differences between new and old comets.

Reference Difference Technique

Roemer (1962) No Light curve analysis
Hughes (1975) No Frequency of outbursts
Sekanina (1975) Yes Activity at large r
Kresák (1977) No Light curve analysis
Marsden et al. (1978) Yes Orbital errors
Weissman (1980) Yes New comet tendency to split a factor of 2.5 higher than for old comets
Delsemme (1985) No Light curve fitting, comparison of ro
Svoren (1986) No Light curve analysis, photometric exponent
Rickman et al. (1991) Yes Nongravitational effects; active surface area
A’Hearn et al. (1995) Yes Active surface area correlated with dynamical age
A’Hearn et al. (1995) Yes Primordial differences in carbon-chain molecule depletion

a clear trend with the amount of active surface area decreas- 4.1.3. Modern observations. A long-term program of
ing for older comets, which could either be interpreted as observation of the activity level of a large number of SP,
evidence that the nuclei of the dynamically older comets HT, LP, and DN comets has been conducted using the fa-
are smaller (primordial condition), or that a smaller frac- cilities on Mauna Kea, the National Optical Astronomy
tion of their surfaces are active (an evolutionary effect). Observatories, and the Hubble Space Telescope. This pro-
Recent work on comet nucleus size distributions, compar- gram has the advantage over previous studies in that the
ing the nuclei of the DN and SP comets, shows that this is dataset has been obtained using standardized equipment,
likely to be an evolutionary effect (Meech et al., 2004). filter bandpasses, and measurement apertures, has system-
Additionally, A’Hearn et al. (1995) found a strong correla- atically followed the orbit of the comets over large fractions
tion of the dust-to-gas ratio with perihelion distance. This of the orbital cycle for SP comets, and has placed con-
implies processing of the surface tied to peak surface tem- straints on the nucleus sizes of the DN comets. From the
perature, although the explanation for why this should af- point of view of the appearance of the comae, the bright-
fect future dust release rates is unclear. Finally, for those ness levels, and the rate of change of brightness with dis-
SP comets that did not experience a recent orbital change, tance, a distinct difference between the different dynamical
no variation was evident in production rates from one ap- comet groups has been observed. Figures 6 and 7 compare
parition to another. the appearance of comets in each dynamical class.

3.9 AU 5.2 AU 6.0 AU 8.5 AU 10.7 AU 12.8 AU

Top row: JF — P/Neujmin 1

Middle row: HF — P/Halley
Bottom row: DN — Shoemaker 1987o

Fig. 6. Comparison of comets from three dynamical classes: SP comet 28P/Neujmin 1, a Jupiter-family comet; 1P/Halley, a HT
comet probably evolved inward from the Oort cloud; and a DN comet, C/1987 H1 (Shoemaker 1987o) on its first passage through the
inner solar system. The images show the different levels of activity in the groups at different r.
330 Comets II

JF — Neujmin 1

13–14 AU 14.8 AU 17–19 AU

5.0–5.5 AU

HF — Halley

DN — Shoemaker 1987o

DN — Shoemaker 1984f

Fig. 7. Same as for Fig. 6, extending the observations to larger r, and adding one DN comet, C/1984 K1 (Shoemaker 1984f).

For the most part, the SP comets in the program rarely

exhibit much visible evidence of coma beyond 2–3 AU.
This is consistent with the finding of A’Hearn et al. (1995)
that these comets are more heavily mantled, and have much
smaller surface areas, and has probably contributed to the
misinterpretation of the Delsemme (1982) curves regarding
the distance at which H2O sublimation begins. The bright-
ness of the HT Comet 1P/Halley, which originated in the
Oort cloud, was significantly brighter than most of the SP
comets at a given heliocentric distance, although even this
comet was seen to be heavily mantled from the Giotto space-
craft, with only 10% of the surface active. In the images, the
comet fades significantly beyond r = 6 AU, and by 12.8 AU
had a brightness consistent with a bare nucleus.
At r = 14 AU, 1P/Halley exhibited a large (∆m > 5 mag)
outburst in brightness (see Fig. 8). This has been interpreted
as a release of gas and dust initiated by the onset of crys-
tallization in the amorphous ice several tens of meters below
the surface (Prialnik and Bar-Nun, 1992).
Sporadic activity at large distances is being more fre-
quently observed with the advent of more sensitive detec- Fig. 8. Composite R-band image of 1P/Halley obtained using the
tors. Chiron has been monitored nearly continuously since University of Hawai‘i 2.2-m telescope on Mauna Kea on Febru-
1989 when the coma was discovered, through its February ary 15, 1991, when the comet was at r = 14.3 AU. The extent of
1996 perihelion to the present. Chiron never gets close the dust coma was at least 2 × 105 km in diameter.
 Meech and Svoren: Physical and Chemical Evolution of Cometary Nuclei 331

peak brightness. Unlike comets that pass closer to the Sun,

Chiron’s surface does not get quickly “renewed” from H2O-
ice sublimation because it never gets warm enough.
The general activity that has been observed in the LP
comets shows that they have significant differences in their
coma appearance, ranging from symmetrical comae, to the
narrow parallel-sided tails seen historically in distant com-
ets. Roemer (1962) and Sekanina (1975), among others,
have commented on the fact that the dust tails of distant
comets often exhibited this peculiar appearance. The coma
in these cases tended to be sharply bounded at the head of
the comet. From dust-dynamical modeling, the shapes of
these tails suggested the presence of large grains with a
small velocity dispersion (Sekanina, 1975). The few LP and
DN comets that have been observed from perihelion out to
between Uranus and Neptune share several characteristics:
(1) The brightness fades much more slowly than for the
periodic comets, even 1P/Halley, suggesting there is likely
a physical difference in the upper layers that affects the heat
Fig. 9. Brightness variations of 2060 Chiron from Mauna Kea, transport. (2) There is significant activity out to large dis-
reduced to unit r and ∆. tances, based on dust-dynamical models — activity continues
in some cases beyond 15 AU (see Fig. 10). Detailed thermal
models will allow exploration of the physical causes — i.e.,
enough to the Sun for significant H2O-ice sublimation (q = if this can be explained by a receding crystallization front.
8.45 AU), yet its absolute brightness has had nearly con- (3) The comets do not seem to exhibit the strong bright-
tinual fluctuations, including two long, slow outbursts near ness fluctuations seen in Chiron; however, this could be a
17 and 12 AU (see Fig. 9). The sporadic brightening of selection effect since Chiron is so bright that it can be fre-
Chiron’s light curve can be reproduced with a model as- quently observed.
suming an amorphous ice nucleus with 60% dust fraction, A recent high-resolution infrared spectroscopic survey
where the activity is driven by crystallization (Prialnik and has measured production rates of several organic species
Bar-Nun, 1992). This not only reproduces the sporadic in a variety of LP and DN comets (Mumma et al., 2001,
brightening that began near aphelion, but also the thermal 2002; Dello Russo et al., 2001). The low formation tem-
measurements and limits on CO and CN production at its peratures and organic compositions provide information

Fig. 10. Comparison of the postperihelion light curves of (a) C/1983 O1 (Cernis), and (b) C/1984 K1 (Shoemaker), shown as filled
triangles. The postperihelion light curve of 1P/Halley is shown as open squares, including the outburst near r = 14 AU, and other SP
comets as dots.
332 Comets II

TABLE 3. Possibly active KBOs and Centaurs.

Object q–Q e a P T Qp ∆r Reference

1996 TO66 38.48–48.67 0.12 43.57 287.6 02/1908 inferred 45.8 [1]
1999 TD10 12.29–190.10 0.88 101.20 1018.1 10/1999 coma? 12.3–12.7 [2]
C/2000 T4 8.56–19.59 0.39 14.10 52.9 05/2002 10 –1–10 –2 8.5–8.6 [3]
2060 Chiron 8.45–18.91 0.38 13.70 50.7 02/1996 3–4 8.45–17.0 [4]
C/2000 B4 6.83–29.22 0.62 18.02 76.5 06/2000 coma? 6.86 [5]
C/2001 M10 5.30–48.01 0.80 26.66 137.7 06/2001 coma 5.30 [6]
q–Q = perihelion–aphelion (AU); e = orbital eccentricity; a = semimajor axis (AU); P = orbital period (yr); T = most re-
cent time of perihelion; Qp = estimated production of dust (kg s–1) or comment regarding activity; ∆r = range of heliocen-
tric distances at which activity has been observed.
References: [1] Hainaut et al. (2000); [2] Choi et al. (2003); [3] Bauer et al. (2003); [4] Meech and Belton (1990);
[5] Kušnirák and Balam (2000); [6] Lawrence et al. (2001).

about the chemical environment in the formation region. 17.5 to 8.5 AU. While many of the volatiles in Table 1 could
The chemistry is not consistent with origins in a thermally in principle be responsible for activity at these distances (in-
or chemically equilibrated region of the solar nebula, rather cluding H2O-ice sublimation for the small end of the range),
it is consistent with irradiated ices on grain surfaces in the it is very likely that the crystallization of amorphous H2O
natal molecular cloud. There is one exception to this, and ice is the driver for the activity. The more difficult activity
that is for Comet C/1999 S4 (LINEAR), which has an un- to explain, if not induced by collision, is the apparent ac-
usual organic composition that is severely depleted in hyper- tivity in 1996 TO66 at r = 45.8 AU. Here it is too cold for
volatiles and methanol and probably consists of materials the ice phase transition, and the most likely driver would
condensed from processed nebular gas in the Jupiter-Saturn be sublimation from frozen volatiles, such as CO, CH4, or
region. C2H6.
4.1.4. Activity in Kuiper belt objects and Centaurs. There
has been recent interest in searching for activity in KBOs 4.2. Secular Fading
before they enter the inner solar system as Centaurs and
SP comets. There is circumstantial evidence for activity in During the active phase, when the comet passes within
one KBO (Hainaut et al., 2000), while others are conduct- the inner solar system, there is considerable evolution of the
ing sensitive searches for activity in these objects (Meech et interior and surface of the comet. This evolution may be
al., 2003). observed as a secular change (decrease) in the brightness of
The classification scheme for Centaurs has evolved over periodic comets. The release of gases will affect the physi-
time. The original definition encompassed all small bodies cal properties of the nucleus such as a change of porosity,
orbiting the Sun between Jupiter and Neptune, but other redistribution of volatiles, and surface dust mantle forma-
more recent definitions include objects with perihelia be- tion. One can expect to observe secular fading as a conse-
tween 5.2 < q < 30 AU. Many objects traditionally classi- quence of a smaller surface area available for sublimation.
fied as SP comets, such as 29P/Schwassmann-Wachmann 1, A very rapid fading of JF comets has been claimed
fall into this category. Some objects, such as 39P/Oterma, (Vsechsvyatskij, 1958), but dismissed as resulting from
which by these definitions may be classified as Centaurs, time-dependent instrumental effects (Kresák, 1985). A dis-
have recently had their orbits perturbed by close Jupiter covery observation is probably near the upper extreme of
encounters. Duncan et al. (2004) uses the Tisserand invari- brightness and by removing just the discovery apparition
ant to classify those objects with T > 3 and semimajor axis observations, there can be a secular brightness decrease of
greater than that of Jupiter as Centaurs. This definition 40% (Svoren, 1991). The active lifetime of a comet often
excludes 29P/Schwassmann-Wachmann 1 and 39P/Oterma. consists of recurring active phases separated by temporary
For the purposes of this chapter, the list of Centaurs and extinctions, and is not truly secular (Kresák and Kresáková,
scattered disk objects provided by B. Marsden on the Minor 1990). If comets do fade, they likely do so very slowly, or
Planet Center Web pages (http://cfa-www.harvard.edu/iau/ episodically. An excellent resource for the study of comet
mpc.html) will be used, and this excludes 29P/Schwass- light curves is the Comet Light Curve Catalogue/Atlas
mann-Wachmann 1 and 39P/Oterma. (Kamél, 1990).
A handful of Centaurs now show possible evidence for
outgassing. These are shown in Table 3. With the exception 5. SUMMARY
of 2060 Chiron, the activity in all the Centaurs in Table 3
was discovered when the objects were at perihelion, rang- Our understanding of activity in comets has been rap-
ing between 5.3 and 12.3 AU. Although Chiron’s activity idly evolving thanks to the contributions from new tech-
was discovered near r = 12 AU (inbound), detailed studies nologies that have allowed observations over a range of
have shown that this object has significant activity from distances, including observations of bare nuclei, and the
 Meech and Svoren: Physical and Chemical Evolution of Cometary Nuclei 333

ability to watch the development of the dust coma. In ad- Schleicher for his helpful review of the chapter; and an anony-
dition, radio astronomy, UV, visible, and infrared spectros- mous reviewer for useful comments. Finally, thanks to H. Weaver
copy are providing us with information about the complex for his patience and understanding during the writing of this chap-
chemical composition of the nuclei. When combined with ter. This work was supported in part by NASA Grant Nos. NAG5-
4495 and NAG5-12236.
powerful new dynamical models of the solar system, and
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336 Comets II
 Weissman et al.: Structure and Density of Cometary Nuclei 337

Structure and Density of Cometary Nuclei

Paul R. Weissman
Jet Propulsion Laboratory

Erik Asphaug
University of California, Santa Cruz

Stephen C. Lowry
Jet Propulsion Laboratory

We are still at a very primitive stage in our understanding of the structure and density of
cometary nuclei. Much of the evidence at our disposal is fragmentary and often indirect. Never-
theless, a compelling picture is beginning to emerge of cometary nuclei as collisionally processed
fractal aggregates, i.e., rubble piles. The evidence comes from observations of split and disrupted
comets, in particular Shoemaker-Levy 9, from theories of planetesimal formation in the early
solar nebula, from a recognition of the role of collisions in the evolution of cometary nuclei, and
from theoretical and experimental studies of the fragmentation and reassembly of asteroids. This
paradigm-shift away from nuclei as monolithic bodies parallels that which has occurred for aster-
oids in the past decade. A related factor that strongly suggests that nuclei contain substantial
macroscopic voids is estimates of the nuclear density, which, like asteroids, show comets to be
“under-dense” compared with their constituent materials. We find that the bulk density of com-
etary nuclei lies in the range 0.5–1.2 g cm–3, with a perhaps “best” current value of 0.6 g cm–3.

1. INTRODUCTION include irradiation by solar and galactic cosmic rays, accre-

tion of and erosion by interstellar grains, heating by nearby
Cometary nuclei are primordial bodies, among the first supernovae and from stars passing through the Oort cloud,
to accrete in the early solar nebula. As such, it has long been the crystallization of amorphous water ice as the nucleus
held (e.g., Delsemme, 1977) that comets preserve a cosmo- is warmed above 120–150 K for the first time, sublimation
chemical record of the composition of the nebula and the of volatiles as the cometary nuclei approach the Sun, and
conditions within it. Additionally, comets may preserve a collisional processing, either in the Kuiper belt or during the
physical record of the accretion process itself, how small ejection of protocomets from the giant planets zone to the
grains and particles came together to form macroscopic Oort cloud (for reviews, see Weissman and Stern, 1998, and
bodies with kilometer dimensions. Investigations of comet- Stern, 2003, and references therein). Another possible modi-
ary nuclei are thus crucial to understanding planet-build- fying mechanism is internal heating by short-lived radio-
ing processes in our solar system, and probably in planetary nuclides in the early solar system (Prialnik and Podolak,
systems around other stars. 1999), although we have no evidence as to whether this did
It is widely accepted that cometary nuclei formed in the or did not occur.
solar nebula through the slow accretion of silicate, organic, Most of these processes only affect a relatively thin layer
and icy grains as material settled to the central plane of the near the nucleus surface. However, collisions can radically
nebula (Weidenschilling, 2004). This slow initial agglom- alter the nucleus structure, ranging from substantial fractur-
eration and accumulation of material produced bodies up ing of the cometary material(s) to total disruption and subse-
to several kilometers in size. In the giant planets zone (5 < quent reassembly of the nucleus. There is a considerable
r < 35 AU) these “icy planetesimals” were then scattered to body of studies of the collisional evolution of asteroidal bod-
distant orbits in the Oort cloud and to escape to interstellar ies, which we suggest is very applicable to the problem of
space by the growing gas giant planets. Beyond ~35 AU the structure of cometary nuclei. We believe they show that,
planetary perturbations were largely incapable of scatter- like asteroids, cometary nuclei probably have a rubble-pile
ing objects to distant orbits so the material there remained structure, although the comets may have followed a some-
in situ in the region we now call the Kuiper belt. Thus, com- what different path to that final state from that of their aster-
etary nuclei were long viewed as having been preserved in oidal cousins.
a near-pristine state in these two dynamical reservoirs. Evidence for the rubble pile nature of cometary nuclei
In the last two decades it has increasingly been recog- comes from observations of split and disrupted comets, in
nized that the nuclei have been modified over the history particular comet Shoemaker-Levy 9 (D/1993 F2), which was
of the solar system by a variety of physical processes. These tidally disrupted by a close encounter with Jupiter, from

337
338 Comets II

theoretical studies of the accretion of icy planetesimals in Some of these ideas were not entirely new to the scien-
the early solar system, from the relatively recent recogni- tific literature. For example, Vorontsov-Velyaminov (1946)
tion that cometary nuclei are collisionally processed objects, notes that Baldet (1927) and Slipher (1927) estimated that
and from studies of the collisional evolution of asteroids, as the nucleus of periodic comet Pons-Winnecke was a com-
noted above. Together, we find that these lines of evidence pact object with dimensions of only 2–3 miles, and that it
create a compelling picture for cometary nuclei as colli- might be a monolithic body. Also, the idea of a “rocket
sionally evolved rubble piles. effect” from evolving gases had previously been proposed
A measurable physical parameter that has strong impli- for the sandbank model, based on desorption of bound gases
cations for the internal structure of cometary nuclei is the from grains as the comets approached the Sun. Even the idea
bulk density. If nuclei are indeed fluffy aggregates or rubble of ice in cometary nuclei had been proposed by Vsekhsvi-
piles, then they may be “under-dense” relative to their con- atsky in 1948. Whipple’s key contributions were his abil-
stituent materials and contain substantial macroscopic voids. ity to combine these disparate ideas into a unified model
Thus, density measurements alone could be used to infer a that explained many aspects of cometary behavior, and his
fluffy or rubble-pile structure. However, density measure- insistence that the nucleus was a single, small, solid body.
ments for cometary nuclei are exceedingly difficult to ob- The debate between advocates of the sandbank and icy-
tain, and at present can only be accomplished indirectly. conglomerate models continued for several decades after
In this chapter we will review our current understand- 1950. Any questions of nucleus “structure” were only in
ing of cometary nucleus structure and density, and the evi- terms of the sandbank vs. the icy conglomerate; Whipple’s
dence that is leading us to conclude that cometary nuclei papers did not comment on the underlying structure of the
are collisionally evolved rubble piles. In section 2 we ex- nucleus. However, during this time observational and theo-
amine the proposed models for cometary nuclei. In section 3 retical evidence in support of the icy-conglomerate model
we review the evidence for such models from spacecraft continued to grow. Among the more notable accomplish-
encounters. In section 4 we discuss evidence for cometary ments were Delsemme’s (e.g., 1971) work on sublimation
rubble piles, including the substantial body of research on rates of water and other volatile ices and Marsden and col-
the structure and evolution of asteroids that we find is very leagues’ (e.g., Marsden et al., 1973) modeling of nongravi-
applicable to this problem. In section 5 we discuss density tational motions in comets using those sublimation models.
estimates for cometary nuclei and the methods employed. Over time, the sandbank model fell into disfavor, finally
Section 6 contains a discussion of these topics and our con- being discarded in 1986 when the Giotto and Vega space-
clusions, and a discussion of expected future spacecraft craft returned images of the nucleus of comet 1P/Halley
measurements. (Fig. 1).

2. PROPOSED MODELS OF COMET 2.2. The Fluffy-Aggregate, Primordial-Rubble-Pile,

NUCLEUS STRUCTURE and Icy-Glue Models

2.1. The Icy-Conglomerate Model The approach of periodic comet Halley in the 1980s
heightened interest in comets and provided the impetus for
The modern era in understanding cometary nuclei began new investigations, both observational and theoretical, into
with Whipple’s classic series of papers (1950, 1951, 1955) the nature of cometary nuclei. These included hypotheses
that first proposed the “icy-conglomerate” model for the with regard to the underlying structure of the nucleus. Two
cometary nucleus. Whipple sought to explain the nongravi- models, proposed almost simultaneously, were the “fluffy
tational motion of periodic comet Encke and others by sug- aggregate” of Donn et al. (1985) and Donn and Hughes
gesting a “rocket effect” from sublimating ices on the sur- (1986), and the “primordial rubble pile” of Weissman (1986).
face of a rotating nucleus. The earlier sandbank model of The primary concept in both these proposals was that com-
Levin (1943), Lyttleton (1948), and others envisioned the etary nuclei were aggregates of smaller icy planetesimals,
cometary “nucleus” as a gravitationally bound swarm of dust brought together at low velocity in a random fashion. With
particles with adsorbed gases, orbiting the Sun. In contrast, little in the way of modifying processes or energy sources
Whipple envisioned the cometary nucleus as a single mac- available to change this initial structure, the cometary nu-
roscopic body composed of a mixture of volatile ices and clei would preserve their highly irregular initial shapes and
“meteoritic material.” Whipple’s papers are impressive in very porous, easily fragmented structure over the history
that he proposed many of the features that have become part of the solar system.
of the standard paradigm for cometary nuclei today. These The arguments of Donn and colleagues came from their
include the formation of nuclei at very low temperatures; studies of the accretion of small grains in the solar nebula,
the low bulk density of cometary nuclei; porosity within the realizing that random accretion would lead to self-similar
nucleus; the low strength, low albedo, and low thermal con- structures at larger spatial scales. Weissman, on the other
ductivity of cometary materials; and the formation of non- hand, pointed out that the total gravitational potential energy
volatile lag deposits on nucleus surfaces, slowly cutting off of a typical cometary nucleus, say 5 km in radius, was not
cometary activity. sufficient to raise the temperature of the cometary material
 Weissman et al.: Structure and Density of Cometary Nuclei 339

(a) (b)

Fig. 1. Images of the nucleus of comet 1P/Halley. (a) Vega 2 image taken on March 9, 1986, from a range of 8031 km at a phase
angle of 28.4°. The spatial resolution is ~160 m/pixel. The image shows the “peanut-like” shape of the nucleus and several large dust
jets emanating from its surface. (b) Composite Giotto image taken on March 13–14, 1986 (© Max-Planck Institute for Aeronomy). The
resolution varies from ~50 m/pixel at upper left to ~320 m/pixel at lower right. Phase angles vary from 89° to 107° in a similar fashion.
Both images showed that the Halley nucleus was a dark, irregular object with a bimodal structure.

by even 1°K, and thus there was no energy source to mold main-belt asteroids, cemented together by an icy-conglom-
it into a single monolithic body. Both Donn et al. and Weiss- erate glue. In the icy-glue model the boulders provided the
man suggested that a fragmentary structure for cometary irregular topography seen in the Giotto images of the Halley
nuclei could help to explain such observed processes as nucleus (Keller et al., 1986) and also helped to explain the
outbursts and splitting, and could provide a mechanism for collimated jets seen emanating from the surface (from ac-
irregular activity on the surfaces of cometary nuclei. tive icy-glue regions between pairs of boulders). Although
Weissman drew analogies with previous work on the rub- it contains some interesting features, the icy-glue model has
ble-pile structure of asteroids (Davis et al., 1979). However, not received wide support because there is no evidence for
he appended the term “primordial” to suggest that the nuclei a population of remnant “boulders” from decaying comets,
were original solar nebula material, and not the products of and it could not explain many of the features of the breakup
earlier, disrupted bodies. We now recognize that collisional of comet Shoemaker-Levy 9 (D/1993 F2).
evolution likely played a role for cometary nuclei also (see All these nucleus concepts are illustrated in Fig. 2. The
section 4.2), and so the nuclei may indeed be reassembled general consensus today is that the fluffy-aggregate and pri-
rubble piles from earlier generations of icy planetesimals. mordial or collisionally evolved rubble-pile models are the
Note that the fluffy-aggregate and primordial-rubble-pile best description of the underlying structure of the cometary
models are not new versions of the sandbank model, as nucleus. Our discussion in the following sections will focus
incorrectly stated by Sekanina (1996). Sekanina erroneously on these two models and why we believe they are the best
equated the newer models with the Vorontsov-Velyaminov current description for the structure of cometary nuclei.
(1946) model, which suggested that cometary nuclei were a Note that whether we use the term “fluffy aggregate” or
swarm “some 25–60 km in diameter . . . composed of [~107] “rubble pile,” we are referring to the same basic concept of
blocks some 160 m in diameter, which are nearly in contact.” a weakly bound agglomeration of smaller icy cometesimals.
In other words, Vorontsov-Velyaminov proposed a swarm of
boulders rather than sand. In contrast, both the fluffy aggre- 3. SPACECRAFT IMAGING OF
gate and primordial rubble pile models require that the sub- COMETARY NUCLEI
fragments of the nuclei are in contact in a single nucleus struc-
ture, and are weakly bonded and/or gravitationally bound. 3.1. Comet 1P/Halley
A third hypothesis, proposed after the Halley spacecraft
flybys, was the “icy-glue” model of Gombosi and Houpis The first resolved images of a cometary nucleus were
(1986). They suggested that comets were composed of po- obtained by the Vega 1, Vega 2, and Giotto spacecraft that
rous refractory boulders with compositions similar to outer- flew past comet 1P/Halley in March 1986 (Sagdeev et al.,
340 Comets II

(a) (b)

(c) (d)

Fig. 2. Artists’ concepts of various models for cometary nuclei: (a) Whipple’s icy conglomerate model as envisioned by Weissman
and Kieffer (1981); (b) the fractal aggregate model of Donn et al. (1985); (c) the primordial rubble pile model of Weissman (1986);
and (d) the icy-glue model of Gombosi and Houpis (1986). All but (d) were proposed prior to the spacecraft flybys of comet 1P/Halley
in 1986.

1986; Keller et al., 1986). The Vega images were taken from face albedo was 0.05 to 0.08, assuming a lunar-like phase
a range of 8–50 × 103 km. Unfortunately, the Vega 1 cam- function and extrapolated to zero phase (Keller et al., 1994).
era was badly out of focus. Still, the images were useful in The nucleus is clearly seen as an elongated object with
determining the overall shape and dimensions of the nu- highly irregular surface topography. The bright spot in the
cleus, as shown in Fig. 1a, taken during the Vega 2 closest right center of the image is a “hill” ~500 m in height, stick-
approach at a range of 8031 km. The “peanut-like” shape of ing up into the sunlight from beyond the terminator. Other
the nucleus is clearly visible. hill-like structures with dimensions of ~500 m are visible
The Giotto images were taken at a much closer range surrounding an apparently flat area at upper left. A feature
and show considerably more detail. A composite Giotto im- near the upper left center of the image was identified early
age of the Halley nucleus is shown in Fig. 1b (Keller et al., on as a crater but more careful examination shows it to be a
1986). The Sun is at upper left in the image. The nucleus is fortuitous arrangement of two pairs of hills, each forming
viewed at a phase angle of 89°–107°; lower-phase images V-shaped ridges. The overall nucleus has a binary appear-
cluster near the upper left. Only about 25% of the nucleus ance with a narrow “waist” at the center. Activity appears
is illuminated by sunlight. The outline of the unilluminated to originate from discrete areas on the nucleus surface some
nucleus is visible at lower right against the bright cometary hundreds of meters in size, rather than from the entire sun-
dust coma. Because this is a composite of many images, the lit area. The apparently inactive areas may be lag deposits
spatial resolution varies from a best value of ~50 m/pixel at of nonvolatile materials, too heavy to be lifted off the nu-
the upper left to ~320 m/pixel at lower right. The last im- cleus surface, or may be part of the original radiation-pro-
age was taken at a range of 1680 km. Bright dust jets ema- cessed crust of the cometary nucleus.
nate from the sunlit portions of the nucleus and obscure the
underlying topography. The projected nucleus dimensions 3.2. Comet 19P/Borrelly
in the image are ~14.0 × 7.5 km. A triaxial solution for the
dimensions of the nucleus, combining images from all three The nucleus of comet 19P/Borrelly, shown in Fig. 3
spacecraft, gave axes of 15.3 × 7.2 × 7.2 km [±0.5 km in (Soderblom et al., 2002), was imaged by the Deep Space 1
each dimension (Merényi et al., 1989)]. The average sur- (DS1) spacecraft on September 22, 2001, from a distance of
 Weissman et al.: Structure and Density of Cometary Nuclei 341

3560 km at a phase angle of 51.6°. The resolution of the and no apparent cooling due to sublimation of surface ices.
image is 47 m/pixel and the Sun is to the left. The overall However, because each infrared spectrum is, in fact, the aver-
nucleus dimensions are ~8.0 × 3.2 km (±0.2 km in each di- age of a swath across the nucleus surface from bright limb
mension), and it is readily seen to have a bimodal structure. to terminator, any small cool regions (such as the sources
Like Halley, the topography is rough, although there also of the jets) would be masked by the much stronger signal
appear to be relatively smooth areas. The smooth areas ap- from the warmer inactive regions.
pear to include several “mesas,” large flat regions raised
above the surrounding terrain. Active jets (not visible in this 3.3. Analysis
version of the image) emanate from the smooth regions near
the center of the sunlit limb (at upper left). Several sharp Neither the Halley nor the Borrelly images are at suffi-
ridges are visible along the terminator and near the narrow cient resolution to understand fully the surface morphology
neck of the nucleus at lower left. No fresh impact craters of these two comets, in particular, the sources of the jets or
down to ~200 m in diameter are visible anywhere on the the nature of the apparently inactive regions. However, im-
illuminated surface. ages of both nuclei unequivocally show a bimodal struc-
Like the Halley nucleus, the surface of 19P/Borrelly is ture. Such structures have not been apparent in spacecraft
dark, with an average albedo of 0.029 ± 0.006 (Buratti et al., flyby images of asteroids, although they are evident in ra-
2003), although some spots have albedos as low as 0.01. The dar images of some near-Earth asteroids (Ostro et al., 2003).
derived phase curve (from both spacecraft and groundbased However, a rubble-pile structure may not readily manifest
data) is similar to that for C-type asteroids. Near-infrared itself in surface features. The exceedingly large craters on
spectra between 1.3 and 2.6 µm show a strongly red slope asteroid 253 Mathilde have been interpreted as evidence of
and a generally featureless spectrum with the exception of an underlying rubble-pile structure (Veverka et al., 1997),
an unidentified feature at 2.39 µm. This feature appears in as any monolithic asteroid would be destroyed by impacts
all spectra and may be associated with hydrocarbon com- large enough to create such craters (see next section). Even
pounds such as polyoxymethelene (Soderblom et al., 2002). more so than asteroids, cometary nuclei may have the abil-
Using the DS1 infrared data, the surface temperature was ity to mask their internal structures through mass wasting
estimated at between 300 and 345 K, consistent with an processes such as sublimation, sintering, and fallback.
equilibrium black-body surface at its distance from the Sun, Both the Halley and Borrelly nuclei show considerable
surface roughness, as might be expected from a rubble-pile
structure, where large chunks may easily break off or be
rotationally dislodged (although both of these are slowly
rotating nuclei). Also, it is interesting that both nuclei look
more alike than different, since we suspect that they likely
originated from different dynamical reservoirs, possibly
with different collisional histories. As a typical Jupiter-family
comet, Borrelly likely originated from the collisionally pro-
cessed Kuiper belt, whereas Halley, with its retrograde orbit,
most likely originated from the Oort cloud and hence the
giant-planets zone (Levison, 1996).

4. EVIDENCE FOR THE RUBBLE-PILE

NATURE OF COMETARY NUCLEI

4.1. Disrupted Comets

The strongest observational evidence for cometary nu-

clei as rubble piles comes from observations of disrupted or
split comets. Most splitting events are random and seem to
occur for no obvious reason. The classic example is comet
3D/Biela, a Jupiter-family comet with a period of 6.6 yr that
was observed in 1772, 1805, 1826, and 1832. The comet was
Fig. 3. Deep Space 1 image of the nucleus of 19P/Borrelly, taken
observed to split during its 1846 apparition and returned as
on September 22, 2001 from a range of 3560 km (Soderblom et
a double comet in 1852. It was never observed again. How-
al., 2002). The phase angle is 51.6° and the resolution is 47 m/
pixel. Like the nucleus of comet Halley, the Borrelly nucleus is ever, intense showers were observed from the related Androm-
dark with irregular topography, but also with large, apparently edid meteor stream in 1872, 1885, and 1892, correspond-
smooth areas, and with jets emanating from discrete areas on the ing to times when 3D/Biela should have returned.
surface (not visible in this version of the image). Also, like Halley, More recently comet LINEAR, D/1999 S4, was observed
the nucleus is clearly bimodal. to disrupt completely as it passed through perihelion in July
342 Comets II

There is at present no known mechanism for explaining

these random splitting events. One proposed mechanism by
Samarasinha (1999), gas pressure release from volatile
pockets, is discussed in section 4.4. Also, Weissman et al.
(2003) have proposed rotational spinup due to asymmetri-
cal outgassing forces as a likely cause. Regardless of the
mechanism, it seems clear that nuclei are fragile objects and
that when they disrupt, they break into subfragments of tens
of meters in dimension.
A second form of disruption event that provides insights
into nucleus structure occurs when a comet passes through
the Roche limit of a planet or the Sun. This has happened
in the case of Jupiter (16P/Brooks 2 in 1886 and D/Shoe-
maker-Levy 9 in 1992; see section 4.6) and even more spec-
tacularly in the case of the Sun (Marsden, 1989). Prior to
Fig. 4. Hubble Space Telescope image of comet LINEAR (D/ 1978, nine “Sun-grazing” comets, those with perihelion dis-
1999 S4) taken on August 5, 2000, showing fragments of the dis- tances less than 0.01 AU (~2 solar radii), had been discov-
integrating nucleus (Weaver et al., 2001). This long-period comet ered by groundbased observers. Eight of those nine were
disrupted close to perihelion at 0.765 AU from the Sun in July in very similar orbits and were known as the Kreutz group.
2000. It was suggested that these were fragments of a larger comet
that had been tidally disrupted on a previous perihelion pas-
sage (e.g., Marsden, 1989). Weissman (1979) showed that
nongravitational accelerations are so great for Sun-grazing
2000 (Weaver et al., 2001) (see Fig. 4). Weaver et al. ob- comets that they can be perturbed to their current orbits with
served at least 16 fragments of D/1999 S4 using the Hubble semimajor axes of ~100 AU in only two or three perihe-
Space Telescope (HST) and Very Large Telescope (VLT), lion passages. Several of the Kreutz comets split during their
and estimated radii of 25–60 m, assuming an albedo of 0.04. perihelion passages and this was used by Öpik (1966) to
There was evidence for secondary components near some estimate nucleus strengths of 104–106 dynes cm–2. To first
fragments, and evidence that the fragments continued to order, this is about the strength of a snowdrift or a pile of
split over time. The SWAN instrument on the Solar and dirt. So cometary nuclei appear to be very weakly bonded.
Heliospheric Observatory (SOHO) observed water produc- Michels et al. (1982) and Sheeley et al. (1985) discov-
tion rates during the breakup (Mäkinen et al., 2001) and ered six additional Kreutz members using the SOLWIND
found that the observations could best be explained by a coronagraph on an Earth-orbiting satellite. None of these
power-law radius distribution for the fragments, N(>r) ∝ comets survived perihelion passage, nor were they detected
r –a, where N is the number of fragments with radius greater from the ground, suggesting that they were relatively small.
than r, with a cumulative slope, a, of 1.74. Interestingly, this An additional 10 Sun-grazers were found by the Solar Max
is close to the slope of 1.59 ± 0.03 found for Jupiter-family spacecraft between 1987 and 1989 (MacQueen and St. Cyr,
cometary nuclei by Weissman and Lowry (2003). 1991). More recently, the SOHO spacecraft has discovered
Weissman (1980) compiled records of observations of 18 ~540 Sun-grazing comets between 1996 and the end of 2002
split comets and showed that 10% of dynamically new com- (Biesecker et al., 2002). Most of these are Kreutz group
ets from the Oort cloud split, vs. 4% for returning long- members, although three other small groups have also been
period comets, and only 1% for short-period comets (per identified, two of which are possibly identified with comet
perihelion passage) (see also Boehnhardt, 2004). The split- 96P/Machholz 1. Biesecker et al. (2002) estimated diameters
ting events did not show any correlation with perihelion dis- for SOHO fragments of several to tens of meters. Weissman
tance, distance above the ecliptic plane, or time of peri- (1983) and Iseli et al. (2002) showed that cometesimals
helion passage. The statistics suggest that the tendency of larger than ~40–120 m in diameter might be expected to
cometary nuclei to split may reflect some intrinsic nucleus survive perihelion passage, as there is insufficient time for
property, such that comets that are likely to split do so early them to sublimate completely.
on, and those that are unlikely to split are able to survive These continuous streams of cometesimals can be readily
for hundreds or even thousands of returns. Note however explained if the progenitor nuclei are aggregates or rubble
that splitting events do not always lead to total disruption piles that disrupted on previous perihelion passages. Small
of the nucleus. For example, comet 73P/Schwassmann- differences in their initial orbits would lead to the large dis-
Wachmann 3 has been observed to shed fragments on at least persion in arrival times (the typical Sun-grazer orbital pe-
two perihelion passages, yet it still returns every 5.4 yr. In riod is 500–1000 yr), particularly if the cometesimals were
fact, the majority of “splitting” events involve one or more freed from the nucleus more than one orbit ago. In many
small fragments breaking off the main nucleus, and the ways the dynamics are very similar to meteoroid streams,
latter surviving the event. although radiation forces likely do not play a major role.
 Weissman et al.: Structure and Density of Cometary Nuclei 343

Note that if all 540 of the SOHO comets discovered thru near-Earth objects (NEOs) and the hazard they present to life
2002 had 10-m diameters, they would add up to a nucleus on Earth. An important issue, then, is the degree to which
less than 100 m in diameter, so although there are many cometary structure can be inferred from what we presently
cometesimals (and many as yet undiscovered), the progeni- know concerning asteroids. As noted above, comets and as-
tor comet need not have been very large. teroids alike appear to be products of moderate to intense
As discussed in section 4.4 below, a monolithic progen- collisional evolution. They both are of a size that sits on the
itor nucleus cannot easily explain the huge numbers of fulcrum between gravity-dominated and strength-dominated
SOHO comets, as hierarchal splitting would likely not result bodies (Asphaug et al., 2003). So the forces of evolution,
in a very large number of fragments. The entire passage of and the forces of equilibrium response to that evolution,
the comet within the solar Roche limit takes only ~3–4 h appear to be at least broadly the same for comets as for
(depending on the nucleus bulk density assumed) and there asteroids.
is not sufficient time for the nucleus to repeatedly split There are, however, obvious differences. Comets and aster-
unless it was already an agglomerate of a huge number of oids are each derived from different dynamical reservoirs
smaller cometesimals, i.e., a rubble pile. Alternatively, Seka- at different initial heliocentric distances, and thus different
nina (2002) has argued that Kreutz-family fragments con- thermal regimes. Comets undergo intense geologic activity
tinue to split randomly around their entire orbits. Since in the form of mass wasting, i.e., sublimation and disrup-
random disruption is so poorly understood, this possibility tion. Impact craters are not expected to be long-lived on an
cannot be ruled out. However, could such a random mecha- active nucleus (and are not observed; see section 2), whereas
nism explain the narrow size distribution of the observed the asteroids are saturated with craters. Another distinction
SOHO comets? Why are larger fragments not observed? Is relates to the nongravitational forces applied to active com-
it really necessary to invoke additional random disruption ets, which can excite their rotational state (Samarasinha and
to explain the Sun-grazing comet streams? Clearly, there Belton, 1995), possibly to the point of shape modification
are still many open questions with regard to the Sun-grazing or disruption (Weissman et al., 2003). Though nongravita-
comets. tional forces are now also proposed for asteroids (Rubincam,
2000), including forces that can alter their rotation over
4.2. Collisional Evolution longer timescales [e.g., the Yarkovsky-O’Keefe-Radzievskii-
Paddack (YORP) effect, named after the scientists who con-
It is easy to show that collisions between cometary nu- tributed to development of the idea; YORP results in rota-
clei are very rare in the classical Oort cloud, the region tional changes on small bodies due to forces from asymmet-
beyond ~104 AU from the Sun that supplies the long-period ric reradiation of absorbed insolation]. A final difference is
comet flux through the planetary region (Oort, 1950). Stern the origin of mechanical strength. Comets, possessed of po-
(1988) found that impact rates would be more significant tentially mobile volatiles, have a means of forming cohesive
in the proposed inner Oort cloud (Duncan et al., 1987), and aggregate structures over time, whereas a dry asteroid may
that all comets there would undergo at least some surface become truly strengthless if it evolves into a rubble pile.
modification due to impacts of collisional debris. The interpretation of highly evolved, rocky asteroids,
More recently, studies of the physical and dynamical especially the common S and V types, has made good prog-
evolution of the more tightly packed Kuiper belt (Duncan ress thanks to the notable success of the Near-Earth Asteroid
et al., 2004) suggested that collisions play a very important Rendezvous (NEAR) mission at asteroid 433 Eros (which is
role (Stern, 1995, 1996; Farinella and Davis, 1996). Addi- generally agreed to be a highly fragmented, gravitationally
tionally, Stern and Weissman (2001) showed that collisions bound rock), together with the Galileo flybys of Gaspra and
between protocomets in the giant-planets zone, prior to their Ida and supported by collisional modeling based on terres-
ejection to the Oort cloud (or to interstellar space), would trial rock types (e.g., Asphaug et al., 1996). But primitive
be catastrophic for much of the initial population. Charnoz asteroids, the type example being 253 Mathilde, represent a
and Morbidelli (2003) confirmed that collisions result in deep perplexity for asteroid science. While evidence of a
substantial erosion of cometesimals during the ejection pro- highly porous interior for Mathilde is no longer in dispute —
cess, although not quite as severely as found by Stern and the measured density from the NEAR Shoemaker flyby is
Weissman. However, the differences in their results are most 1.3 ± 0.2 g cm–3 (Veverka et al., 1997) — the nature of this
likely attributable to differences in the respective models porosity is entirely unclear. Is Mathilde microporous, in the
and in the specific cases run. Regardless, this new view of manner of the cometary dust balls proposed by Greenberg
the collisional history of cometary nuclei is essentially a and Hage (1990), and recently proposed by Housen et al.
complete reversal of the picture of cometary nuclei as un- (1999) to explain Mathilde’s giant craters? If so, is it cohe-
processed aggregates from the primordial solar nebula. sive, as one might expect for microscale grain structure?
Thus, we must consider what effect collisions might have Or does Mathilde, and the other primitive asteroids with
on the internal structure of cometary nuclei. Fortunately, this comparable densities [as determined by analyses of their
question has received significant attention in recent years satellite orbits (Merline et al., 2003)], possess huge voids
through studies of the collisional processing of asteroids, as one would expect from collisional disruption and reas-
spurred on in large part by the increasing attention given to sembly of major fragments (Benz and Asphaug, 1999)? In
344 Comets II

studying the structure of cometary nuclei and asteroids, we in the impacted components, with few pathways of trans-
learn of their origins and evolution. mission to neighboring components. Moreover, a coarse
rubble pile tends to result in ejection of most impact prod-
4.3. Monoliths, Rubble Piles, and Porosity ucts (Asphaug et al., 2003) rather than absorption by com-
paction. Whether a comet is macroporous or microporous,
To describe the interiors of small bodies in the solar stress wave transmission is hindered due to the great attenu-
system we require a dictionary of well-defined and agreed- ation of poorly consolidated ice and rock, making the sur-
upon terms. Richardson et al. (2003) recently reviewed this vival of porous comets and asteroids more likely during
topic with regard to asteroids; for comets one must add to impact, as demonstrated by the experiments of Ryan et al.
this the complexity of mantle development (e.g., Brin and (1991) and Love et al. (1993) and by numerical (Asphaug
Mendis, 1979) and melting of the interior due to short-lived et al., 1998) and scaled simulations (Housen and Holsapple,
radionuclides (Prialnik and Podolak, 1999), both of which 2003).
might significantly alter the internal structure.
Monoliths are objects of low porosity and significant 4.4. Volatiles and Cohesion
strength, and are good transmitters of elastic stress. Mono-
liths in an impact-evolved population must be smaller than A volatile-rich aggregate (such as an icy cometary nu-
the size that would accumulate its own impact ejecta. Es- cleus) is more cohesive than a dry aggregate (such as an
cape velocity for a constant density body is proportional to asteroidal rubble pile) due to the facilitation of mechanical
its size (approximately 1 m/s per km of diameter for spheres bonding, either directly (e.g., van der Waals forces) or in-
of ice), so that bodies larger than some transition size evolve directly during episodes of sublimation and frost deposi-
into gravitational aggregates. Monoliths can be fractured by tion (Bridges et al., 1996). For gravity as low as on a typical
impact bombardment, in which case their tensile strength cometary nucleus, frost or other fragile bonds can be cri-
is compromised and may be reduced to zero, i.e., shattered. tical to long-term survival during impact or tidal events.
A fractured or shattered monolith might transmit a com- Comet Shoemaker-Levy 9, for example, could never have
pressive stress wave fairly well, provided pore space has disrupted during its 1992 tidal passage near Jupiter at a
not been introduced between the major fragments. Tensile perijove of only 1.3 jovian radii had the tensile strength
stress, however, is not supported across a fracture. across the comet exceeded ~103 dynes cm–2 (Sekanina et al.,
A rubble pile includes any shattered body whose pieces 1994), weaker than snow. Asphaug and Benz (1994, 1996)
are furthermore translated and rotated into a loose packing. calculated a maximum tensile strength of only ~30 dynes
Stress waves of any sort are poorly transmitted across a cm–2 for Shoemaker-Levy 9 in order for it to fragment from
rubble pile, although intense shocks may propagate by a hypothetical monolithic body into ~20 pieces (see below),
crushing and vapor expansion. Primordial rubble piles are and therefore proposed a cohesionless rubble-pile structure
objects that accreted as uncompacted cumulates to begin for this comet and gravitational clumping (as opposed to
with. Collisional rubble piles are primordial rubble piles that fragmentation) as the cause of its “string of pearls” post-
have subsequently undergone collisional evolution. perijove structure. It matters greatly whether a comet is truly
Because much of our discussion regarding comets relates strengthless or only extraordinarily weak. Note, however,
to primordial and collisional rubble piles, we must also dis- that Shoemaker-Levy 9 may have been previously dis-
tinguish between macroscopic (coarse) and microscopic (fine) rupted, although not catastrophically, during its ~60 yr or
porosity. An asteroid or cometary nucleus consisting of quin- more orbiting Jupiter, and thus the tensile strength deter-
tillions of tiny grains might exhibit considerable cohesion mined by Asphaug and Benz may not be typical of other
and perhaps support a fractal-like “fairy-castle” porosity. The cometary nuclei.
total energy of contact bonds divided by the total mass of a There is a converse effect to the presence of volatiles,
granular asteroid, its overall cohesional strength, is inversely in that their vapor expansion might help fuel a comet’s dis-
proportional to grain diameter, so that a coarse aggregate assembly during hypervelocity collisions. The energy of
is weaker than a fine one, if all else is equal (Greenberg, vaporization for ice is approximately 10 times lower than
1998). On the other hand, a highly porous, finely commi- that for rock, and the impact speed required to establish a
nuted body might accommodate significant compaction. shock wave is also lower (on the other hand, impact speeds
Impact cratering on microporous bodies might provide in the outer solar system are also lower). The effect of super-
counter-intuitive results, involving crushing and capture of volatiles such as CO, should they exist in sufficient quanti-
impacting material (e.g., Housen and Holsapple, 1990) ties within the nucleus, would have an even more pro-
rather than ejection. nounced effect upon the expansion of impact ejecta, in a
A coarse rubble pile by contrast has far fewer contact manner that has not yet been characterized. And so, while
surfaces distributed over the same total mass, and would volatiles may provide some kind of structural integrity to
therefore behave much differently. Asphaug et al. (1998) an aggregate body, they may also reduce the size or speed
used a coarse rubble pile as a starting condition for impact of impactor required for catastrophic disruption. Samara-
studies, and found that the impact shock wave gets trapped sinha (1999) offered expanding volatiles, propagating from
 Weissman et al.: Structure and Density of Cometary Nuclei 345

the Sun-warmed exterior to the interior of a coarsely porous ders of magnitude from model to model), but the concept
comet, as an explanation for the disruption of comet LIN- was established that beyond some size, rubble piles might
EAR D/1999 S4 near perihelion. However, Weaver et al. exist.
(2001) and Mumma (2001) found a fairly low CO abun- The quantity ρQ*S has dimensions of strength. It happens
dance (<1%) in the disrupted comet. CO is typically the to be close to the corresponding static tensile strength of
most abundant volatile ice in cometary nuclei after water. ice and rock in laboratory impact experiments (Fujiwara
This brings up the final important effect of porosity, et al., 1989). Tensile strength was therefore used as an easily
which is the tremendously efficient insulating property of measured proxy for ρQ*S in early disruption theory. Upon
granular media in vacuum. Weissman (1987) and Julian et this basis, it was concluded that primitive asteroids, comets,
al. (2000) showed that the surface thermal inertia for comet and early planetesimals (which are presumably of lower ten-
Halley was at least an order of magnitude less than that for sile strength than laboratory ice and rock) would be easily
solid water ice. If cometary nuclei have low thermal conduc- disrupted, and that survivors (the objects we see today)
tivities, then it is extremely difficult to transport energy dur- would be strong, intact bodies, and regolith would be thin
ing a single perihelion passage to volatile reservoirs at depth. or absent (Housen et al., 1979; Veverka et al., 1986). The
In addition, it is difficult to reconcile the buildup of pres- transition between strength-dominated, monolithic bodies
sure within the nucleus with an open rubble-pile structure. and gravity-dominated rubble piles was expected to occur
at ~100 km because (1) the transition should occur when
4.5. The Case for Strength central pressure ~2πGr2ρ2/3 equals rock strength; this tran-
sition occurs at about 100 km diameter for icy or rocky
Within the context of collisional evolution, the rubble- targets; and (2) it should occur when gravitational binding
pile hypothesis was first formalized by Davis et al. (1979) energy per volume equals rock strength Y; neglecting con-
in their modeling of size distributions among various small- stants this yields rρ = (Y/G)½, and r on the order of several
body populations. They defined a threshold specific energy hundreds of kilometers, again whether for ice or rock.
Q*D (impact kinetic energy per target mass) required to both With distinct ways of viewing small-body structure con-
shatter mechanical bonds and accelerate half the mass to verging upon a transition to the gravity regime at ~100-km
escape trajectories. Shattering requires a lower specific sizes, the idea seemed safe that all but the largest comets
energy Q*S < Q*D to create fragments, none larger than half and asteroids were monolithic. Certainly by the time of the
the target mass, not necessarily accelerating those fragments spacecraft encounters with comet Halley in 1986, the idea
to dispersal. For small rocks, Q*D → Q*S, whereas for large of structurally integral comets appeared to be on a solid
bodies, Q*S /Q*D → 0. Whenever Q*S << Q*D, the probability foundation.
of a shattering impact (which involves a smaller impactor) There were, however, some very serious problems with
becomes far greater than the probability of dispersal, in this conclusion. For one thing, the same collisional model-
which case a body might be expected to evolve into a pile ing required that bodies smaller than ~100 km would be
of rubble, unless other effects (such as melting and com- unlikely to survive over billions of years, in contrast with
paction) were to dominate. The steeper the impactor popu- their abundant population (see Chapman et al., 1989). An
lation size distribution, the more likely it is that shattering even more compelling argument against structural integrity
will dominate dispersal, i.e., that the population evolves into was the manner in which comets came apart so effortlessly
rubble piles. in tidal and random disruption events (see section 4.1). As
Davis et al. (1979) expressed impact strength as the sum we shall now see, the resolution to this dilemma appears
of the shattering strength plus the gravitational binding to be that impact strength and tensile strength are not sim-
energy of the target ply related, and may even be inversely correlated. That is
to say, structurally weak bodies are capable of absorbing
Q*D = Q*S + 4πρGr2/5 (1) large quantities of impact energy that would disrupt struc-
turally strong bodies.
where r is the radius of a spherical target and ρ is its density. Experiments (Love et al., 1993) and modeling (Asphaug
Equation (1) is called energy scaling: On a graph of Q*D vs. et al., 1998, 2003) have shown that loosely bonded aggre-
r it plots as a horizontal line (Q*D ~ Q*S = constant), transi- gates can survive a projectile that would shatter an equal-
tioning at some size to a gravity-regime slope of 2 (Q*D ∝ mass monolith into small pieces. It is now believed that
r2). The size corresponding to this break in slope is known some of the most fragile bodies in the solar system — po-
as the strength-gravity transition for catastrophic disruption. rous aggregates with little or no cohesion — can be highly
[The strength-gravity transition for catastrophic disruption resistant to catastrophic disruption owing to their ability to
must be distinguished from the strength-gravity transition dissipate and absorb impact energy. In other words, there
for planetary cratering. An object in the gravity regime for is no longer any rationale for adopting tensile strength as a
disruption (Earth is one) can certainly have strength-con- measure of an object’s catastrophic disruption threshold, and
trolled craters.] Subsequent analysis has changed the slopes with this tenet no longer supportable, the edifice of strength
in both regimes (the predicted transition size varies by or- scaling crumbles. Furthermore, ejection velocities from
346 Comets II

fragile bodies are correspondingly low, enabling them to Shoemaker-Levy 9 sparked new investigations in a num-
hold on to their pieces (in the strength regime, ejecta veloc- ber of areas. Melosh and Schenk (1993) were quick to see
ity would scale with the square root of strength). Like palm the correlation between the SL9 morphology and the mor-
trees that bend in a storm, rubble-pile comets may survive phology of many mysterious crater chains (“catenae”) (Pas-
collisions that would shatter and disperse monolithic bodies. sey and Shoemaker, 1982) on Ganymede and Callisto, and
ascribed a common formation mechanism. The first and
4.6. Shoemaker-Levy 9 simplest model for the tidal disruption (Scotti and Melosh,
1993) proposed that the ~20 observed fragments were in-
Discovered in March 1993 (Shoemaker et al., 1993), tact “cometesimals” each a few 100 m across, bound to-
comet Shoemaker-Levy 9 (D/1993 F2) (SL9) was seen to be gether gravitationally as a coarse rubble pile that separated
a chain of ~20 discrete nuclei in an eccentric orbit around in Jupiter’s tidal field. Scotti and Melosh ignored bonding
Jupiter (Fig. 5). Dynamical integrations of the orbits of the between the cometesimals, and assumed that the comet was
nuclei backward in time brought them together at a previ- not rotating at the time of perijove passage, and that its
ous perijove passage on July 7.8, 1992, at only 1.31 jovian pieces (although gravitationally bound to begin with) did
radii, inside Jupiter’s Roche limit. Other dynamical integra- not interact gravitationally thereafter. The actual analysis
tions suggested that the comet had been in orbit around involved two massless test particles representing the inner
Jupiter for ~60 yr, although that figure is somewhat uncer- and outer points of the comet, launched with identical ve-
tain (Chodas and Yeomans, 1996). locity from two slightly offset perijoves. This offset — the
Dobrovolskis (1990) and Asphaug and Benz (1996) pro- comet diameter — was then constrained by the measured
vided overviews of tidal disruption theory as it pertains to length of the fragment chain. Scotti and Melosh derived a
small solar system bodies. Dobrovolskis developed his own parent comet diameter of ~2 km, considerably smaller than
theory for the initiation and propagation of cracks inside the prevailing 10-km estimate based on modeling (Sekanina
tidally strained elastic spheres. This insightful formal trea- et al., 1994) and the 7.7-km estimate based on HST images
tise on the Jeffreys (1947) regime was published only two (Weaver et al., 1994), although Weaver et al. cautioned that
years before the breakup of SL9, and set the stage for inter- their estimates only provided upper limits to the progeni-
pretation of SL9 as a solid elastic body (that is to say, a mono- tor nucleus diameter.
lithic mass of rock and ice). Supported by the strength- Asphaug and Benz (1994) tried a different approach, first
regime analyses discussed above, theorists were accustomed modeling a solid elastic sphere undergoing Jeffreys (1947)
to thinking about small bodies as elastic solids. regime disruption. They reproduced the theoretical result of
For Shoemaker-Levy 9, however, there can be no doubt Dobrovolskis (1990), although the allowed strength had to be
that it was a body of extraordinarily low cohesion, less than lower than the small tidal stress. While there was no prob-
that of dry snow. The equilibrium tidal stress at the center lem breaking the comet in two if a small enough strength
of a homogeneous sphere is approximately GMpρcrc2/R3, was allowed, splitting it into 4, or 8, or 16 pieces was im-
where Mp is the mass of the planet (Jupiter), ρc and rc are possible. Once the nucleus breaks in two, the tidal stress
the density and radius of the comet, and R is the distance to drops by a factor of four, and must build up to its previous
the center of the planet. This is 103 dynes cm–2 for a 1-km value for further fragmentation to occur. In order to come
comet of density 0.6 g cm–3 at SL9’s perijove of 1.31 RJ. apart into ~20 pieces by the time of perijove passage, frac-
(Note also that tidal stress and lithostatic overburden both ture would have to begin at a strength lower than ~30 dynes
scale with r2c, which is the foundation for the scale-similarity cm–2, about a million times weaker than cold water ice.
to follow.) Sensing a dead end, Asphaug and Benz (1994) began to
reproduce the scenario of Scotti and Melosh (1993) explic-
itly, beginning with ~20 spheres (“grains”) in close contact,
modeled using an N-body code with Jupiter as the central
mass. In these models, self-gravitation was observed to form
clumps or pairs among the grains unless density was de-
creased to very low values (0.05 g cm–3). For reasonable
densities, the number of observable fragments (clumps) was
always significantly lower than the number of grains. To
form ~20 fragments, ~100 or more grains had to be as-
sumed — no longer really a cometesimal model, but a
Fig. 5. Hubble Space Telescope image of the tidally disrupted
rubble-pile model instead. For N > 200 initial grains, self-
comet Shoemaker-Levy 9 (D/1993 F2) (SL9) in January 1994
(Weaver et al., 1994). Note that the brightest nuclei are near the similarity took over, and what was revealed was a process
center. These corresponded to the largest nuclei, as determined responding not only to gravity, but to self-gravitational in-
from the brightness of the SL9 impact events on Jupiter (Nichol- stability (Chandrasekhar, 1961). And so there were serious
son, 1996; Crawford, 1997), and matched the prediction of problems with the Dobrovolskis and the Scotti and Melosh
Asphaug and Benz’s (1994, 1996) rubble-pile model. models, as applied to SL9.
 Weissman et al.: Structure and Density of Cometary Nuclei 347

Fig. 6. A 500-“grain” simulation of the breakup of comet Shoemaker-Levy 9 by Asphaug and Benz (1996). The initial nucleus is
1.5 km in diameter and the grains have bulk densities of 0.5 g cm–3. (a) The unperturbed nucleus with the grains in close hexagonal
packing and a void space of 27%; (b) the distorted nucleus at perijove, 1.3 RJ: arrows show velocity vectors relative to the center of
mass; (c) perijove + 2 h, 3.5 RJ: the nucleus is a cigar-shaped chain, 10 km in length; (d) perijove + 10 h, 12 RJ: the grains have
already clumped into a chain of subnuclei.

Still, the idea of a solid elastic comet was difficult to This smaller comet would become a 10-km-long “cigar” by
refute, despite its fatal shortcomings. In the first detailed t = 2 h (see Fig. 6), rotating at the same rate as deduced by
kinematical model for the breakup, Sekanina et al. (1994) Sekanina et al. (1994). This turns out to be the time that
proposed a large (10-km minimum diameter) nucleus that self-gravity among the comet fragments could be ignored,
underwent sudden brittle fragmentation about 2 h after as was done in Sekanina et al.’s kinematical model. Thus,
perijove with Jupiter, by showing that the orbits of individ- all aspects of the rubble-pile description are consistent with
ual SL9 fragments diverge from an ~10-km body at t ≈2 h the kinematic requirements.
[1.5 h in Sekanina et al. (1994); 2.5 h in Sekanina (1996)]. Asphaug and Benz (1994), and shortly thereafter Solem
This did not mean, however, that the undistorted parent nu- (1994, 1995), estimated the size of the parent nucleus by
cleus was 10 km across, or that it underwent brittle failure. correlating their models with the length of the fragment
Rather, Asphaug and Benz (1996) found that these values chain as first observed almost nine months after the break-
were entirely consistent with a 1.5-km-diameter rubble-pile up, yielding a best fit of 1.5 km diameter if the parent nu-
nucleus undergoing tidal distortion during perijove passage. cleus was not rotating, and 1.0 km if it was rotating pro-
348 Comets II

grade with a period of 6 h (a retrograde rotating progenitor chains of reassembled, virtually strengthless rubble piles of
was not possible, as this would have prevented the forma- small icy planetesimals whose common quality were their
tion of the highly symmetric chain that was observed). In similar bulk densities. While models involving strength
addition, the rubble-pile models predicted the appearance of effects can be tuned (Sekanina et al., 1994; Sekanina, 1996)
the reassembled fragment string, with the largest objects near to satisfy the constraints of Shoemaker-Levy 9, they fail
the center of the “string of pearls” (see Fig. 5). The 1.5-km miserably when applied to the more general problem of
diameter for the SL9 progenitor was near the median for all catenae craters.
disrupted comets striking Ganymede and Callisto as found SL9 provides a statistic of one. Whether all comets are
by Schenk et al. (1996), making the progenitor a typical, strengthless is open to debate, because tidal breakup admits
rather than an unusually large, cometary nucleus (see Weiss- a bias, in that comets passing through the Roche zone that
man and Lowry, 2003). do not disrupt (strong bodies) bear no record of surviving
this passage, other than being torqued into a new spin state
4.7. Catenae and losing any loose surface material. For every disrupted-
comet crater chain on Ganymede and Callisto, there could
The catenae, i.e., crater chains, on Ganymede and Cal- be several impact craters by comets that had equally close
listo (see Fig. 7) also provide important clues to the struc- Roche encounters with Jupiter but did not suffer disruption.
ture of cometary nuclei. Schenk et al. (1996) showed that However, the number of catenae on the observed surfaces
there is no correlation between the estimated parent nucleus of Ganymede and Callisto is the same as one would expect
size for the catenae (based on well-known crater-scaling (Schenk et al., 1996) if every Jupiter-grazing comet dis-
relationships) and the number of craters produced. Catenae rupted in this fashion. While there is no guarantee that every
formation is self-similar across all sizes, from approximately comet in the Jupiter family is a rubble pile, catenae statis-
tens to hundreds of kilometers. These data would imply, tics provide strong evidence that most are. The breakup of
within the context of the Melosh and Scotti cometesimal SL9, and by extension the cometary breakups recorded at
model, that larger comets are composed on average of pro- Ganymede and Callisto, constitute a direct record of comet-
portionately larger cometesimals. But this is at odds with ary structure. The other direct record, that of cometary spin
our understanding of how comets accrete. Weidenschilling’s state, has further implications that are also consistent with
(1997) cometesimal model, for example, suggests that the the rubble-pile structure of comets (see section 5.3).
building-block size for comets should be independent of the
diameter of the final comet. Furthermore, the largest cra- 5. DENSITY OF COMETARY NUCLEI
ters are found in the center of the catenae, as predicted by
rubble-pile tidal disruption simulations. The only economi- 5.1. Direct Measurement of Mass and Volume
cal explanation for scale-similarity and for large central
fragments is that the catenae were formed by impacts of In discussing the density of cometary nuclei, it is first
necessary to clearly define our terms. Following Britt et al.
(2003) we define the “grain density,” ρg, as the mass of an
object divided by the volume that is occupied by solid
grains. This is an intrinsic property of the material involved.
For example, the grain density of water ice at 0°C is
0.917 g cm–3 (Hodgman, 1962). The “bulk density,” ρb, of
an object is its mass divided by its total volume, including
voids and pore spaces. The porosity of an object is (1 – ρb /
ρg). Generally, in astronomy, we measure the bulk density
of distant objects and, unless otherwise noted, that is the
quantity we will be discussing in what follows.
To estimate the density of a body, we must measure its
mass and its volume. Both of these measurements are very
difficult for cometary nuclei. Volume can be estimated from
direct spacecraft imaging (see section 2) or from telescopic
observations that can yield the approximate radius and axial
ratio of individual nuclei (Lamy et al., 2004). By far the
most common technique is to perform charge-coupled-de-
vice (CCD) photometry of nuclei when they are far from
Fig. 7. The Enki catena crater chain on Ganymede as imaged
by the Galileo spacecraft on April 5, 1997. The total chain of 13 the Sun and (presumably) inactive, and then to assume a
craters is ~160 km in length. Note that the largest craters are near typical cometary albedo of 0.03–0.04 for the nuclei (e.g.,
the center of the chain, as predicted by the Asphaug and Benz Licandro et al., 2000; Lowry et al., 2003). If a rotational
(1994, 1996) simulations, and as observed for comet Shoemaker- lightcurve can be obtained, then it is also possible to derive
Levy 9. a lower limit to the axial ratio of the nucleus (e.g., Lowry
 Weissman et al.: Structure and Density of Cometary Nuclei 349

and Weissman, 2003). If many lightcurves are available tric lightcurve via empirical relationships such as that of
(something we do not have yet for any nucleus), then it is Festou (1986), and then combined with equation (3) to solve
possible to derive a full three-dimensional shape model for the mass. Unfortunately, this method is highly model
(e.g., Kaasalainen et al., 2003). dependent and the assumptions applied are numerous. For
Estimating nuclei masses is considerably more difficult. example, it is not possible to constrain the directionality of
Cometary nuclei are too small to appreciably perturb other the rocket forces without knowledge of the location of the
bodies in the solar system. Even close spacecraft flybys active areas and the rotational state of the nucleus. Thermal
have been unsuccessful to date because of the low cometary lag effects, which are due to unknown values of the sur-
masses and the high flyby speeds. The gravitational pertur- face thermal inertia, must also be factored in. A more de-
bation by a comet or asteroid on a passing spacecraft can tailed discussion of the theory of cometary nongravitational
be estimated by the impulse approximation forces and outgassing physics can be found in Yeomans et
al. (2004).
∆V = 2GMc/DV∞ (2) In situ observations from the Vega and Giotto spacecraft
encounters with comet 1P/Halley provided, for the first
where ∆V is the change in velocity of the spacecraft, di- time, accurate measurements of the dimensions and hence
rected along a line connecting the cometary nucleus and the volume of a comet’s nucleus (Wilhelm et al., 1986). This
point of closest approach of the spacecraft, G is the gravi- allowed Rickman (1986) to estimate a bulk density of 0.1–
tational constant, Mc is the mass of the nucleus, D is the 0.2 g cm–3 for the Halley nucleus. This early paper was
closest approach distance, and V∞ is the flyby velocity at widely accepted as indicative of extremely low bulk densi-
infinity. If we take a typical 5-km-radius nucleus with a den- ties for cometary nuclei. This view was further strengthened
sity of 1 g cm–3, and a spacecraft flying by at 100 km dis- by Rickman et al. (1987), who studied 29 short-period com-
tance at a velocity of 30 km s–1, the velocity perturbation ets and found that their bulk densities were all below 0.5 g
is 2.3 × 10 –3 cm s–1, about an order of magnitude less than cm–3, indicating a highly porous internal structure.
the current detection capability of spacecraft radio track- However, others found higher values for the nucleus den-
ing systems. sity. An independent estimate for 1P/Halley by Sagdeev et
al. (1988) found a value of 0.6 (+0.9, –0.4) g cm–3. A de-
5.2. Nongravitational Force Estimates tailed analysis of the many factors and uncertainties in-
volved in these calculations led Peale (1989) to conclude
At present the only means for estimating nucleus mass is that the density of Halley could be anywhere from 0.03 to
by modeling the expected acceleration of comets due to the 4.9 g cm–3, with a preferred value near 1.0 g cm–3. Even
“rocket effect” from sublimation of water ice on a rotating Rickman (1989) revised his earlier value for Halley and
nucleus, and comparing that with the observed nongravi- increased the estimated density to 0.28–0.65 g cm–3.
tational motion of the comet. This method was pioneered More recently, Skorov and Rickman (1999) used a more
by Rickman (1986, 1989), who showed that the change in refined method and indicated that the earlier method of
the orbital period, ∆P, caused by the nongravitational forces Rickman (1989) underestimated the momentum transfer that
(neglecting accelerations normal to the orbital plane) is re- produces the nongravitational acceleration. They determined
lated to the acceleration j by that the earlier density estimates should be increased by a
factor of ~1.8. Thus, their new Halley density estimates
1 P P were 0.5–1.2 g cm–3.
6π(1 – e2) 2
e jt
∆P =
n2 p∫
0
jr sinθ dt + ∫R
0 h
(3) Combining spacecraft and groundbased imaging of 19P/
Borrelly during the DS1 flyby in 2001, Farnham and Coch-
ran (2002) calculated the orientation of the rotation pole and
where P is the orbital period; t is time; e, n, and p are the compared this with published nongravitational terms to com-
orbital eccentricity, mean motion, and semilatus rectum pute a nucleus mass of 3.9 × 1016 g and a density of 0.49
respectively; θ is the true anomaly; and jr and jt are the radial (+0.34, –0.20) g cm–3. For Borrelly, the primary jet structure
and transverse components of the nongravitational accel- appears to be fortuitously aligned with the rotation axis. Such
eration. The force from the outflow of gas and dust in the an alignment means that nucleus rotation and thermal lag
orbital plane is given by effects will not significantly influence the resulting non-
gravitational motion of the body. Indeed, Yeomans (1971)
pointed out that although significant nongravitational acceler-
F= − ∑Q m v
i
i i i (4) ations are present for this comet, they have remained essen-
tially constant since its discovery in 1904. However, Davids-
son and Gutiérrez (2003) have estimated a lower bulk den-
where Qi are the production rates of the different volatile sity of 0.18 to 0.30 g cm–3 for Borrelly, barely in agreement
species that have masses mi and emission velocities vi. This with the Farnham and Cochran (2002) value. As was the
rocket force is related to the nucleus mass M by F = Mj. case for 1P/Halley, density estimates derived from nongravi-
Equation (4) can be evaluated from the observed heliocen- tational force estimates appear to still be fairly uncertain.
350 Comets II

5.3. Shoemaker-Levy 9 eration at the apex of a rotating prolate spheroid: 2a(2π/

Prot), where a is the semimajor axis of the spheroid and Prot is
As discussed previously, the appearance of comet Shoe- the nucleus rotation period. To evaluate g we solve the fol-
maker-Levy 9 provided unique insights into the nature of lowing integral (Luu and Jewitt, 1992)
cometary nuclei. Asphaug and Benz (1994, 1996) and Solem
(1994, 1995) were able to explain many of the observed 1
2
2 2f 2
characteristics of SL9’s “string of pearls” appearance by as-
suming that the pre-breakup nucleus was a strengthless rub-
g = −2πGρba ∫0
1 − f2 +
s
− 1 ds (5)

ble pile of hundreds of smaller icy planetesimals. Asphaug

and Benz and Solem found that density played a key role where f is the ratio of the semiminor to semimajor axes,
in determining the final, post-breakup configuration of this b/a; G is the gravitational constant; ρb is the spheroid bulk
swarm of planetesimals. For densities less than ~0.3 g cm–3, density lower limit; and s is the distance along the semi-
the resulting chain of clumps was highly diffuse. For den- major axis in units of a. By setting the integral of equa-
sities greater than 1.0 g cm–3, the planetesimals formed a tion (5) equal to the expression for the centripetal accelera-
single, major central clump, unless the progenitor nucleus tion given above we obtain
happened to have significant prograde rotation.
These outcomes were found, as expected from dimen- 2π
− =
sional analysis, to be self-similar for any density, when the P2rotGρb
perijove distance was normalized to the density-dependent
(6)
2f 2(1 − f 2) 2 + f 2 ln f 2 − f 2 ln 2 − f 2 + 2 1 − f 2
1
Roche limit. For SL9, where the perijove was known, the
morphology of the chain thus narrowly constrained the nu-
(1 − f 2)
3
cleus density. The result was that the SL9 progenitor nucleus 2

needed to have a bulk density of about 0.6 ± 0.1 g cm–3

(Asphaug and Benz, 1996) or ~0.5 g cm–3 (Solem, 1995). We can infer shape information from the rotational light-
Asphaug and Benz also found that a fast, prograde rotation curve of the nucleus via time-series photometric measure-
led to somewhat higher density estimates, on the order of ments. If we assume that the brightness variation is purely
1.0 g cm–3. shape induced and not caused by a variation in albedo
Note again that the values above are the effective bulk den- across the nucleus surface, then the nucleus can be modeled
sity of the progenitor nucleus, not the individual cometes- as a triaxial ellipsoid with semiaxes a, b, and c, where a >
imals. Assuming random reassembly with similar macropo- b and b = c. A lower limit to the axial ratio can be estimated
rosity, the bulk density of the final SL9 nuclei post-breakup using f –1 = a/b = 100.4∆m, where ∆m is the range of observed
would be similar, or perhaps somewhat lower than the val- magnitudes. As an example we consider the lightcurve of
ues above, given the low relative velocity of the reaccretion Comet 22P/Kopff (Lowry and Weissman, 2003). If we sub-
and the lack of time for compaction processes to work (i.e., stitute f = 0.6 and Prot = 12.3 h into equation (4), we get ρb ≥
sintering, inward coma diffusion, etc). Crawford (1997) 0.11 g cm–3 for the Kopff nucleus. The density measurement
used a hydrocode with advanced thermodynamics to obtain is a lower limit because we use the projected axial ratio, a/b,
best matches to the Galileo NIMS observations of the SL9 which is a lower limit to the true axial ratio, since the orien-
impacts (Carlson et al., 1997). Crawford’s best fit was for tation of the rotation axis is unknown. Also, the nucleus does
impactor densities of 0.25 g cm–3, and for a parent comet not necessarily need to be spinning at its rotational disrup-
with the same mass as derived by Asphaug and Benz (1994). tion limit.
These density values are somewhat lower than what we ex- Lightcurves for a number of cometary nuclei have been
pect from a reassembled rubble pile. However, the effec- published to date. The corresponding values for the light-
tive bulk density of the impactors may have been reduced curve-derived rotation periods and projected axial ratios are
as the rubble piles again began to gravitationally distort and shown in Fig. 8. The derived rotation periods range from
extend in Jupiter’s gravitational field just prior to impact. 5.2 to 29.8 h, while the projected axial ratios, a/b, range
Also, the accompanying debris cloud (see Fig. 6) around from 1.02 to 2.48. The inferred, lower-limit nucleus bulk
each impactor may have worked to increase the effective densities are given by the position of each comet in the fig-
cross-section in Crawford’s calculations, even though most ure and range from 0.02 to 0.56 g cm–3, consistent with den-
of the mass was concentrated in the central object. sity values determined through other methods.
Figure 8 is reminiscent of one found for asteroid rota-
5.4. Rotation Period: Shape Relationship tion periods and shapes by Pravec et al. (2003, see their
Fig. 5) where there is a sharp edge in the distribution of
Knowledge of the shape and rotation period of the nu- asteroids (with diameters >0.15 km) at a rotation period of
cleus allows a lower limit to be calculated for the nuclear about 2.2 h, corresponding to a density of ~2.5 g cm–3.
density, i.e., the minimum density required in order to with- Pravec et al. interpret this result as evidence for small aster-
stand centripetal disruption under the assumption of negli- oids being “loosely bound, gravity-dominated aggregates
gible cohesive strength. The density is derived by setting the with negligible tensile strength.” Although the statistics for
gravitational acceleration, g, equal to the centripetal accel- the comets are relatively poor so far, we are perhaps see-
 Weissman et al.: Structure and Density of Cometary Nuclei 351

ing a similar “edge” at a density of ~0.6 g cm–3. Note also note, however, that Holsapple’s calculations do not explain
in Fig. 8 that there is a trend for the fastest-rotating nuclei the sharp edge seen for the vast majority of small asteroids
to have lower values of a/b, which may reflect the inability in the rotation rate vs. elongation plot of Pravec et al.
of the rubble-pile nuclei to maintain extended shapes near (2003). The existence of that edge strongly implies that
the rotational disruption limit. many of these bodies are indeed acting as if they were
The database of rotational lightcurves for transneptunian strengthless (or, to be more exact, have cohesive strengths
objects (TNOs) continues to grow (Sheppard and Jewitt, ≤102 dynes cm–2). Thus we believe that the density lower
2002), and the inferred lightcurve-derived density lower limits shown in Fig. 8 are indeed likely to be meaningful.
limits are typically in the range 0.1–0.4 g cm–3. These val-
ues are consistent with those for cometary nuclei, which is 5.5. Additional Methods for Inferring
reassuring given that the TNOs are believed to be the likely Nucleus Densities
source for most of the Jupiter-family comets in Fig. 8 (Levi-
son, 1996). An alternative method for estimating nucleus densities
Recently Holsapple (2003) has suggested that modest relies on measurements of the density of dust particles origi-
cohesive strengths, on the order of a few times 104 dynes nating from comets. Anhydrous interplanetary dust particles
cm–2, could allow even fast-rotating, elongated asteroids to (IDPs), widely believed to be derived from comets, have
survive as rubble piles. This value is similar to the tensile typical bulk density values of 0.7–1.2 g cm–3 (Fraundorf et
strengths inferred for cometary nuclei (see section 4.1). We al., 1982), including voids that were likely once filled with
ices. Although these densities are indeed consistent with bulk
densities obtained from other methods, they are still some-
what uncertain, since the nucleus porosity, the degree of
volatile loss from the particles, and the degree of compac-
tion during atmospheric entry are largely unknown. Also,
Maas et al. (1990) found mean densities ranging from 0.2–
6.0 g cm–3 for individual dust particles detected during the
Halley spacecraft encounters consistent, although not par-
ticularly constraining.
By combining models of interstellar dust accretion with
observational constraints provided by the Halley encounters,
Greenberg and Hage (1990) found porosities of 0.6–0.83 for
dust in the cometary coma, which in turn led to estimated
comet nucleus densities of 0.26–0.60 g cm–3. Additionally,
Greenberg (1998) combined results of his core-mantle inter-
stellar dust model, the solar system abundances of the ele-
ments, the composition of dust from comet Halley, and data
on the volatile molecules in cometary comae to set an upper
limit to the density of fully packed cometary material of
~1.65 g cm–3. This would be what we referred to earlier as
the “grain density” [see Weidenschilling (2004) and Sykes
et al. (2004) for discussions of accretion mechanisms and
IDPs].
If the bulk density of cometary nuclei are on the order
of 0.6 g cm–3 as suggested above, then the nuclei have a
porosity of 0.64, assuming Greenberg’s (1998) grain den-
sity for cometary materials. Is such a value reasonable? Britt
Fig. 8. Lightcurve-derived rotation periods and projected axial and Consolmagno (2001, see also Britt et al., 2003) showed
ratios, a/b, for 13 Jupiter-family comets and 1 Halley-type comet. that several C-type asteroids (plus Deimos) have macropo-
Their inferred density lower limits are given by their position on rosities of ~40%, although the average C-type porosity is
this plot. Constant-density curves for values of 0.02, 0.06, 0.2, ~27%. Macroporosities of 60% or more are seen for two
0.6, and 2.0 g cm–3 have been overplotted for comparison. The M-type (metallic) asteroids. The C-type asteroids are likely
inferred bulk density lower limits range from 0.02 to 0.56 g cm–3, to be a reasonable analog for cometary nuclei, given the
consistent with density values determined through other methods
similarity between carbonaceous materials and the nonvola-
(see text). Lightcurve data references: [1] Meech et al. (2001),
tile component of cometary materials. So a cometary nu-
[2] Fernández et al. (2002), [3] Lamy et al. (2001), [4] Meech et
al. (2000), [5] A’Hearn et al. (1989), [6] Lamy et al. (1998), cleus porosity value of 0.64 seems somewhat high, although
[7] Delahodde et al. (2001), [8] Meech et al. (1993), [9] Boehn- not necessarily unreasonable. Note that all the 40% poros-
hardt et al. (2002), [10] Millis et al. (1988), [11] Osip et al. (1995), ity asteroids involved in these measurements are consider-
[12] Fitzsimmons and Williams (1994), [13] Luu and Jewitt (1992), ably larger than typical cometary nuclei (d = 53–214 km),
[14] Lowry and Weissman (2003), [15] Jewitt et al. (2003). except for Deimos (d = 12 km). The porosity of Deimos is
352 Comets II

actually very poorly determined and could be anywhere with 67P/CG in August 2014. A key experiment is the Comet
from 15% to 62%. If we perform the reverse calculation Nucleus Sounding Experiment by Radiowave Transmission
and assume a porosity of 40% for cometary nuclei, then we (CONSERT) (Barbin et al., 1999). CONSERT is a radar
obtain a density of 1.0 g cm–3 using Greenberg’s value. tomography experiment consisting of a transponder on the
Rosetta lander and a radar transmitter/receiver on the Ro-
6. DISCUSSION AND SUMMARY setta orbiter. If the lander is able to survive several weeks
or months on the nucleus surface, it will allow the orbiter
The nature of cometary nuclei has been, and continues sufficient time to orbit the nucleus many times, obtaining
to be, among the more elusive questions of solar system numerous ray paths through the nucleus. The experiment
science. The icy-conglomerate model was a major paradigm is somewhat hampered by the fact that there is only one
shift in our understanding of comets when it was first pro- lander (two were originally planned). However, CONSERT
posed by Whipple in 1950. Fifty years of evidence has should yield considerable insight into the interior of the
proved the basic correctness of that model. But as with any 67P/CG nucleus, including the location and dimensions of
problem in science, we always want to look at the question any substantial voids.
in more detail. The gravity mapping experiment onboard Rosetta will
In this chapter we have presented a long list of evidence provide additional evidence on the internal structure of the
that suggests that the underlying structure of icy-conglomer- nucleus (Pätzold et al., 2001). Mapping of higher harmon-
ate cometary nuclei is a collisionally processed rubble pile of ics in the 67P/CG gravity field, coupled with a detailed
smaller icy planetesimals. That evidence includes (1) space- shape model obtained from the Rosetta imaging experiment,
craft imaging of comets Halley and Borrelly that show a OSIRIS (Thomas et al., 1998), will provide evidence of den-
bimodal structure and rough, chaotic topography for both sity inhomogeneities within the nucleus, as well as an overall
nuclei; (2) observations of randomly disrupted comets, sug- measure of the bulk density of the nucleus. The Rosetta space-
gesting that they are extremely fragile objects; (3) obser- craft may orbit as close as 1 km to the surface of 67P/CG.
vations of Sun-grazing comets including the more than 540 A third source of information is the imaging experiment
objects discovered by the SOHO spacecraft, which have itself, which will provide submeter-resolution images of the
estimated diameters of ~10 m; (4) recent theoretical studies entire nucleus surface. These images should provide suffi-
that show that cometary nuclei have been subjected to mod- cient resolution to understand the mechanisms creating the
erate to intense collisional processing; (5) recent theoreti- nucleus morphology, and may provide evidence of faults,
cal studies of the collisional evolution of asteroids that show substructure, or other landforms that help to reveal the in-
that small bodies in the solar system need not be mono- ternal structure of the nucleus.
lithic; (6) comet Shoemaker-Levy 9, which can best be ex- Besides Rosetta, there are two comet flyby missions that
plained by the tidal disruption and reassembly of a rubble may yield improved imaging of nuclei, and certainly will
pile nucleus; (7) the catenae on Ganymede and Callisto that be able to address the question of diversity between differ-
show that Shoemaker-Levy 9 is not unique, but rather is rep- ent comets. The first is the Stardust mission, which was
resentative of a common solar system process; (8) the low launched in February 1999 and flew by comet 81P/Wild 2
density estimates for cometary nuclei, suggesting that they in January 2004 (Brownlee et al., 2000). Stardust is de-
are under-dense relative to their constituent materials; and signed to capture cometary dust particles in the coma and
(9) the rotation-shape relationship for observed cometary return them to Earth for analysis in terrestrial laboratories
nuclei that shows a possible cutoff in the distribution simi- in 2006. However, it also includes an imaging system that
lar to that seen for rubble-pile asteroids, albeit at a differ- can be expected to produce nucleus images comparable to,
ent density value. or perhaps somewhat better than, those from DS1.
Together, we believe that this evidence makes a com- The second mission is Deep Impact, which will be
pelling case for cometary nuclei as collisionally processed launched in December 2004 and will fly by comet 9P/
rubble piles. Although this may seem to be a leap of faith Tempel 1 in July 2005, deploying a ~370-kg impactor that
to some readers, we feel that it is one made on firm grounds. will strike the nucleus and (perhaps) create a significant
This paradigm shift has already occurred for asteroids and crater (Meech et al., 2000). Deep Impact carries an ad-
we believe that the time is now right for a similar paradigm vanced imaging system on both the flyby spacecraft and
shift for cometary nuclei. the impactor that should provide us with the best nucleus
The final resolution of this question requires the detailed images of any mission to date, with a resolution of only a
study of a cometary nucleus (or many nuclei) at close range, few meters per pixel. In addition, the impact experiment
something that can only be accomplished using a nucleus- itself may yield insights into the strength of cometary ma-
orbiting spacecraft, and perhaps may even require a nucleus terials and the structure of the nucleus. However, because
lander. The Rosetta mission of the European Space Agency both Stardust and Deep Impact are fast flybys, neither is
(Schwehm, 2002) includes experiments designed to inves- capable of making a mass determination for their respec-
tigate the internal structure of the nucleus of periodic comet tive nuclei.
67P/Churyumov-Gerasimenko (hereafter, 67P/CG). Rosetta, Sadly, the Comet Nucleus Tour (CONTOUR) mission was
to be launched in February 2004, is expected to rendezvous lost in August 2002 due to a spacecraft failure. CONTOUR
 Weissman et al.: Structure and Density of Cometary Nuclei 353

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358 Comets II
 Prialnik et al.: Modeling Comet Nuclei 359

Modeling the Structure and Activity of Comet Nuclei

Dina Prialnik
Tel Aviv University

Johannes Benkhoff
DLR Berlin

Morris Podolak
Tel Aviv University

Numerical simulation of the structure and evolution of a comet nucleus is reviewed from
both the mathematical and the physical point of view. Various mathematical procedures and
approximations are discussed, and different attempts to model the physical characteristics of
cometary material, such as thermal conductivity, permeability to gas flow, drag of dust grains,
and dust mantling, are described. The evolution and activity of comets is shown to depend on
different classes of parameters: defining parameters, such as size and orbit; structural param-
eters, such as porosity and composition; and initial parameters, such as temperature and live
radioisotope content. Despite the large number of parameters, general conclusions or common
features appear to emerge from the numerous model calculations — for different comets —
performed to date. Thus, the stratified structure of comet nuclei, volatile depletion, and the role
of crystallization of ice in cometary outbursts are discussed.

1. INTRODUCTION increasing sophistication during the past two or three de-

cades. A list of symbols and constants used in the math-
Although comets have been observed and studied since ematical formulation of comet nucleus models is given in
antiquity, the comet nucleus is a much more recent concept: Table 1.
“It has been stated that within the head of a comet there is
usually a bright point termed the nucleus. This is the only 1.1. Historical Perspective
part of its structure that excites any suspicion of a solid
substance.” (Robert Grant, History of Physical Astronomy, The simplest view of a comet nucleus is that of an ac-
1852). Even now, only two comet nuclei (Halley and Bor- tive surface enveloping an inert interior. It stems from the
relly) have been observed at close distances, where their assumption that solar radiation — exterior to the nucleus —
shapes and sizes can be clearly seen, and none has yet been is the only energy source responsible for cometary activity.
probed beneath the surface. Nevertheless, it is the nucleus Thus the Sun’s gravity determines the dynamic history of a
that, by its structure and composition, determines the be- comet and solar energy determines its thermal history. Given
havior of a comet in a given orbit. a composition of ice and dust, the thermal properties of
One of the striking features of comet nuclei is their var- cometary material appear to be such that the skin depth as-
ied, often unexpected, behavior. Some exhibit outbursts sociated with the orbital cycle is much smaller than the
when they are close to the Sun, others when they are far radius, and hence an inert interior seems to be justified. This
from the Sun. Some show a drastic reduction in their gas is also the reason for considering comets as pristine, un-
outflow for several orbits, during which they have a dis- altered objects, relics of the formation of the solar sys-
tinctly asteroidal appearance. Some nuclei suddenly split tem. This naive view will be shown to have changed con-
into several smaller pieces, while others remain whole even siderably in recent years. Nevertheless, the simplest among
when they pass sufficiently close to the Sun to be affected comet nucleus models deal with the surface and assume
by tidal forces. In short, every comet nucleus seems to have constant properties over its entire extent (albedo, emissiv-
its own special pattern of behavior. Thus it is a real chal- ity, and dust/ice mass ratio), completely neglecting any
lenge to develop a theory of comet nucleus behavior that energy exchange with the interior. The earliest model based
is rich enough to allow for this wealth of idiosyncrasy, al- on these assumptions was that of Squires and Beard (1961);
beit based on a handful of relatively simple processes, such later models were calculated by Cowan and A’Hearn (1979).
as are expected of a moderately large icy rock floating in They provided solutions for the power balance equation at
space. Remarkably, such a theory — or model — seems to the nucleus boundary to obtain the variation of surface tem-
be possible and has aroused growing interest and achieved peratures and gas and dust production rates as a function of

359
360 Comets II

TABLE 1. List of symbols.

A Albedo P orb Orbital period v Velocity

a Semimajor axis P spin Nucleus spin period vth Thermal velocity
c Specific heat Pα Partial gas pressure Xα Mass fraction of species α
dH Heliocentric distance Pα Saturated vapor pressure ε Emissivity
e Eccentricity Qrad Radioenergy generation rate ζ Angle of insolation
F Energy flux Qα Surface sublimation flux θ Latitude
fα Fraction of trapped gas qα Volume sublimation rate ϑ Declination
G Gravitational constant R Radius of nucleus κ Thermal diffusivity
g Gravitational acceleration Rg Ideal gas constant λ Crystallization rate
Hac Heat of crystallization r Radial distance from center µ Molecular weight
Hα Latent heat of sublimation rd Dust grain radius ν Kinematic viscosity
J Mass flux r*d Critical dust grain radius ξ Tortuosity
K Thermal conductivity rp Pore radius ρα Partial density of ice species
k Boltzmann constant S Surface to volume ratio rα Partial density of gas species
L Solar luminosity T Temperature rα Density of solid species
l Mean free path T Tensile strength σ Stefan-Boltzmann constant
M Mass of nucleus t Time τ Characteristic timescale
M Solar mass u Energy per unit mass Ψ Porosity
mα Molecular mass of species α V Volume ω Hour angle

heliocentric distance. A so-called “standard model” emerged, et al., 1974), so far ignored. This study explored the con-
based on power balance for a unit area normal to the solar sequences of crystallization of amorphous ice and the asso-
direction ciated release of latent heat on the temperature profile. It
revealed intermittent bursts of crystallization, an effect that
(1 − )L = εσT 4 + m H2O /2πkT (1)
was studied in considerably more detail by Prialnik and
H 2O H 2O Bar-Nun (1987), reviving an earlier suggestion that com-
4πd 2H etary outbursts might be linked with the crystallization pro-
cess. In parallel, cometary activity due to volatiles other than
assuming the surface to be entirely covered by water ice. H2O was studied by Fanale and Salvail (1987).
The total incident energy depends on the cross-sectional The next step in the study of comet nuclei by numerical
area of the nucleus, whereas evaporation and reradiation of simulations was prompted by the detailed observations of
energy occur over the entire hemispherical surface facing Comet P/Halley when it passed perihelion in 1986, which
the Sun. However, since regions not normal to the incident revealed that the nucleus had a very low bulk density, indi-
radiation receive less energy by a cosine factor and are at a cating a high porosity (Rickman, 1989). Further evidence
lower temperature, less energy is lost from these regions in favor of porosity is provided by the presence in cometary
by evaporation and radiation. Therefore, in view of the great ejecta of molecules from volatile ices, which cannot sur-
uncertainties in the physical properties of cometary material, vive in the warm subsurface layers. The origin of such
the comet was treated as a two-dimensional (2-D) disk of molecules must therefore be in the deeper, colder layers of
area πR2 facing the Sun. Combined with observed produc- the nucleus. Pores act as conduits for the transport of gases
tion rates, this model is often used in order to estimate the trapped in comet nuclei. Mekler et al. (1990) initiated a
nucleus size (or at least the size of its active surface area). detailed study of the effect of porosity on the cometary
Diurnal temperature variations over the surface of the nucleus. They developed a model of gas flow through a
nucleus were first studied by Weissman and Kieffer (1981, porous medium, allowing for vaporization from the pore
1984) and by Fanale and Salvail (1984). Heat conduction walls, and used this model for the simplest case of a po-
to the interior was now considered as well, but only in a rous pure-water-ice nucleus. They found that for a given
thin subsurface layer. The possibility of an outer dust mantle distance from the Sun there is a critical depth above which
enveloping the icy nucleus was first considered by Mendis the gas flows out of the nucleus, and below which it flows
and Brin (1977) and Brin and Mendis (1979), and subse- toward the center. Laboratory experiments performed by the
quently pursued by many others. Heat conduction through- KOSI group around the same time (Spohn et al., 1989)
out the entire nucleus was first explored by Herman and confirmed these findings and promoted the study of gas
Podolak (1985), who solved the heat diffusion equation for flow through porous comet nuclei. The basic model of low-
the one-dimensional (1-D) case of a homogeneous spheri- density flow through a porous medium has been adapted
cal nucleus. It was prompted by the suggestion that comet- by a number of research groups (e.g., Espinasse et al., 1991;
ary ice could be amorphous and its subsequent crystalliza- Steiner and Kömle, 1991; Prialnik, 1992; Tancredi et al.,
tion could provide an internal source of energy (Patashnik 1994; Benkhoff and Huebner, 1995). More recently, at-
 Prialnik et al.: Modeling Comet Nuclei 361

tempts have been made to include the flow of dust particles 1.2. Basic Assumptions Derived from Observations
through the pores as well (Orosei et al., 1995; Podolak and
Prialnik, 1996). It is now commonly agreed that porosity The structure of a comet nucleus may be modeled as a
must be included in order to properly understand cometary highly porous agglomeration of grains made of volatile ices
behavior. A different question that has been repeatedly ad- and dust, with a size distribution that probably spans many
dressed concerns the end state of comets. Unless they are orders of magnitude. The dominant volatile component is
disrupted by tidal forces or destroyed by collisions with water ice, while the other volatiles, such as CO, CO2, HCN,
larger bodies, comet nuclei are expected to evaporate and N2, etc., are mixed with the water ice or incorporated in it,
disintegrate, leaving behind a trail of debris. But they may either in the form of clathrate-hydrates, or as trapped gases
also become extinct — asteroid-like — if a dust mantle within the (amorphous) ice matrix. Having been formed at
forms at the surface, quenching all types of cometary ac- low temperatures and pressures, cometary ice is believed
tivity. This line of investigation started with the early work to be amorphous (Mekler and Podolak, 1994). Laboratory
of Shul’man (1972), followed by numerous studies of vari- experiments indicate that amorphous ice is capable of trap-
ous aspects of the dust mantle, culminating in detailed evo- ping large amounts of gas and most of this trapped gas es-
lutionary models of transition objects between comets and capes when the ice crystallizes (Bar-Nun et al., 1987). Thus,
asteroids (e.g., Coradini et al., 1997a,b). whereas H2O molecules are released within a narrow tem-
As the prevailing idea of pristine comet nuclei interiors perature range, when the ice sublimates, the other volatiles
began to give way to more elaborate pictures of these ob- may be released in different temperature ranges. Crystalliza-
jects, another internal heat source — radioactive decay, tion, as well as sublimation from the pore walls in the deep
commonly considered for large bodies of the solar sys- cometary interior, may be triggered (and sustained) either
tem — came into focus. The first to have considered radio- by a heat wave advancing inward from the surface, or due
active heating of comet nuclei were Whipple and Stefanik to internal heat release by radioactive isotopes contained in
(1966): They found that the decay of 40K, 235U, 238U, and the dust, or else by the release of latent heat that accompa-
232Th caused the internal temperature to rise to a peak of nies the transformation of amorphous into crystalline ice.
~90 K (from an initial 0 K) on a timescale of some 108 yr. These are, in fact, the three main — and perhaps only —
About 10 years later, Lee et al. (1976) presented strong evi- sources of energy available to comets. Their typical prop-
dence that the short-lived radionuclide 26Al had been pres- erties are summarized in Table 2. The radioactive source is
ent in the early solar nebula. Further evidence strengthening important particularly during the long period of time spent
this conclusion has accumulated ever since. The idea of by comets outside the planetary system, far from the Sun.
internal heating of comet nuclei by the decay of 26Al gained Close to the Sun, it is far less efficient than solar radiation,
impetus following early studies by Irvine et al. (1980) and and hence negligible. The most important radionuclide is
Wallis (1980), who showed that it may lead to melting of the short-lived isotope 26Al. Observational evidence points
the ice, which would have implications for early formation toward an interstellar isotopic ratio 26Al/27Al ≈ 5 × 10–5 (e.g.,
of organic molecules and the origin of life (see Thomas et MacPherson et al., 1995), implying an initial mass frac-
al., 1997). Thus heating by radioactive decay has been tion X0(26Al) ≈ 7 × 10–7 in the solar nebula dust (rock) and
considered in a number of comet nucleus models under presumably an order of magnitude less, on average, in ob-
various conditions and assumptions. Whether or not liquid jects such as comets, for which the time of aggregation did
water could have been present in comet nuclei during their not exceed a few million years (Lugmair and Shukolyukov,
early stages of evolution, and if so, under which conditions, 2001). In contrast to these sources, the exoergic crystalli-
is still debated. The question of whether and to what extent zation of amorphous water ice is not an independent source,
comets are pristine bodies that hold clues to the formation since it occurs above a threshold temperature that must be
of the solar system is still open. Finally, would it be pos- attained by means of other energy sources. Crystallization
sible for comet nuclei to have had liquid cores, but at the may occur at any evolutionary stage, and may propagate
same time preserved their outer layers in pristine form? either inward or outward.
These are some of the questions that have prompted the Once gas is released from the ice in the interior of the
development of increasingly sophisticated models of comet nucleus, its pressure will cause it to flow to the surface.
nuclei. The number of studies devoted to the evolution and Gases moving through the pores drag with them small dust
activity of comet nuclei and to the complex processes in-
volved is steadily growing. The effort is twofold: under-
standing and providing a usable mathematical formulation TABLE 2. Energy sources and their characteristics.
of the processes on the one hand, and incorporating these
Solar Radiation Radioactivity Crystallization
processes in numerical simulations of the structure and
evolution of comet nuclei on the other. Section 3 will be Surface source Body source Local source
devoted to the former and section 4 to the latter. The set of ∝ R2/dH2 ∝ R3Xrad ∝ Xa–iceH ac
evolutionary equations will be presented in section 2, and Cyclic Declining Transient
conclusions as well as suggestions for future work, in sec- Inward moving wave Homogeneous Thin front
Late evolution Early evolution Induced
tion 5.
362 Comets II

particles that have detached from the solid matrix. The

larger particles may eventually block the pores; the smaller
ones may flow all the way with the gas.
The free gases present in the interior of a comet are ex-
pected to affect the thermal and mechanical structure of the
nucleus by contributing to the conduction of heat through
advection or recondensation and by building up internal
pressure. This pressure may surpass the tensile strength of
the already fragile, grainy configuration and result in crack-
ing of the porous matrix and outbursts of gas and dust.
Accumulation of large particles on the nucleus surface may
lead to the formation of a sealing dust mantle that may par-
tially (or fully) quench the comet’s activity.
All these processes are taken into account in models of
the evolution and activity of comet nuclei, as will be shown
in the next section. Internal processes depend on physical
properties characteristic of cometary material, which will
be discussed in sections 3 and 4.

1.3. Approximations Required by Modeling

Comet nuclei are too small for self-gravity to be of im-

portance, hence they are not necessarily spherical. However, Fig. 1. Schematical representation of numerical grids for a spin-
a nonspherical object is far more difficult to model. In addi- ning nucleus, commonly used in model calculations. Dots indi-
tion, the number of free parameters for an arbitrary shape cate radial directions along which heat conduction is computed;
tends to infinity. Thus models must assume some form of lateral conduction is only included in the 2.5-D model, and only
symmetry and sphericity, requiring a single dimensional along the meridian, as shown.
parameter — the (effective) radius R is the common as-
sumption. The simplest among spherical models are 1-D,
considering a spherically symmetric nucleus, which implies tributions of such wedges over one spin period. This is
an evenly heated surface, although in reality only one hemi- essentially a 2.5-dimensional (2.5-D) calculation. The next
sphere faces the Sun at any given time, and even its sur- step is to take into account both diurnal and latitudinal so-
face is not evenly irradiated. This approximation is known lar flux variations (Gutiérrez et al., 2000; Julian et al., 2000;
(somewhat loosely) as the “fast-rotator” approximation. It is Cohen et al., 2003), considering, however, only radial heat
a good approximation for the interior of the nucleus, below conduction, i.e., neglecting lateral conduction. This quasi
the skin depth; it is valid for the surface far away from the three-dimensional (3-D) approach is amply justified by the
Sun, where diurnal temperature variations are small. extremely low heat conductivity of cometary material; the
However, in order to obtain an accurate surface tempera- characteristic heat diffusion time between the equator and
ture distribution and its diurnal change at any heliocentric pole (as between surface and center) is of the order of the
distance, one must adopt the so-called “slow-rotator” ap- lifetime of a comet (see Table 5 below). The different mod-
proach, which takes into account the diurnal and latitudi- els are shown schematically in Fig. 1; of course, calcula-
nal solar flux variations. This type of model requires a far tions use much finer meshes than the ones shown.
greater amount of computing time, since much smaller time The advantage of the negligible self-gravity of comets
steps — a small fraction of the spin period — must be used is that the structure of the nucleus may be assumed incom-
in the numerical integration over time. pressible despite the low strength of the porous material.
A first attempt in this direction was to consider a point By comparing the hydrostatic pressure at the center with
on the equator of a spinning nucleus and translate the diur- the material strength, we obtain the condition for incom-
nal temperature change obtained into a map of the equato- pressibility
rial temperature at any given time. Such a procedure (Benk-
hoff and Boice, 1996; Benkhoff, 1999) may be described as ρR < 3 /2πG (2)
a 1.5-dimensional (1.5-D) model. An upper limit for the pro-
duction rate is obtained by using the maximum noon flux where C is the compressive strength. Even for as low a
for the entire surface of the sunlit hemisphere. A more ad- value as C ≈ 10 kPa (see section 3.8), this implies
vanced model is achieved by considering a wedge of sur-
face elements aligned along a meridian (Enzian et al., 1997, ρg/cm3Rkm < 10
1999). Thus the latitudinal effect is taken into account and
the total production rate is obtained by summing the con- which is amply satisfied by the typical sizes and densities
 Prialnik et al.: Modeling Comet Nuclei 363

of comet nuclei. Therefore, the equations that determine the ∂ρg, α

structure and evolution of comets are those of energy con- + ∇ ⋅ Jα = ƒα λρa + qα
∂t
servation and of mass conservation for the various compo- (9)
∂ρs,α
nents. Momentum conservation (hydrostatic balance) is not = − qα
required for the solid matrix and can be replaced by a pre- ∂t
scribed (usually constant) density profile; for the gas spe-
cies, expressions for the flux in different regimes are used. The equation of energy conservation is

2. EVOLUTION EQUATIONS AND

∂
SOLUTION METHODS
∂t
[ρu] + ∇ ⋅ (F + ∑u
α
g, α Jα ) = (10)

2.1. Mass and Energy Conservation

where S stands for all the available energy sources and
Consider a composition of water ice and vapor, dust, and sinks,
other volatiles, which, as we have seen, may be frozen, free,
or trapped in the amorphous water ice. For each volatile
species α we distinguish — when necessary — between two
phases, solid (denoted by index s) and gas (index g), which
= λρa ac + Q rad − ∑q
α
α α (11)

have, e.g., different specific heat coefficients. For water, the

solid phase may be either amorphous (index a) or crystal- Here [ρu] represents the sum over all species and all phases
line (index c); water vapor will be denoted by index v and (although the contribution of the gas phases is small and
dust by d. Then the mass density and porosity are given hence sometimes neglected), u = ∫c(T)dT, and
respectively by
F = –K∇T (12)
ρ = ρa + ρc + ρv + ∑α
(ρs, α + ρg,α ) + ρd (3)
Combining the energy and mass conservation equations, we
obtain the heat transfer equation, which can replace equa-
Ψ = 1 − (ρa + ρc)/ H 2O − ∑ρ
α
s, α / α − ρd/ d (4) tion (10)

We note that densities refer to mass per unit volume of

∂uα
∑ρ ∑c J
nucleus material. Since the gas resides in the pores, the
− ∇ ⋅ (K∇T) + α α ⋅ ∇T = (13)
actual gas density within the pores will be ρg,α/Ψ and the α
∂t
α α
partial pressure, assuming an ideal gas, will be

with the advantage being that the temporal derivatives of the

g ρg, αT
Pα = (5) variables are now separated. The above set of time-depen-
Ψµα dent equations is subject to constitutive relations u(T), λ(T),
qα(T, Ψ, rp), Jα(T, Ψ, rp), and K(T, Ψ, rp), which require
Local thermodynamic equilibrium is assumed to prevail, additional assumptions for modeling the structure of the
that is, all components in all phases, as well as radiation, nucleus. They will be discussed in some detail in the next
share the same local temperature. It is further assumed that section. The most widely used expressions or values for the
gases trapped in the amorphous ice do not affect its heat thermal properties of cometary H2O ice and dust are given
capacity or density. Let f be the total fraction of occluded in Table 3. Ice properties have been measured and turned
gas, Σα fα = f. Thus the equations of mass conservation are into empirical temperature-dependent relations by Klinger
(1980, 1981), and more recently by Ross and Kargel (1998).
∂ ρa
= − λρa (6)
∂t TABLE 3. Thermal properties of
cometary H2O ice and dust.
∂ρc
= (1 − ƒ)λρa − q v (7) Property Relation Units
∂t
Specific heat: ca, cc 7.49T + 90 J kg –1 K–1
Specific heat: cv = 3R gµ 1.385 × 103 J kg –1 K–1
∂ρv
+ ∇ ⋅ Jv = q v (8) Specific heat: cd ~800 J kg –1 K–1
∂t Thermal conductivity: Kc 567/T J m–1 s–1 K–1
Thermal diffusivity: κa 3.13 × 10 –7 m2 s–1
Thermal conductivity: Kd ~0.1– 4 J m–1 s–1 K–1
for H2O in all its phases, and similarly
364 Comets II

2.2. Boundary Conditions is lost by a comet during a perihelion passage. We are thus
faced with two vastly different length scales, which imply
The set of evolution equations must be supplemented by different timescales as well. On the evolutionary timescale
initial and boundary conditions. For the heat transfer equa- of the comet the thin boundary layer may be assumed to
tion, the boundary conditions refer to the flux F(r) on the be in (quasi) steady-state. Its ice may be assumed to have
open interval r0 < r < R, where r0 = 0 when the entire comet crystallized. The gas fluxes from the interior may be taken
is considered, or 0 < r0 < R, when only an outer layer is as constant and their contribution to heat conduction may
considered in a plane-parallel calculation. At the ends of be neglected. In addition, plane-parallel geometry is justi-
this interval we have fied in this case and hence the equations that have to be
solved near the surface as a function of depth z are
F(r0) = 0 (14)
dJv(T, Pv)/dz = qv(T, Pv) (20)

F(R) = εσT(R, t )4 + dF(T)/dz = –qv(T, Pv)H (21)

L (15)
Q − (1 − ) cosξ The boundary conditions for this layer are equation (15) at
4πd H(t)2
R and given temperature at the lower boundary, where it is
fitted to the rest of the comet. This procedure, suggested by
The local solar zenith angle is given by Prialnik (1992) was also employed by Tancredi et al. (1994).
An alternative approach to the macroscopic equations of
cosξ = cosθ cosω cosδ + sinθ sinδ (16) gas diffusion in a porous volatile medium is a kinetic model,
which provides gas fluxes as well as gas production and
where δ is the declination (see also Sekanina, 1979; Fanale loss rates, for a given temperature distribution (Skorov and
and Salvail, 1984). The factor F ≤ 1 represents the frac- Rickman, 1995; Skorov et al., 2001). It is particularly suited
tional area of exposed ice, since the surface material is a to the surface layer of the nucleus, near the pore openings.
mixture of ice and dust (Crifo and Rodionov, 1997) In this case the gas pressure at the surface is no longer re-
quired as a boundary condition, but rather it results from the
−1 calculation.
ρd
= 1+ ice (17) The initial conditions must be guessed, and since the
ρice d comet nucleus as a whole never reaches steady-state below
a skin depth of the order of meters to several tens of meters,
The function dH(t) is given in terms of the changing eccen- these conditions play a significant role. This explains the
tric anomaly E by the familiar celestial mechanics equations importance attached to the early evolution of comets at large
distances from the Sun, which determines the interior con-
t = a3/ GM (E – e sinE) (18) figuration of comet nuclei when they enter the inner plan-
etary system and become active.
dH = a(1 – e cosE) (19)
2.3. Numerical Schemes
Similarly to the heat flux, the mass (gas) fluxes vanish at
r0. At the surface R the gas pressures are those exerted by The system of nonlinear, time-dependent, second-order
the coma; in the lowest approximation they may be assumed partial differential equations (6)–(9) and (10) or (13) is
to vanish: Pα(R,t) = 0. [For a more elaborate discussion turned into a set of difference equations that are solved
concerning the boundary conditions to be assumed for the numerically. They constitute a two-boundary value prob-
gas pressure at the surface and their effect, see Crifo et al. lem that requires relaxation methods for its solution. Let
(2004).] We should note that when the entire comet is con- the time and space domains be divided into finite intervals
sidered, mass and heat fluxes must vanish at the center. δtn = tn – tn – 1 and ∆ri = ri – ri – 1 (0 ≤ i ≤ I), such that t0 =
However, at the lower boundary of a finite layer, other 0, r0 = 0, and ri = R. The solution for the change of the tem-
conditions may equally be imposed (for example, a fixed perature profile will be represented by a series of stepped
temperature and corresponding vapor pressures), but only functions T ni , where Ti is the temperature within the inter-
by adopting vanishing fluxes are energy and mass conser- val ∆ri. For the simple (linear) case of heat transfer with
vation secured. constant coefficients, there are several possibilities for com-
In a porous medium the surface is not well defined and bining the space and time derivatives into a difference equa-
a surface layer of finite (rather than vanishing) thickness tion for the transport equation, among which the most com-
supplies the outflowing vapor. Mekler et al. (1990) have mon are the explicit scheme, which can be solved directly;
shown that the surface layer where most of the vapor is the fully implicit scheme, which, upon rearranging terms,
generated is considerably thinner than the layer of ice that results in a system of I linear equations requiring the in-
 Prialnik et al.: Modeling Comet Nuclei 365

version of a tridiagonal matrix for its solution; and the

Crank-Nicholson scheme, which is a modified implicit form
that requires the inversion of a tridiagonal matrix as well.
The explicit scheme has the disadvantage that time-steps
are restricted by the Courant-Friedrichs-Levy condition, δt ≤
(∆r)2/2K, for a given space discretization; thus time-steps
may become prohibitively small when a fine mesh is re-
quired in order to resolve sharp temperature gradients. The
implicit schemes, on the other hand, are unconditionally
stable for all values of the time-step. However, they require
a far greater amount of computations for each time-step,
prohibitively large in the case of a large spatial grid, or in
the 2- or 3-D cases. The Crank-Nicholson scheme has the
advantage of being second-order accurate in time, whereas
the fully implicit one, as the explicit scheme, is only first-
order accurate in time. The fully implicit scheme, on the
other hand, is best suited for stiff equations, i.e., when there
are two or more very different timescales on which the tem-
perature is changing (as is the case in comets). The reason is
that the implicit scheme converges to the steady-state solu-
tion for large time-steps.
The same methods apply to the more complicated case
when the heat capacity and thermal conductivity are func-
tions of the temperature, and there is also a temperature-
dependent source term (such as equation (13)). In this case,
the difference equations of the implicit schemes must be
linearized and solved iteratively. Another numerical method
of solution of the nonlinear heat equation is the predictor-
corrector method, essentially a two-step iterative procedure.
Each iteration (or step) requires the inversion of a tridiag-
onal matrix. A comparison of different algorithms that were
used to compute the evolution of a comet nucleus model for Fig. 2. Model results for (a) H2O production rates of a pure ice
the same set of physical parameters is shown in Fig. 2. Each nucleus and (b) surface temperature of a dust-mantled nucleus, at
of the numerical methods mentioned above was adopted in the subsolar point as function of time for five revolutions in Comet
one or the other of these algorithms, which also differ in P/Wirtanen’s orbit as computed by five different algorithms (W. F.
other numerical parameters (for details, see Huebner et al., Huebner et al., personal communication, 2002).
1999). The results are remarkably similar; the agreement
at low perihelion distances is excellent, but this is expected
since most of the solar radiation is spent in sublimation. dure is that equal volume intervals ensure a better radial
Differences arise at larger distances and provide an estimate resolution near the nucleus surface, where ∂T/∂r is steeper.
of the error-bars expected from model calculations, which Similarly, choosing the eccentric (or true) anomaly angle
are otherwise difficult to assess. as the temporal variable naturally leads to smaller time steps
Although ∂∂ut = c(T) ∂∂Tt , the time difference should be taken near perihelion, where changes are more rapid.
for the energy, rather than for the temperature, in order to
ensure energy conservation in the numerical scheme. Fi- 2.4. Computational Approximations
nally, in the case of a 1-D spherical coordinate system, it is
convenient to choose the volume V enclosed within a sphere We note that the evolution equations are coupled through
of radius r for the space variable, rather than r, for then the the source terms and the gas fluxes, which are functions of
equation retains the form of the plane-parallel one. From both temperature and pressure, and hence must be solved
the physical point of view, it would be even better to adopt simultaneously. This is extremely time consuming, consid-
the mass enclosed within a sphere of radius r as space vari- ering that the equations are strongly nonlinear. Simplify-
able, but if the mass is allowed to change during evolution ing approximations may be used under special conditions.
as a result of internal sublimation and gas flow, the volume If the effective permeability of the medium is sufficiently
is a better choice. In this case the flux through r must be high, the time derivative on the lefthand side of the mass
replaced by the energy crossing the spherical surface of ra- conservation equation for the gas phases (equation (8))
dius r per unit time. An additional advantage of this proce- becomes negligible. Neglecting it is tantamount to a quasi-
366 Comets II

steady-state approximation, where gas densities and produc- but in either case the problem of calculating the conduc-
tion rates change only as far as the temperature distribu- tivity through such a porous material remains essentially
tion changes. Thus equations (9) are replaced by the same. For the canonical model of a porous ice matrix,
the pores can themselves be filled, at different times, with
∇ ⋅ Jα = q α smaller grains, H2O vapor, or other gases. The grains em-
∂ρs,α (22) bedded in the water-ice matrix, the grains and gases flow-
= − qα ing through the pores, and even radiation passing through
∂t
the pores will each affect the rate of heat transport through
In this way we strictly have to solve only one time-depen- the nucleus. This is a complex problem that has a rather
dent equation supplemented by structure (space-dependent) long history.
equations. This constitutes a huge computational advantage, To begin, let us consider a simple idealized medium
particularly in a long-term evolutionary calculation, where consisting of bulk H2O ice permeated by spherical, gas-free
a detailed account of gas flow through the porous medium, pores. If these pores do not transport energy, they will re-
coupled with heat transfer, would require a prohibitively duce the overall conductivity of the medium. If Ks is the
large amount of computing time. Combining equations (22) bulk conductivity of solid ice, then the conductivity of the
and integrating over volume, we obtain porous ice will be K = φKs, where φ < 1. The key problem is
to determine the value of φ. Smoluchowski (1981) suggested
− Ms, α = Jα (R, t)4πR 2 (23) that this reduction would be proportional to the cross-sec-
tional area of the pores. Since the volume of void is pro-
which means that the total mass of gas ejected through the portional to the porosity Ψ, its cross-sectional area should
comet’s surface per unit time is equal to the total amount be proportional to Ψ2/3. We might expect, therefore, that
of gas evaporated throughout the nucleus per unit time for
each species. This approximation is valid for nonabundant φ ≈ 1 – Ψ2/3 (24)
species, for which the bulk density is low. It breaks down
when the net gas sublimation rate is negative, i.e., when In a later paper, Smoluchowski (1982) used a formula
recondensation surpasses sublimation. This approach has originally developed by Maxwell (1873). If we consider
been recently adopted by Choi et al. (2002) in long-term spherical grains of conductivity Kp embedded in a matrix of
evolutionary calculations of Kuiper belt objects. It is also conductivity Ks, and the grains occupy a small fraction of
applied for the outermost layer of the nucleus, as already the total volume, Ψ, then the conductivity of the combined
mentioned in section 2.2. medium is reduced relative to that of the matrix by a factor
A different approximation with the same computational
K
advantage — reduction of the number of time-dependent (2 − 2Ψ ) + (1 + 2Ψ ) Kp
equations — has been used in other studies (e.g., Coradini φ= Kp
s
(25)
et al., 1997a) for the nucleus interior. It assumes that when (2 + Ψ ) + (1 − Ψ ) K
s
both the ice and gas phases are present, the gas density is
equal to the saturated vapor density, which is a function of This formula is actually the first term in an expansion, and
temperature. Strictly, this would imply that no evaporation/ neglects effects of mutual “shadowing” by the grains. It is
condensation could take place. However, as the temperature therefore exact only for the case of small Ψ. Higher-order
changes, the saturated density (pressure) changes with it, terms were later added by Rayleigh (1892), which extended
and this change can be translated into a rate of evaporation/ the applicability to larger values of Ψ. But precisely because
condensation. This is an excellent approximation for the the Maxwell formula neglects shadowing, it gives an up-
interior of the nucleus, where the pressures are indeed found per limit to φ. A lower limit can be obtained by inverting
to attain saturation; it implies, however, that there is suffi- the problem: Let the matrix be composed of grain mate-
cient material in both phases to allow instantaneous adjust- rial and the grains be composed of ice. Then
ment. It is not valid, therefore, for minor volatile compo-
K
nents and fails close to the surface of the nucleus. The two K p 2Ψ K s + (3 − 2Ψ )
p

simplifying approximations are thus complementary. φl = (26)

K s (3 − Ψ ) K p + Ψ
K s
3. PHYSICAL PROCESSES
The spherical grains embedded in the ice matrix may be
3.1. Heat Conduction in a Porous Medium replaced by pores, in which case Ψ is the porosity, and the
pore conductivity due to the flux carried by radiation is
Cometary H2O ice can be viewed as the matrix that
comprises the bulk of the nucleus, but within this matrix Kp = 4εσrpT3 (27)
there are grains of dust, occluded gases, and pores. Reach
et al. (2000) have recently suggested that the grains domi- Squyres et al. (1985) used an expression due to Brails-
nate and form the background matrix with ice as the filler, ford and Major (1964) for φ
 Prialnik et al.: Modeling Comet Nuclei 367

Kp series of models and fitting analytic functions to the results,

8K s
φ= A+ A2 + (28) this Monte Carlo approach allows one to find φ for a given
4K s Kp porosity

where (1 − Ψ/ Ψc ) α( Ψ) ≤ φ
≤ (1 − Ψm / Ψc )α ( Ψm ) ln(1 − Ψ) / ln(1 − Ψm ) (32)
Ks α(Ψ) = 4.1Ψ + 0.22
A = (2 − 3Ψ ) + 3Ψ − 1
Kp Ψc = 0.7
Ψm is the minimal possible porosity of the medium (essen-
They also pointed out that if the matrix material is actually tially, its microporosity). If the pore size distribution is
composed of ice grains, and the area of contact between known as well, the value of φ within this range can be
adjoining grains is small, the resultant conductivity of the uniquely determined. A comparison of the different expres-
medium will be reduced even further by a so-called Hertz sions is shown in Fig. 3.
factor, the area of contact between material grains relative to The agreement goes only as far as the trend of decreasing
the cross-sectional area. A different expression, known as conductivity with increasing porosity. The low conductiv-
Russel’s formula, was used in other studies (see Espinasse ity of porous comet-analog material was also demonstrated
et al., 1991) experimentally (e.g., Benkhoff and Spohn, 1991; Kömle et
al., 1996; Seiferlin et al., 1996). It should be mentioned that
K
Ψ 2/3 Kp + (1 − Ψ2/3) in addition to the pores that result from the grainy struc-
φ= s
K
(29) ture of the ice-dust matrix, there are almost certainly addi-
Ψ− Ψ 2/3 + 1 − Ψ2/3 ( Ψ1/3 − 1) Kp tional micropores in the ice. These may be inherent to the
s
structure of ice formed by slow deposition of water vapor
Steiner and Kömle (1991) proposed still another theo- at low temperature (Kouchi et al., 1994), or may result from
retical expression dissociation of clathrate-hydrates in the ice (Blake et al.,
1991). They should have little direct influence on the con-
Kp ductivity of the medium (unless they are correlated in space
φ = 1− 1− Ψ Ψ +
Ks and form cracks), and will not affect the density apprecia-
(30) bly, but they will allow the gas to flow through the medium
B + 1 Kp more freely.
1 − Ψ ς + (1 − ς)
B Ks + K p

where

B = 1.25[(1 – Ψ)/Ψ]10/9

is a deformation factor, and ς is a flattening coefficient,

which is essentially the Hertz factor. This factor depends
on the details of the structure of the medium and cannot be
determined a priori.
Haruyama et al. (1993) and Sirono and Yamamoto
(1997) used effective medium theory to derive

Kp
φ −1 φ− Ks
Ψ+ (1 − Ψ ) = 0 (31)
1+ ( 1
Ψc
−1 φ ) Kp
Ks
+ ( 1
Ψc )
−1 φ

where Ψc is the percolation threshold of the medium (Stauf-

fer and Aharony, 1994). None of these approaches, how-
ever, allows for a distribution of pore sizes, yet the pore-size
distribution will certainly affect the resultant conductivity.
Recently, a new approach was adopted by Shoshany et
Fig. 3. Correction factor to the thermal conductivity resulting
al. (2002). Using a Monte Carlo procedure, they modeled from porosity, as a function of porosity, for different models: Max-
a 3-D fractal medium made of ice and voids. A tempera- well’s upper (MaxU) and lower (MaxL) limits, Smoluchowski’s
ture gradient was assumed across this medium and the 3-D relation (Smo), Squyres et al.’s relation (Squ), and the Monte Carlo
equations of heat transfer were solved to obtain the energy fractal model (M-C, see text). When applicable, two ratios of the
flux, which yields the effective conductivity. By running a pore to solid conductivity are considered, as shown on the figure.
368 Comets II

3.2. Amorphous–Crystalline Transition in H2O Ice from the decay of 26Al (e.g., Mahoney et al., 1984). Fur-
thermore, Srinivasan et al. (1999) detected for the first time
Ordinary ice has a crystalline structure, but when water 26Mg in a differentiated meteorite, and therefore could con-

vapor condenses at low temperatures, the molecules do not firm the role of 26Al in the differentiation of meteoritic par-
have sufficient energy to take up the proper sites in the ent bodies. Thus it is already widely used in thermal model-
crystal, and an amorphous material is produced. The ther- ing of asteroids [see Merk et al. (2002) and references
mal conductivity of amorphous ice (see Table 3) is much therein]. Indeed, for small silicate bodies such as asteroids,
lower than that of crystalline ice, and its temperature de- accretion models predict growth times in the range between
pendence has an opposite trend, K ∝ T rather than K ∝ T–1. 104 yr and 1 m.y., depending on whether conditions allow
Experiments by Kouchi et al. (1992) indicate that the con- for runaway accretion or not. Hence the comparably short
ductivity may be as much as four orders of magnitude lower. lifetime of 26Al and the growth time of asteroidal bodies
These authors suggest that their low value may be the re- are compatible. Comets, on the other hand, formed much
sult of the very slow deposition procedure used, which cre- farther from the Sun and hence took longer to accrete. But
ates a network of connected micropores. This network, even in this case formation times may have been sufficiently
which is actually a system of cracks, will leave “islands” short to allow for live 26Al. For example, Weidenschilling
of disconnected amorphous ice that will substantially lower (1997) showed that it is possible to grow large icy bodies
the conductivity. A similar behavior is observed in amor- of a radius of about 40 km within 2.5 × 105 yr in the re-
phous semiconductors. Again, we see that porosity effects gion at 30 AU. All the observational evidence points toward
may significantly alter the conductivity of a material. an interstellar isotopic ratio of 26Al/27Al ≈ 5 × 10–5, imply-
Amorphous ice is unstable and tends to spontaneously ing an initial mass fraction X0(26Al) ≈ 7 × 10–7 in dust (rock)
convert to crystalline ice. Measurements by Schmitt et al. and presumably an order of magnitude less in objects whose
(1989) have shown that the rate of crystallization is given by time of aggregation did not exceed a few million years.
The rate of heating by a radioactive isotope of relative
λ(T) = 1.05 × 1013e–5370/T s–1 (33) abundance Xrad,0 within the dust is given by

Crystallization has a number of consequences. First, the Qrad = ρdXrad,0H radτ –1

rade
–t/τrad (34)
conductivity through the medium will change with time.
This will be due mainly to the intrinsic difference in con- where H rad is the energy released per unit mass upon decay
ductivity between the two phases. In addition, however, the and τrad is the decay time constant. The total contribution
two phases differ in density, as amorphous ice is denser than is obtained by summing over the different species. The major
crystalline ice by 2–7%. The precise difference depends on long-lived sources of radioactive heating — 40K, 232Th,
the rate of deposition [see Jenniskens and Blake (1994) and 235U, and 238U — together provide some 3 × 10 –11 J kg –1 s–1.

references therein], but in any case the phase change will The short-lived 26Al, assuming an initial mass fraction X0 ~
subject the medium to stresses that may cause a change in 5 × 10–8, could have provided as much as 2 × 10–8 J kg–1 s–1.
porosity. This will further affect the thermal conductivity.
A second consequence comes from the fact that amor- 3.4. Sublimation and the Surface/Volume Ratio
phous ice has the ability to trap volatiles. Extensive studies
by Bar-Nun and co-workers [see Bar-Nun and Owen (1998) The porous structure of the comet nucleus allows for an
and references therein] have explored the dependence of the internal process that is otherwise confined to the cometary
composition of the trapped gases, their relative abundances, surface: sublimation of ice from the pore walls or conden-
and their rates of release on the temperature of deposition sation onto them. The rate of sublimation — mass per unit
of the ice, and on the rate at which the medium is heated. volume of cometary material per unit time — is given by
In particular, they find that gas release accompanies the
change in crystal structure. The amorphous-crystalline
µα
phase change should therefore lead to an increase in the q α = S( Ψ, rp ) ( α ( T) − Pα ) (35)
activity of the nucleus. 2π gT
Finally, the phase change releases latent heat, and this
provides an internal heat source for the medium. The mea- where the term in square brackets represents the sublima-
sured value is H ac = 9 × 104 J kg–1 (Klinger, 1981). As the tion rate per unit surface area. Thus the property of the
phase change is irreversible, this heat source is a sporadic porous structure that affects sublimation is the surface to
one, and occurs only once in any given mass element of volume ratio S, defined as the total interstitial surface area
the comet. of the pores Ap per given bulk volume V

3.3. Radioactive Heat Production S = Ap /V (36)

The most potent radioenergy source for comets is the Its evaluation requires some model of the porous configu-
short-lived radionuclide 26Al, which gained renewed inter- ration. As a simple example, consider the specific surface
est owing to the detection of interstellar 1.809 MeV γ-rays of a porous material made of identical spheres of radius rs
 Prialnik et al.: Modeling Comet Nuclei 369

in a cubical packing. In this case As = 4πrs2N, where N is the We note that the two models behave differently with
number of spheres in the given volume V. Obviously, V = changing porosity: As Ψ decreases, the surface to volume
(2rs)3N, which yields S = π/2rs. If the solid spheres are re- ratio of capillaries tends to zero, while that of spheres in-
placed by spherical pores embedded in a solid matrix, the re- creases to a maximum. Toward high porosities, on the other
sult is the same. Clearly, fine materials have a much greater hand, the surface to volume ratio of spheres tends to zero.
specific surface than coarse materials. Consider now a more It is, however, difficult to visualize either a low-porosity me-
realistic case of a granular medium of spherical grains of n dium made up of a bundle of individual capillaries, or a
different sizes, so that the number of grains of radius ri (1 ≤ high-porosity one made up of widely separated spheres.
i ≤ n) is Ni. The total area and volume of these spheres are Therefore, in numerical modeling that allows for a chang-
ing porosity — due, for example, to vigorous sublimation
n
As = ∑ 4πr N
i =1
2
i i = Ap
or condensation — it would be advisable to change from
one model to the other as the porosity changes. The mod-
(37) els yield equal values of S for Ψ = 0.6. Among other rela-
n
Vs = ∑
i=1
4
3
πri3N i
tions that have been suggested in the literature, we find
(Kaponen et al., 1997)

respectively. By definition, V = Vs /(1 – Ψ), whence S ∝ – Ψ ln Ψ (43)

n

∑ ƒ /r = 3(1 − Ψ)/r
Beside the major ice component H2O, comet models
S = 3(1 − Ψ ) i i p (38)
usually include several other components of higher vola-
i=1
tility (CO, CH4, CO2, CH3OH, HCN, NH3, H2S, C2H2 ,
where rp is the harmonic mean radius weighted by fi, the C2H6, C3H4). For each species, an empirical formula for the
volume fraction occupied by spheres of radius ri. As be- saturated vapor pressure is used, of the form
fore, pores and grains may be interchanged.
Another case, often used in comet nucleus modeling, is P = Ae –B/T (44)
that of a bundle of cylindrical tortuous capillary tubes that do
not cross each other (Mekler et al., 1990). The tortuosity is The coefficients for A and B for different ices are given in
defined as the ratio of the capillary length to the sampled Table 4. The coefficients for water and carbon monoxide
thickness. For a given length L and unit cross-sectional area may be found in Fanale and Salvail (1984). The other pa-
we have rameters are extrapolated from fits to data found in the
Handbook of Chemistry and Physics (Lide, 2003).
n
The latent heat of sublimation H is calculated from the
Ap = ∑ 2πr N ξ L
i=1
i i
(39)
Clausius-Clapeyron equation

V =1⋅ L
1 ∂P µ
= (45)
where ri is the capillary radius (1 ≤ i ≤ n), Ni is the number P ∂T T 2 g
of capillaries of radius ri crossing a unit area, and ξ is the
typical capillary tortuosity. Thus Using the empirical equation (44), we obtain B = µH /R g,
implying constant values for H .
n
S= ∑ 2πr N ξ
i =1
i i (40)
TABLE 4. List of coefficients for the pressure equation.

On the other hand, A Value B Value

Ice Component Symbol (1010 Nm–2) (Kelvin)
n
Ψ= ∑ πr N ξ
i=1
2
i i (41)
Water
Carbon monoxide
H2O
CO
356.
0.12631
6141.667
764.16
Carbon dioxide CO2 107.9 3148
Methane CH4 0.597 1190.2
which leads to Propyne C3H4 3.417 3000
Propadine C3H4 2.382 2758
n Ethane C2H6 0.459 1938
S = 2Ψ ∑ ƒ /r = 2Ψ/r
i =1
i i p (42) Methanol
Hydrogen cyanide
CH3OH
HCN
8.883
3.8665
4632
4024.66
Hydrogen sulphide H2S 1.2631 2648.42
where rp is the harmonic mean radius weighted by fi, the Ammonia NH3 61.412 3603.6
volume fraction occupied by capillaries of radius ri. Acetylene C2H2 9.831 2613.6
370 Comets II

3.5. Gas Flow and Permeability bundle of capillaries, we obtain for the mass flux

The gas released in the interior of the nucleus, either by 1/2

8 m
sublimation from the pore walls or as a result of crystalli- JKn = − Φ ∇(P/ T ) (52)
zation of amorphous ice, will diffuse through the pores. 3 2πk
Flow through a porous medium will depend on the proper-
ties of the medium and the properties of the flowing mate- where Φ, defined as the permeability of the medium, is ob-
rial itself. A simple formulation for fluid flow through a tained by using equation (41) and the same weighting func-
porous medium was derived experimentally by Darcy as tion as in the calculation of S for the same model (equa-
early as 1856 and has become known as Darcy’s law tion (42))

Φ = Ψrp/ξ2 (53)
1
J ∝ ∇P (46)
ν Another common relation between Φ and Ψ, known as the
Kozeny law, is of the general form
where ν is the kinematic viscosity of the fluid; in the case
of an ideal gas Φ ∝ Ψ3/(ξ2S2) (54)
1
ν≈ lvth (47) For a relatively low porosity, near the percolation limit Ψc,
3 below which there is no continuous flow through the me-
and dium, the relation is of the form

Φ ∝ (Ψ – Ψc)µ
8kT
vth = (48) (55)
πm µ = 2.8

The simple law (equation (46)) is, however, only approxi- However, when the pore size is increased, the condition
mately correct. Kn > 1 may no longer apply. The flow becomes a con-
The flow regime for a gas in a porous medium is deter- tinuum (Poiseuille), or viscous flow, dominated by colli-
mined by the Knudsen number defined as the ratio of the sions between particles
mean free path of a gas molecule to the pore diameter
l 3 Ψrp2 σα mπ 1/2
P
Kn = (49) JPo = − ∇P (56)
2rp 16 ξ2 2k 3 T 3/2
If n is the gas number density and σα the kinetic cross sec-
tion of a gas molecule, then For the intermediate regime, Kn ~ 1, semiempirical inter-
polation formulae are commonly used, of the general form
1 kT
l= = (50) J = a1JKn + a2JPo, known as the Adzumi equation, with fixed
σα n σα P
(empirically determined) coefficients a1 and a2. Each one
(Note that the cross section is usually defined as πd2, where of the flow equations is suitable for a set of given condi-
d is the molecular diameter; it may also include a factor tions. But when Kn is neither uniform nor constant, as in
2 if velocity effects are taken into account.) The highest the case of an evolving comet, the above formulae do not
ice temperature attained in comet nuclei is of the order of ensure a smooth transition between the two flow regimes
200 K; substituting in equation (50) σH2O ≈ 2.5 × 10 –15 cm2 as the Knudsen number changes from Kn >> 1 to Kn << 1.
and P ≈ P H2O (200 K), we obtain l ≈ 4 cm. Hence so long A more suitable interpolation may be obtained by noting
as the average pore size is less than 1 mm, we have Kn >> 1, that if the temperature is uniform, equation (52) reduces to
meaning that the flow of gas through the pores is a free an expression similar in form to equation (56). This sug-
molecular, or Knudsen flow, where collisions of the gas gests an interpolation similar to the Adzumi equation
particles with the pore walls are much more frequent than
collisions between particles. In this regime, the amount of
9π 1
mass passing through a cylindrical tube per unit time is J= 1+ JKn (57)
given by 256 Kn

which varies continuously from JKn for Kn >> 1 to JPo for

8rp3 πm
j= − ∇(P/ T ) (51) Kn << 1.
3ξ 2k When two gases (e.g., H2O vapor and CO) are flowing
through the same medium, they are treated independently,
(see Mekler et al., 1990). Adopting again the model of a namely each flux is computed according to equation (57).
 Prialnik et al.: Modeling Comet Nuclei 371

Since the molecular flow is driven by the partial pressure, interior of the nucleus. Near the surface, where the main
whereas the viscous flow is driven by the total pressure, this driving force is provided by water vapor sublimating from
is strictly correct in the Knudsen regime, and also in the case the pore walls, conditions are even more favorable.
of immiscible flows (see Bouziani and Fanale, 1998). For- So far we have neglected the effect of gravity. A gravi-
tunately, the flux of initially trapped gas is overwhelmingly tational acceleration g would change the solution in equa-
dominant in the interior of the comet, while the H2O flux tion (61) for the velocity to
becomes dominant in a very thin outer layer of the nucleus
(a few centimeters), where most of the sublimation occurs. vd(t) = (vg – gτ)(1 – e –t/τ) (62)
The interaction between gases is therefore restricted to this
layer. At high flow rates turbulence may arise, and equa- Hence the effect is negligible so long as gτ << v. For a con-
tion (57) may no longer hold. This is indicated by the Rey- stant nucleus density ρ, and at depths that are much smaller
nolds number exceeding a critical value of order 1000. When than R, we have g = (4π/3)GρR. For parameters character-
the Reynolds number is routinely evaluated during evolu- istic of cometary interiors (resulting in the above estimate
tionary calculations, it is always found to remain smaller of τ) this condition is amply satisfied. It will break down
than 100, and therefore equation (57) may be safely applied. for very large dust grains (see discussion of critical radius
in the next section), but the flow of such grains would in
3.6. Drag on Dust Grains any case be prevented by the small pore size.
In conclusion, to a good approximation, the dust grain can
As the ice sublimates from the porous nucleus matrix, be taken to move at the same speed as the gas. The differ-
dust grains are released into the gas stream. Transport of ence is that while the gas can move fairly freely through the
dust must therefore be considered in addition to gas flow, nucleus by diffusing through pores (or, if need be, through
a problem that is only now beginning to be studied. micropores), a dust grain can only move through those pores
We have seen that the flow of gas through porous comet that are large enough to accommodate it. Several models
nuclei is typically a free molecular (Knudsen) flow. The have been suggested to treat this problem. Podolak and
drag force on a dust grain of radius rd in the Knudsen re- Prialnik (1996) proposed that the dust motion be treated
gime is as a random walk. Shoshani et al. (1997) treat the porous
medium as a sequence of filters, each with a size distribu-
Fdrag ≈ 2πr 2dρvth(vg – vd) (58) tion of holes. The pores are viewed as cylinders extending
from these holes. The distance between filters is the aver-
up to a numerical factor of order unity (Öpik, 1958), where age distance one would travel in a cylindrical pore before
vg is the gas velocity and vd is the dust grain velocity. Com- the radius of the pore changed significantly. Assuming a
bining equations (58) and (48) and dividing by the mass of given dust grain speed and given size distributions for grains
the (spherical) dust grain, we obtain the grain’s acceleration and for pores, they follow the change in dust size distribu-
tion as the dust migrates through the nucleus. They also
dvd 1
= (vg − vd ) (59) show how the trapping of dust grains affects the porosity
dt τ(rd) and permeability of the medium.
where rd is the density of the grain and the characteristic More recently, Shoshany et al. (1999) used Monte Carlo
time τ, a function of the dust grain radius for given flow calculations to explore the behavior of dust migration in a
conditions, is medium with randomly distributed pores. They found that
the effective speed of dust particles is lower than that found
m by the random walk model for all porosities, although the
τ≈ d
rd (60)
ρ kT difference decreases for Ψ → 0 or Ψ → 1 as expected. They
also found that only the smallest dust grains (of order of the
The dust grain velocity (assuming a constant gas velocity) pore size) traversed the medium for any distance. Larger
is thus grains could not find sufficiently many large pores to travel
freely, and they got trapped after moving only a short dis-
vd(t) = vg(1 – e –t/τ) (61) tance. Large grains that are observed in a comet coma were
most likely lifted off directly from the surface. Smaller
For conditions that are typical of cometary interiors (a grains may have a component originating deeper in the
few meters to a few tens of meters below the surface), where nucleus. The exponent obtained from fitting a power law
crystallization of amorphous ice takes place and trapped gas to the observed grain size distribution in the coma may
is released, or where volatile species (such as CO) subli- therefore not accurately reflect the grain size distribution
mate, we find τ ≈ 0.5(rd/1 µm) s, so that even 10-µm par- within the nucleus itself.
ticles can reach 90% of the gas velocity in about 10 s. For Recent studies (Skorov and Rickman, 1995, 1998, 1999)
gas velocities typical of such conditions, the particle will have begun to focus on the details of the interaction of the
have traveled during that time interval a distance of much gas flow with the individual dust grains. These Monte Carlo
less than 1 m. This length scale is considerably smaller than computations follow the flow of gas molecules in the Knud-
the typical length scale over which conditions change in the sen regime as they leave the surface of the nucleus and
372 Comets II

interact with the dust grains above it. This work studies the overall gas flux and adopting, in the lowest approximation,
gas kinetic flow as a function of capillary length, inclina- a drag coefficient CD ≈ 2. When sublimation at the surface
tion angle, and temperature gradient along the pores at the is the dominant component, then equation (64) reduces to
surface of the nucleus. It also follows the velocity distribu- πr2dP (T). The effective gravitational force, diminished by the
tion of the gas molecules, and how it is affected by interac- centrifugal force, is
tion with the dust grains. Like all Monte Carlo computa-
tions, this program is advancing slowly, but is beginning to 4π 3 3π cos2 θ
produce important insight into the gas-dust interaction. Fgrav = rd d g 1 − (65)
How do these studies contribute to the numerical simu- 3 GρPspin
2

lation of a comet nucleus evolution? As the effective rate

of flow of dust particles clearly depends on the particle size, with g = 4πGρR/3, but the correction term is small so long
we may assume in numerical calculations the dust grain as Pspin < 3 h. Thus roughly
radii to be distributed over a discrete range rd,1, rd,2, … rd,N,
(T)
according to some distribution function ψ(rd) (such as a rd* ≈ (66)
power law). The size of a dust particle may be assumed to Gρ d R
remain unchanged, thus ignoring possible breakup or coa- The problem of dust mantle formation was first studied
lescence of dust grains. Hence particles in each size cat- by Brin and Mendis (1979), who related the mantle thick-
egory may be treated as independent species. The local flux ness D at a particular point in the orbit to its thickness at
of dust particles of radius rd,n is therefore given by an earlier point by

Jd,n = βnρd,nvg D[d H (t )] = D[d H (t − δt )](1 − Θ) +

Q (67)
It is the coefficient βn that must be determined by the dust (1 − Ω)X d δt
d
flow model (cf. Horanyi et al., 1984). For example, Podolak
and Prialnik (1996) adopt where Ω is the fraction of dust released from ice and car-
ried away by the sublimating gas, and Θ is the additional
βn ∝ log[1 – ψ(rd,n)]/log[(1 – ψ(rd,n))ψ(rd,n)] part of the mantle removed by the increased gas flux. For
a grain size distribution ψ(rd) within a range [r min max
d , r d ] and
The mass conservation equation for these particles is a critical grain size r*d(t), which changes along the orbit, the
functions Ω and Θ can be calculated and thus the develop-
∂ρd, n
+ ∇ ⋅ Jd, n = 0 (63) ment and evolution of this dust mantle can be followed. The
∂t rate of growth of the mantle is determined by the param-
We note that there is no source term in equation (63); the eter (1 – η), where
implicit assumption in this simple approximation is that any r *d
dust grain that can be dragged (allowance being made for
η=
∫ r min
d
ψ(rd )rd3drd
the critical radius and the local average pore radius) is r max
∫
d
dragged with the gas. ψ(rd )rd3drd
r min
The results expected from any dust flow model are the d

grain size distribution of the ejected dust and the changing This simple approach deals, however, only with the mass
pore structure of the medium through which the dust flows. of the mantle, regardless of its structure.
For example, the large dust grains left behind on the nucleus One approach to modeling the structure of the dust
surface form a dust mantle, which, in turn, affects the rate mantle is to assume that the ice sublimates freely at the
of heat and gas flow at the surface. nucleus surface, carrying with it the smaller (than critical
size) dust grains, while the larger grains are left behind. At
3.7. Dust Mantle Formation the beginning, these large dust grains are isolated from each
other, but as more and more grains accumulate, the surface
The eventual formation of a dust mantle on the surface of becomes evenly covered and starts interfering with the es-
a comet nucleus may be modeled in different ways, the essen- cape of smaller and smaller grains. The porosity of the dust
tial parameter being the critical dust grain radius, which rep- mantle decreases and eventually drops below that of the
resents the radius of the largest particle that can leave the nucleus. This idea of trapping and compaction, introduced
comet, as determined by the balance of forces acting on a by Shul’man (1972), was adopted by Rickman et al. (1990)
dust grain. The drag force exerted by the gas flux at the in modeling the dust mantle. They showed that if the grain
surface is size distribution follows a power law with an index of about
–3.5, the smallest grains left behind contribute the most to
Fdrag = 1
C πr 2
2 D d ∑v J
α
α α ≈ πrd2 ∑v J
α
α α
(64) forming the dust mantle. The gas flow through such a man-
tle can be modeled by considering gas diffusion through
summing over the different species that contribute to the this porous medium. If the gas pressure is high enough, the
 Prialnik et al.: Modeling Comet Nuclei 373

dust mantle can be blown off, and the process will start energy of the material is decreased thereby. Cook applies
anew. The process depends both on latitude and on the in- this picture to a fractal material composed of successive
clination of the rotation axis. A dust mantle will inhibit gas generations of spherical aggregates. This picture may be
sublimation when most of the surface, close to 100%, is useful for modeling the strength of comet nuclei.
covered by grains (e.g., Prialnik and Bar-Nun, 1988), a In a weak porous medium, thermal stresses (Kührt,
result that was confirmed by the KOSI experiments (Grün 1984) and internal pressure exerted by gas that accumulates
et al., 1993). in the pores may break the fragile solid matrix. For ex-
Eventually, the pore size of the dust mantle may become ample, a model of a typical comet given in Prialnik et al.
too small to allow particles to escape and a large amount (1993) yields internal water vapor pressures exceeding 2 ×
of small grains will become permanently trapped. This may 105 Pa. This is comparable to the above strength estimates
lead to a very stable and efficient dust crust with a high for cometary ice. If the stress, σm, on a material exceeds
cohesive strength, which may surpass the vapor pressure its tensile strength T, then that material will undergo ten-
building up in the porous material underneath the mantle sile fracture. If the stress is negative (compression) and ex-
(Kührt and Keller, 1994). As a consequence, the gas is ceeds the compressive strength C , the material will undergo
driven toward the interior and refreezes, forming an ice shear fracture. In a spherical shell of radius r, the tangen-
layer of increased density (Prialnik and Mekler, 1991). This tial stress is given by
effect was actually observed in the KOSI comet simulation
experiments (Spohn et al., 1989). σm 1 dP
= − (69)
r 2 dr
3.8. Tensile Strength and Fracture of the Nucleus
(Morley, 1954), so that fracture should occur when
The material strength of comet nuclei is very low. Al-
though the range of values resulting from different estimates dP 2
− > (70)
is wide, all values indicate a weak material. The strength dr r
deduced from tidal breakup of Sun-grazing comets is 102–
104 Pa (Sekanina, 1984; Klinger et al., 1989). Laboratory In general C >> T, so that only tensile fracture needs to be
experiments lend further support to the low strength esti- considered. Prialnik et al. (1993) present a simple algorithm
mates derived from observations: The typical strengths of for dealing with this effect. They assume that the porosity
the ice crusts measured in the KOSI experiments were in of the medium remains unchanged, but the average pore
the 105-Pa range (Kochan et al., 1989). radius increases as a result of fracture. When the local pres-
A simple model for the strength of a medium composed sure gradient is high enough so that condition (70) is satis-
of spherical grains was developed by Greenberg et al. fied (for example, due to crystallization and release of
(1995). Taking the nominal dipole-dipole interaction to be trapped gas), the local average radius of the pores is in-
~10 –2 eV, they obtain for the tensile strength creased by a factor proportional to (r/2T )dP/dr. Then a re-
laxation time is allowed so that the gas can flow through the
−2 enlarged pores, after which condition (70) is tested again.
rd
= 6.1 × 102 (1 − Ψ )β Pa (68) The energy of deformation of the matrix is small compared
0.1 µm with the energy released by the amorphous-crystalline tran-
sition, and may be neglected. This procedure can also allow
where 1 ≤ β ≤ 12 is the number of contact points per par- for the effect of strain hardening, whereby the strength of
ticle. The strength and Young’s modulus for a medium com- a material is increased due to deformation. In this case one
posed of ice grains linked into chains by intermolecular can allow the tensile strength of the material to increase
forces is computed by Sirono and Greenberg (2000). They along with the increasing pore size.
show that these forces are strong enough to hold an assem- In summary, as a result of fracture, the size distribution
blage of grains together even when its self-gravity will not. of pores will vary throughout the nucleus. In addition, sin-
They derive 3 × 102 Pa for the tensile and 6 × 103 Pa for tering (Kossacki et al., 1999) or pore blocking by small dust
the compressive strength, when applied to the tidally split grains may alter pore sizes as well as consolidate the ma-
Comet Shoemaker-Levy 9. terial. Massive recondensation of volatiles on pore walls has
Rotational stability against breakup of fast-rotating com- a similar effect. A subject for future work is to incorporate
ets provide an independent means of estimating the strength additional processes such as grain growth by sintering and
of cometary material. Computations of this kind have been the elimination of pores by densification. An excellent re-
presented by Davidsson for solid spheres (Davidsson, 1999) view of the relevant processes is given by Eluszkiewicz et al.
and for biaxial ellipsoids (Davidsson, 2001). Cook (1989) (1998). We are again faced with a complex internal process
considers a medium composed of bulk material permeated for which we must account based on very little information.
by cracks. The energy of such a medium will be a sum of Moreover, the pore size distribution measured at the sur-
the elastic strain energy in the bulk material and the surface face of a comet nucleus need not represent the distribution
energy along the crack. The crack will spread if the total in the deeper layers. However, extensive studies of crater
374 Comets II

formation in ice targets (Arakawa et al., 2000) have shown

that the crater depth scales as the square root of the impact
energy. More importantly, the crater pattern depends not
only on the energy of the impactor, but also on the details of
the layering of the ice. Thus future measurements of cra-
ters on comet nuclei may yield clues to their underlying
structure.

3.9. Characteristic Timescales

Each process mentioned in this section has its own char-

acteristic timescale and the competition between these
timescales will determine to a large extent the evolution-
ary pattern of the comet nucleus that will be discussed in
the next section:
1. The thermal timescale, obtained from the energy con-
servation equation (10), which in its simplest form (with-
out sources and advection) is a heat-diffusion equation.
Distinction must be made between the thermal timescale
of amorphous ice τa–ice, crystalline ice τc–ice, and dust τdust.
For a layer of thickness ∆r and average temperature T we Fig. 4. Timescales of different evolutionary processes (see text)
have as a function of temperature. The solar timescale is given for dis-
tances of 1 and 10 AU (dash-dot lines); the thermal timescale for
τa–ice = (∆r)2ρac(T)/Ka (71) ice is shown for two depths (10 cm and 10 m).

and similar expressions for τc–ice and τdust. As a rule, τc–ice <
τa–ice < τdust; as we have seen in section 3.1, porosity in- radioactive species may be added; the only relevant one
creases all these timescales considerably. being that of 26Al. A comparison of these timescales is
2. The timescale of gas diffusion τgas, which is also the shown in Fig. 4, where they are plotted against tempera-
timescale of pressure release, obtained from the mass con- ture, assuming an average pore size of 10 µm and a poros-
servation equation, which (without sources) can be regarded ity of 0.5, and considering heliocentric distances of 1 and
as a diffusion-type equation for the release of gas pressure: 10 AU and depths of 10 cm and 10 m (since the diffusion
timescales for heat and gas depend on depth). These time-
1/2
3 (∆r)2 2πm scales will be helpful for understanding the results of nu-
τgas = (72)
4 Ψrp kT merical calculations presented in the next section.

3. The timescale of crystallization τac, which is also the 4. MODELING RESULTS AND
timescale of gas-release and pressure buildup: INTERPRETATION: STRUCTURE AND
EVOLUTION OF COMET NUCLEI
τac = λ(t)–1 = 9.54 × 10–14e5370/T s (73)
4.1. Input Parameters
4. The timescales of sublimation of the different vola-
tiles, τsubl–H2O for water, τsubl–CO for CO and τsubl–CO2 for In order to follow the evolution of a comet nucleus struc-
CO2, and so forth: ture by means of the equations displayed in section 2, in-
cluding the physical processes described in section 3, we
ρc still need to specify a number of different types of param-
τsubl–H2O = (74)
SP H2O m H2O / 2πkT eters:
1. Defining parameters. These identify a comet and
and similar expressions for τsubl–CO, τsubl–CO2, and so forth. include orbital parameters (semimajor axis and eccentric-
5. The insolation timescale τ , which concerns the skin ity), the nucleus size, given by an average radius, its mass
of the comet nucleus that is heated by absorption of solar (or bulk density), and its spin period, all of which may be
radiation. determined observationally.
2. Initial parameters. These are required for the solu-
4πd2H tion of the time-dependent equations and must be guessed.
τ = (κ c Pspin /πρc c) ρc cT (75)
L (1 – ) As these equations are not expected to reach equilibrium
(steady-state), the initial conditions are not likely to be “for-
To these, the constant characteristic times of decay of the gotten.” They include the initial temperature, or tempera-
 Prialnik et al.: Modeling Comet Nuclei 375

ture profile; compositional parameters (mass fractions of the TABLE 5. Estimates of characteristic properties of comets.
different volatiles and dust); and structural parameters, such
as porosity, average pore size or pore size distribution, as Dependence on
well as the nature of the water ice, whether crystalline or Property Parameters Value
amorphous. In fact, one of the main goals of modeling is
1/2
to determine these properties by comparing their observ- 2Ka 3/2
Orbital skin depth 18 m
able consequences to actual observations (see Prialnik, ρc
2002). Regardless of details, initial homogeneity is adopted
as a rule. PspinK 1/2
3. Physical parameters. These are parameters related Diurnal skin depth 0.1 m
πρc
to the various physical processes discussed in section 3.
They supplement the parameters in the former group and,
R2ρc
in principle, should have been determined by them, had the Thermal timescale 8 × 104 yr
π2K
detailed structure of comet nuclei been better understood.
Among them are albedo and emissivity, associated with
πL R2
surface properties, as well as thermal conductivity coeffi- Insolation per orbit 1018 J
2 a(1 − e 2)
cients, tensile strength, and so forth, associated with bulk
material properties. These parameters can be determined by
2
laboratory experiments, although caution must be exercised, R
Production rate (ph) 1.3 × 1030/s
since laboratory samples are scaled down by orders of 4µ a (1 − e)
magnitude. In situ measurements should eventually provide
much more reliable input data. 1
Erosion per orbit 1.7 m
8 ρ a (1 − e 2 )
4.2. Analytical Considerations: Characteristic
Properties of the Comet Nucleus
Max. temperature 4πa2 (1 − e)2 Q 205 K
=1
Adopting typical values for the physical properties of
cometary material in general, simple estimates may be de-
Day-night range (ph) Td ρcK dT 1
rived for the characteristics of the nucleus structure and
(see equation (79)) ∫Tn π Pspin Q
=
2
23 K
evolution, in terms of the defining parameters just men-
tioned, as shown in Table 5. These provide insight into the
nature of comet nuclei, as well as instructive guidelines for Life time 8 R ρ a (1 − e 2 ) 3 × 103 yr
building numerical models of their structure and evolution.
For example, the skin depth and thermal timescale help in
Note that G = GM = 1.152 × 1010 m3/2 s–1; L = L /H ; values
defining an adequate numerical grid, or discretization, in
listed in the last column were obtained using the following param-
space and time, while the mass loss rate and life span indi- eters: a = 10 AU, e = 0.9, resulting in a perihelion (ph) distance of
cate what the size of such a grid should be. The tempera- 1 AU, R = 5 km, ρ = 7 × 102 kg/m3, Pspin = 10 h, K = 0.6 J/
ture (calculated from equation (1) for the subsolar point) (m s K), c = 8 × 102 J/(kg K).
indicates what thermochemical processes are to be expected.
These, however, are only crude estimates. The detailed
behavior of comet nuclei is obtained by applying the full face, equation (15), with –K∇TR substituted for F(R) on the
set of equations given in section 2, and including complex lefthand side
input physics, as discussed in section 3. Since the evolu-
tion of nuclei, as already indicated by the crude estimates, (1 − )L
cos ξ = εσT 4 + K∇TR + QH (76)
is largely determined by their defining parameters, numeri- 4πd 2H
cal models are mostly applied to individual comets, rather
than to comets in general, and even then the results may The incoming solar flux depends mainly on the Sun-comet
diverge, as compositional and structural parameters vary. distance, the rotational state, spin period, scattering prop-
Detailed examples of the application of thermal evolution erties of the coma (neglected here), and the reflectivity of
models to individual comets are given by Meech and Svoren the surface; thermal reradiation depends on the emissivity;
(2004). Typical characteristics of the structure and activity heat transported in and out of the nucleus is a function of
of comet nuclei are discussed in the rest of this section. the thermal conductivity with all its related parameters; and
the energy dissipated in sublimation depends on the com-
4.3. Surface and Internal Temperatures position. For illustration, we choose in the following dis-
cussion models of the small, fast-spinning, short-period
In order to understand the surface temperatures of comet Comet P46/Wirtanen, the former target of the European
nuclei, we may use the power balance equation at the sur- mission Rosetta.
376 Comets II

To begin, we distinguish between two extreme cases. The

first extreme is to assume that no ices or volatile materials
are present at the surface, which then consists of a porous
dust layer where gas sublimated in the interior of the nu-
cleus can flow through. Thus the thermal conductivity and
matrix structure are the key parameters influencing the
surface temperature (Ts). The other extreme is a free subli-
mation regime, where it is assumed that only water ice is
present on the surface. Here the energy used for sublima-
tion of the gas dominates in the power balance equation,
at least at heliocentric distances smaller than 2–3 AU. This
leads to much lower surface temperatures, as shown in
Fig. 5, where results for Ts(dH) at different “comet day”
times, obtained from calculations for inactive surfaces
(Figs. 5a,b) and for pure ice surfaces (Fig. 5c), are com-
pared. In order to investigate the influence of the thermal
conductivity of the mantle on the thermal evolution of the
nucleus, we distinguish between a high and a low conduc-
tivity mantle. The high value K = 0.1 Wm–1 K–1 (top panel)
is still about a factor of 10 less than the conductivity of typi-
cal solid minerals on Earth, so as to account for porosity
and for the loose structure of cometary material. For the
low conductivity case, a 100-fold smaller value is assumed.
The highest surface temperatures are obtained at noon
at the subsolar point; nighttime temperatures are much
lower. At perihelion, the difference between the highest
temperature (370 K at noon) and the lowest one (about
180 K at night) is about 190 K, assuming a dust surface.
At the intermediate distance of 3 AU, the maximum day
temperature is about 210 K, while night temperatures are
about 140 K. At aphelion the day-night variations are the
smallest, about 30 K.
When a much lower thermal conductivity is assumed for
the mantle, the difference between day and night tempera-
tures increases significantly. At perihelion, the day-night
variation is about 300 K (Tmax ≈ 380 K, Tmin ≈ 80 K) and
at aphelion the difference is still quite large, 120 K (Tmax ≈
180 K, Tmin ≈ 60 K). The reason is that in the low conduc-
tivity case the thermal reradiation power is almost the same
as the solar input and the thermal conductivity power is
almost null. In the high conductivity case, on the other hand,
the power transported by heat conduction into the nucleus
is about 10% of the incoming solar input. At night, stored
internal energy is transported from the interior to the sur-
face. This transport, too, is more efficient in case of a high
matrix conductivity. Therefore, we obtain smaller tempera-
ture differences between day and night and also obtain
lower maximum and higher minimum temperatures. The
transition from inward to outward heat conduction is not
exactly in tune with the insolation power. This transition may
be observable: Tracers could be the flux of minor volatiles
that depend on the accumulated energy. In the high-con-
ductivity mantle models there is a delay due to the thermal
inertia of the material. This delay is vanishingly small in Fig. 5. Surface temperatures as a function of distance from the
the case of low conductivity. An effect similar to the day- Sun for different “comet day” times. A comparison is shown be-
night effect and the associated thermal lag also appears on tween (a),(b) inactive surfaces and (c) pure ice surfaces. Results
the much longer timescale of orbital evolution, where pre- from model calculations for Comet P46/Wirtanen.
 Prialnik et al.: Modeling Comet Nuclei 377

inner amorphous part, where conductivity is poor (see sec-

tion 3.2) and the temperature profile steep.
The diurnal temperature variation may be generally under-
stood and estimated by the following simple argument. The
rate of cooling, or the cooling flux Fcool(T), on the night-
side is given by equation (15), setting the insolation rate to
zero and assuming a pure ice composition

Fcool(T) = εσT4 + Q(T)H (77)

This is balanced by the heat lost from an outer layer down

to a depth equal to the skin depth corresponding to the spin
period of the nucleus, s = KPspin/(πρc) . Thus, over a time
interval dt, measured in units of the spin period, the tem-
perature will change by an amount dT given by

Fcool (T) dt = −ρscdT =

(78)
− ρc(T)K(T)/(πPspin ) dT

Fig. 6. Temperature profiles in the upper layer of a nucleus which, integrated over half a spin period, yields
model in the orbit of P/Wirtanen at several points along the orbit,
pre- and post-perihelion, as marked. The typical steep rise in tem-
Tmax ρc(T)K(T)/(πPspin ) 1
perature in curve 4 is due to heat released in crystallization, which
proceeds at a fast rate at that point. We note the shift of the surface ∫Tmin Fcool (T)
dT =
2
(79)
due to erosion.
where Tmax – Tmin is roughly the temperature difference
between the subsolar and antisolar points. The day-night
perihelion temperatures are typically lower than post-peri- temperature difference as function of Tmax is shown in Fig. 7
helion ones at the same heliocentric distance. for three values of the Hertz factor.
For the free sublimation regime — active areas with no
dust mantle on the surface — the results will change sig-
nificantly. Close to the Sun, at noon, the highest Ts is about
203 K, nearly the free sublimation temperature of water at
about 1 AU. The lowest Ts at night is about 115 K, which
yields day-night variations of about 90 K at perihelion. At
about 3 AU, a maximum of about 190 K and night mini-
mum of ~105 K can be expected. At aphelion, the day-night
variations are again the smallest and amount to about 65 K
(Tmax ≈ 165 K, Tmin ≈ 100 K). The large difference between
an active and an inactive surface is that in the former most
of the insolation power is consumed by water sublimation.
Surface temperatures are thus limited by the free sublima-
tion temperature of water ice, a strong energy sink that does
not allow temperatures to increase any further. Lower tem-
peratures also reduce the thermal reradiation power, which
depends on the temperature to the fourth power.
The heat transported inward serves in part to increase
the internal energy of the nucleus, and in part is absorbed
in sublimation of volatiles. Heating of the subsurface lay-
ers during one revolution is illustrated in Fig. 6 for an
amorphous ice nucleus model. The affected region is barely
a few meters deep; the layer of temperature inversion at
large dH is barely a few centimeters thick. The change in
slope of the profile occurs at the boundary between the Fig. 7. Analytical estimate for the surface temperature difference
outer crystalline layer, which is an efficient heat conductor between the subsolar and antisolar points for several values of the
leading to a mild temperature variation with depth, and the Hertz factor.
378 Comets II

In terms of timescales (Fig. 4), we note that the timescale

of solar heating at 1 AU intersects the sublimation time-
scales at temperatures ~25 K for CO, ~80 K for CO2, and
~160 K for H2O. When these temperatures are attained and
if the corresponding ices are found near the surface, the
solar energy will be absorbed in sublimation. Consequently,
the surface temperature will rise much more slowly. We note
that in all cases conduction to the interior is negligibly slow.
A steady state will be reached at slightly higher tempera-
tures, when the timescale of gas diffusion for a thin sub-
surface layer intersects the sublimation timescales: ~30 K
for CO, ~100 K for CO2, and ~200 K for H2O. These are
the expected surface temperatures of comets near 1 AU,
when the corresponding ices are exposed. If a mixture of
ices is present, the temperature will be determined by the
most volatile among them.

4.4. Production and Depletion of Volatiles

The solar energy flux reaching the nucleus — after be-

ing partly scattered or absorbed by the coma — is to some Fig. 8. Mass fraction of crystalline H2O ice and of CO ice (multi-
small part reflected (low albedo of the nucleus) and in part plied by 10) in the upper layer of a comet model for the orbit of
reradiated in the IR (high emissivity). A small fraction is P/Wirtanen, at the subsolar point. The initial composition is Xa =
transported into the interior of the nucleus by conduction 0.5, fCO = 0.05, and Xd = 0.5. We note the advance of crystalliza-
and to a very small degree by radiation in pores. The rest tion accompanied by freezing of the CO gas flowing inward in
the cold regions below the crystallization front. The drop of Xc
(the bulk at small distances from the Sun) is absorbed at
near the surface is due to sublimation. The model is the same as
the surface and used to evaporate (sublimate) water ice. The
that of Fig. 6.
amount of water vapor released depends on the dust cover
on the surface. A dust cover a few millimeters thick causes
most of the incident energy to be reradiated, leaving only
a small fraction for sublimation of water ice. Heat that is
conducted into the interior of the porous nucleus may reach Because of heat and gas diffusion, the nucleus will be
ices more volatile than water ice. In a comet nucleus, many chemically differentiated in layers. The least-volatile ma-
different volatile species are expected to be present (see terial (dust) will be at the top of the nucleus. It will be fol-
Table 4). If the ice is crystalline, then volatile ices are fro- lowed by a layer of dust and water ice. In the deepest layers
zen out as separate phases. As heat diffuses inward, each we would find dust and all ices, including the most vola-
volatile constituent forms its own sublimation front depend- tile species (such as CO and CH4). At the surface of the
ing on its enthalpy of vaporization. If amorphous ice is nucleus, water and other more volatile ices evaporate, leav-
present it will change to crystalline ice, forming an addi- ing a layer of dust behind. Dust particles entrained by the
tional front, this time exothermic, for the phase transition. gas into the coma will heat up in sunlight, and the organic
At this front, gases trapped by the amorphous ice will be component (hydrocarbon polycondensates) will be vapor-
released. As an ice species evaporates the gas pressure at ized. Polymerized formaldehyde (POM) plays an important
the sublimation front increases toward its maximum (equi- role in the dust in producing short-lived formaldehyde gas,
librium) value at that temperature. The pressure forms a gra- which quickly dissociates into CO. The distributed coma
dient that is negative in the outward direction and positive source for the CO must be subtracted from the total CO
in the inward direction. This pressure gradient drives the release rates in order to obtain production rates resulting
gas flow. The gas flowing outward will diffuse through the from gas released by the nucleus. A major goal of comet
comet nucleus and escape through its surface into the coma. research is to determine conditions in the solar nebula based
The gas flowing inward will recondense a short distance on the chemical composition of comet nuclei. However, the
below the sublimation or crystallization front and release nucleus composition cannot be directly observed and must
its latent heat. This is an additional heat transport mecha- be deduced from the observed composition of the coma.
nism into the interior, which surpasses advection by flow- Taking advantage of new observing technology and the
ing gas (Prialnik, 1992; Steiner and Kömle, 1993). It was early detection of the very active Comet Hale-Bopp (C/1995
observed by Benkhoff and Spohn (1991) during the KOSI O1), researchers were allowed for the first time to deter-
experiments on cometary ice analogs. Recondensation oc- mine the coma abundance ratios of different species over a
curs within a thermal skin depth. The effect is illustrated large range of heliocentric distances. The results supported
in Fig. 8. the hypothesis that coma abundances do not reflect in a
 Prialnik et al.: Modeling Comet Nuclei 379

simple way the composition of the nucleus. Abundance 4.5. Dust Ejection and Mantle Formation
ratios of different species may change by factors as large
as several hundred, going from heliocentric distances of r ≈ The basic process of dust ejection and mantle formation
1 AU to r ≈ 7 AU. Thus chemical modeling of the coma is quite simple: As water and other — more volatile — ices
coupled to gas-dynamic flow is first required (see Crifo et evaporate, the gas flux drags with it dust particles with radii
al., 2004) in order to provide the true, distance-dependent smaller than the critical radius r*d (which varies with tem-
composition of volatiles released from the nucleus. Nucleus perature), while the larger particles accumulate on the sur-
models should then be tested against these results along the face, eventually creating an inactive mantle. If at all points
orbit for as large a range of distances as possible in order of the orbit (that is, for all values of the surface tempera-
to deduce the composition of the nucleus. An example of ture) r*d(T) < rdmax, a permanent mantle will form and grow
this procedure, based on the work of Huebner and Benkhoff thicker with repeated orbital revolutions. In time, the insu-
(1999), is given in Fig. 9, which shows the mixing ratio of lating effect of the mantle will quench sublimation and
CO relative to H2O using cubic fits to the release rates ob- hence dust entrainment as well. The difficulty in modeling
tained by combining observational data from Comet Hale- this process is due to the large uncertainties in the param-
Bopp for H2O (from OH) and CO covering the spectrum eters involved. Thus, whereas the observed size distribution
range from radio to UV. The heavy dashed curve is the re- of dust grains concerns the small particles, it is the large
sult of model calculations for a mixture of 35% amorphous particles that determine the rate of formation of the mantle.
H2O, 7% CO2, 13% CO (50% trapped in the amorphous Moreover, the physical properties of the mantle may be
ice), and 45% dust. The CO2 has very little influence on largely affected by organic material that acts as a glue be-
the results. The mixture is close to what one would expect tween dust grains (Kömle et al., 1996). Consequently, one
from the condensable component of molecules forming at of the main goals of model calculations is to examine the
low temperatures from a mixture of elements with solar effect of parameter variations. Podolak and Herman (1985)
abundances. Although the result is below the fit, it must be showed that the growth and stability of the mantle is af-
kept in mind that the CO from distributed sources has not fected by the thermal conductivity, a high conductivity
been subtracted from the observed CO flux. acting as a heat sink. The effect of a variable albedo was
studied by Orosei et al. (1995). They showed that dust ac-
cumulation and darkening of the surface can cause an in-
crease in the energy absorbed by the nucleus to such an
extent as to increase ice sublimation and dust drag to the
point of complete removal of the mantle. In such a case the
comet would become whiter and colder and buildup of the
mantle could start anew, leading to alternating phases of
activity and hibernation. The importance of cohesive forces
within the refractory material was stressed by Kührt and
Keller (1994), who showed that mantles may withstand the
vapor pressure building up underneath and thus explain the
seemingly permanent inactivity of a large fraction of the
nucleus.
Cometary activity declines considerably during the build-
up of a dust mantle. A very thin dust layer, on the order of
a few centimeters or less, is capable of diminishing the com-
etary activity by a large factor (e.g., Prialnik and Bar-Nun,
1988; Coradini et al., 1997b; Capria et al., 2001). At the
same time, the surface temperature becomes much higher,
as we have seen in section 3.7 and Fig. 5. If a dense ice
crust builds up below the dust mantle, the activity is
quenched to an even higher degree (Prialnik and Mekler,
1991). In these cases the activity is limited to exposed
patches of ice. Rickman et al. (1990) show — by numerical
simulations of mantle growth — that even stable mantles
are sufficiently thin to be broken occasionally by thermal
cracks, explosion of gas pockets, or minor collisions, al-
lowing localized activity.
The second goal of models involving dust is to explain
the observed dust production rates. Here too the results are
Fig. 9. The mixing ratio of CO relative to H2O using cubic fits largely dependent on unknown parameters. An example of
to the release rates (see text). From Huebner and Benkhoff (1999). dust ejection from a comet nucleus resulting from dust
380 Comets II

reaches the critical temperature Tc ~ 110–120 K, the latent

heat released at the front causes it to rise still further. The
higher temperature, in turn, causes crystallization to pro-
ceed even faster and thus a runaway process develops. The
rise time and the timescale of outbursts thus triggered
should be on the order of τc–ice(Tc) = τac(Tc). According to
Fig. 4, it is about 100 days for crystallization for a depth
of 10 m (and it will be ~1 day for a depth of 1 m). This
means that fluctuations (and outbursts) at small heliocen-
tric distances should occur on much shorter timescales than
at large heliocentric distances. Observations appear to con-
firm this conclusion.
The competition between τac and τgas should indicate
when an instability is likely to occur. We recall that the
crystallization timescale is also the timescale of gas release
and pressure buildup (assuming gas is occluded in the
amorphous ice), while the diffusion timescale of the gas is
also the timescale of pressure relaxation. If τac > τgas, the
pressure is released sufficiently rapidly to prevent mechani-
cal instability; however, if τgas >> τac, gas would accumu-
late more rapidly than it is removed and large stresses may
Fig. 10. Dust and gas production rates for a model of Comet result from pressure buildup. Thus, if the temperature of
Hale-Bopp. The dotted line represents the production rate of H2O amorphous ice at a certain depth exceeds a critical value,
alone; the dashed line is the total gas flux, including H2O, CO, it could lead to a state of instability. This situation may be
and CO2. The ice/dust mass ratio for the nucleus is 1. From avoided either if the temperature decreases, which is pos-
Prialnik (2002). sible if the thermal timescale is sufficiently short, or if the
pore size increases, thereby reducing τgas. However, accord-
ing to Fig. 4, the thermal timescales for both amorphous
carried out from the interior, as well as blown off of the and crystalline ice are longer than τgas by 2–3 orders of
surface, is shown in Fig. 10. magnitude. Hence only expansion of the pores may arrest
the development of an instability, once it occurs. However,
4.6. Crystallization and Outbursts the analysis of timescales does not provide clues for the
magnitude of the pressure and pressure gradients in rela-
Comets are often found to be active at heliocentric dis- tion to the strength of the material, nor to the outcome of
tances far beyond the limit of ~5 AU, within which the unstable conditions. This necessitates detailed numerical
activity may be explained by sublimation of water ice in- computations, and the establishment of an algorithm for
duced by insolation. Crystallization of amorphous ice has treating fracture.
long been recognized as a suitable mechanism for explain- Numerical models of the evolution of cometary nuclei
ing such distant bursts of activity (Patashnik et al., 1974; find that crystallization progresses in spurts, their onset,
Smoluchowski, 1981; Espinasse et al., 1991; Weissman, duration, and extent in depth being largely determined both
1991; Prialnik and Bar-Nun, 1992). by the structure, composition, and thermal properties of the
Considering the timescales of crystallization, heat con- nucleus and by the comet’s orbit (e.g., Herman and Podolak,
duction and sublimation, we find that at very low tempera- 1985; Prialnik and Bar-Nun, 1987, 1990; Espinasse et al.,
tures conduction dominates, meaning that heat released by 1991, 1993; Tancredi et al., 1994). Crystallization may be
a local source will be efficiently removed. Crystalline ice initiated by the heat wave propagating inward from the
is a much better heat conductor than amorphous ice and insolated comet surface to the crystalline-amorphous ice
hence heat will flow predominantly to the surface through boundary, provided that after reaching this boundary, it still
the growing outer crystalline layer. Thus, as long as the carries sufficient energy for significantly raising the local
temperature of the outer layer of the nucleus is below the temperature. However, once this has occurred and the
critical temperature where τac intersects τc–ice (see Fig. 4), boundary has moved deeper into the nucleus, later heat
the rate of heating by crystallization will be very slow. As waves originating at the surface will be too weak when
the crystallization rate is much more sensitive to tempera- reaching the boundary to rekindle crystallization. A quies-
ture than the conduction rate (of crystalline ice), it will cent period would thus ensue, until the surface recedes (by
eventually surpass the rate of heat conduction. For example, sublimation) to a sufficiently short distance from the crys-
at a depth of 10 m, the conduction timescale surpasses the talline-amorphous ice boundary. At this point, a new spurt
crystallization timescale close to 120 K. Crystallization is of crystallization will take place. Since in the meantime the
triggered by some heat source that causes the temperature interior temperature of the ice has risen to some extent, crys-
to rise; when the temperature at the crystallization front tallization will advance deeper into the nucleus than at the
 Prialnik et al.: Modeling Comet Nuclei 381

previous spurt. This will in turn affect the time span to the optimal parameter combination was found after numerous
next spurt of crystallization, since the rate of surface reces- trials of parameter combinations that proved far less suc-
sion for a given comet is roughly constant (see Table 5). In cessful. They found that spurts of crystallization started
conclusion, crystallization would appear to be triggered spo- close to aphelion. As a rule, the CO production rate de-
radically, preferentially at large heliocentric distances, creased slightly as the model comet approached the Sun
where comets spend most of their time. This could explain from aphelion. This should explain the puzzling fading of
the distant activity — outbursts and possibly splitting — of Chiron between 1970 and 1985 (i.e., from ~18 AU to
comets. ~14 AU). The model produced the required CO emission
The release of gas trapped in the amorphous ice provides rates, explained by release of trapped gas, and reproduced
the link between crystallization and the eruptive manifes- the estimated surface (color) temperatures at different points
tations of comets, of which a few examples will be given of the orbit as derived by Campins et al. (1994). Capria et
below. We have already shown that numerical simulations al. (2000) also explained Chiron’s activity by gas trapped
are based on many simplifying assumptions, and often adopt in amorphous ice, although they also mentioned the possi-
parameters that are not well known. Hence they should not bility of CO ice close to the surface, which would imply that
be expected to accurately reproduce any particular observed Chiron has been inserted into its present orbit only recently
outburst. Rather, such simulations should account for the (cf. Fanale and Salvail, 1997).
basic characteristics of the observed outbursts. 4.6.3. Erratic activity of Comet Schwassmann-Wach-
4.6.1. Distant outbursts of Comet P/Halley. The behav- mann 1 (SW1). The orbit of Comet SW1 is nearly circular
ior of Comet P/Halley at large heliocentric distances, be- and confined between the orbits of Jupiter and Saturn.
yond 5 AU, was characterized by outbursts of various mag- Despite the fact that at such heliocentric distances the sub-
nitudes; during the most significant one, at 14 AU (West limation of H2O ice is negligible, this comet exhibits irregu-
et al., 1991), the total brightness increased by more than lar activity — unpredictable changes in its lightcurve.
5 mag and an extended coma developed. The outburst sub- Froeschlé et al. (1983) suggested that this might be associ-
sided on a timescale of months. Klinger and his collabora- ated with crystallization of amorphous ice. This suggestion
tors (see Espinasse et al., 1991; Weissman, 1991) and was further strengthened by the detection of CO released
Prialnik and Bar-Nun (1992) showed that these features can by the comet (Senay and Jewitt, 1994; Crovisier et al.,
be explained by ongoing crystallization of amorphous ice 1995), since although SW1 is too distant for H2O ice sub-
in the interior of the porous nucleus, at depths of a few tens limation, its surface is too hot for the survival of CO ice.
of meters. According to this model, enhanced outgassing Subsequently, Klinger et al. (1996) showed by model cal-
results from the release of trapped gas during crystalliza- culations that the CO production pattern can be explained
tion of the ice. The orbital point where the gas flux reaches and simulated by gas trapped in the amorphous ice and
its peak was found to be strongly dependent upon the po- released from the ice upon crystallization. The chaotic be-
rosity of the comet nucleus. Thus, for example, in the case havior results from the highly nonlinear temperature depen-
of a spherical nucleus of porosity ~0.5 (Prialnik and Bar- dence of the processes involved.
Nun, 1990), crystallization is found to occur on the out- 4.6.4. Distant activity of Comet Hale-Bopp. Comet
bound leg of Comet P/Halley’s orbit, at heliocentric dis- Hale-Bopp (C/1995 O1) was characterized by an unusually
tances between 5 and 17 AU (depending on the pore size bright coma at a distance of about 7 AU from the Sun.
assumed, typical pore sizes being 0.1–10 µm). Similar re- Observations performed by Jewitt et al. (1996) detected a
sults were obtained by Schmitt et al. (1991). The duration very large flux of CO molecules, which increased dramati-
of an outburst is the most difficult to predict: Depending cally. Such brightening is unlikely to have resulted from
on the pore size and on the mechanical properties of the surface (or subsurface) sublimation of CO ice in response
ice, it may vary over three orders of magnitude. A time span to insolation. In any case, CO ice should have been depleted
of a few months lies within this range and is therefore pos- much earlier in the orbit, since at 7 AU the surface tem-
sible to obtain for a suitable choice of parameters. perature is already above 100 K, considerably higher than
4.6.2. Preperihelion activity of 2060 Chiron. Chiron, the sublimation temperature of CO. In this case as well the
first classified as an asteroid, was observed to develop a unusual activity could be explained on the basis of crystal-
coma at random intervals before it reached perihelion (in lization and release of occluded CO accompanied by ejec-
1996) in its 50-year orbit. Marcialis and Buratti (1993) tion of dust entrained by the gas (Prialnik, 1999, 2002;
summarized its brightness variations: The first episode of Capria et al., 2002).
coma formation occurred in 1978, during the middle of the
decline in brightness; the second episode, in 1989, when 4.7. Early Evolution of Comets: Effect of
the coma reached vast dimensions, coincided with the maxi- Radioactivity
mal brightness. Even near aphelion Chiron underwent a
major outburst that lasted several years. Prialnik et al. Formation of comets, like star formation, is still an ob-
(1995) were able to obtain a model that agreed remarkably ject of study and thermal evolution during formation has
well with the observational data by adopting a composition barely been considered (Merk, 2003). But attempts to esti-
of 60% dust and 40% amorphous ice, occluding a fraction mate the possible effect of radioactive heating on young
0.001 of CO and assuming a low emissivity (ε = 0.25). The comet nuclei have been made in a number of different stud-
382 Comets II

ies under different assumptions and approximations [see

Prialnik and Podolak (1995) and references therein, and
more recently, De Sanctis et al. (2001) and Choi et al.
(2002) and references therein]. There is general agreement
that the long-lived radionuclides should have no or little
effect on objects below about 50 km in radius; thus 26Al is
considered as the energy source. Using again Fig. 4 as a
guide, we find by extrapolation that at a depth of 1 km the
thermal timescale of amorphous ice becomes comparable
to the decay time of 26Al, meaning that the ice may barely
be heated. It will certainly be heated at larger depths, a few
kilometers and beyond. There, eventually, the internal tem-
perature will become sufficiently high for crystallization to
set in, providing an additional internal heat source (Podolak
and Prialnik, 1997). At the same time, however, the ther-
mal timescale will decrease, crystalline ice being a much
better heat conductor than amorphous ice. In addition, if
the nucleus is sufficiently porous, the gases released upon Fig. 11. Contour plots of the relative radius r/R up to which the
crystallization will be able to escape to the outer regions nucleus core crystallizes due to radiogenic heating during forma-
of the nucleus and will carry the heat away efficiently. tion by accretion. From Merk (2003).
Hence, only in still larger comet nuclei (beyond 10 km) will
the internal temperature continue to rise.
If the internal temperature becomes such that the layers of the nucleus. This will reduce the porosity in those
timescale of sublimation is shorter than the timescale of layers and enrich them in condensed volatiles. As the comet
radiogenic heat release, then most of the released energy nears the Sun and the outer layers heat up, these gases will
will be absorbed in sublimation of ice from the pore walls, be released and the comet will show enhanced activity.
starting with the most volatile species. If, in addition, the
radius is such that the timescale of gas (vapor) diffusion is 5. CONCLUSIONS AND DIRECTIONS
lower than the timescale of sublimation, then sublimation FOR FUTURE WORK
will consume the radiogenic heat so long as there is ice,
since the vapor will be efficiently removed. A steady state 5.1. General Conclusions
will develop, without further heating of the ice matrix.
Regarding H2O, it is worth mentioning that the tempera- In spite of the sparse information regarding the cometary
ture of such a steady state would be considerably lower than interior, the complexity of the processes that may take place
the melting temperature of ice. On the other hand, if the within them, and the uncertainties involved, the general
porosity of the ice is very low and the average pore size conclusion that emerges from simulations of the evolution
very small, τgas may become sufficiently high for gas re- of comet nuclei is that, essentially, a nucleus model of
moval to become inefficient. In such cases the internal tem- porous, grainy material, composed of gas-laden amorphous
perature may rise to the melting point of ice (cf. Yaboushita, ice and dust, is capable of reproducing the activity pattern
1993; Podolak and Prialnik, 2000). of comets. Three types of cometary activity, all associated
Calculations of the long-term evolution of comets far with the flow of volatiles through and out of a porous
from the Sun under the influence of radioactive heating nucleus, are identified. They have observable outward mani-
show that the internal temperatures attained may be suffi- festations on the one hand, and lasting effects on the struc-
ciently high for comets to have become depleted of volatiles ture of the nucleus on the other.
that sublimate below ~40–50 K, initially included as ices 1. Sublimation of volatiles from the pore walls and the
(De Sanctis et al., 2001; Choi et al., 2002). Less-volatile subsequent flow of vapor is the source of gas for the coma
species may have been partly lost as well. Observation of and tail, but may also lead to the formation of a dense ice
such volatiles in comets suggests that they originate from crust below the surface of the nucleus. Gases flowing to the
amorphous H2O ice undergoing crystallization. This means interior may refreeze when reaching sufficiently cold re-
that, despite radioactive heating, a substantial fraction of the gions, at depths correlated with the volatility of the gas. The
H2O ice has retained its pristine form, i.e., the innermost resulting effect is a stratified nucleus configuration.
region is crystalline, and the outer region is composed of 2. Crystallization of amorphous ice, accompanied by the
amorphous ice. Figure 11 shows the relative radius of the release of heat as well as trapped gases, may account for
inner part of the nucleus that has crystallized during early cometary outbursts and may also result in fracture of the
evolution, as a function of the comet’s radius and distance porous material.
from the Sun (Merk, 2003). 3. Drag of dust grains by the flowing gas leads to ejec-
Although much of the released gas will escape the tion of the small particles seen in the dust coma and tail,
nucleus entirely, some will become trapped in the cold outer while accumulation of the large particles on the surface of
 Prialnik et al.: Modeling Comet Nuclei 383

ing crucial (or critical) parameters. As a result, explanations

for observed behavior may be ambiguous; i.e., different
parameter combinations, within the same model, may lead
to similar results. Consequently, additional input is required
both from laboratory studies and from observations.
The input required from laboratory studies includes
(1) pressure curves at low temperatures, (2) latent heat meas-
urement, (3) thermal conductivity of mixtures, and (4) sub-
limation studies of mixtures. From observations we need
more information on dynamical properties (spin axis, rota-
tion period, orientation, and shape of nucleus). It would be
interesting to determine and understand whether a potato,
rather than spherical, shape is typical of small bodies of
negligible self-gravity. Upcoming in situ measurements
should provide information about the porous structure —
porosity and pore size — as well as strength. The interplay
among the different methods of research applied to comet-
Fig. 12. Schematic layered structure of a cometary nucleus (ar- ary nuclei is illustrated in Fig. 13.
bitrary scales). From Prialnik (1999).
5.3. Where Do We Go from Here?

In the course of this review we have mentioned a rather

the nucleus may lead to the formation of a sealing dust man- long list of assumptions that are common to most theoreti-
tle that would turn the comet into an asteroid-like object. cal studies to date. Simplifying assumptions are justified
In conclusion, the thermal evolution and activity pattern when a theory is still young and ridden by uncertainties.
of a porous comet nucleus differs significantly from the old Now that it has matured, we may safely enter the next stage,
view of a solid icy body that is mainly controlled by sub- where more sophisticated methods and models should be
limation from the surface in response to solar heating. The developed. We suggest a few below, following the order of
structure that emerges is shown schematically in Fig. 12. the review’s sections. In some cases, first steps have already
The thermal evolution of comet nuclei may be divided been taken.
into two phases: a long phase — of the order of the solar 5.3.1. Numerical methods. (1) Use of adaptive grid
system’s age — spent at large distances from the Sun (in methods for dealing with receding surfaces during late evo-
the Oort cloud or the Kuiper belt), and a second, much lution, as well as growing mass during very early stages.
shorter phase, spent in orbit around the Sun within the plan- (2) Development of full-scale 3-D models that allow for
etary system. There is, of course, an intermediate, transient lateral flow both of heat and of gas. (3) Inclusion of bound-
phase during which a periodic comet is gradually perturbed ary conditions accounting for the nucleus-coma interaction.
into its final, steady orbit. The notion that the thermal evo- (4) Implementation of modern methods for the simulta-
lution process really begins when a comet enters the sec- neous solution of a multiple component nucleus.
ond phase of its life, becoming a “new” comet, is beginning
to be doubted. New comets, which have often been de-
scribed as pristine objects that have undergone no (or little)
alteration during their lifetime in the distant outskirts of the
solar system, are now suspected to have been heated to the
point of melting of the H2O ice. Nevertheless, they are still
believed to constitute a source of solar nebula material.
Much of the fascination and interest comets have aroused
was due to the clues they were believed to hold to the for-
mation of the solar system. This may still be true, at least
for a fraction of comets, or for a fraction of every comet.
In addition, comets are now invoked to explain the forma-
tion of life.

5.2. Required Input Data from Observations

and Experiments

The success of the thermal evolution theory just de-

scribed in explaining the structure and activity of comet Fig. 13. The role of nucleus models in the coordinated study of
nuclei is hindered by the huge lack of information regard- comets.
384 Comets II

5.3.2. Physical processes. (1) Coupling between gas ice analogs in vacuo. Science, 245, 58–551.
phases and rigorous treatment of mixtures. (2) Construction Bouziani N. and Fanale F. P. (1998) Physical chemistry of a het-
of models for fracture and for crack propagation. (3) Treat- erogeneous medium: Transport processes in comet nuclei.
ment of surface properties, such as irregularities, shadow- Astrophys. J., 499, 463–474.
Brailsford A. and Major K. G. (1964) The thermal conductivity
ing, and mixed thermal properties, as well as radiative
of aggregates of several phases, including porous materials. Br.
transfer in the outermost porous layer (e.g., Davidsson and
J. Appl. Phys., 15, 313.
Skorov, 2002a,b). (4) Modeling of the material structure of Brin G. D. and Mendis D. A. (1979) Dust release and mantle
the dust mantle on the nucleus surface. development in comets. Astrophys. J., 229, 402–408.
5.3.3. Modeling the evolution of comet nuclei. (1) Mod- Campins H., Telesco C. M., Osip D. J., Rieke G. H., Rieke M. J.,
eling comet formation by accretion. (2) Long-term evolu- and Schulz B. (1994) The color temperature of (2060) Chiron:
tion over the age of the solar system, considering potential A warm and small nucleus. Astron. J., 108, 2318–2322.
gravitational interactions and orbital evolution. (3) Model- Capria M. T., Coradini A., De Sanctis M. C., and Orosei R. (2000)
ing comet ⇔ asteroid transition (e.g., Coradini et al., Chiron activity and thermal evolution. Astron. J., 119, 3112–
1997a). (4) Modeling nucleus shape evolution as a result 3118.
of uneven ablation. Capria M. T., Coradini A., De Sanctis M. C., and Bleckai M. I.
(2001) P/Wirtanen thermal evolution: Effects due to the pres-
The purpose of modeling comet nuclei is not to predict
ence of an organic component in the refractory material. Planet.
their behavior based on an initial set of parameters. Given
Space Sci., 49, 907–918.
the large number of parameters and their wide range of Capria M. T., Coradini A., and De Sanctis M. C. (2002) C/1995
possible values, predictions may be misleading. Rather, the O1 Hale-Bopp: Short and long distance activity from a theo-
true purpose of modeling is to reproduce the observed retical model. Earth Moon Planets, 90, 217–225.
cometary behavior, in order to deduce internal properties Choi Y.-J., Cohen M., Merk R., and Prialnik D. (2002) Long-term
of comet nuclei that are inaccessible to observation. The evolution of objects in the Kuiper belt zone — effects of insola-
closer the numerical simulations are to observed reality, the tion and radiogenic heating. Icarus, 160, 300–312.
more reliable will be our inferences on the elusive nature Cohen I. B. and Whitman A. (1999) Isaac Newton — The Prin-
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for the evolution of shape and temperature distribution of
ginning of life as well. In the words of Isaac Newton: “I
comet nuclei — application to Comet 46P/Wirtanen. New
suspect that the spirit which is the smallest but most subtle
Astron., 8, 179–189.
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388 Comets II
PART V:
THE GAS COMA
 Bockelée-Morvan et al.: The Composition of Cometary Volatiles 391

The Composition of Cometary Volatiles

D. Bockelée-Morvan and J. Crovisier
Observatoire de Paris

M. J. Mumma
NASA Goddard Space Flight Center

H. A. Weaver
The Johns Hopkins University Applied Physics Laboratory

The composition of cometary ices provides key information on the chemical and physical
properties of the outer solar nebula where comets formed, 4.6 G.y. ago. This chapter summa-
rizes our current knowledge of the volatile composition of cometary nuclei, based on spectro-
scopic observations and in situ measurements of parent molecules and noble gases in cometary
comae. The processes that govern the excitation and emission of parent molecules in the radio,
infrared (IR), and ultraviolet (UV) wavelength regions are reviewed. The techniques used to
convert line or band fluxes into molecular production rates are described. More than two dozen
parent molecules have been identified, and we describe how each is investigated. The spatial
distribution of some of these molecules has been studied by in situ measurements, long-slit IR
and UV spectroscopy, and millimeter wave mapping, including interferometry. The spatial dis-
tributions of CO, H2CO, and OCS differ from that expected during direct sublimation from
the nucleus, which suggests that these species are produced, at least partly, from extended sources
in the coma. Abundance determinations for parent molecules are reviewed, and the evidence
for chemical diversity among comets is discussed.

1. INTRODUCTION ucts are called daughter products. Although there have been
in situ measurements of some parent molecules in the coma
Much of the scientific interest in comets stems from their of 1P/Halley using mass spectrometers, the majority of re-
potential role in elucidating the processes responsible for the sults on the parent molecules have been derived from remote
formation and evolution of the solar system. Comets formed spectroscopic observations at ultraviolet (UV), infrared (IR),
relatively far from the Sun, where ices can condense, and and radio wavelengths. The past decade has seen remark-
the molecular inventory of those ices is particularly sensi- able progress in the capabilities at IR and radio wavelengths,
tive to the thermochemical and physical conditions of the in particular, and over two dozen parent cometary molecules
regions in the solar nebula where material agglomerated into have now been detected. Many new identifications were
cometary nuclei. An important issue is the extent to which obtained in Comet C/1996 B2 (Hyakutake), which passed
cometary ices inherited the molecular composition of the within 0.1 AU of Earth in March 1996, and in the excep-
natal presolar dense cloud vs. the role of subsequent chem- tionally active Comet C/1995 O1 (Hale-Bopp). We discuss
istry and processing in the solar nebula (Irvine et al., 2000a; how each of these molecules was identified, how the spec-
Ehrenfreund et al., 2004; Lunine and Gautier, 2004). troscopic data are used to derive abundances, and we de-
Though a variety of subtle evolutionary mechanisms oper- scribe the abundance variations observed among comets.
ated for cometary nuclei during their long storage in the We also discuss our current knowledge of the noble gas
Oort cloud and Kuiper belt (Stern, 2003) and, for short- abundances in cometary nuclei, as these are potentially diag-
period comets, during their many passages close to the Sun, nostic of the role played by cometary bombardment on the
the bulk composition of cometary nuclei is still regarded to formation and evolution of planetary atmospheres. Noble gas
be in large part pristine, except possibly for the most vola- abundances are also key indicators of the temperature con-
tile ices. Thus, observing comets today provides a window ditions and condensation processes in the outer solar nebula.
through which we can view an earlier time when the planets The spatial distribution of several molecules has been in-
were forming. vestigated in situ, by IR and UV long-slit spectroscopy, and
In this chapter, we discuss our current knowledge of the by radio mapping. We present observational evidence for
composition of cometary nuclei as derived from observa- the presence of extended sources of molecules in the coma.
tions in cometary comae of molecular species that subli- The brightness distribution and velocity shifts of radio emis-
mate directly from the nucleus. In the common cometary sion lines are diagnostic of the outgassing pattern from the
terminology, which will be used here, these species are nucleus, and recent results obtained by millimeter interfer-
called parent molecules, while their photodestruction prod- ometry are presented.

391
392 Comets II

Isotopic abundances often provide important insights into ing the surface of Earth, cometary UV investigations are
the evolutionary history of matter, and we discuss the vari- generally conducted from space platforms.
ous isotopic data that have been obtained for cometary par- Most parent molecules have strong fundamental bands
ent molecules. of vibration in the 2.5–5 µm region, where there is abun-
For molecules having at least two identical nuclei, the dant solar flux for exciting infrared fluorescence and where
internal energy levels are divided into different spin spe- thermal radiation and reflected sunlight from dust is not
cies (ortho and para in the simplest case), and we discuss very strong. This near-IR spectral region, which is partly
how the observed distribution among these spin species may accessible from Earth-based observations, has been a rich
provide information on the formation temperature of comet- source of molecular identifications in cometary comae. The
ary nuclei. first high-spectral-resolution measurements (λ/δλ ~ 105–
106) in this region were made during observations of Comet
2. INVESTIGATION OF 1P/Halley from the NASA Kuiper Airborne Observatory
PARENT MOLECULES (KAO) in 1985. The entire region was explored at modest
spectral resolution by the Infra Krasnoe Spectrometre (IKS)
2.1. Daughter Products instrument onboard the Vega probe to 1P/Halley (λ/δλ ~ 50)
and, more recently, by the Infrared Space Observatory (ISO)
Most of the cometary species observed at optical and UV observations of Comet Hale-Bopp and 103P/Hartley 2 (λ/
wavelengths are radicals, atoms, and ions that do not sub- δλ ~ 1500). The advent of sensitive, high-dispersion spec-
limate directly from the nucleus but are instead produced trometers at the NASA Infrared Telescope Facility (IRTF)
in the coma, usually during the photolysis of the parent and Keck telescopes revolutionized this field. Their spec-
molecules, but also by chemical reactions. The discussion tral resolving power (~20,000) allows resolution of the ro-
of these secondary species in cometary comae is covered tational structure of the vibrational bands, which is very
in this book by Feldman et al. (2004). The only exception important for investigating the internal excitation of the mol-
is that CO Cameron band emission, some of which is pro- ecules and for unambiguously identifying molecules in the
duced in a prompt process following the photodissociation spectrally confused 3.3–3.6 µm region, where the funda-
of CO2, is discussed below. mental C–H stretching vibrations lie for all hydrocarbons.
Infrared spectroscopy is particularly useful for studying
2.2. Mass Spectrometry symmetric molecules, which do not have permanent electric
dipole moments and thus cannot be observed in the radio
The Giotto spacecraft, which flew by 1P/Halley in March range.
1986, was equipped with two mass spectrometers suitable Radio spectroscopy is a powerful technique for studying
for composition measurements: the Neutral Mass Spec- molecules in cold environments via their rotational transi-
trometer (NMS) and the Ion Mass Spectrometer (IMS). tions. This technique has produced many discoveries of com-
These two instruments had a mass resolution of 1 amu/q etary parent molecules and is more sensitive than IR and
and mass ranges of 12–50 and 1–57 for NMS and IMS, UV spectroscopy for comets observed at large heliocentric
respectively. The Positive Ion Cluster Composition Analyser distances. With a few exceptions, observations have been
of the Rème Plasma Analyser also had some capabilities made in the 80–460 GHz frequency range from ground-
for studying ions in the 12–100 amu/q range. These instru- based telescopes. The Submillimeter Wave Astronomy Sat-
ments provided much new information on the molecular and ellite (SWAS) and the Odin satellite, which observed the
isotopic composition of cometary volatiles, as detailed in 557 GHz H2O rotational line in several comets, initiated
section 5 and section 9. However, the analyses of these data investigations of submillimetric frequencies not observable
were not straightforward, owing to the limited mass reso- from Earth. Radio spectrometers provide high spectral reso-
lution and the need for detailed chemical modeling to de- lution (λ/δλ ~ 106–107), which permits investigations of gas
duce neutral abundances from the ion mass spectra (see kinematics through line profile measurements (typical com-
review of Altwegg et al., 1999, and references therein). etary line widths are ~2 km s–1), and which eliminates most
ambiguities related to line blending, galactic confusion, or
2.3. Spectroscopy instrumental effects. Most detected molecules were ob-
served in several lines, thereby securing their identification.
Most electronic bands of cometary parent molecules fall
in the UV spectral region. As discussed in section 3.1.2, the 3. EXCITATION PROCESSES:
electronic states of polyatomic molecules usually predisso- LINE/BAND INTENSITIES
ciate, so the absorption of UV sunlight by these species
leads to their destruction rather than fluorescence. As a re- 3.1. Overview: Main Processes
sult, the UV study of cometary parent molecules reduces to
investigations of diatomic molecules (e.g., CO and S2) and The interpretation of line or band intensities of parent
the atoms present in nuclear ices, specifically noble gases. molecules in terms of column densities and production rates
Since the terrestrial atmosphere blocks UV light from reach- requires the knowledge of the processes that govern their
 Bockelée-Morvan et al.: The Composition of Cometary Volatiles 393

excitation and emission in the coma. Two kinds of excita- Einstein coefficients Av'v" in the range 10–100 s–1, and band
tion mechanisms can be distinguished: radiative processes excitation rates gv"v' of a few 10–4 s–1. Harmonic and com-
and collisional excitation. bination bands have intrinsic strengths, and thus excitation
3.1.1. Radiative vibrational excitation. For most parent rates, much smaller than those of the fundamental bands.
molecules, the main radiative excitation process is radiative The pumping from excited vibrational states is also weak.
excitation of the fundamental bands of vibration by direct Indeed, their population is negligible with respect to the
solar radiation (Mumma, 1982; Yamamoto, 1982; Crovisier population of the ground vibrational state. This can be dem-
and Encrenaz, 1983; Weaver and Mumma, 1984). The pump- onstrated easily. If we ignore collisional excitation, which
ing rate glu (s–1) for an individual ro-vibrational transition is negligible for vibrational bands as explained in sec-
l → u is given by tion 3.1.5, and do not consider possible deexcitation of the
v' excited state to vibrational states other than the ground
c3 wu state (this corresponds to pure resonant fluorescence), then
glu = Aul J(νul) (1)
8πhν3ul wl the population nv' of this v' band at equilibrium between
solar pumping and spontaneous decay is
where the lower level l belongs to the v" vibrational state
(v" = 0 for fundamental bands), and the upper level u be-
gv"v'
longs to the excited v' vibrational state. νul is the frequency nv' = nv" (4)
of the transition, wl and wu are the statistical weights of the Av'v"
lower and upper levels, respectively, and Aul is the sponta-
neous emission Einstein coefficient for u → l. J (νul) is the where nv" is the population of the ground vibrational state
energy density per unit frequency of the radiation field at v" = 0. Combining equations (3) and (4), nv' /nv" only de-
the frequency νul. The solar radiation in the infrared can pends upon the frequency of the band and heliocentric dis-
be described approximately by a blackbody at Tbb = 5770 K tance r, and is equal to a few 10 –6 at 1 AU from the Sun
and having solid angle Ωbb (Ωbb /4π = 5.42 10 –6 r –2, where for most bands. It can be also shown that the timescale for
r is the heliocentric distance in AU). Then equilibration of this excited v' vibrational state is 1/Av'v",
typically a fraction of second: The total vibrational popu-
Ωbb wu lations reach radiative equilibrium almost instantly after
glu = Aul(ehνul/kTbb – 1) –1 (2)
release of the molecules from the nucleus. For the same rea-
4π wl
sons (low populations and small radiative lifetimes), steady-
The band excitation rate gv"v', which is the relative number state is achieved locally for the rotational levels within the
of molecules undergoing vibrational v" → v' excitation vibrational excited states. As will be discussed later, this is
through all possible l → u transitions within the (v',v") band generally not the case for the rotational levels in the ground
at frequency νv'v", can be approximated by (Crovisier and vibrational state.
Encrenaz, 1983) Besides the direct solar radiation field, the vibrational
bands can be radiatively excited by radiation from the nu-
Ωbb cleus and the dust due to scattering of solar radiation or
gv"v' = Av'v"(ehνv'v"/kTbb – 1) –1 (3)
4π their own emission in the thermal infrared. Crovisier and
Encrenaz (1983) showed that all these processes are negli-
Av'v" is the band spontaneous emission Einstein coeffi- gible, except excitation due to dust thermal emission, which
cient, which can be related to the total band strength meas- can be important in the inner comae of active comets for
ured in the laboratory. Practically, the individual spontaneous vibrational bands at long wavelengths (>6.7 µm).
emission rates Aul required to compute the individual excita- 3.1.2. Radiative electronic excitation. The electronic
tion rates glu (equation 2) can be derived from absorption bands of diatomic and polyatomic molecules fall in the UV
line intensities measured in the laboratory. The HITRAN range. Owing to the weak solar flux at these wavelengths,
(Rothman et al., 2003) and GEISA (Jacquinet-Husson et al., the excitation rates of electronic bands are small compared to
1999) databases list absorption line intensities and frequen- vibrational excitation rates. For example, the total excitation
cies for ro-vibrational and pure rotational transitions of many rate of the A1Π state of CO by the absorption of solar pho-
molecules. More extensive databases for pure rotational tran- tons near 1500 Å, which leads to resonance fluorescence in
sitions are those of the Jet Propulsion Laboratory (Pickett the CO A1Π–X1Σ+ Fourth Positive Group, is ~1–2 × 10 –6 s–1
et al., 1998) and the University of Cologne (Müller et al., at r = 1 AU (Tozzi et al., 1998). The latter is roughly two
2001). For linear or symmetric-top molecules without elec- orders of magnitude smaller than the excitation rate by solar
tronic angular momentum, simple formulae approximate the radiation of the CO v(1–0) band at 4.7 µm [2.6 × 10 –4 s–1
Aul and glu quantities as a function of the total band Einstein at 1 AU (Crovisier and Le Bourlot, 1983)]. Therefore, the
coefficient Av'v" and excitation rate gv"v', and the rotational populations of the ground state rotational levels are not sig-
quantum numbers (Bockelée-Morvan and Crovisier, 1985). nificantly affected by electronic excitation. In addition, elec-
Typically, the strongest fundamental vibrational bands of tronic bands of polyatomic molecules are often dissociative
cometary parent molecules have spontaneous emission or predissociative, and their excitation by the Sun generally
394 Comets II

only produces weak UV fluorescence. This explains why

cometary parent molecules are rarely identified from their
electronic bands in UV spectra. The resonance transitions of
neutral atoms, including the noble gases that may be present
in the nucleus, are at UV and far UV (FUV) wavelengths,
but the excitation rates are relatively small because of the
low solar flux in these regions. The electronic excitation of
CO and S2, as observed in UV cometary spectra, is reviewed
in section 3.4. The computation of electronic excitation rates
does not differ much in principle from that of vibrational
excitation rates. However, in the UV range the solar spec-
trum shows strong and narrow Fraunhofer absorption lines,
and cannot be approximated by a blackbody. This fine struc-
ture results in absorption probabilities that depend on the
comet’s heliocentric radial velocity, as first pointed out by
Swings (1941) for the CN radical. This so-called Swings ef-
fect can introduce large variations in the fluorescence emis-
sion spectrum of electronic bands.
3.1.3. Radiative rotational excitation and radiation trap-
ping. Pure rotational excitation by sunlight is negligible
because of the weakness of the solar flux at the wavelengths
of the rotational transitions. However, at r > 3 AU, rotational
excitation by the 2.7 K cosmic background radiation com-
petes with vibrational excitation (which varies according to
r–2), and must be taken into account in fluorescence calcu-
lations (Biver et al., 1999a).
In the specific case of the H2O molecule, the rotational
excitation is strongly affected by self-absorption effects.
Owing to large H2O densities in the coma, many rotational
H2O lines are optically thick and trap line photons emitted Fig. 1. (a) Rotational population distribution of HCN as a func-
by nearby H2O molecules. This was modeled by Bockelée- tion of distance to nucleus for a comet at 1 AU from the Sun with
Morvan (1987) in the local approximation, using an escape Q(H2O) = 1029 molecules s–1 (from the model of Biver et al.,
probability formalism. The net effect of radiation trapping is to 1999a). (b) H2O local density n(H2O), electronic density ne and
delay the radiative decay of the rotational levels to the lower temperature Te in the model. The gas kinetic temperature is 50 K
states and to maintain local thermal equilibrium at a lower throughout the coma. The population distribution evolves from
thermal equilibrium in the inner coma, to fluorescence equilib-
density than would have been required in optically thin con-
rium in the outer coma. The discontinuities at 2 × 103 km are due
ditions (Weaver and Mumma, 1984; Bockelée-Morvan,
to the sharp rise of the electron temperature, from 50 to 10,000 K.
1987). The lower rotational states of H2O are affected by this
process up to distances of a few 10 4 km when the H2O pro-
duction rate Q(H2O) is ~1029 molecules s–1.
3.1.4. Fluorescence equilibrium. When the excitation efficient. The timescale for rotational equilibration, which
is determined solely by the balance between solar pump- is mainly controlled by pure rotational relaxation for mole-
ing and subsequent spontaneous decay, this establishes a cules having a nonzero electric dipole moment (vibrational
condition called fluorescence equilibrium. For the rotational relaxation is more rapid), exceeds 10 4 s for most detected
levels within the ground vibrational state, fluorescence equi- molecules. Some molecules never reach equilibrium during
librium is reached in the outer, collisionless coma. For mole- their lifetime.
cules with large dipole moments (µ) and large rotational 3.1.5. Collisional excitation. Collisions, generally in-
constants, such as H2O (µ = 1.86 D) or HCN (µ = 2.99 D), volving H2O molecules and/or electrons, are important in
infrared excitation rates are generally small compared to the determining the rotational excitation of molecules in the
vibrational and rotational Einstein A-coefficients, so that inner coma. For comets at large heliocentric distances, where
most of the molecules relax to the lowest rotational levels the CO production rate is much larger than the H2O produc-
of the ground vibrational state (Fig. 1). Heavy molecules tion rate, collisional excitation is provided by CO. Collisions
with small dipole moment (e.g., CO with µ = 0.11 D) and with ions are generally considered to be unimportant for
symmetric species will have, in contrast, a warm rotational parent molecules, but this question has not yet been prop-
distribution at fluorescence equilibrium. The rotational erly addressed.
population distribution gets colder as the comet moves far Owing to the low temperatures throughout the inner coma
from the Sun because vibrational excitation becomes less [10–100 K (cf. Combi et al., 2004)], collisions do not signi-
 Bockelée-Morvan et al.: The Composition of Cometary Volatiles 395

ficantly populate either the vibrational or electronic levels lar excitation by e––H2O collisions exceeds that by H2O–
of molecules, and the steady-state vibrational and electronic H2O collisions at cometocentric distances >3000 km from
population distributions are determined by radiative pro- the nucleus. Neutral H2O collisions dominate in the inner
cesses. Collisions can quench the fluorescence of vibrational coma because the n(H2O)/n(e–) local density ratio is very
bands, but this is generally unimportant, except possibly large (Fig. 1). Observational evidence for the important role
within a few kilometers of the surface of the nucleus (Cro- played by collisions with electrons is now abundant [e.g.,
visier and Encrenaz, 1983; Weaver and Mumma, 1984). Biver et al. (1999a) for the excitation of HCN]. So far, the
Collisions thermalize the rotational population of the modeling of this process is subject to large uncertainties,
ground vibrational state at the kinetic temperature of the as the electron density and temperature in the coma are not
gas. The collision rate C (s–1) is given by well-known quantities. Figure 1 shows an exemple of the
electron density and temperature profiles used by Biver et
C = σcn(rc)v (5) al. (1999a) for modeling excitation by collisions with elec-
trons. These profiles are based on measurements made in
where σc is the collision cross-section, n(rc) is the local situ in Comet Halley, and the dependences with H2O pro-
density of the collision partner at the cometocentric distance duction rate and heliocentric distance expected from theo-
rc, and v is the relative speed of the impinging species. To retical modeling.
treat collisional excitation properly, we must understand 3.1.6. Non-steady-state calculations. The evolution
how collisions connect individual rotational states, that is, of the population distribution with distance to the nucleus
specify the collision cross-sections σij for each i → j tran- has been studied for a number of molecules: CO (Chin
sition. However, there is little experimental or theoretical and Weaver, 1984; Crovisier and Le Bourlot, 1983), H2O
information on collisional processes involving neutral mol- (Bockelée-Morvan, 1987), HCN (Bockelée-Morvan et al.,
ecules (H2O or CO). Not only are the line-by-line cross- 1984), H2CO (Bockelée-Morvan and Crovisier, 1992),
sections not available, but the total cross-sections for colli- CH3OH (Bockelée-Morvan et al., 1994), and linear mole-
sional deexcitation, which could, in principle, be derived cules (Crovisier, 1987). Collisional excitation by electrons
from laboratory measurements of line broadening, are poorly was included in more recent works (e.g., Biver et al., 1999a).
documented for most cometary species. In current cometary These studies solve the time-dependent equations of statis-
excitation models, total cross-sections of ~1–5 ×10 –14 cm2 tical equilibrium, as the molecules expand in the coma
are assumed (e.g., Chin and Weaver, 1984; Bockelée-Morvan,
1987; Crovisier, 1987; Biver et al., 1999a), based on the
∑p ∑n p
dni
broadening of CO and H2O lines by collisions with H2O. = −ni ij + j ji (6)
Chin and Weaver (1984) introduced a ∆J dependence on dt j≠i j≠i
the rotational CO–H2O cross-sections and pointed out that
collisional excitation of CO is rather insensitive to this de- where the transition rate pij from level i to j, of energy Ei
pendence as long as the total cross-section is fixed. and Ej respectively, may involve collisional excitation (Cij),
The role of electron collisions in controlling rotational radiative excitation (gij), and/or spontaneous decay (A ij)
populations was first investigated in detail by Xie and terms. If we omit radiation trapping effects
Mumma (1992) for the H2O molecule. This study was moti-
vated by the need for large cross-sections to interpret the pij = Cij + gij if Ei < Ej (7)
relative line intensities of the ν3 H2O band in Comet 1P/
Halley observed preperihelion with the KAO. It was previ- pij = Cij + Aij if Ei > Ej (8)
ously recognized that, in the inner coma, inelastic collisions
with H2O would cool hot electrons to the temperature of The coupled differential equations (equation (6)) are
the gas, transferring their translational energy into rotational “stiff”, as they contain rates with time constants differing
H2O excitation (Ashihara, 1975; Cravens and Korosmezey, by several orders of magnitude, and their solution requires
1986). Unlike neutral-neutral collisions, theoretical determi- special techniques, such as the Gear method (cf. Chin and
nations of rotational cross-sections are available for colli- Weaver, 1984). In contrast, the fluorescence equilibrium
sions involving electrons. Relatively simple formulae were solution can be simply computed by matrix inversion.
obtained using the Born approximation by Itikawa (1972), Figure 1 shows the evolution of the population of the
which show that cross-sections are directly proportional to lowest rotational levels of the HCN molecule with distance
the rotational Aul of the transitions and are also a function to the nucleus. At some distance in the coma, collision exci-
of the kinetic energy of the colliding electrons. Cross-sec- tation can no longer compete with rotational spontaneous
tions are large for molecules with large dipole moments decay, and the population distribution evolves to fluores-
(Aul ∝ µ2), typically exceeding those for neutral-neutral cence equilibrium. Because radiative lifetimes vary among
collisions by two or three orders of magnitude for electrons the levels, the departure from local thermal equilibrium
thermalized at 50 K. Using the electron temperature and (LTE) occurs separately for each rotational level. The size
density profile measured in situ by Giotto, Xie and Mumma of the LTE region also varies greatly among molecules, as
(1992) showed that, for a Halley-type comet, the molecu- shown in Crovisier (1987), where the evolution of the rota-
396 Comets II

tional population distribution is computed for a number of lar column density that is related to the molecular produc-
linear molecules. Molecules with small dipole moments tion rate (section 4).
(e.g., CO) have long rotational lifetimes and correspondingly In the radio domain, line intensities are usually expressed
larger LTE regions. Symmetric molecules with no dipole in term of equivalent brightness temperatures TB, where TB
moment, such as CO2, cannot relax to low rotational levels; is related to Ful through the Rayleigh-Jeans limit (hν << kT)
high rotational levels become more and more populated as of the Planck function. The line area integrated over velocity
the molecules expand in the coma. in K km s–1 is then related to the column density through
Low-lying rotational levels maintain thermal populations
up to a few 103 km from the nucleus in moderately active hc3Aul
comets (QH2O ≈ 1029 molecules s–1) near 1 AU from the ∫ TBdv =
8πkν2ul
〈Nu〉 (10)
Sun. This implies that the thermal approximation is a good
one to describe the rotational structure of vibrational bands In most observational cases, radio antennas are sensitive
observed by long-slit spectroscopy (section 3.3). On the to molecules present in the intermediate region between
other hand, the thermal equilibrium approximation may not thermal and fluorescence equilibrium. Time-dependent ex-
be valid for the interpretation of rotational line emission citation models, as described in section 3.1.6, are thus re-
observed in the radio range, owing to the large beam size quired to derive 〈N〉 from the observed line area ∫ TBdv.
of radio antennas. Because these models rely on ill-known collisional excita-
tion parameters (section 3.1.5), observers try, as much as
3.2. Rotational Line Intensities possible, to observe several rotational lines of the same
molecule. This permits them to determine the rotational
When rotational lines are optically thin and spontane- temperature that best describes the relative population of
ous emission dominates over absorption of the continuum the upper states, given the observed line intensities. The
background and stimulated emission, their line flux Ful (in inferred rotational temperature can then be compared to that
W m–2 or Jy km s–1) is given by predicted from modeling, thereby constraining the free
parameters of the model. Methanol has multiplets at 165
Ω and 157 GHz that sample several rotational levels of same
Ful = hνulAul〈Nu〉 (9)
4π quantum number J. Their observations are particularly use-
ful, as the rotational temperature derived from these lines
where Ω is the solid angle subtended by the main beam of is similar to the kinetic temperature in the collisional re-
the antenna. (The diffraction-limited beam pattern of circular gion (Bockelée-Morvan et al., 1994; Biver et al., 1999a,
radio antennae is well approximated by a two-dimensional 2000). This is also the case of the 252-GHz lines shown in
gaussian, which width at half power defines the main-beam Fig. 2. Other series of lines (e.g., the 145- or 242-GHz
solid angle.) 〈Nu〉 is the column density within the upper multiplets of CH3OH, or the HCN lines) exhibit rotational
transition state u, and is obtained by volume integration over temperatures that are intermediate between the kinetic tem-
the beam pattern of the density times the fractional popu- perature of the inner coma and the rotational temperature
lation in the upper state. When nu is constant within the at fluorescence equilibrium. These lines can be used to
beam, 〈Nu〉 is equal to nu〈N〉, where 〈N〉 is the total molecu- constrain the collision rates. Constraints can also be ob-

Fig. 2. Wideband spectrum of Comet Hale-Bopp observed on February 21.7, 1997 at the CSO showing twelve J3–J2 A lines of CH3OH,
the 56–45 line of SO, and, in the image sideband at 254.7 GHz, the J(28–27) line of HC3N (Lis et al., 1999).
 Bockelée-Morvan et al.: The Composition of Cometary Volatiles 397

tained from observations at offset positions from the nucleus curate derivation of the production rate. Figure 3 shows the
(Biver et al., 1999a). H2O ν3 band of H2O observed with ISO in Comet Hale-
Most rotational lines observed in comets are optically Bopp at 2.9 AU from the Sun (Crovisier et al., 1997), and
thin because of small molecular column densities. The only the synthetic spectrum that best fits the data with Trot =
exceptions encountered were the J(4–3) HCN line observed 29 K. Figure 4 shows examples of groundbased IR spectra
in C/1996 B2 (Hyakutake) (Lis et al., 1997; Biver et al., for Comets Hyakutake and C/1999 H1 (Lee) at r ~ 1 AU,
1999a) and Hale-Bopp (Meier et al., 1998b), the H2O ro- where several lines of H2O and CO are detected: From
tational lines observed with ISO in Comet Hale-Bopp (Cro- Boltzmann analyses of the line intensities, Trot was esti-
visier et al., 1997), and the 110 –101 line of H2O observed mated to ~75 K for both comets (Mumma et al., 2001b).
with the SWAS and Odin satellites in a few comets (Neufeld Opacity effects in the solar pump and for the emitted
et al., 2000; Lecacheux et al., 2003). For the H2O 110 –101 photons, if present, would affect the effective line-by-line
line, self-absorption effects result in asymmetric line shapes, infrared fluorescence emission rates and the intensity distri-
indeed observed in high-resolution spectra obtained with bution within the bands. This was investigated by Bockelée-
Odin (Lecacheux et al., 2003). Morvan (1987) for the ν2 and ν3 bands of H2O, and ac-
counted for in the determination of the ortho-to-para ratio
3.3. Intensity of Ro-Vibrational Lines and of H2O from the ISO spectra (Crovisier et al., 1997) (Fig. 3;
Vibrational Bands section 10). The opacity of the CO2 ν3 band observed by
VEGA/IKS in 1P/Halley was taken into account for accu-
As for pure rotational lines, the line flux Ful (W m–2) of rate measurement of the CO2 production rate in this comet
optically thin ro-vibrational lines u → l (u within v', l within (Combes et al., 1988). Since optical depth effects are stron-
v") is given by equation (9), where Ω is the solid angle ger in the inner coma, the spatial brightness profile of an
corresponding to the field of view. Ful can be also expressed optically thick line falls off less steeply with distance to the
as a function of the emission rate (the so-called g-factor) of nucleus than under optically thin conditions. Optical depths
the line gul = Aulnu (s–1), assuming nu to be constant within of OCS ν3 and CO v(1–0) ro-vibrational lines were evalu-
the field of view ated (Dello Russo et al., 1998; DiSanti et al., 2001; Brooke
et al., 2003), in order to investigate whether this could ex-
Ω
Ful = hνul gul〈N〉 (11) plain their relatively flat spatial brightness distributions in
4π Comet Hale-Bopp (section 7), but the effect was found to
Neglecting collisional excitation, the emission rate gul is be insignificant.
related to the fractional populations nj within the ground
vibrational state v = 0 through 3.4. Electronic Bands

∑n g
j,v = 0
j ju
The parent molecules studied via electronic bands at UV/
FUV wavelengths are CO, S2, and, indirectly, CO2 (Fig. 5).
gul = Aul
∑∑ A
(12) Two other potential constituents of the nucleus, H2 and N2,
uj can also fluoresce at UV and FUV wavelengths. H2 was
v j
recently detected during observations of two long-period
where the summation in the denominator is made over all comets with the Far Ultraviolet Spectroscopic Explorer
possible vibrational decays (v' → v = 0 and v' → v hot- (FUSE); however, the amount measured was consistent with
bands, including the v' → v = v" band to which the u → l all the H2 being derived from the photolysis of H2O, rather
transition belongs). In the righthand term of equation (12), than from sublimation of frozen H2 in the nucleus (Feldman
the gju coefficients are the excitation rates due to solar pump- et al., 2002). Further discussion of cometary H2 can be
ing defined in equation (2). Equation (12) is readily ob- found in Feldman et al. (2004). Although electronic exci-
tained by solving equation (6) for the nu population within tation of N2 usually leads to predissociation, fluorescence
v', assuming steady-state (section 3.1.1) and neglecting ro- can occur in the (0,0) band of the Carroll-Yoshino system
tational decay within v', which is much slower than vibra- (c4'1Σ+u–X1Σ+g) at 958.6 Å. Several cometary spectra were
tional decays. taken with FUSE to search for fluorescence from N2, but
The band flux is related to the total emission rate of the only upper limits were derived (P. D. Feldman, personal
band gv'v" through a formula similar to equation (11). In the communication, 2003) (see section 5.6.1).
case of pure resonance fluorescence, gv'v" is equal to the Observations of CO in the UV range are discussed in
band excitation rate gv"v' given in equation (3). section 5.2. The calculation of g-factors for the CO A–X
In most cases, individual g-factors are computed assum- bands is discussed by Tozzi et al. (1998), and g-factors for
ing LTE in the ground vibrational state. The retrieved mo- the B–X, C–X, and E–X bands are discussed by Feldman
lecular column densities (and production rates) may then et al. (2002). Generally, the Swings effect (see section 3.1.2)
depend strongly on the assumed rotational temperature. In is small for all the UV bands of CO, with g-factor varia-
Comet Hale-Bopp and other bright comets, many ro-vibra- tions of only ~20% with heliocentric radial velocity.
tional lines were observed for most molecules, allowing Emission in the CO Cameron band system near 2050 Å
measurement of the rotational temperature Trot and an ac- (a3Π–X1Σ+) was discovered during Hubble Space Telescope
398 Comets II

Fig. 3. The region of the ν3 band of water observed with the ISO short-wavelength spectrometer in Comet C/1995 O1 (Hale-Bopp)
on 27 September and 6 October 1996 (top). Line assignations are indicated. The synthetic fluorescence spectrum of water that is the
best fit to the data (bottom) corresponds to Q(H2O) = 3.6 × 1029 molecules s–1, Trot = 28.5 K and OPR = 2.45. Adapted from Crovisier
et al. (1997).

Fig. 4. Detection of CO and H2O in Comets C/1996 B2 (Hyakutake) and C/1999 H1 (Lee) in the 4.7-µm region (from Mumma et
al., 2001b). Several lines of the CO v(1–0) and H2O ν1–ν2 and ν3–ν2 bands are present. The relative intensities of CO and H2O lines
are reversed even though the rotational temperatures were similar for the two comets, providing graphic evidence of the dramatically
different CO abundance in these two comets.
 Bockelée-Morvan et al.: The Composition of Cometary Volatiles 399

Fig. 5. Portions of the ultraviolet (UV) spectra of C/1996 B2 (Hyakutake) taken on 1996 April 1 with the HST. All the parent mol-
ecules detected at UV wavelengths are represented: The top panel shows multiple bands in the Fourth Positive Group of CO; the
middle panel shows several bands of the CO Cameron system, which is thought to be produced mainly by prompt emission following
the photodissociation of CO2, and the bottom panel shows multiple bands of the B–X system of S2. Figure adapted from Weaver
(1998).

(HST) observations of 103P/Hartley 2 (Weaver et al., 1994), they are electric dipole forbidden, which means that reso-
and this spurred a reanalysis of earlier data acquired with nance fluorescence cannot be the excitation mechanism.
the International Ultraviolet Explorer (IUE) that resulted in The Cameron bands can be excited during the photodisso-
the detection of Cameron band emission in several other ciation of CO2, producing CO molecules in the a3Π state
comets (Feldman et al., 1997). The Cameron bands involve that can then decay to the ground state on a timescale of
transitions between triplet and singlet electronic states, i.e., ~10 ms in a process called prompt emission (Weaver et al.,
400 Comets II

1994). In this case, the CO Cameron band emission is di- sity is then integrated along the line of sight to obtain the
rectly proportional to the CO2 production rate, and its inten- column density.
sity can be used to estimate the CO2 abundance in exactly For the case of a circular observing aperture centered on
the same way that observations of the O1D line near 6300 Å the nucleus, if the aperture subtends a distance at the comet
can be used to probe the H2O production rate (cf. Feldman that is much smaller than the scalelength (L = vτ) of the
et al., 2004). Unfortunately, electron impact on CO also molecule, the average column density within the aperture
produces Cameron band emission fairly efficiently, and this is given by
complicates the interpretation of the spectra when both CO
and CO2 are comparably abundant. When spectra are taken Q
〈N〉 = (14)
at sufficient resolution to resolve the rotational structure in vd
the Cameron bands, the two competing excitation mecha-
nisms can be easily distinguished because the CO molecules where d is the aperture diameter.
produced during the photolysis of CO2 are rotationally If the aperture size is much larger than the scalelength
“hot”, with a rotational temperature about five times larger of the molecule, then
than for the CO excited by electron impact (Mumma et al.,
1975). 4Qτ
〈N〉 = (15)
S2 has been observed through its B3Σ–u–X3Σ–g system in πd2
the near-UV in several comets (section 5.5). Because of its
very short lifetime (≈500 s), S2 is concentrated within a When equations (14) and (15) are not applicable, other
small spatial region near the nucleus and observations with methods must be used to relate the column density to the
high spatial resolution (<500 km) are required to detect it. production rate. While convenient tabulations are available
The photodissociation rate and the B–X g-factor of S2 are for both circular (Yamamoto, 1982) and square (Hoban et
comparable. Thus, a time-dependent model of the excita- al., 1991) apertures, the continually increasing power of
tion is required for accurate interpretation of the emission computers makes the direct integration of equation (13)
(Kim et al., 2003; Reylé and Boice, 2003). simple, fast, and accessible to most researchers.
Cometary emission in electronic bands is generally pro- In the limit cases of equations (14) and (15), 〈N〉 depends
duced by resonance fluorescence, as are the great majority of on either v or τ. In the intermediate cases, the column den-
cometary emissions observed at optical and near-IR wave- sity depends on both the lifetime and velocity. Lifetimes
lengths. However, the anomalous intensity ratio of the CO have been computed for many parent molecules (Huebner
C–X and B–X bands in the FUSE spectrum of C/2001 A2 et al., 1992; Crovisier, 1994) under both solar maximum
(LINEAR) suggests that some of the B–X emission is pro- and solar minimum conditions and have accuracies of ~20–
duced by e–-impact on CO, while the presence of a “hot” 30% for the well-documented species. But the photodisso-
component in the C–X emission is suggestive of an excita- ciation rates of several cometary molecules (e.g., H2CS,
tion process involving CO2 (Feldman et al., 2002). As pre- SO2, NH2CHO) are unavailable or uncertain by factors of
viously discussed, the CO Cameron bands can be excited several. Expansion velocities for some molecules can be
by both photodissociative and e–-impact processes. determined from analysis of observed radio line profiles,
but usually the outflow velocities are uncertain by ~30%.
4. DETERMINATION OF There is also the problem that the outflow velocity changes
PRODUCTION RATES with position in the coma, as molecules are accelerated by
photolytic heating in the coma, but typically observers adopt
For estimating relative molecular abundances in the an average outflow speed that is appropriate for the size of
nucleus, the measured column densities (or local densities the aperture used (i.e., smaller velocities used for smaller
in the case of in situ measurements) are converted into apertures).
molecular production rates, i.e., outgassing rates at the nu- For molecules released by an extended source, such as
cleus. This step requires a good description of the molecu- H2CO (section 7), the Haser formula for daughter species
lar spatial distributions. Most studies use the Haser model (see Combi et al., 2004) is generally used to describe their
(Haser, 1957), which assumes that the parent molecule is spatial distribution. Inferred production rates then strongly
sublimating from the surface of the nucleus at a constant depend on the scalelength of their parent source, Lp, espe-
rate and expands radially outward at constant velocity. cially when the field of view samples cometocentric dis-
Under these conditions, the local density in the coma n is tances smaller than Lp. Any underestimate of Lp will result
given by in an underestimate of the production rate. In this context,
there are some uncertainties in the production rates derived
Q from radio observations of distant comets for which subli-
n(rc) = e – (rc – rn) /vτ (13)
4πr2cv mation from icy grains is likely and not taken into account
in most studies (A’Hearn et al., 1984; Biver et al., 1997;
where Q is the production rate, rc is the distance from the Womack et al., 1997; Gunnarsson et al., 2002). H2CO pro-
center of the nucleus, rn is the radius of the nucleus, v is duction rates obtained in Comet Hale-Bopp at large r are
the outflow speed, and τ is the molecular lifetime. The den- uncertain as well, as there is little information on the he-
 Bockelée-Morvan et al.: The Composition of Cometary Volatiles 401

liocentric variation of the H2CO parent scalelength (see 1986; Larson et al., 1989), but the strong 2.7-µm funda-
section 7). mental bands (ν1 and ν3) blanket this entire region from the
With sufficient spatial resolution and mapping, the ra- ground. However, groundbased IR observations of Comets
dial distribution of molecules can be investigated, and pro- 1P/Halley and C/1986 P1 (Wilson) indicated the presence
duction rates can be more accurately determined. Section 7 of excess flux near 2.8 µm that could not be attributed to
discusses how native and extended sources of CO molecules H2O fundamental bands (Tokunaga et al., 1987; Brooke et
are extracted from the analysis of long-slit spectra. al., 1989), but was consistent with the expected flux from
The spatial distribution of cometary molecules is certainly H2O hot-bands (Bockelée-Morvan and Crovisier, 1989). The
much more complex than assumed by the Haser model. As hot-band emissions in this spectral region were more ex-
discussed elsewhere in this book (e.g., Crifo et al., 2004), tensively sampled by ISO in Comet Hale-Bopp (Fig. 3).
the production rate may vary on short timescales, outgas- High spectral dispersion surveys of the 2.9-µm region ob-
sing from the nucleus may not be isotropic, and the expan- tained in Comets C/1999 H1 (Lee) and 153P/2002 C1
sion velocity increases with distance from the nucleus and (Ikeya-Zhang) with NIRSPEC at the Keck telescope re-
may have day/night asymmetries. Anisotropic outgassing vealed multiple lines of the ν1 + ν3 – ν1, (ν1 + ν2 + ν3)–(ν1 +
and/or velocity variations have been considered in a few ν2), and 2ν1 – ν1 H2O hot-bands (Mumma et al., 2001a;
radio studies, using information provided by the line shapes Dello Russo et al., 2004).
and mapping (e.g., Gunnarsson et al., 2002; Veal et al., In other spectral regions, the terrestrial atmosphere is
2000). generally transparent to H2O hot-band emissions. Hot-band
emission from H2O was detected in Comets C/1991 T2
5. OBSERVATIONS OF (Shoemaker-Levy), 6P/d’Arrest, and C/1996 B2 (Hyakutake)
PARENT MOLECULES using bands near 2 µm (ν1 + ν2 + ν3 – ν1 and 2ν2 + ν3 – ν2)
(Mumma et al., 1995, 1996; Dello Russo et al., 2002a).
In this section, we review the in situ measurements and Production rates were obtained for all three comets, and a
spectroscopic investigations of parent molecules and noble rotational temperature was obtained for H2O in Comet Hya-
gases. The production rates relative to H2O (also called abun- kutake (Mumma et al., 1996). A survey of the CO (1–0)
dances in the text) measured in several well-documented band (4.7 µm) in Comet Hyakutake revealed new emissions
comets near their perihelion are listed in Table 1. Upper that were identified as nonresonance fluorescence from the
limits for several undetected molecules are given in Table 2. ν1 – ν2 and ν3 – ν2 hot-bands of H2O (Mumma et al., 1996;
Dello Russo et al., 2002a). As H2O and CO can be sampled
5.1. Water simultaneously (Fig. 4), preference was given to the 4.7-µm
region thereafter (e.g., C/1995 O1 Hale-Bopp (Weaver et al.,
Water is the most abundant constituent of cometary ices 1999b; Dello Russo et al., 2000), 21P/Giacobini-Zinner
and its production rate is used for quantifying cometary (Weaver et al., 1999a; Mumma et al., 2000), C/1999 H1 (Lee)
activity and for abundance determinations. Its presence in (Mumma et al., 2001b), C/1999 S4 (LINEAR) (Mumma et
cometary comae was definitively established in the 1970s al., 2001a).
from observations of H and OH, which showed that these The rotational lines of H2O also cannot be observed from
species were produced in appropriate quantities and with the ground, except for a line of one of the trace isotopes
spatial distributions and velocities consistent with H2O pho- (HDO — see section 9). Lines in the far-IR, especially the
tolysis (see the review of Festou et al., 1993). 212–101, 221–212 and 303–212 lines near 180 µm, were ob-
Water is difficult to measure directly. The fundamental served by ISO in Comet Hale-Bopp (Crovisier et al., 1997).
bands of vibration, especially ν3 near 2.7 µm, cannot be The fundamental ortho rotational line, 110–101 at 557 GHz,
observed from the ground because of strong absorption in was observed using SWAS (Neufeld et al., 2000) and the
the terrestrial atmosphere. This band was observed in 1P/ Odin satellite (Lecacheux et al., 2003) in C/1999 H1 (Lee),
Halley and C/1986 P1 (Wilson) from the KAO (Mumma et 153P/2002 C1 (Ikeya-Zhang), and several other comets.
al., 1986; Larson et al., 1989), in 1P/Halley with the Vega/ These lines are very optically thick, which means that the
IKS IR spectrometer (Combes et al., 1988), and with ISO derivation of accurate H2O production rates requires a reli-
in Comets Hale-Bopp and 103P/Hartley 2 (Crovisier et al., able model for the H2O excitation and radiative transfer.
1997, 1999a,b) (Fig. 3).
Nonresonance fluorescence bands (hot-bands) of H2O 5.2. Carbon Monoxide and Carbon Dioxide
have weaker g-factors, but some are not absorbed by tellu-
ric H2O and thus can be observed from the ground. Direct 5.2.1. Carbon monoxide (CO). The CO molecule was
absorption of sunlight excites molecules from the ground discovered in comets during a sounding rocket observation
vibrational state to a higher vibrational state, followed by of C/1975 V1 (West), when resonance fluorescence in the
cascade into an intermediate level that is not significantly Fourth Positive Group (A1Π–X1Σ+) near 1500 Å was de-
populated in the terrestrial atmosphere (Crovisier, 1984). tected in the UV spectrum (Feldman and Brune, 1976).
Hot-band emission from H2O ν2 + ν3 – ν2 was first detected Emission in these bands has been detected subsequently in
near 2.66 µm in high-dispersion airborne IR spectra of nearly every bright (mV < 7) comet observed at UV wave-
Comets 1P/Halley and C/1986 P1 (Wilson) (Weaver et al., lengths with IUE (cf. Feldman et al., 1997), the HST (cf.
402 Comets II

TABLE 1. Production rates relative to water in comets.

C/1995 O1 C/1996 B2 C/1999 H1 C/1999 S4 153P/2002 C1

Molecule 1P/Halley (Hale-Bopp) (Hyakutake) (Lee) (LINEAR) (Ikeya-Zhang)
H2O 100 100 100 100 100 100
CO 3.5*, 11[1] 12*,[13], 23[13,14] 14*,[25,26], 19–30[25,27,28] 1.8[36] –4[37] ≤0.4[41], 0.9[42] 2[45], 4–5[46,47]
CO2 3–4 [2,3] 6†,15
CH4 <0.8[4] 1.5[16] 0.8[16,29] 0.8[38] 0.14[42] 0.5[16]
C2H2 0.3[1] 0.1[16] –0.3[17] 0.2[30] –0.5[31] 0.27[38] <0.12[42] 0.18[48]
C2H6 0.4[1] 0.6[17] 0.6[29] 0.67[38] 0.11[42] 0.62[49]
CH3OH 1.8[5,6] 2.4[14] 2[27,28] 2.1[38] –4[39] <0.15[42] 2.5[46,47]
H2CO‡ 4[2,7,8] 1.1[14] 1[27,28] 1.3[39] 0.6[41] 0.4[47]
HCOOH 0.09[14] <0.1[43]
HCOOCH3 0.08[14]
CH3CHO 0.02[18]
NH2CHO 0.015[14]
NH3 1.5[9] 0.7[19] 0.5[32,33] <0.2[50]
HCN 0.1[10,11] 0.25[14,20] 0.1[27,28] –0.2[34] 0.1[38] –0.3[39] 0.1[42] 0.1[47] –0.2[48]
HNCO 0.10[14] 0.07[28] 0.04[47]
HNC 0.04[14,21] 0.01[28,35] 0.01[39] 0.02[43] 0.005§,[47]
CH3CN 0.02[14] 0.01[33] 0.01[47]
HC3N 0.02[14] <0.01[47]
H2S 0.4[6] 1.5[14] 0.8[27] <0.9[39] 0.3[43] 0.8[47]
OCS 0.4[14,22] 0.1[36] <0.2[47]
SO2 0.2[14]
CS2 0.2[12] 0.2[14] 0.1[27] 0.08[39] 0.12[43] 0.06[47] –0.1[45]
H2CS 0.05[23]
NS ≥0.02[24]
S2 0.005[37] 0.002[40] 0.0012[44] 0.004[45]
*Production from the nucleus; see text.
† Value at heliocentric distance r = 1 AU extrapolated from the value of 20% measured at r = 2.9 AU, assuming that [CO ]/[CO] did not
2
change with r.
‡ H CO abundances refer to production from an extended source.
2
§ Measured at r ~ 1 AU; increased up to 0.02% at r ~ 0.5 AU (N. Biver et al., personal communication, 2003; Irvine et al., 2003).

References: [1] Eberhardt (1999); [2] Combes et al. (1988); [3] Krankowsky et al. (1986); [4] Altwegg et al. (1994); [5] Bockelée-
Morvan et al. (1995); [6] Eberhardt et al. (1994); [7] Meier et al. (1993); [8] Mumma and Reuter (1989); [9] Meier et al. (1994);
[10] Despois et al. (1986); [11] Schloerb et al. (1986); [12] Feldman et al. (1987); [13] DiSanti et al. (2001); [14] Bockelée-Morvan
et al. (2000); [15] Crovisier et al. (1997); [16] Gibb et al. (2003); [17] Dello Russo et al. (2001); [18] Crovisier et al. (2004a); [19] Bird
et al. (1999); [20] Magee-Sauer et al. (1999); [21] Irvine et al. (1998); [22] Dello Russo et al. (1998); [23] Woodney (2000); [24] Irvine
et al. (2000b); [25] DiSanti et al. (2003); [26] McPhate et al. (1996); [27] Biver et al. (1999a); [28] Lis et al. (1997); [29] Mumma et
al. (1996); [30] Mumma et al. (2003); [31] Brooke et al. (1996); [32] Palmer et al. (1996); [33] Bockelée-Morvan (1997); [34] Magee-
Sauer et al. (2002a); [35] Irvine et al. (1996); [36] Woodney et al. (1997); [37] Weaver et al. (1996); [38] Mumma et al. (2001b);
[39] Biver et al. (2000); [40] Feldman et al. (1999); [41] Weaver et al. (2001); [42] Mumma et al. (2001a); [43] Bockelée-Morvan et
al. (2001); [44] Weaver (2000); [45] Weaver et al. (2002b); [46] DiSanti et al. (2002); [47] N. Biver et al. (personal communication,
2003); [48] Magee-Sauer et al. (2002b); [49] Dello Russo et al. (2002b); [50] Bird et al. (2002).

Weaver, 1998), and sounding rockets (cf. Feldman, 1999). J(2–1) line at 230 GHz was first observed in 29P/Schwass-
More recently, resonance fluorescence in several bands of mann-Wachmann 1 (Senay and Jewitt, 1994) at r ≈ 6 AU,
the Hopfield-Birge system (B1Σ+–X1Σ+, C1Σ+–X1Σ+, and and subsequently in a few bright comets. In Comets Hya-
E1Π–X1Σ+) has been detected between 1075 Å and 1155 Å kutake and Hale-Bopp, the J(1–0) and J(3–2) lines were also
in spectra measured by FUSE (Feldman et al., 2002). observed. The J(2–1) line was detected out to r = 14 AU in
Through the end of 2002, CO emission had been detected Comet Hale-Bopp with the Swedish-ESO Submillimetre
in a total of 12 comets at UV wavelengths, with [CO/H2O] Telescope (SEST) (Biver et al., 2002a).
abundances ranging from ~0.4% to nearly 30%. The first clear detection of the lines of the v(1–0) IR
The radio lines of CO are intrinsically weak because of band of CO near 4.7 µm was obtained during observations
the small dipole moment of this molecule. However, these of Comet Hyakutake (Mumma et al., 1996; DiSanti et al.,
lines are the most easily detected gaseous emissions for 2003). Eight lines of this band were detected in emission,
comets at large heliocentric distances (r > 3 AU). The CO using CSHELL spectrometer at the NASA/IRTF. CO has
 Bockelée-Morvan et al.: The Composition of Cometary Volatiles 403

TABLE 2. Molecular upper limits in Comet Hale-Bopp r > 2.9 AU. This higher value is likely due to the higher
from radio observations (from Crovisier et al., 2004). volatility of CO2 compared to H2O. The value of 6% given
in Table 1 is that extrapolated to 1 AU, using the Q(CO2)/
Molecule (X)/(H2O) Q(CO) ratio of ~0.3 measured at 2.9 AU.
H2O 100 As discussed in section 3.4, the presence of CO2 is also
H2O2 <0.03 indirectly inferred from observations of the CO Cameron
CH3CCH <0.045 bands near 2050 Å, which can be emitted via prompt emis-
CH2CO <0.032 sion following the photodissociation of CO2. In practice,
C2H5OH <0.10 these UV bands can only be used to derive accurate CO2
CH3OCH3 <0.45
production rates when the comet is CO-depleted, or is bright
CH3COOH <0.06
enough to allow observations with sufficient spectral reso-
Glycine I <0.15
HC5N <0.003 lution (λ/δλ > 1500) to unambiguously identify the sepa-
C2H5CN <0.01 rate emissions from CO2 photodissociation and electron
CH2NH <0.032 impact on CO, which overlap in low-resolution data.
CH3SH <0.05
NaOH <0.0003 5.3. Methanol (CH3OH), Formaldehyde (H2CO),
NaCl <0.0008 and Other CHO-bearing Molecules

5.3.1. Methanol (CH 3 OH). The identification of

CH3OH was first suggested by Knacke et al. (1986) to ex-
plain the 3.52-µm feature seen near the broad 3.3–3.5-µm
been detected in every comet observed since then with emission in several low-resolution spectra of 1P/Halley.
CSHELL and with NIRSPEC at the Keck Observatory (eight Hoban et al. (1991) observed the 3.52-µm feature in Comets
Oort cloud comets and one Jupiter-family comet) (Mumma C/1989 Q1 (Okazaki-Levy-Rudenko), C/1989 X1 (Austin),
et al., 2003; Weaver et al., 1999a,b). Selected spectra of C/ C/1990 K1 (Levy), and 23P/Brorsen-Metcalf, and showed
1999 H1 (Lee) and Comet Hyakutake are shown in Fig. 4. that its properties were consistent with fluorescence from
CO rotational temperatures were obtained from Boltzmann low-temperature (70 K) CH3OH in the ν3 band. Figure 6
analyses of the measured spectral line intensities and were displays 3.2–3.7-µm spectra of Comets C/1989 X1 (Aus-
used to extrapolate total production rates from the observed tin) and C/1990 K1 (Levy) showing CH3OH emission.
lines. For eight Oort cloud comets observed by IR ground- Definite identification of CH3OH in cometary comae was
based spectroscopy through the end of 2002, the total CO obtained from the detection of several J(3–2) rotational lines
abundance ranged from 1% to 24% relative to H2O (Mumma at 145 GHz in Comets C/1989 X1 (Austin) and C/1990 K1
et al., 2003). (Levy) at the 30-m telescope of the Institut de Radioastron-
CO was investigated by mass spectrometry in 1P/Halley omie Millimétrique (IRAM) (Bockelée-Morvan et al., 1991,
with the Giotto NMS (Eberhardt et al., 1987). As detailed 1994).
in section 7.1, these measurements revealed that part of the Methanol has now been observed in many comets, both
CO originated from an extended source. Native and ex- at radio and IR wavelengths, and the CH3OH abundances
tended sources of CO were separately quantified in a few inferred from radio and IR spectra are generally consistent
comets from long-slit IR observations (section 7.2). Among (Table 1). In Comet Hale-Bopp, ~70 rotational lines were
eight Oort cloud comets observed at IR wavelengths, the detected at millimeter and submillimeter wavelengths (Biver
native abundance [CO/H2O] varies by more than a factor et al., 1999b). Methanol rotational lines often appear as
of 40 [0.4–17% (Mumma et al., 2003) (section 8). multiplets in radio spectra (Fig. 2), whose analysis provides
5.2.2. Carbon dioxide (CO2). The presence of carbon clues to the temperature and excitation conditions in the
dioxide in cometary comae was indirectly established a long coma (see section 3.2). High-resolution Keck/NIRSPEC
time ago from the existence of CO+2 in cometary tails (see spectra obtained in the 3-µm region in Comets C/1999 H1
Feldman et al., 2004). It was confirmed by the detection (Lee) and C/1999 S4 (LINEAR) show the P, Q, R structure of
of the CO2 ν3 band at 4.26 µm. This band is very strong the ν3 band and present, near 3.35 µm, many ro-vibrational
(g-factor = 2.6 × 10 –3 s–1), but it cannot be observed from lines belonging to the ν2 and ν9 CH3OH bands (Mumma et
the ground because of strong absorption from terrestrial al., 2001a,b).
CO2. The ν3 band has only been observed by Vega/IKS in The ν 2 and ν9 CH3 stretching modes of CH3OH are
1P/Halley (Combes et al., 1988), and by ISO in Comets responsible for about half the total intensity of the 3.3–
Hale-Bopp (Crovisier et al., 1997, 1999a) and 103P/ 3.5-µm emission feature (Hoban et al., 1993; Bockelée-
Hartley 2 (Colangeli et al., 1999; Crovisier et al., 1999b). Morvan et al., 1995). Synthetic spectra, as modeled by
CO2 was also observed in 1P/Halley from the mass 44 peak Bockelée-Morvan et al., are shown in Fig. 6. Other weaker
in the Giotto NMS mass spectra (Krankowsky et al., 1986). CH3OH combination bands should contribute as well. The
The inferred CO2 production rate relative to H2O was 3–4% rotational structure of these bands is not yet available, which
in 1P/Halley and 8–10% in 103P/Hartley 2. It was >20% makes it difficult to identify new hydrocarbons or CHO-
in Comet Hale-Bopp, but this comet was only observed at bearing molecules in this spectral region.
404 Comets II

(Combes et al., 1988; Mumma and Reuter, 1989) This de-

tection is controversial, however, as this band was not de-
tected in groundbased IR spectra of 1P/Halley and several
other comets (e.g., Reuter et al., 1992). The detection of
H2CO by IR long-slit spectroscopy is difficult, owing to its
low abundance and daughter-like density distribution. Re-
cently, DiSanti et al. (2002) reported the detection of the
Q branch of the H2CO ν1 band in high-resolution spectra
of 153P/2002 C1 (Ikeya-Zhang) obtained with CSHELL at
the NASA/IRTF.
A detection of the 110–111 line of H2CO at 6 cm wave-
length in Comet 1P/Halley using the Very Large Array
(VLA), announced by Snyder et al. (1989), is controversial.
If real, it would lead to an exceptionally high abundance
of H2CO (see discussion in Bockelée-Morvan and Crovisier,
1992). The first definite detection of H2CO at millimeter
wavelengths (312–211 at ~226 GHz) was in Comet C/1989
X1 (Austin) at IRAM (Colom et al., 1992). Since then, this
molecule has been observed via several lines at millimeter
and submillimeter wavelengths in several comets. H2CO
was monitored at radio wavelengths in Comet Hale-Bopp
(Biver et al., 1997, 1999b, 2002a) (see Fig. 7). It exhibited a
steep heliocentric production curve (~r –4.5) over the entire
range 1 ≤ r ≤ 4 AU, which contrasted with the r –3–r –2 evo-
lution observed for most molecules. This behavior is related

Fig. 6. 3.2–3.7-µm spectra of Comets C/1989 X1 (Austin) and

C/1990 K1 (Levy) (thick line). The continuum flux due to ther-
mal emission and scattered light from dust grains has been sub-
tracted. The contributions of the methanol bands (ν2, ν3, and ν9
at 3.33, 3.37, and 3.52 µm respectively) are shown in thin lines.
The residual emission spectra, after subtracting methanol emis-
sion, are shown in dashed line. Figure adapted from Bockelée-
Morvan et al. (1995).

Besides the 3.52-µm band, CH3OH is identified in 1P/

Halley from the peak at 33 amu/q present in Giotto IMS
and Giotto NMS mass spectra, which is essentialy due to
CH3OH+2 (Geiss et al., 1991; Eberhardt et al., 1994). Eber-
hardt et al. inferred a CH3OH abundance relative to H2O that
is consistent with the value derived from the 3.52-µm band.
The [CH3OH/H2O] abundance ratios measured up to
now range from less than 0.15% in Comet C/1999 S4 (LIN-
EAR) to 6%, with many comets around ~2% (see section 8).
5.3.2. Formaldehyde (H2CO). Cometary H2CO was
first identified in 1P/Halley, from the signature of its pro-
tonated ion in mass-spectra obtained with Giotto NMS
(Meier et al., 1993). Its spatial distribution was found to Fig. 7. Gas production curves in Comet Hale-Bopp from radio
differ from that expected for a parent molecule, suggesting observations at IRAM, JCMT, CSO, and SEST telescopes (Biver
the presence of a extended source of H2CO in the coma (see et al., 2002a). OH production rates are from observations of the
the discussion in section 7). Its ν1 band near 3.59 µm was 18-cm lines at the Nançay radio telescope. Inverted triangles in-
possibly detected in the Vega/IKS spectrum of 1P/Halley dicate upper limits in cases of nondetection.
 Bockelée-Morvan et al.: The Composition of Cometary Volatiles 405

to the production mechanism of H2CO, which became more at 244.83 GHz with IRAM/PdBi (Crovisier et al., 2004a).
efficient when the comet approached the Sun. Several marginal features at the frequencies of CH3CHO
The Q(H2CO)/Q(H2O) production rate ratio refering to lines are also present in IRAM 30-m spectra (Crovisier et
the extended H2CO production has been estimated to 4% al., 2004a). These molecules, which are ubiquitous compo-
for Comet 1P/Halley. This ratio ranges from 0.13 to 1.3% nents of star-forming regions, are much less abundant than
for comets in which H2CO has been investigated at milli- CH3OH and H2CO (Table 1): ~0.1% relative to H2O for
meter wavelengths (Biver et al., 2002b). HCOOH and HCOOCH3, and ~0.02% for CH3CHO. Further
5.3.3. Other CHO-bearing molecules. Several new or- work on archive millimeter spectra of Comet Hale-Bopp led
ganic CHO-bearing molecules were identified in Comet to the identification of ethylene glycol (HOCH2CH2OH)
Hale-Bopp with millimeter spectroscopy thanks to its high (Crovisier et al., 2004b) with an abundance of 0.25% rela-
gaseous activity. Formic acid (HCOOH) was detected from tive to water.
four J(10–9) lines near 225 GHz using the Plateau de Bure
interferometer (PdBi) of IRAM in single dish mode (Fig. 8) 5.4. Symmetric Hydrocarbons
(Bockelée-Morvan et al., 2000). Methyl formate (HCOOCH3)
is one of the most complex cometary molecule detected in Symmetric hydrocarbons lack a permanent dipole mo-
the gas phase. A blend of eight J(21–20) rotational transi- ment and their excited electronic states predissociate, hence
tions at ~227.56 GHz was detected in low-resolution spectra only their ro-vibrational bands are observable in cometary co-
of Comet Hale-Bopp obtained at the IRAM 30-m telescope mae. Since 1996, CH4, C2H2, and C2H6 have been detected
(Bockelée-Morvan et al., 2000) (see Fig. 8). Acetaldehyde in many comets. The overall appearance of the 3.0-µm re-
(CH3CHO) has been detected from its 130,13–120,12 A+ line gion, which is particularly rich in emission lines from hy-
drocarbons and other species, is shown in Fig. 9 for Comet
C/1999 H1 (Lee). A tentative detection of C4H2 was also
obtained in Comet 153P/2002 C1 (Ikeya-Zhang) (Magee-
Sauer et al., 2002b). Searches for C2H4, C3H6, C3H8, and
C6H6 have been negative so far (M. Mumma, personal com-
munication, 2003).
5.4.1. Methane (CH4). CH4 was first clearly detected
spectroscopically in Comet Hyakutake, through ground-
based observations of five lines of the ν3 band at 3.3 µm
(Mumma et al., 1996). Earlier attempts to detect methane
are reviewed in Mumma et al. (1993). Methane has been
detected in every comet searched since then, including
Comet Hale-Bopp, C/1999 S4 (LINEAR), C/1999 H1 (Lee)
(Figs. 9a,b), C/1999 T1 (McNaught-Hartley), C/2001 A2
(LINEAR), C/2000 WM1 (LINEAR), and 153P/2002 C1
(Ikeya-Zhang). Its abundance [CH4/H2O] ranged from 0.14%
to 1.4% in the sample (Gibb et al., 2003) (see section 8).
5.4.2. Acetylene (C2H2). C2H2 was first detected in
Comet Hyakutake, through three lines of its ν3 band at
3.0 µm (Brooke et al., 1996). The Oort cloud comets sam-
pled up to now are consistent with [C2H2/H2O] = 0.2–0.5%
(Table 1), excepting C/1999 S4 (LINEAR) for which the
abundance relative to H2O was significantly lower (<0.12%
at the 2σ limit) (Mumma et al., 2001a) (see section 8). The
abundance retrieved from in situ measurements of 1P/Hal-
ley was ~0.3% (Giotto NMS) (Eberhardt, 1999).
5.4.3. Ethane (C2H6). C2H6 was first detected in Comet
Hyakutake, when emissions in four Q-branches of its ν7
band (3.35 µm) were measured (Mumma et al., 1996). C2H6
Fig. 8. Spectra of SO (CSO, February 21), SO2 (IRAM/PdBi, has been detected in every comet searched since then
March 18, 20, 21), OCS (CSO, March 26), HC3N (CSO, Febru- (Mumma et al., 2003). Among Oort cloud comets, the abun-
ary 20), HNCO (CSO, February 19), NH2CHO (IRAM 30-m,
dance is remarkably constant ([C2H6/H2O] ~ 0.6% (Table 1),
April 5), HCOOH (IRAM/PdBi, March 20–21), and HCOOCH3
the sole exception being C/1999 S4 (LINEAR) (Mumma et
(IRAM 30-m, April 5) observed in Comet Hale-Bopp in 1997. The
velocity frame is with respect to the comet nucleus velocity. The al., 2001a). The abundance retrieved from in situ measure-
dashed line superimposed on the observed spectrum of HCOOCH3 ments of Comet Halley was 0.4% (Giotto NMS) (Eberhardt,
is a synthetic profile, which takes into account that the HCOOCH3 1999). However, C2H6 was significantly depleted in 21P/
line at ~225.562 GHz is a blend of eight transitions whose posi- Giacobini-Zinner, the quintessential C2-depleted Jupiter-
tions are shown. From Bockelée-Morvan et al. (2000). family comet (Mumma et al., 2000; Weaver et al., 1999a;
406 Comets II

Fig. 9. High-dispersion spectra of Comet C/1999 H1 (Lee) obtained on August 21, 1999 with NIRSPEC at the Keck telescope in the
3-µm region. The dashed line shows a synthetic spectrum of the atmospheric transmittance. Adapted from Mumma et al. (2001b).

A’Hearn et al., 1995). The ν5 band (3.45 µm) of C2H6 was IRAM 30-m telescope in Comets C/1989 X1 (Austin) and
detected in Comets Hale-Bopp, Lee, and C/2001 A2 (LIN- C/1990 K1 (Levy) (Bockelée-Morvan et al., 1991; Crovisier
EAR), but it has not yet been quantitatively analyzed (M. et al., 1991a). It was subsequently observed in several other
Mumma, personal communication, 2003). comets (Biver et al., 2002b), but only through its two milli-
metric lines at 169 and 217 GHz. The H2S/H2O ratio ranges
5.5. Sulfur-bearing Molecules from 0.12% to 1.5%.
Protonated H2S was identified in ion mass spectra of
5.5.1. CS radical tracing carbon disulfide (CS2). The Comet 1P/Halley, from which a [H2S]/[H2O] abundance of
CS radical, which is observed at both UV and radio wave- 0.4% was derived. This value is within the range of values
lengths (see Feldman et al., 2004) is thought to trace CS2. measured in other comets (Eberhardt et al., 1994).
The inferred CS2 abundances range from 0.04% to 0.3% 5.5.3. Sulfur monoxide and dioxide (SO and SO2). SO
(Meier and A’Hearn, 1997). CS2 has a very short lifetime and SO2 have so far been detected only in Comet Hale-
(~500 s at r = 1 AU), and the spatial brightness profiles of Bopp, through several rotational transitions at radio wave-
CS measured during the UV observations are consistent lengths (Lis et al., 1999; Bockelée-Morvan et al., 2000) (see
with the hypothesis that CS is derived from a short-lived Figs. 2 and 8). The 65–54 line of SO at 219.949 GHz was
parent. imaged with IRAM/PdBi, and shows a brightness distri-
5.5.2. Hydrogen sulfide (H2S). Hydrogen sulfide was bution consistent with a daughter distribution (Wink et al.,
first detected through its 110–101 line at 169 GHz at the 1999). It is likely that SO can be fully explained by the
 Bockelée-Morvan et al.: The Composition of Cometary Volatiles 407

photodissociation of SO2 (Bockelée-Morvan et al., 2000). abundance relative to H2O Q(NS)/Q(H2O) is highly uncer-
Before these detections, Kim and A’Hearn (1991) derived tain, but estimated to ≥0.02% (Irvine et al., 2000b).
upper limits on Q(SO)/Q(H2O) and Q(SO2)/Q(H2O) pro-
duction rate ratios from the absence of their electronic bands 5.6. Nitrogen-bearing Molecules
in the UV, which are much lower than those inferred from
the radio observations of Comet Hale-Bopp (0.3% and 0.2% With an abundance of ~0.5% relative to H2O, NH3 is
for SO and SO2 respectively): A reappraisal of the g-fac- apparently the dominant N-bearing cometary molecule. The
tors of these bands is certainly necessary. abundance of the super volatile molecule N2 in cometary
5.5.4. Carbonyl sulfide (OCS). OCS was first detected nuclei, which would constrain the formation conditions of
through its J(12–11) radio line at 145.947 GHz by Woodney these objects in the solar nebula, is the subject of continu-
et al. (1997) in Comet Hyakutake, and confirmed by sev- ing debate.
eral other radio lines in Comet Hale-Bopp (Fig. 8) (Lis et 5.6.1. N2. As mentioned in section 3.4, FUSE searches
al., 1999; Bockelée-Morvan et al., 2000). Lines of the for UV fluorescence from N2 have been unsuccessful. The
strong ν3 band at 4.85 µm (g-factor of 2.6 × 10 –3 s–1) were upper limit on the [N2/H2O] ratio in two long-period comets
observed by Dello Russo et al. (1998) in Comets Hyakutake [C/2001 A2 (LINEAR) and C/2000 WM1 (LINEAR)] was
and Hale-Bopp. In the latter comet, the long-slit infrared <0.2%, while the [N2/CO] ratio in those same two comets
observations suggested an extended source for OCS (sec- was <30% (P. D. Feldman, personal communication, 2003).
tion 7.2). Inferred Q(OCS)/Q(H2O) are 0.1% and 0.4% for Mass spectrometry in Comet Halley has also not been
Comets Hyakutake and Hale-Bopp respectively. very helpful in constraining the N2 abundance because of
5.5.5. Thioformaldehyde (H2CS). H2CS was detected the accidental coincidence in the masses of N2 and CO
by one rotational line (716–615 at 244 GHz) in Comet Hale- (Eberhardt et al., 1987).
Bopp with the 12-m radio telescope of the National Radio The presence of N2 in comets is indirectly inferred from
Astronomy Observatory (NRAO) (Woodney et al., 1999). emissions in the B2Σ+u–X2Σ+g First Negative System of the
Its abundance relative to H2O has been evaluated to 0.05% N+2 ion near 3910 Å. During observations ranging from early
by Woodney (2000). in the twentieth century all the way up to the 1986 appari-
5.5.6. Disulfur (S2). The S2 molecule was discovered tion of 1P/Halley, detections of this band have been claimed
during IUE observations of C/1983 H1 (IRAS-Araki-Alcock) in many comets (e.g., Wyckoff et al., 1991, and discussion in
when several bands of the B3Σu– –X3Σg– system near 2900 Å Cochran et al., 2000). N2 abundances of ~0.02% relative
were detected (A’Hearn et al., 1983). A reanalysis of those to H2O have been derived from these observations. However,
data using improved spectral reduction techniques and re- high-spectral-resolution observations of some recent comets
vised g-factors (Budzien and Feldman, 1992) suggests that [122P/de Vico, C/1995 O1 (Hale-Bopp), and 153P/2002 C1
the [S2/H2O] abundance varied from 0.007% to 0.25% dur- (Ikeya-Zhang)] did not detect the N+2 band (Cochran et al.,
ing the course of the observations. 2000; Cochran, 2002), with upper limits of ≤10 –5–10–4 on
The most common form of solid sulfur is S8, and the the abundance of N2 relative to CO. Thus, the reality of the
discovery of S2 in a comet was the first detection of this detection of the N+2 ion in the low-resolution spectra of
unusual molecule in any astronomical object. The lifetime comets observed earlier may be questioned, especially con-
of S2 is very short (a few hundred seconds at r = 1 AU), sidering the severe spectral blending by emissions from
which means that exceptional spatial resolution (roughly a CO+, CO+2, CH, and CH+ bands in this same region, and
few hundred kilometers at the comet) is generally required to potential confusion with N+2 emissions from airglow and
detect it. Thanks to the close approach to Earth of C/1996 B2 aurora.
(Hyakutake) and the high spatial resolution available from 5.6.2. Ammonia (NH3). Ammonia was tentatively de-
HST, S2 has now been detected in four other comets, with tected from its 24-GHz inversion line in Comet C/1983 H1
[S2/H2O] abundances in the range 0.001–0.005% (Table 1). (IRAS-Araki-Alcock) by Altenhoff et al. (1983). Confirmed
Thus, whatever its origin, S2 seems to be ubiquitous in com- detections of several inversion lines were obtained in Com-
ets, at least the long-period ones, although its abundance ets Hyakutake (Palmer et al., 1996) and Hale-Bopp (Bird
apparently varies over a large range. Note, however, that et al., 1997, 1999; Hirota et al., 1999), from which abun-
the derived S2 abundances are usually strongly dependent dances of ~0.5% were derived (Table 1). An upper limit of
on the assumed S2 lifetime, whose uncertainty could inflate 0.2% was measured for Comet 153P/2002 C1 (Ikeya-Zhang)
the true abundance variation. (Bird et al., 2002).
5.5.7. NS radical. NS was detected through the two The infrared ν1 band of NH3 at 3.00 µm was detected
J(15/2–13/2) e and f radio transitions at the James Clerk in Comets Hale-Bopp (tentatively) (Magee-Sauer et al.,
Maxwell Telescope (JCMT) by Irvine et al. (2000b) in 1999) and 153P/2002 C1 (Ikeya-Zhang) (K. Magee-Sauer
Comet Hale-Bopp. The origin of this molecule is puzzling; et al., personal communication, 2003).
NS is a radical that is unlikely to be present in cometary ices, Ammonia was also indirectly investigated from the bands
but no plausible parent could be found. Because its spatial of its photodissociation products NH and NH2, which are
distribution and photodissociation rate are unknown, its easily observed in the visible (see Feldman et al., 2004).
408 Comets II

From detailed chemical modeling, Meier et al. (1994) in- (Ikeya-Zhang) (N. Biver et al., personal communication,
vestigated the relative contributions of NH+3 vs. OH+ and 2002). Its abundance relative to H2O is in the range 0.04–
NH+4 vs. H2O+ at masses 17 and 18 in Giotto NMS spectra. 0.1%.
They inferred an NH3 abundance of 1.5% in Comet 1P/Hal- 5.6.6. Formamide (NH2CHO). NH2CHO was detected
ley, a factor 2–3 times higher than the values measured in by several radio lines in Comet Hale-Bopp at CSO and
Comets Hyakutake and Hale-Bopp. IRAM and the inferred abundance is 0.015% (Fig. 8) (Lis
5.6.3. Hydrogen cyanide (HCN) and hydrogen isocya- et al., 1999; Bockelée-Morvan et al., 2000).
nide (HNC). HCN was firmly detected in Comet Halley
from its J(1–0) line at 88.6 GHz by several teams (Despois 5.7. Noble Gases
et al., 1986; Schloerb et al., 1986, 1987; Winnberg et al.,
1987). It is now one of the easiest parent molecules to ob- The noble gases (He, Ne, Ar, Kr, and Xe, in order of
serve from the ground and can serve as a proxy for moni- increasing atomic mass and decreasing volatility) are both
toring gas production evolution. It is also found to be in chemically inert and highly volatile. Thus, their abundances
remarkably constant ratio with H2O production (~0.1% ac- in cometary nuclei are especially diagnostic of the comet’s
cording to radio measurements, see section 8), so that it can thermal history. However, remote observations of the noble
be used to evaluate relative molecular abundances (Biver gases are difficult because their resonance transitions lie in
et al., 2002b). the far-UV spectral region (λ ≤ 1200 Å), which is acces-
HCN is also observed in the infrared through its ν3 band sible only from space and is outside the wavelength range
at 3.0 µm (Brooke et al., 1996; Magee-Sauer et al., 1999; covered by the HST and the Chandra X-ray observatory.
Mumma et al., 2001b). The spectrum of Comet Lee in Searches for several noble gases (He, Ne, and Ar) have been
Fig. 9c shows many ro-vibrational lines of HCN. For some attempted by sounding rockets (Green et al., 1991; Stern et
comets, there is a factor of two discrepancy between infra- al., 1992, 2000), the Hopkins Ultraviolet Telescope (Feld-
red and radio determinations of the HCN abundance rela- man et al., 1991), the Extreme Ultraviolet Explorer (EUVE)
tive to H2O (Table 1). (Krasnopolsky et al., 1997), the Solar and Heliospheric
HNC, an isomeric form of HCN that is unstable in usual Observatory (SOHO) (Raymond et al., 2002), and FUSE
laboratory conditions, was first detected from its J(4–3) line (Weaver et al., 2002a), but there has not yet been a convinc-
at 363 GHz in Comet Hyakutake (Irvine et al., 1996). It was ing detection of any noble gas sublimating from a cometary
then observed in Hale-Bopp by several groups (Irvine et nucleus.
al., 1998; Biver et al., 2002a; Hirota et al., 1999) and in 5.7.1. Helium. Helium is the lightest and most vola-
several other comets (Biver et al., 2002b; Irvine et al., tile of the noble gases, and significant amounts could be
2003). The origin of HNC is subject to debate. For Comet frozen in cometary nuclei only if the equilibrium tempera-
Hale-Bopp, an increase of the HNC/HCN ratio (from 0.03 to ture never rose above a few kelvins. For this reason, the
0.15) was observed when the comet approached the Sun and detection of emission in the He resonance line at 584 Å dur-
became more active; this was interpreted as a clue to chemi- ing EUVE observations of Comet Hale-Bopp was not in-
cal conversion of HCN to HNC in the coma, which becomes terpreted in terms of the production of He atoms sublimat-
more efficient in a denser coma (Irvine et al., 1998). How- ing from the nucleus (Krasnopolsky et al., 1997). Rather,
ever, high HNC/HCN ratios were also observed in Comets the emission could be fully explained by invoking charge
Hyakutake, C/1999 H1 (Lee), and C/2001 A2 (LINEAR), exchange between He II solar wind ions and cometary neu-
which were only moderately productive (Table 1). The tral species, which produces He in an excited state that can
HNC/HCN ratio seems to be rather inversely correlated with then relax radiatively [i.e., the same excitation mechanism
r (Biver et al., 2002b; Irvine et al., 2003), which would favor responsible for cometary X-rays; see Lisse et al. (2004)].
a production due to thermo-desorption from heated grains. Thus, observations of He emission from comets do not shed
5.6.4. Methyl cyanide (HC3N) and cyanoacetylene any light on the thermal history of cometary nuclei, but they
(CH3CN). Two other nitriles are observed in comets. can be used as probes of the solar wind conditions and of the
CH3CN was first detected in Comet Hyakutake with the interaction between cometary neutrals and the solar wind.
IRAM interferometer in single-dish mode through a series 5.7.2. Neon. Neon is also highly volatile, with a subli-
of rotational lines at 92 GHz (Dutrey et al., 1996). HC3N mation temperature of ~10 K under solar nebula conditions.
was first detected in Comet Hale-Bopp through several rota- Fortuitously, the Ne resonance line at 630 Å overlaps the
tional lines (Lis et al., 1999; Bockelée-Morvan et al., 2000 strong solar O V line, which boosts the Ne g-factor upward
(see Fig. 2). These two molecules are 10 times less abun- by a factor of ~100 relative to what it would be if only the
dant than HCN (Table 1). solar continuum was available for the excitation. A sensitive
5.6.5. Isocyanic acid (HNCO). A single radio line of search for this Ne line in Comet Hale-Bopp with EUVE re-
HNCO was observed at the Caltech Submillimeter Observa- sulted in an upper limit on the [Ne/O] abundance that was
tory (CSO) in Comet Hyakutake (Lis et al., 1997). Confir- depleted by a factor of ~25 relative to the solar value in the
mation was obtained by detection of several rotational lines ice phase, and by a factor of ~200 in total (gas + dust) (Kras-
in Comet Hale-Bopp (Fig. 8) (Lis et al., 1999; Bockelée- nopolsky et al., 1997). An even more sensitive upper limit
Morvan et al., 2000). It was also observed in 153P/2002 C1 was obtained for Comet Hyakutake; [Ne/O] was depleted by
 Bockelée-Morvan et al.: The Composition of Cometary Volatiles 409

a factor of 700 in ice and by more than 2600 in total rela- tion of PAHs in cometary nuclei remain open issues requir-
tive to the solar value (Krasnopolsky and Mumma, 2001). ing further investigation. Some problems that still need to
5.7.3. Argon. There was a claimed detection of the be addressed more rigorously include the excitation mecha-
two principal resonance lines of Ar at λ = 1048.22 and nism for PAHs, which is thought to be dominated by elec-
1066.66 Å during a sounding rocket observation of Comet tronic pumping in the UV followed by intermode conver-
Hale-Bopp in 1997 (Stern et al., 2000). The deduced [Ar/ sion to excitation of the numerous PAH vibrational modes;
O] ratio was rather high, 1.8 ± 0.96 times the solar value how PAHs are released from cometary refractories to the gas
of [Ar/O] = (46 ± 8) × 10 –4, but the CO abundance was phase; and the lifetime of PAHs in cometary comae (Joblin
also high (≈12%) (DiSanti et al., 2001), indicating that et al., 1997).
Comet Hale-Bopp retained highly volatile material. Recent In addition to the detected molecules discussed above
high-spectral-resolution observations of comets with FUSE and listed in Table 1, upper limits have been set for many
(Weaver et al., 2002a) demonstrate that there are other lines other species from dedicated or serendipitous searches at
that can be confused with Ar emission in low-resolution radio and IR wavelengths. A selection of upper limits ob-
spectra like those of Stern et al. (2000), which makes the tained from radio observations of Comet Hale-Bopp (Cro-
Ar detection in Comet Hale-Bopp questionable. visier et al., 2004a) is listed in Table 2.
Sensitive searches for Ar have been made with FUSE Numerous unidentified features have been detected in
in two long-period comets, C/2000 WM1 (LINEAR) and C/ cometary spectra. This indicates that new cometary species
2001 A2 (LINEAR) (Weaver et al., 2002a). Argon was not are still to be identified, pending further theoretical spec-
detected in either comet, and the [Ar/O] abundance was troscopic investigations and laboratory measurements. Uni-
depleted by at least a factor of 10 (5σ result) relative to the dentified lines observed in the visible and UV domains are
solar value. These large Ar depletions may not be surpris- presumably due to atoms, radicals, or ions (cf. Feldman et
ing because the abundance of CO, which has comparable al., 2004). Likely, many of these unidentified lines are due
volatility to Ar, was also very low in these comets (below to already known cometary species (e.g., C2, NH2, …).
1%). The upper limit on [Ar/O] for the only CO-rich comet In the IR, several unidentified bands have been noted for
observed by FUSE so far, C/1999 T1 (McNaught-Hartley) a long time. This is the case for the 2.44-µm band (Johnson
with [CO/H2O] ≈ 13%, was not very constraining, no larger et al., 1983) and for the 3.3–3.5-µm broad band, which can
than the solar abundance at the 5σ level. be only partly attributed to C2H6 and CH3OH (see discus-
Given the string of null results discussed above, infor- sion in section 5.3.1). We have strong indications that the
mation on the noble gas content in cometary nuclei may 3.4–3.5-µm excess emission shown in Fig. 6 mainly arises
not be obtained until a mass spectrometer makes sensitive from gas-phase fluorescence and not from refractory organ-
in situ measurements. ics (Bockelée-Morvan et al., 1995). Recently, many uniden-
tified lines have been detected in IRTF/CSHELL and Keck/
5.8. Other Molecules and Upper Limits NIRSPEC high-resolution spectra (e.g., Magee-Sauer et al.,
1999; Mumma et al., 2001b). Some of these latter lines could
Polycyclic aromatic hydrocarbons (PAHs) are thought to be due to CH3OH, whose IR spectrum is still poorly under-
be an important constituent of interstellar matter, respon- stood. Considering that the IR spectra of simple, stable mol-
sible for the ubiquitous emission bands near 3.28, 7.6, and ecules are well known, we could conclude that the unidenti-
11.9 µm (C–H stretching, C–C stretching, and C–H bend- fied lines are probably due to radicals or to more complex
ing modes respectively). Are PAHs also present in comets? molecules. A few unidentified lines have also been noted
An emission band near 3.28 µm has been observed in some in the radio domain, but they were observed with limited
comets (e.g., Davies et al., 1991; Bockelée-Morvan et al., signal-to-noise ratio.
1995) (see Fig. 6) and tentatively attributed to PAHs in the
gas phase, although other species, such as CH4 and OH 6. HELIOCENTRIC EVOLUTION
prompt emission are also contributing at this wavelength. OF PRODUCTION RATES
This PAH band was not observed in Comet Hale-Bopp,
either from the ground or with ISO, but the ISO spectra Extensive studies of the evolution of the outgassing of
were obtained at relatively large heliocentric distances (r > many comets as a function of heliocentric distance are avail-
2.7 AU) where the PAHs may not be emitting efficiently. able from the observation of daughter species [e.g., Schlei-
Moreels et al. (1993) claimed to detect phenanthrene (C14H10) cher et al. (1998) for 1P/Halley, Rauer et al. (2003) for
in the near-UV spectrum of 1P/Halley measured by the Hale-Bopp]. Spectroscopic observations of parent mole-
three-channel spectrometer on Vega, but this result has not cules, however, were generally conducted during the most
been confirmed by any other observation. Perhaps the best active phase of the comets (i.e., near perihelion), when the
suggestion for cometary PAHs comes from the identifi- signals received from Earth are expected to be the stron-
cation of napthalene, phenanthrene, and other PAHs in laser gest. Monitoring along comet orbit was only possible for a
ablation studies of dust collected in the terrestrial strato- few bright comets, such as Comet Halley [HCN at r = 0.6–
sphere that is thought to be of cometary origin (Clemett et 1.8 AU (Schloerb et al., 1987)], Hyakutake [HCN, CH3OH,
al., 1993). In summary, the presence and precise composi- CO, H2CO, H2S at r = 0.24–1.9 AU (Biver et al., 1999a)],
410 Comets II

and C/1999 H1 (Lee) [H2O, HCN, CH3OH, H2CO at r < curring in the coma (see Crifo et al., 2004). However, data
1.7 AU (Biver et al., 2000; Chiu et al., 2001)]. The early acquired so far provide limited information due to the lack
discovery at r = 7 AU of Comet Hale-Bopp and its excep- of spatial coverage and resolution. Radio and long-slit IR
tional intrinsic activity [Q(H2O) = 1031 molecules s–1 at spectra provide numerous examples of anisotropic distri-
perihelion] provided the first opportunity to follow the evo- butions with day/night asymmetries, which will not be dis-
lution of the production rates of a number of molecules over cussed here. Rather, we will focus on studies of the radial
a much larger heliocentric range. Figure 7 shows the result distribution of molecular species in the coma. Some spe-
of a monitoring performed at radio wavelengths (Biver et cies can be released directly from the nucleus, and also can
al., 2002a) during which many molecules were detected up be produced in the coma from other precursors. The former
to r = 4–5 AU, and up to 14 AU in the case of CO. Long- source is said to be direct (or native), while the latter is said
slit spectroscopy in the infrared covered the 0.9–4.1-AU to be extended (or distributed). The native and extended
range for CO, the 0.9–4-AU range for C2H6, and the 0.9– sources exhibit different radial distributions, and can be
1.5-AU range for H2O (DiSanti et al., 2001; Dello Russo recognized in this way.
et al., 2000, 2001).
Gas production curves are almost the only observational 7.1. Radial Distribution from In Situ Measurements
tools we have to obtain informations regarding the nature
and physical state of cometary ices, and their thermal prop- The discovery of extended sources of molecules in the
erties and sublimation mechanisms. A review of the various coma was one of the highlights of the space investigation
processes involved in cometary activity, and of the math- of 1P/Halley. The best examples were for CO (Eberhardt
ematical models developed so far, is presented by Prialnik et al., 1987) and H2CO (Meier et al., 1993). Their densi-
et al. (2004). Gas production curves also complement use- ties measured by NMS along the path of the Giotto space-
fully visual light curves for the study of seasonal effects, craft do not match those expected for a parent molecule.
dust mantling, etc. (see Meech and Svoren, 2004). A funda- Only one-third (~3.5% relative to H2O) of the total CO was
mental question that arises and can be addressed observa- released directly from the nucleus, the remainder (~7.5%)
tionally from gas production curves is to which extent pro- being produced from an extended source in the coma (Eber-
duction rate ratios reflect the bulk composition inside the hardt et al., 1987; Eberhardt, 1999). H2CO in Comet Halley
nucleus. Both numerical simulations and laboratory experi- was produced mainly, and perhaps totally, from an extended
ments show that the link is not simple, at least for the most source (Meier et al., 1993). The region containing the ex-
volatile species. tended sources extended to ~104 km from the nucleus.
The monitoring performed in Comet Hale-Bopp showed Meier et al. (1993) estimated the scalelength of the parent
that the coma composition changed with heliocentric dis- source of H2CO to be 1.2 times the photodissociative scale-
tance. CO was the main escaping gas at large r (Fig. 7). The length of H2CO that corresponds to ~5000 km. According
H2O production rate surpassed that of CO for r < 3 AU. to Eberhardt (1999), there is also indication of a second
Capria et al. (2000) showed that the heliocentric behavior extended source of H2CO with a much longer scalelength.
of CO production (roughly in r –2 from r = 0.9 to 14 AU) These discoveries sparked keen interest in identifying the
can be explained if CO is present in the nucleus both as nature of the extended sources.
pure ice and as trapped gas in amorphous H2O ice that Proposed sources for extended H2CO focus on the de-
would be immediately below the surface. This trapped gas composition of (native) polymerized H2CO (Meier et al.,
is released during the amorphous to crystalline phase tran- 1993), possibly polyoxymethylene (POM) (Mitchell et al.,
sition. In contrast, models considering only the sublimation 1987, 1989; Huebner, 1987). Recent laboratory work dem-
of pure CO ice fail in reproducing the observed heliocen- onstrates that adequate monomeric H2CO can be produced
tric dependence. by thermal decomposition of POM, if cometary grains are
As seen in Fig. 7, distinct trends are observed among the 4% POM by mass in Comet Halley (Cottin et al., 2004).
various molecules. As already discussed, the steep produc- Photolysis of monomeric H2CO was suggested as a sig-
tion curves of HNC and H2CO are likely related to an ex- nificant source for extended CO in 1P/Halley. According
tended production in the coma (see sections 5.3.2 and to Meier et al. (1993), the photodissociation of H2CO pro-
5.6.3). Steep production curves when compared to, e.g., vides about two-thirds of the extended CO source. Accord-
HCN are also observed for CS and OCS (Woodney, 2000; ing to Eberhardt (1999), H2CO could even fully account
Biver et al., 2002a). A pre-/postperihelion asymmetry is also for the extended CO source after a reanalysis of the data.
apparent for all molecules. In contrast, in Comet Hale-Bopp, H2CO was found to be
only a minor contributor to extended CO as its production
7. SPATIAL DISTRIBUTION OF PARENT rate was much below that of CO extended production (sec-
MOLECULES AND EXTENDED SOURCES tion 7.2.1). Carbon suboxide (C3O2) was suggested as a
source of CO (Huntress et al., 1991), but the upper limit
The study of the spatial distribution of parent molecules derived from Vega IKS spectra (C3O2 < 0.1%) (Crovisier
provides clues on the distribution of the outgassing at the et al., 1991b) was well below the minimum value (7.5%)
surface of the nucleus and on gas dynamics processes oc- required to produce the amount of extended CO inferred
 Bockelée-Morvan et al.: The Composition of Cometary Volatiles 411

Fig. 10. Observations of Comet Hale-Bopp with IRTF/CSHELL. (a) Image of thermal continuum at 3.5 µm (λ/δλ = 70). The east-
west slit is indicated. (b) Spatial profiles of CO, H2O, and dust along the slit. (c) Rotational temperatures for CO along the slit.
(d) Symmetric Q-curves showing the rise to terminal values. From DiSanti et al. (2001).

from the Giotto observations. An alternative view, that OCS (Dello Russo et al., 1998) and CO (Weaver et al.,
Giotto flew through a jet enriched in CO, was proposed by 1999b; DiSanti et al., 1999, 2001; Brooke et al., 2003),
Greenberg and Li (1998) to interpret the NMS observations. although the ratio of native to extended source production
rates for CO remains controversial. In contrast, the column
7.2. Radial Distribution from density profiles for H2O (Weaver et al., 1999b; Dello Russo
Long-Slit Spectroscopy et al., 2000; Brooke et al., 2003), C2H6 (Weaver et al.,
1999b; Dello Russo et al., 2001; Brooke et al., 2003), CH4
7.2.1. Infrared results. When a molecule is released (Weaver et al., 1999b; Brooke et al., 2003), and HCN
directly from the nucleus, its column density is expected (Magee-Sauer et al., 1999) were consistent with release
to vary, in first approximation (i.e., Haser model and ρ << solely from the nucleus.
vτ), as ρ–1, where ρ is the distance between the line of sight The technique is illustrated for Comet Hale-Bopp in
and the nucleus (i.e., the impact parameter). If an extended Fig. 10 from DiSanti et al. (2001). An image of the thermal
source is also present, the variation of column density with continuum near 3.5 µm (λ/δλ ~ 70) reveals dust enhance-
r is much flatter. Under favorable circumstances, this dif- ments to the northeast and northwest (sunward) of the nu-
ference can be used to extract the two sources separately. cleus (Fig. 10a). High-dispersion spectra were measured
In Comet Hale-Bopp, extended sources were identified for with the slit positioned as shown. The intensity profiles
412 Comets II

measured along the slit show that CO is extended to the

east while H2O is symmetric about the nucleus and the dust
is extended to the west (Fig. 10b).
To extract the contribution of the native and extended
CO sources, DiSanti et al. (2001) developed the method of
Q-curves, as shown in Fig. 10d. The intensities measured
at symmetric positions along the slit are first averaged to
minimize the effects of outflow asymmetry. An apparent
production rate can be then derived from the intensity
measured at a specific location using equation (11) and the
formula that links the column density to the production rate
under the idealized assumption of spherical outflow at con-
stant velocity. The resulting Q-curve (Fig. 10d) rises from
the nucleocentric value to a terminal value that is taken to
represent the total production rate for the species. The
nucleus-centered value is always too low, owing to slit
losses induced by seeing, drift, guiding error, and other
observing factors, but the terminal value is reached quickly
for molecules released directly from the nucleus (e.g., H2O,
C2H6, CH4, dust). Molecules having an extended source rise
Fig. 11. Mosaicked image of HCN J(1–0) main hyperfine com-
more slowly to the terminal value (e.g., CO, OCS) (com-
ponent (F = 2–1) obtained on April 6, 1997, for Comet Hale-Bopp
pare Q-curves for CO, H2O, and dust; Fig. 10d). with the BIMA array. Contour interval: 0.23 K averaged over
It was estimated that ~70% of OCS was produced from 3.5 km s–1. The angular resolution is 10". From Wright et al.
an extended source in Comet Hale-Bopp near perihelion (1998).
(Dello Russo et al., 1998). At large heliocentric distance
(4.1 AU < r < 2 AU), the spatial profile of CO was consis-
tent with its release solely from the nucleus. However, nucleus but may have a lifetime that is significantly longer
within 2 AU an extended source was activated, and it sup- than the theoretical value (Weaver et al., 2002b).
plied at least half the total CO released thereafter (0.9 AU <
r < 1.5 AU) (DiSanti et al., 2001); using a different ap- 7.3. Millimeter Wave Mapping/Interferometry
proach involving explicit modeling of both parent and
daughter spatial distributions, Brooke et al. (2003) estimated Mapping of rotational emission lines was only attempted
that ~90% of the observed CO was derived from the ex- in a few comets. Most investigations were performed in
tended source at r = 1 AU, in apparent contradiction with Comets Hyakutake and Hale-Bopp, due to their exceptional
the conclusions of DiSanti et al. (2001). The abrupt onset brightnesses. Focal plane arrays and on-the-fly mapping
and constant fractional production of the extended source (which consists in moving the telescope beam across the
thereafter suggest a thermal threshold for release from small source at a constant velocity) provided extended coverage
CHON grains, rather than photolysis of a precursor volatile. of the molecular emissions with single-dish telescopes, al-
Monomeric H2CO was at most a minor contributor to ex- though with limited spatial resolution (10" at most) [(e.g.,
tended CO in Comet Hale-Bopp. Carbon dioxide is admit- Lovell (1999) using QUARRY at the Five College Radio
tedly a significant source of CO. However, it cannot explain Astronomy Observatory (FCRAO)]. Large maps using con-
the extended CO source observed in the IR, which has a ventional techniques were also obtained (e.g. Hirota et al.
scalelength much smaller than the CO2 photodissociation (1999) at the Nobeyama 45-m telescope; Biver et al. (1999a)
scalelength. In Comet Hyakutake, CO was abundant and it at JCMT). Interferometry techniques have been successfully
was released almost entirely from the nucleus (DiSanti et used for the first time, and provided angular resolutions up
al., 2003). to 2". Numerous observations were performed in Comet
7.2.2. Ultraviolet results. The advent of the long-slit Hale-Bopp with the IRAM Plateau de Bure interferometer,
capability of the Space Telescope Imaging Spectrograph the array of the Berkeley-Illinois-Maryland Association
(STIS) on HST now permits extremely high-spatial resolu- (BIMA), and the Owens Valley Radio Observatory (OVRO).
tion studies of CO and S2. However, the small g-factors for Interferometric maps of rotational lines of CO, HCN (e.g.,
the CO emissions makes this approach feasible only for the Fig. 11), H2S, CS, SO, H2CO, HNC, DCN, HDO, and
brightest comets. While the g-factors are much larger for S2, CH3OH were obtained (Blake et al., 1999; Veal et al., 2000;
its abundance is so low that poor signal-to-noise is a problem Wink et al., 1999; Wright et al., 1998; Woodney et al., 2002).
in this case as well. Nevertheless, accurate spatial bright- In contrast to other spectral domains, additional information
ness profiles for S2 were recently obtained in 153P/2002 C1 on the spatial distribution along the line of sight can be
(Ikeya-Zhang) and indicate that S2 probably originates in the extracted from the radio maps by analyzing the line shapes.
 Bockelée-Morvan et al.: The Composition of Cometary Volatiles 413

Maps of Comet Hale-Bopp show the presence of gas- ecules. That of HCN was found consistent with theoretical
eous jets. The images obtained by Blake et al. (1999) with predictions, while a photodissociation rate 10 times larger
OVRO show HNC, DCN, and HDO emissions offset by a than the commonly accepted value is suggested for CS.
few arcseconds with respect to the dust continuum emis-
sion, interpreted as due to jets enriched in these molecules. 8. MOLECULAR ABUNDANCES AND
No such offsets were observed for other species mapped CHEMICAL DIVERSITY AMONG COMETS
with millimeter interferometry. Veal et al. (2000) observed
structures in HCN J(1–0) maps obtained with BIMA, which According to current theories, comet formation in the
varied and disappeared on timescales ~2 h. These variations solar nebula extended over a wide range of heliocentric
may trace rotating HCN jets, as observed for CO. Indeed, distances for both Oort cloud comets [also called nearly
a sinusoidal temporal variation in the spectral shift of the isotropic comets (Dones et al., 2004)] and Jupiter-family
CO J(2–1) line was observed at IRAM/PdBi (Henry et al., comets [now recognized as a subclass of the ecliptic com-
2002; Henry, 2003). Both the period of this sinusoid, which ets (Duncan et al., 2004; Morbidelli and Brown, 2004)],
is consistent with the nucleus rotation period, and the time which suggests that comets could display diversity in their
modulation of the signals received by the antenna pairs, chemical composition depending on the local temperature
suggest the existence of a CO spiraling jet. From the maps and nebular composition where they formed. If there was
of Comets Hyakutake and Hale-Bopp (Biver et al., 1999a; significant mixing of nebular material across large ranges
Wink et al., 1999), H2CO clearly appears extended with a in heliocentric distance, even individual cometary nuclei
parent scalelength consistent with that derived for 1P/Halley could exhibit chemical inhomogeneity.
from the in situ measurements. Coarse radio mapping in Chemical diversity among comets is indeed observed for
C/1989 X1 (Austin) gave similar results (Colom et al., both parent volatiles and daughter species. From a study of
1992). In contrast, the HCN and H2S maps of Comet Hale- radicals (OH, CN, C2, C3, NH) in 85 comets, A’Hearn et al.
Bopp (Wink et al., 1999; Wright et al., 1998) are consistent (1995) proposed the existence of two classes of comets,
with parent molecule distributions. As discussed in sec- depending on their C2/CN ratio: “typical” comets and “C2-
tion 5.5.3, the interferometric observations of SO show that depleted” comets. They found that about one-half the Ju-
this species does not follow a parent density distribution, and piter-family comets (JFCs) were C2-depleted, but the frac-
suggest the photolysis of SO2 as the main source of SO tion of C-depleted nearly isotropic comets was much smaller.
(Wink et al., 1999). The meaning of this depletion is clouded by two factors.
Other observational clues for extended sources obtained First, the relative production of C2 and CN from several pos-
by radio observations concern distant comets. Gunnarsson sible gas and dust precursors is not known. Second, the
et al. (2002) mapped the CO J(2–1) line in Comet 29P/ present volatile composition of a JFC may not reflect its
Schwassmann-Wachmann 1 with the SEST telescope. They original volatile composition. Jupiter-family comets typi-
concluded that there was a large (~70%) contribution of CO cally have low-inclination, prograde orbits with periods less
coming from an extended source, likely sublimating icy than ~20 years, and they are subjected to much greater in-
grains. No such imaging was performed in Comet Hale- solation than the nearly isotropic comets. Thus, some JFCs
Bopp when far from the Sun. However, the CO line shapes may have experienced thermal fractionation while in their
of Comet Hale-Bopp at large r resemble those of 29P/ present orbits.
Schwassmann-Wachmann 1, which led Gunnarsson et al. Surveys of parent volatile abundances show strong evi-
(2003) to suggest that sublimating grains were also contrib- dence for chemical diversity among comets (Fig. 12 and
uting to the CO production in Comet Hale-Bopp when at Table 1). Among the Oort cloud comets (OCCs), the native
r > 4 AU. These line profiles are asymmetric, and character- CO abundance varies by a factor of ~40 (0.4–17%) rela-
ized by a pronounced peak on the blue wing of the line, and tive to H2O. The abundance of extended CO varies by a
a redshifted part of lower intensity. This blue peak would similar amount, but the two sources are not correlated. The
correspond to nuclear production toward the Sun, while the comet-to-comet differences in native CO are presumably
redshifted component is the red part of a symmetric pro- attributable to intrinsic variation in the amount of CO ice
file due to the secondary source. Much more symmetric frozen into cometary nuclei. The CO2 abundance varied by
radio lines were observed for CH3OH, H2CO, and OH at a factor of five (2.5–12%) among five comets (Feldman et
r > 3.5 AU (Biver et al., 1997; Womack et al., 1997). These al., 1997), although this conclusion rests on the assump-
results are consistent with a relative contribution of the icy tion that the observed CO Cameron band emission was due
grains vs. nucleus outgassing being more important for solely to the photodissociation of CO2. Infrared investiga-
CH3OH, H2CO, and H2O than for CO. This may be not sur- tions of CO2 in three comets indicate CO2/H2O variations
prising given the lower volatilities of CH3OH, H2CO, and by at least a factor of 2.
H2O ices compared to CO ice. Infrared observations of hydrocarbons in a handful of
Snyder et al. (2001) used the maps of HCN J(1–0) and comets (Mumma et al., 2003; Gibb et al., 2003) show that
CS J(2–1) obtained in Comet Hale-Bopp with the BIMA the CH4 abundance varies by a factor of ~10 (0.14–1.4%),
array to measure the photodissociation rates of these mol- apparently without correlation with CO. Thus, one cannot
414 Comets II

The comets that are abundant in CH3OH are also abundant

in H2CO. No clear correlation is found between the rela-
tive abundances and the dynamical origin of the comets,
or their dust-to-gas ratios.
From UV observations of the CS radical by IUE and
HST of 19 comets (Meier and A’Hearn, 1997), the CS2
abundance varies from 0.04% to 0.3%.
Perhaps one should not be surprised to find significant
chemical diversity among even a small sample of nearly
isotropic comets because, as stated earlier, the comets from
the Oort cloud were probably formed over a large range of
heliocentric distances. The most recent dynamical models
suggest that comets now in the Oort cloud were contrib-
uted in roughly equal numbers by each giant planet and the
Kuiper belt (Dones et al., 2004). The chemical diversity
found to date suggests that comets from various regions of
the protoplanetary disk are present in today’s Oort cloud
and can provide a window on this crucial period in solar
system development. However, many more comets must be
sampled and additional parent molecules measured to estab-
lish overall taxonomic classes of comets from their chem-
istry and related parameters.

9. ISOTOPIC COMPOSITION

Isotopic ratios are an important diagnostic of the physi-

cal conditions that prevailed during the formation of com-
etary volatiles, as well as isotopic exchange and mixing
Fig. 12. Abundances relative to water in comets. The range of processes that may have occurred in the solar nebula be-
measured values is shown in the gray portions. The number of fore their incorporation into comets. Since most detections
comets for which data are available is given in the right. For CO, of parent molecules postdate 1985, it is not surprising that
abundances refer to total CO (native and distributed sources). the detection of their isotopomers is rare. We summarize
most of the measurements in Table 3.
The first measurements of the D/H ratio in H2O were
define a “typical” abundance for either CO or CH4. The obtained in Comet Halley from mass-resolved ion-spectra
C2H6 abundance shows less diversity, with six OCCs show- of H3O+ acquired by the IMS (Balsiger et al., 1995) and
ing ~0.4–0.7% and only C/1999 S4 (LINEAR) differing NMS (Eberhardt et al., 1995) instruments onboard Giotto.
greatly. In the same group of comets, the C2H2 abundance These independent data provided precise D/H values, which
was typically 0.2–0.3%, but it was significantly lower in combined give a D/H value of ~3 × 10 –4. Thanks to the
C/1999 S4. The CH3OH abundance is ~2% in 14 comets availability of sensitive groundbased instrumentation in the
(including all four JFCs sampled) observed in the infrared, submillimeter domain, HDO was detected in Comets Hya-
but three OCCs had much lower abundances [C/1990 K1 kutake (Fig. 13) and Hale-Bopp from its 101–000 line at
(Levy), C/1996 Q1 (Tabur), and C/1999 S4] and two had 464.925 GHz (Bockelée-Morvan et al., 1998; Meier et al.,
much higher abundances [C/1989 X1 (Austin), 109P/Swift- 1998a). The derived D/H values are in agreement with the
Tuttle]. determinations in 1P/Halley. Blake et al. (1999) reported
From radio observations of about 25 comets (including the interferometric detection of the 211–212 HDO transition
6 JFCs), Biver et al. (2002b) studied the production rates at 241.562 GHz in Comet Hale-Bopp and derived a D/H
of HCN, HNC, CH3CN, CH3OH, H2CO, CO, CS, and H2S value one magnitude larger in jets compared to the sur-
relative to H2O. Hydrogen cyanide is the best-studied mol- rounding coma. A serendipitous detection of the 312–221
ecule. In contrast to other species, the distribution of the HDO line at 225.897 GHz in Comet Hale-Bopp was also
HCN/H2O ratios is strongly peaked, with most comets reported by Crovisier et al. (2004a).
around 0.1%. Observed in more than 10 comets, CH3OH, DCN was detected in Comet Hale-Bopp with the JCMT
H2CO, and H2S show large variations. The distribution of from its J(5–4) rotational transition at 362.046 GHz (Meier
CH3OH/H2O ratios follows that measured from infrared et al., 1998b). The inferred D/H value in HCN is 2.3 × 10 –3,
spectra. The H2CO/H2O abundance ranges from 0.4% to i.e., seven times larger than the value in H2O. The same
1.3% in 12 comets, but is significantly lower (≤0.15%) in value is reported by Crovisier et al. (2004a) from a mar-
21P/Giacobini-Zinner. H2S/H2O varies from 0.4% to 1.5% ginal detection of the J(3–2) DCN line at the IRAM 30-m
in 10 comets, but is only 0.12% in C/2000 WM1 (LINEAR). telescope. Interferometric observations of this J(3–2) DCN
 Bockelée-Morvan et al.: The Composition of Cometary Volatiles 415

TABLE 3. Isotopic ratios in comets.

Ratio Molecule Comet Value Method* Reference

D/H H2O Halley (3.08+0.38
–0.53 ) × 10
–4 m.s.† Balsiger et al. (1995)
Halley (3.06 ± 0.34) × 10 –4 m.s.† Eberhardt et al. (1995)
Hyakutake (2.9 ± 1.0) × 10 –4 r.s. Bockelée-Morvan et al. (1998)
Hale-Bopp (3.3 ± 0.8) × 10 –4 r.s. Meier et al. (1998a)
HCN Hale-Bopp (2.3 ± 0.4) × 10 –3 r.s. Meier et al. (1998b)
H2CO Halley <2 × 10 –2 m.s.‡ Balsiger et al. (1995)
Hale-Bopp <5 × 10 –2 r.s. Crovisier et al. (2004a)
CH3OH Halley <~1 × 10 –2 m.s.§ Eberhardt et al. (1994)
Hale-Bopp <3 × 10 –2 r.s.¶ Crovisier et al. (2004a)
Hale-Bopp <8 × 10 –3 r.s.** Crovisier et al. (2004a)
NH3 Hyakutake <6 × 10 –2 v.s.†† Meier et al. (1998c)
Hale-Bopp <4 × 10 –2 r.s.‡‡ Crovisier et al. (2004a)
CH4 153P/2002 C1 <1 × 10 –1 i.s. Kawakita et al. (2003)
H2S Hale-Bopp <2 × 10 –1 r.s. Crovisier et al. (2004a)
CH Hyakutake <3 × 10 –2 v.s. Meier et al. (1998c)
12 C/13 C C2 four comets§§ 93 ± 10 v.s. Wyckoff et al. (2000)
CN Halley 95 ± 12 v.s. Kleine et al. (1995)
CN five comets¶¶ 90 ± 10 v.s. Wyckoff et al. (2000)
CN Hale-Bopp 165 ± 40 r.s. Arpigny et al. (2003)
CN C/2000 WM1 115 ± 20 r.s. Arpigny et al. (2003)
HCN Hyakutake 34 ± 12*** r.s. Lis et al. (1997)
HCN Hale-Bopp 111 ± 12 r.s. Jewitt et al. (1997)
HCN Hale-Bopp 109 ± 22 r.s. Ziurys et al. (1999)
HCN Hale-Bopp 90 ± 15 r.s. Lis et al. (1999)
14 N/15 N CN Hale-Bopp 140 ± 35 v.s. Arpigny et al. (2003)
CN C/2000 WM1 140 ± 30 v.s. Arpigny et al. (2003)
HCN Hale-Bopp 323 ± 46 r.s. Jewitt et al. (1997)
HCN Hale-Bopp 330 ± 98 r.s. Ziurys et al. (1999)
16 O/18 O H2O Halley 518 ± 45 m.s. Balsiger et al. (1995)
H2O Halley 470 ± 40 m.s. Eberhardt et al. (1995)
H2O 153P/2002 C1 450 ± 50 r.s. Lecacheux et al. (2003)
32 S/34 S S+ Halley 23 ± 6 m.s. Altwegg (1996)
CS Hale-Bopp 27 ± 3 r.s. Jewitt et al. (1997)
H2S Hale-Bopp 17 ± 4 r.s. Crovisier et al. (2004a)
* m.s.: mass spectrometry; r.s.: radio spectroscopy; v.s.: visible spectroscopy; i.s.: infrared spectroscopy.
† From H O +.
3
‡ From HDCO+.
§ CH DOH and CH OD averaged.
2 3
¶ For CH OD.
3
** For CH2DOH.
†† From NH.
‡‡ From NH D.
2
§§ Mean ratio in C from observations in C/1963 A1 (Ikeya), C/1969 T1 (Tago-Sato-Kosaka), C/1973 E1 (Kohoutek), and C/1975 N1
2
(Kobayashi-Berger-Milon).
¶¶ Mean ratio in CN from five comets: 1P/Halley, C/1990 K1 (Levy), C/1989 X1 (Austin), C/1989 Q1 (Okazaki-Levy-Rudenko), and

C/1995 O1 (Hale-Bopp).
*** Ratio possibly affected by line blending.

line lead to DCN/HCN values in jets, which are again signi- or visible spectroscopy of daughter species (Table 3). Most
ficantly larger than the single-dish value (Blake et al., 1999). of these upper limits exceed a few percent and may be not
We note that these differences in isotopic abundance ratios easily improved from further groundbased observations
for different regions of the coma (e.g., in and out of jets) unless a comet as bright as Comet Hale-Bopp is coming.
must be confirmed by higher-quality interferometric obser- The measurements of isotopes other than D in cometary
vations before too much effort is expended interpreting volatiles are limited. In Comet Hale-Bopp, rotational tran-
these differences. sitions of HC15N, H13CN, and C34S were detected, leading
Finally, upper limits for several other D-bearing mol- to isotopic ratios that are compatible with the terrestrial
ecules were obtained, mainly by millimeter spectroscopy values 12C/13C = 89, 14N/15N = 270, and 32S/34S = 24 (Jewitt
416 Comets II

ecules with three H atoms (e.g., NH3 or CH3OH); A, E, and

F for molecules with four H atoms (e.g., CH4); and so forth.
Conversions among different species in the gas phase by
radiative transitions or by collisions are strictly forbidden.
Conversions are presumably very slow in the solid phase
as well, although various proton-exchange mechanisms do
exist in that case.
The ortho-to-para population ratio (OPR) can be evalu-
ated from the rotational distribution of the molecules. When
there is equilibrium at a temperature T

∑ (2J + 1)exp
E
(2Io + 1) −
o levels
kT
OPR = (16)
∑
E
(2Ip + 1) (2J + 1)exp −
p levels
kT
Fig. 13. The 101–000 line of HDO at 465 GHz observed in Comet
C/1996 B2 (Hyakutake) with the CSO (Bockelée-Morvan et al., where o and p refer to the ortho and para rotational levels.
1998). J and E are the rotational quantum number and energy of
the levels respectively. For high temperatures, the popula-
tions tend to equilibrate to their statistical weights, 2I + 1.
Thus, the high-temperature OPR limit is 3 for H2O, 1 for
et al., 1997; Ziurys et al., 1999). From a tentative detection NH3, … (see discussions by Crovisier, 1984; Mumma et
of H234S, Crovisier et al. (2004a) deduced a 32S/34S ratio al., 1993).
30% lower than the terrestrial value. In Comet Hyakutake, From observations of the ν3 band of H2O with the KAO,
Lis et al. (1997) inferred a 12C/13C ratio in HCN three times Mumma et al. (1993) reported an OPR of 2.5 ± 0.1 for 1P/
lower than the terrestrial value. However, the J(3–2) H13CN Halley (Tspin ≈ 29 K) and 3.2 ± 0.2 for C/1986 P1 (Wilson)
line used for this measurement is partly blended with a SO2 (Tspin > 50 K). From observations with ISO (Fig. 3), the
line, so this result is uncertain. Regarding the 18O/16O ra- OPR was 2.45 ± 0.10 for Comet Hale-Bopp and 2.76 ± 0.08
tio, which has only been measured in H2O, in situ measure- for 103P/Hartley 2 (Crovisier et al., 1997, 1999b), corre-
ments in 1P/Halley are consistent with the terrestrial value sponding to Tspin = 28 ± 2 K and 36 ± 3 K, respectively.
of 500 (Table 3). H18 2
O has been detected through its fun- Kawakita et al. (2001, 2002) measured the OPR of the
damental ortho line at 547.7 GHz in Comet 153P/2002 C1 NH2 radical in Comets C/1999 S4 (LINEAR) and C/2001
(Ikeya-Zhang) by Lecacheux et al. (2003), and the derived A2 (LINEAR). Following symmetry conservation laws,
H18
2
O/H162
O ratio is consistent with that obtained by mass decay products maintain the spin distribution of the origi-
spectrometry in 1P/Halley. nal molecules during photolysis, so that the OPR of NH3
Lines of 13CN [mainly in the B2Σ+–X2Σ+ v(0–0) system] may be traced from that of NH2. Kawakita et al. derived
and 13C12C (Swan bands) were identified in visible spectra an OPR for NH3 of 1.17 ± 0.04 and 1.12 ± 0.03, respec-
of several comets. All measurements give a C-isotopic ra- tively, for the two LINEAR comets, corresponding to a spin
tio in the CN and C2 radicals consistent with the terrestrial temperature of ~30 K.
value [Table 3; see data for individual comets in Wyckoff et Several other cometary molecules (H2CO, CH3OH, hy-
al. (2000)]. These isotopic ratios may not fully reflect the drocarbons, … ) are likely to have OPR effects that are
values in HCN and C2H2, as other sources of CN and C2 worthy of investigation. The spin species of methane were
radicals are suspected to be present in the coma. Arpigny found to be consistent with Tspin > 40–50 K (Weaver et al.,
et al. (2003) report anomalous C14N/C15N ratios (~140) in 1997; Gibb et al., 2003). Formaldehyde was also investi-
Comets Hale-Bopp and C/2000 WM1 (LINEAR). This is gated from its radio rotational lines, but no reliable OPR
much less than the ratio HC14N/HC15N = 270 observed in could be derived because only a few lines could be probed.
Comet Hale-Bopp, pointing to an additional, still unidenti- The cold spin temperatures retrieved for cometary H2O
fied, source of CN. and NH3 presumably have a meaning related to the history
of these species in the nucleus or even before, i.e., con-
10. ORTHO-TO-PARA RATIOS nected with their formation:
1. Reequilibration in the nucleus. We would then ex-
Molecules with H atoms at symmetrical positions may pect different spin temperatures for different comets, de-
exist in different nuclear-spin species according to the sum pending on their present orbit and dynamical history, which
I of the spins of their H atoms. These spin species are called does not seem to be the case. 30 K corresponds to the equi-
ortho (I = 1) and para (I = 0) for molecules with two H librium temperature at r ~ 100 AU, under present solar sys-
atoms (e.g., H2, H2O, H2S, H2CO, … ); A and E for mol- tem conditions.
 Bockelée-Morvan et al.: The Composition of Cometary Volatiles 417

2. Water formation. The cold spin temperature would troscopy and the compilation of comprehensive spectro-
rule out a gas phase formation, since reactions leading to scopic databases are also needed for further progress.
H2O are exothermal and would form H2O at a high tem- An alternative approach is in situ analysis by space ex-
perature. Rather, the low OPR values suggest formation on ploration, as will be performed by the Rosetta mission.
grains, where H2O would reequilibrate at the grain tempera- Mass spectroscopy and gas chromatography could be much
ture (Tielens and Allamandola, 1987). The ortho-to-para more sensitive than remote sensing.
conversion of H2 on interstellar grains is very fast — on the Perhaps the ultimate answers regarding cometary com-
order of 60 s. Thus, low OPR values are consistent with position will only be revealed by the analysis, at leisure on
cometary H2O originating in the interstellar medium. Earth, of returned samples of cometary ices. Unfortunately,
3. Fractionation of spin species. It is also possible that there is not yet any approved space mission with this as its
one of the spin species is favored by condensation or ab- goal, but we can hope for such a mission in the not too
sorption on interstellar or cometary grains, as is indeed distant future.
observed in laboratory experiments such as condensation The cost and difficulty of encounter missions with com-
of D2O on a cold matrix or selective absorption of H2O on ets will limit, probably for a long time, in situ investiga-
charcoal (Tikhonov and Volkov, 2002). tions to a very small number of objects chosen among the
short-period comets. Ground- and Earth-orbit-based obser-
11. PERSPECTIVES vations will still be needed for the systematic investigation
of a large sample of objects, in order to study their diver-
The situation regarding the detection and abundance sity. Only then will we truly be able to address the role that
determinations of cometary parent molecules has drastically comets played in the formation and evolution of the solar
changed since the publication of Comets (Wilkening, 1982). system and their relation to the interstellar medium.
At that time, CO was the only parent molecule that had been
directly identified. Generally, one had to rely on deducing Acknowledgments. H.A.W. acknowledges financial support
the identity of the parents from observations of their daugh- by NASA through grant HST-GO-8276.01-A from the Space
ter products. A half dozen species were proposed in these Telescope Science Institute, which is operated by the Association
pioneering times, including H2O, CO2, CH4, NH3, all of of Universities for Research in Astronomy, Inc., under NASA
Contract NAS5-26555, and through FUSE Grant NAG5-10921.
which have been confirmed by recent observations.
We now have firm, direct identifications of two dozen
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424 Comets II
 Feldman et al.: Spectroscopy of Fragment Species in the Coma 425

Spectroscopic Investigations of Fragment

Species in the Coma
Paul D. Feldman
The Johns Hopkins University

Anita L. Cochran
University of Texas

Michael R. Combi
University of Michigan

The content of the gaseous coma of a comet is dominated by fragment species produced by
photolysis of the parent molecules issuing directly from the icy nucleus of the comet. Spec-
troscopy of these species provides complementary information on the physical state of the coma
to that obtained from observations of the parent species. Extraction of physical parameters re-
quires detailed molecular and atomic data together with reliable high-resolution spectra and
absolute fluxes of the primary source of excitation, the Sun. The large database of observa-
tions, dating back more than a century, provides a means to assess the chemical and evolution-
ary diversity of comets.

1. INTRODUCTION mation, spectrophotometric data may be used to quantita-

tively derive column abundances of the observed species
In 1964, P. Swings delivered the George Darwin lecture from which, with suitable modeling (see Combi et al., 2004),
(Swings, 1965) on the one-hundredth anniversary of the first the relative abundance of the parent species in the cometary
reported spectroscopic observation of a comet. He described ice could be deduced. Note that for some species, particu-
a century of mainly photographic observations of what were larly C2 and C3, the identity of the parent still remains am-
recognized to be fragment species resulting from photo- biguous. Long-slit spectroscopy at high spatial resolution
chemical processes acting on the volatile species released has provided constraints on the photochemical parameters
from the cometary nucleus in response to solar heating. The used in the models and also has served to probe physical
features identified in the spectra were bands of the radicals conditions in the coma that produce deviations from the
OH, NH, CN, CH, C3, C2, and NH2; the ions OH+, CH+, purely photochemical models. Similar analyses are also pos-
CO+2 , CO+, and N+2; Na I; and the forbidden red doublet of sible with narrowband photometric imaging (see Schleicher
O I (Swings and Haser, 1956; Arpigny, 1965). By the time and Farnham, 2004).
of the publication of the book Comets (Wilkening, 1982) Advances in infrared (IR) and radio technology, together
18 years later, optical spectroscopy had become quantitative with the timely apparitions of several active comets during
photoelectric spectrophotometry (A’Hearn, 1982) and had the past 10 years, have led to the identification of more than
been extended to the radio and vacuum ultraviolet (UV) two dozen parent volatile species in the coma (see Bockelée-
(Feldman, 1982), yet the inventory of species detected grew Morvan et al., 2004). During this same time enhancements
slowly. In the visible, the Sun-grazing Comet Ikeya-Seki in optical and UV technology have also permitted more de-
(C/1965 S1) showed the metals K, Ca+, Ca, Fe, V, Cr, Mn, tailed investigations of the spectra of (mainly) fragment spe-
Ni, and Cu (Preston, 1967), presumably from the vaporiza- cies, leading to a more complete picture of the entire coma.
tion of refractory grains, and H2O+ was identified in Comet The availability of state-of-the-art optical instrumentation at
Kohoutek (C/1973 E1) a few years later. In the UV, the con- a given cometary apparition ensures the acquisition of data-
stituent atoms H, O, C, and S were detected together with sets with good temporal coverage and comparability to the
CS and CO, the first “parent” molecule to be directly identi- historical record for purposes of assessing diversity among
fied spectroscopically (Feldman and Brune, 1976). comets. The high sensitivity of optical detectors also means
The spectra of the observed radicals are necessarily com- that fragment species can be detected at larger heliocentric
plex and detailed analyses of high-resolution spectra dem- distances than any of the parents (cf. Rauer et al., 2003).
onstrated that the observed emission was produced for the While notable advances have been made in spaceborne UV
most part by fluorescence of solar radiation. With this infor- spectroscopic instrumentation, notably STIS on the Hubble

425
426 Comets II

Space Telescope (HST) and the Far Ultraviolet Spectroscopic cludes both allowed radiative decays (such as from the A2Σ+
Explorer (FUSE) satellite, these resources are limited and state of OH) as well as those from metastable states such
cometary observations are relatively few. as O(1D), whose lifetime is ~130 s. The O I 1D–3P doublet at
6300 and 6364 Å has been used extensively as a ground-
2. PHYSICAL PROCESSES based surrogate for the determination of the water produc-
tion rate with the caveat that other species such as OH, CO,
2.1. Photolysis of Parent Molecules and CO2 may also populate the upper level. When the den-
sity of H2O is sufficient to produce observable 6300 Å emis-
The photolytic destruction of water, the dominant mo- sion, it may also produce collisional quenching of the 1D state,
lecular species in the coma of comets at distances near 1 AU and this must be included in the analysis. The analogous
from the Sun, has been extensively studied (see Combi et 1D– 3P transitions in C occur at 9823 and 9849 Å and can

al., 2004). It may proceed through multiple paths depend- similarly give information about the production rate of CO.
ing on the energy of the incident solar photon (here given Carbon atoms in the 1D state, whose lifetime is ~4000 s, are
as the threshold wavelength): known to be present from the observation of the resonantly
scattered 1Po–1D transition at 1931 Å (Tozzi et al., 1998).
H2O + hν → OH + H 2424.6 Å To date the IR lines have only been detected in Comets 1P/
→ OH(A2Σ+) + H 1357.1 Å Halley and Hale-Bopp (C/1995 O1) (Oliversen et al., 2002).
→ H2 + O(1D) 1770 Å
→ H2 + O(1S) 1450 Å 2.2. Excitation Mechanisms
→ H + H + O(3P) 1304 Å
→ H2O+ + e 984 Å The extraction of coma abundances from spectrophoto-
→ H + OH+ + e 684.4 Å metric measurements of either the total flux or the surface
→ H2 + O+ + e 664.4 Å brightness in a given spectral feature has been summarized
→ OH + H+ + e 662.3 Å by Feldman (1996) and we repeat some of the salient points
here. We note that the uncertainty in the derived abundances
Many of the fragments can be further broken down: may include not only the measurement uncertainty, but also
uncertainties in the atomic and molecular data and, in the
OH + hν → O+H 2823.0 Å case of surface brightness measurements, uncertainties in
→ OH+ + e 928 Å the model parameters used. One must be careful in compar-
H2 + hν → H+H 844.79 Å ing abundances and production rates derived by different
→ H+2 + e 803.67 Å observers for the same comet at a given time to assure that
→ H + H+ + e 685.8 Å comparable physical and model parameters are used.
O + hν → O+ + e 910.44 Å In the simplest case we begin with the total number of
H + hν → H+ + e 911.75 Å species i in the coma

The last two reactions may also occur by resonant charge Mi = Qiτi(r) (1)
exchange with solar wind protons. Photoelectrons produced
in the ionization process, particularly those from the strong where Qi is the production rate (atoms or molecules s–1) of
solar He II line at 304 Å, also lead to secondary dissocia- all sources of species i and τi(r) is the lifetime of this spe-
tion and ionization (Cravens et al., 1987) and may contrib- cies at heliocentric distance r, τi(r) = τi(1 AU)r2.
ute to the observed emissions. For an optically thin coma, the luminosity, in photons
Similar equations may be written for other cometary cm–2 s–1, in a given atomic or molecular transition at wave-
species and many, particularly some of the more abundant length λ, is
ones such as CO and CO2, produce many of the same frag-
ment species. Huebner et al. (1992) have compiled a very L(λ) = Mig(λ,r) (2)
useful list of photodestruction rates for a large number of
molecules that includes many polyatomic species that have where the fluorescence efficiency, or “g-factor”, g(λ,r) =
been identified as being present in the cometary ice (see g(λ,1 AU)r –2, is defined by Chamberlain and Hunten (1987)
Table 1 of Bockelée-Morvan et al., 2004). in cgs units as
For the case of H2O, all the fragment species listed
above, with the exception of H+ and H+2, have been detected
πe 2 2
spectroscopically. The second through fourth reactions g(λ,1 AU) = λ fλπ F ω photons s–1 atom–1 (3)
mc2
listed above leave the product atom or molecule in an ex-
cited state that leads to “prompt” emission of a photon. This
provides a means for mapping the spatial distribution of the Here, e, m, and c have their usual atomic values; λ is the
parent molecule in the inner coma. Prompt emission in- transition wavelength; fλ is the absorption oscillator strength;
 Feldman et al.: Spectroscopy of Fragment Species in the Coma 427

πF is the solar flux per unit wavelength interval at 1 AU; absorption of a solar photon is less than the probability that
and w is the albedo for single scattering, defined for a line the species will be dissociated or ionized, so that the ground
in an atomic multiplet as state population is not affected by fluorescence and can be
described by a Boltzmann distribution at a suitable tempera-
Aj ture corresponding to the cometary environment where the
ω= (4) species was produced. For prompt emission, such as that
Σ jA j from CO produced by photodissociative excitation of CO2
(Mumma et al., 1975), the rotational temperature of the CO
and Aj is the Einstein transition probability. At low and mod- will be ~5 times larger than the rotational temperature of the
erate spectral resolution, a given multiplet is not resolved CO2 because of the factor of 5 in the rotational constants
and in this case w = 1. For diatomic molecules, fluorescence and the need to conserve angular momentum in the disso-
to other vibrational levels becomes important and the evalua- ciation process. Similarly, prompt emission of OH will also
tion of w depends to a large degree on the physical conditions be characterized by a “hot” rotational distribution (Bertaux,
in the coma. Note that this definition differs from equation (3) 1986; Budzien and Feldman, 1991).
of Bockelée-Morvan et al. (2004) in that a blackbody cannot 2.2.2. Swings and Greenstein effects. Swings (1941)
be used to represent the solar flux, particularly in the UV, pointed out that because of the Fraunhofer absorption lines
and that a high-resolution spectral atlas is required to ac- in the visible region of the solar spectrum, the absorption
count for the Fraunhofer structure in the solar spectrum. of solar photons in a given molecular band would vary with
Then, for a comet at a geocentric distance ∆, the total the comet’s heliocentric velocity, r, leading to differences
flux from the coma at wavelength λ is in the structure of a band at different values of r when ob-
served at high spectral resolution. This effect is now com-
monly referred to as the Swings effect. Even for observa-
L(λ) Q g(λ, r)τ i(r)
F (λ) = = i photons cm–2 s–1 (5) tions at low resolution, the Swings effect must be taken into
4π∆2 4π∆2 account in the calculation of total band g-factor, and this
has been done for a number of important species such as
Note that the product g(λ,r)τi(r) is independent of r. OH, CN, and NH. A particularly important case is that of
Unfortunately, the scale lengths (the product of lifetime the OH A2Σ+–X2Π (0,0) band at ~3085 Å, which is often
and outflow velocity) of almost all the species of interest used to derive the water production rate (Scheicher and
in the UV are on the order of 105–106 km at 1 AU. Thus, A’Hearn, 1988).
total flux measurements require fields of view ranging from While this effect was first recognized in the spectra of
several arcminutes to a few degrees. This has been done radicals in the visible, a similar phenomenon occurs in the
only rarely (Woods et al., 2000). Again assuming an opti- excitation of atomic multiplets below 2000 Å, where the
cally thin coma, the measured flux in the aperture, F'(λ), can solar spectrum makes a transition to an emission line spec-
be converted to an average surface brightness (in units of trum. For example, the three lines of O I λ1302 have widths
rayleighs), B(λ) of ~0.1 Å, corresponding to a velocity of ~25 km s–1, so that
knowledge of exact solar line shapes is essential to a reli-
B(λ) = 4π10–6F'(λ)Ω–1 (6) able evaluation of the g-factor for this transition (Feldman
et al., 1976; Feldman, 1982).
where Ω is the solid angle subtended by the aperture. The A differential Swings effect occurs in the coma since
brightness, in turn, is related to Ni, the average column den- atoms and molecules on the sunward side of the coma, flow-
sity of species i within the field of view by ing outward toward the Sun, have a net velocity that is dif-
ferent from those on the tailward side, and so if the absorp-
B(λ) = 10–6g(λ,r)Ni (7) tion of solar photons takes place on the edge of an absorp-
tion (or emission) line, the g-factors will be different in the
At this point the evaluation of Qi from Ni requires the use sunward and tailward directions. Differences of this type
of a model of the density distribution of the species i (see will appear in long-slit spectra in which the slit is placed
Combi et al., 2004). along the Sun-comet line. This effect was pointed out by
2.2.1. Fluorescence equilibrium. The excitation of the Greenstein (1958). An analog in the far-UV has been ob-
electronic transitions of the radicals observed in the visible served in the case of O I λ1302. The measurement of a
and near-UV, which may have many photon absorption and Greenstein effect in OH in Comet 2P/Encke has been used
emission cycles in their lifetime, leads to “fluorescence to derive the outflow velocity of water and consequently the
equilibrium” of the rotational levels within the ground vi- nongravitational acceleration of the comet (A’Hearn and
brational level. This process and the various factors that Schleicher, 1988).
affect it are fully discussed in section 3.1.4 of Bockelée- 2.2.3. Bowen fluorescence. As noted above, in the
Morvan et al. (2004). In contrast, in the far-UV, where the UV, with the exception of the H I Lyman series, solar line
solar flux is low, it is often the case that the probability of widths are such that for comets with heliocentric velocities
428 Comets II

>25 km s–1, the available flux at the center of the absorbing ments of the solar flux by integrating the cross section
atom’s line is reduced to a very small value. It was thus sur- λ th
prising that the O I λ1302 line appeared fairly strongly in the
observed spectrum of Comets Kohoutek (C/1973 E1) and
Jd = ∫
0
πF σd dλ (8)

West (C/1975 V1), whose values of r were both >45 km s–1 These rates may also be estimated from the threshold en-
at the times of observation. The explanation invoked the ergies shown in the table of reactions given in section 2.1,
accidental coincidence of the solar H I Lyman-β line at since the solar flux is decreasing very rapidly to shorter
1025.72 Å with the O I 3D–3P transition at 1025.76 Å, cas- wavelengths. Processes with thresholds near 3000 Å have
cading through the intermediate 3P state (Feldman et al., lifetimes on the order of 104 s, those with thresholds near
1976). This mechanism, well known in the study of plane- 2000 Å an order of magnitude longer, while those with
tary nebulae, is referred to as Bowen fluorescence (Bowen, thresholds below Lyman-α, such as most photoionization
1947). The g-factor due to Lyman-β pumping is an order of channels, have lifetimes on the order of 106 s, all at 1 AU.
magnitude smaller than that for resonance scattering, but In addition to uncertainties in the details of the absorption
sufficient to explain the observations. Lyman-β is also co- cross sections, further uncertainty is introduced into the
incident with the P1 line of the (6,0) band of the H2 Lyman calculation of Jd by the lack of exact knowledge of the solar
system (B1Σ+–X1Σ+g ), leading to fluorescence in the same flux at the time of a given observation due to the variabil-
line of several (6,v") bands. Three such lines have recently ity of the solar radiation below 2000 Å, and most impor-
been detected in the FUSE spectra of Comet C/2001 A2 tantly, below Lyman-α. The solar UV flux is known to vary
(LINEAR) (Feldman et al., 2002). considerably both with the 27-d solar rotation period and
It is interesting to note that fluorescence excited by solar with the 11-yr solar activity cycle, the latter reaching fac-
H I Lyman-α was considered by Haser and Swings (1957) tors of 2 to 4 for wavelengths shortward of 1000 Å (Lean,
but considered unlikely based on the state of spectroscopic 1991). Also, at any given point in its orbit, a comet may
knowledge at that time. Lyman-α fluorescence of CO in the see a different hemisphere of the Sun than what is seen from
Fourth Positive system was first detected in the spectrum Earth. The compilation of photodestruction rates of Hueb-
of Venus (Durrance, 1981) and observed in 1996 in Comet ner et al. (1992) uses mean solar fluxes to represent the ex-
Hyakutake (C/1996 B2) (Wolven and Feldman, 1998). treme conditions of solar minimum and solar maximum and
2.2.4. Electron impact excitation. We noted above that also includes the evaluation of the excess energies of the
photoelectron impact excitation may also contribute to the dissociation products.
observed emissions, particularly in the UV. However, a very
simple argument, based on the known energy distribution 3. SPECTROSCOPIC OBSERVATIONS
of solar UV photons, demonstrates that this is only a minor
source for the principal emissions. Since the photoioniza- 3.1. Ultraviolet Observatories in Space
tion rate of water (and of the important minor species such
as CO and CO2 ) is on the order of 10–6 s–1 at 1 AU, and the The first observations of comets in the spectral region
efficiency for converting the excess electron energy into ex- below 3000 Å were made from space in 1970 by the Orbit-
citation of a single emission is on the order of a few percent, ing Astronomical Observatory (OAO-2). The spectrum of
the effective excitation rate for any emission will be on the Comet Bennett (C/1969 Y1) showed very strong OH emis-
order of 10–8 s–1 or less at 1 AU (Cravens and Green, 1978). sion at ~3085 Å and H I Lyman-α emission, at 1216 Å,
Since the efficiencies for resonance scattering or fluores- principal dissociation products of H2O (Code et al., 1972).
cence for almost all the known cometary emissions are one Feldman (1982) reviewed satellite and sounding rocket ob-
to several orders of magnitude larger, electron impact may servations made before the launch of the International Ul-
be safely neglected except in a few specific cases. These traviolet Explorer (IUE) satellite observatory in 1978 and
are the forbidden transitions, where the oscillator strength the early results from IUE, which observed more than 50
(and consequently the g-factor) is very small. Examples in- comets before it was shut down in September 1996 [see
clude the O I 5S2–3P2,1 doublet at 1356 Å, the O I 1D–3P red Festou and Feldman (1987) for a review of the principal
lines at 6300 and 6364 Å, observed in many comets, and results through 1986].
the CO Cameron bands (Weaver et al., 1994; Feldman et The HST, launched in 1990, made a significant advance
al., 1997). However, the excitation of these latter two is in UV sensitivity and provided the ability to observe in a
dominated by prompt emission in the inner coma. Some of small field of view very close to the nucleus. Two spectro-
the emissions below 1200 Å observed in the FUSE spec- graphs, the Goddard High Resolution Spectrograph (GHRS),
trum of Comet C/2001 A2 (LINEAR) have also been at- which utilized solar blind detectors exclusively for UV spec-
tributed to electron impact (Feldman et al., 2002). troscopy, and the Faint Object Spectrograph (FOS), were
2.2.5. Solar cycle variation. The relative abundance of used extensively through 1997 (Weaver, 1998). In February
a fragment species depends on the absorption cross section of that year they were replaced by the Space Telescope Im-
(σd) and the solar flux seen by the comet. The rate coeffi- aging Spectrograph (STIS), which provided further en-
cient Jd is evaluated at 1 AU using whole-disk measure- hancements including long-slit spectroscopy with an angular
 Feldman et al.: Spectroscopy of Fragment Species in the Coma 429

TABLE 1. Principal optical spectroscopic features

of cometary fragment species.

Species* Transition System Name Wavelength (Å)

OH A2Σ+–X2Πi (0,0) 3085
CN B2Σ+–X2Σ+ (0,0) Violet 3883
A2Π–X2Σ+ (2,0) Red 7873
C2 d3Πg–a3Πu (0,0) Swan 5165
A1Πu–X1Σ+g (3,0) Phillips 7715
D1Σ+u–X1Σ+g (0,0) Mulliken 2313
C3 A1Πu–X1Σ+g Comet Head Group 3440–4100
CH A2∆–X2Π (0,0) 4314
B2Σ––X2Π (0,0) 3871, 3889
CS A1Π–X1Σ+ (0,0) 2576
NH A3Πi–X3Σ– (0,0) 3360
NH2 A2A1–X2B1 4500–7350

O I 1D 1 D– 3P 6300, 6364
O I 1S 1 S– 1D 5577
C I 1D 1 D– 3P 9823, 9849

CO+ B2Σ+–X2Σ+ (0,0) First Negative 2190

A2Π–X2Σ+ (2,0) Comet Tail 4273
CO+2 B2Σu–X2Πg 2883, 2896
A2Πu–X2Πg Fox-Duffendack-Barker 2800–5000
CH+ A1Π–X1Σ+ (0,0) Douglas-Herzberg 4225, 4237
OH+ A3Π–X3Σ– (0,0) 3565
H2O+ A2A1–X2B1 4270–7540
N+2 B2Σ+–X2Σ+ (0,0) First Negative 3914
*CO is both a dissociation product and a native molecular species and is discussed by
Bockelée-Morvan et al. (2004).

resolution of 50 milliarcsec. Except for some early results jority of extant cometary spectra were obtained in the mod-
on Comet Hale-Bopp (C/1995 O1) (Weaver et al., 1999), erate-resolution mode, an example of which is shown in
the spectroscopic results from STIS observations of several Fig. 1, with fewer than 25 comets observed at high spectral
comets remain to be published, although a few will be de- resolving powers. The choice of the spectral bandpass is gen-
scribed below. Finally, we note the launch in 1999 of FUSE, erally dependent on the detector. Some groundbased spectro-
which provides access to the spectral region between 900 graphs are capable of being used at ~3085 Å to observe the
and 1200 Å at very high spectral resolution (Feldman et al., OH (0,0) band, but low detector quantum efficiency and poor
2002; Weaver et al., 2002). atmospheric throughput make such observations difficult.
Typically, slit widths of 2–4 arcsec on the sky are used
3.2. Optical Capabilities when obtaining cometary spectra, with the spectral resolu-
tion defined in part by this width. One exception is obser-
As mentioned in the introduction, the spectrum of a vations obtained with an imaging Fabry-Pérot spectrograph
comet was first observed in 1864. From then until the 1970s, where the resolution is obtained by tuning the etalons (cf.
optical cometary spectra were primarily obtained using pho- Magee-Sauer et al., 1988) and a large region of the sky can
tographic plates. At that point, observations began to switch be imaged onto the detector. Fabry-Pérot instruments gen-
over to photoelectric detectors of various types; optical com- erally have a very limited bandpass but work at relatively
etary spectra are obtained currently almost exclusively using high spectral resolving powers.
CCD detectors. Since comets are spatially large, it is desirable to obtain
The optical spectrum of comets is quite dense because spectra at different positions in the coma. Generally, this is
it consists mostly of molecular bands. The principal spec- done either by use of a “long” slit (generally 30–150 arcsec)
tral features are listed in Table 1. Optical spectra are gen- or by repositioning the telescope to image different regions
erally obtained in one of two spectral resolution regimes: of the coma or both. In order to sample all directions in the
moderate resolving powers of R = λ/∆λ ~ 600, which allow coma with a long slit instrument, the slit must be rotated to
detection of complete bands but not individual lines, or R > different position angles on the sky and additional observa-
10,000, which allow detection of individual lines. The ma- tions obtained. Alternatively, a fiber-fed spectrograph can
430 Comets II

Fig. 1. Optical/near-IR CCD spectrum of Comet 109P/Swift-Tuttle obtained November 26, 1992. This spectrum is a composite of a
UV/blue spectrum of Cochran (personal communication) and a red/near-IR spectrum of Fink and Hicks (1996). The cometary spectrum
has been divided by a solar spectrum to show the cometary emissions. The two-pixel resolution was ~7 Å for the blue and ~14 Å for the red
half. The upper panel shows the spectrum scaled by the strongest feature while the lower panel has an expanded ordinate to show the
weaker features. The main features are labeled in one of the panels. This spectrum is typical of comets in the inner solar system.

use fibers placed throughout the coma to obtain spatial in- 3.4. Radio
formation. The fiber pattern can be linear or can sample in
many directions simultaneously. Fluorescence pumping through the UV transitions of
In addition to spectra, cometary comae may be studied the OH radical produces a deviation of the population of
using narrow-band photometry or wide-field imaging (see the hyperfine and Λ-doublet levels of the X2Π3/2 (J = 3/2)
Schleicher and Farnham, 2004). Narrow-band photometry ground state from statistical equilibrium (Despois et al.,
allows for observations of fainter comets and the outer re- 1981; Schleicher and A’Hearn, 1988). Depending on the
gions of the comae; spectra allow for discrimination between heliocentric velocity, this departure may be either “inverted”
crowded spectral features but suffer from small apertures or “anti-inverted,” giving rise to either stimulated emission or
resulting in longer integration times. absorption against the galactic background at 18 cm wave-
length. This technique has been used extensively since 1973
3.3. Infrared to monitor the OH production rate in comets (Crovisier et
al., 2002). The resulting radio emissions are easily quenched
Rapid advances in near-IR (~1–5 µm) spectroscopic in- by collisions with molecules and ions, the latter giving rise
strumentation, particularly at the Keck Telescopes and the to a fairly large “collision radius” that must be accounted
Infrared Telescope Facility at Mauna Kea, have led to much for in interpreting the derived OH column density.
new information about the molecular composition of the
inner coma. Representative spectra given by Mumma et al. 4. WATER PRODUCTS
(2001) disclose the presence of a wide variety of cometary
organic molecules, discussed in detail in Bockelée-Morvan 4.1. Hydroxyl Radical
et al. (2004). The exception is OH, which appears mainly in
transitions from highly excited rotational levels, implying The OH radical is the easiest dissociation product of
that the excitation source is prompt emission following the water to observe, and is often used to determine the pro-
dissociation of water. duction rate of water and to serve as a standard to which
 Feldman et al.: Spectroscopy of Fragment Species in the Coma 431

all other coma abundances are compared. Fortunately, there served nearly simultaneously by IUE. A similar result was
are three separate largely self-consistent datasets that pro- obtained for Comet 21P/Giacobini-Zinner (Combi and Feld-
vide measurements of OH in a large number of comets man, 1992).
made during the past 20 years or more. However, the deter- Bockelée-Morvan and Gérard (1984) also noted asym-
mination of water production rate from the data differs for metries in both the velocity structure and the spatial distribu-
the three and the derived rates are often not in agreement. tion of the 18-cm lines in three comets, which they attrib-
The first is the set of groundbased photometric measure- uted to asymmetrical outgassing of the nucleus. A similar
ments at ~3085 Å made through standardized narrow-band result was reported by A’Hearn and Schleicher (1988) us-
filters, exemplified by the work of A’Hearn et al. (1995). ing the Greenstein effect to demonstrate asymmetrical out-
These measurements are discussed in Schleicher and Farn- gassing of the nucleus of Comet 2P/Encke.
ham (2004). The second is the set of observations of the OH has also been detected in high-resolution IR spectra
18-cm radio lines of OH in more than 50 comets made at near 3 µm of several recent comets (Brooke et al., 1996;
the Nançay radio telescope dating back to 1973 (Crovisier Mumma et al., 2001). From the spatial profiles of individual
et al., 2002). The third set, also comprising over 50 comet- lines, Brooke et al. (1996) demonstrated that the lines origi-
ary apparitions between 1978 and 1996, is the spectroscopic nating from high rotational levels follow that of the parent
measurement of OH fluorescence at ~3085 Å from the or- molecule, H2O, and therefore that these lines arise from
biting IUE. This satellite was in geosynchronous Earth orbit prompt emission, while the lower excitation lines were flat-
and its optical performance, which was monitored continu- ter and the result of UV fluorescence. These observations
ously, did not degrade significantly with time, ensuring a have not yet been quantitatively exploited for the determi-
reliable calibration of all the observations. There are also nation of production rates. The OH A2Σ+–X2Π (0,0) band
many other spectroscopic observations of OH in both the at ~3085 Å also exhibits a “hot” rotational distribution near
radio and the UV, the latter from both HST and from high- the nucleus due to prompt emission (Bertaux, 1986). Detec-
altitude groundbased observatories. tion of this prompt emission, which dominates fluorescence
Interpretation and intercomparison of the radio and UV only at distances of less than 100 km from the nucleus,
observations are dependent on an accurate knowledge of the requires high spatial resolution, which was afforded the IUE
UV pumping of the inversion of the Λ-doubled ground state by the close approach of Comet IRAS-Araki-Alcock (C/
of the molecule, as described above in section 3.4. The two 1983 H1) to Earth in 1983 (Budzien and Feldman, 1991).
measurements are fundamentally different and so the com- Finally, we note that the UV (0,0) band, in fluorescence
parison relies on extensive modeling, both of the spatial equilibrium, consists of a small number of individual lines
distribution and outflow velocity of the OH radicals in the that are well separated at a spectral resolution of ≤1 Å. This
coma, and of the solar excitation process. With high spec- led A’Hearn et al. (1985) to calculate the analogous spec-
tral resolution in the UV, the individual ro-vibrational lines trum of OD. While they found that the strongest lines of OD
of the band can be resolved and such measurements serve as are separable from the OH lines, and are particularly en-
a validation of the fluorescence calculation, which depends hanced at heliocentric velocities between –30 and –5 km s–1,
in turn on a high-resolution spectrum of the Sun (Scheicher attempts to date to detect these lines with both IUE and HST
and A’Hearn, 1988). But this resolution cannot match that have not been successful.
available with the 18-cm radio lines, which in velocity space
can reach ~0.3 km s–1, thus permitting the determination of 4.2. Atomic Hydrogen
the kinematic properties of the outflowing gas (Bockelée-
Morvan and Gérard, 1984; Bockelée-Morvan et al., 1990; Following the first observation of the large H I Lyman-α
Tacconi-Garman et al., 1990). Bockelée-Morvan et al. coma surrounding Comet Bennett (C/1969 Y1) in 1970 by
(1990) demonstrated variations in OH velocity with both two Earth-orbiting spacecraft (Code et al., 1972; Bertaux
cometocentric and heliocentric distance from an extensive et al., 1973), this emission has been observed in a large
set of observations of Comet 1P/Halley. Collisional quench- number of comets both with imaging detectors and spectro-
ing of the ground state inversion affects the radio lines but graphs on a variety of sounding rockets, orbiting observa-
not the UV, but the strongest UV lines can saturate at OH tories, and various other spacecraft. Initial modeling of the
column densities that are reached near the nucleus, and spatial distribution, taking into account the excess velocities
small field-of-view observation from HST show indications of multiple sources, solar radiation pressure, and radiative
of this effect. With their models constrained by the velocity transfer effects, was summarized by Keller (1976). A more
measurements, Bockelée-Morvan et al. (1990) and Gérard complete discussion of the physics involved in the photo-
(1990) were able to reconcile the water production rates chemical production of H atoms and their subsequent non-
derived from the 18-cm observations with those derived LTE (local thermodynamic equilibrium) collisional coupling
from IUE observations of Comet 1P/Halley over an ex- to the coma is given in Combi et al. (2004). In this section
tended range of heliocentric distance. Modeling by Combi we will limit the discussion to spectroscopic observations
and Feldman (1993) was able to achieve agreement between made at sufficient resolution to allow the determination of
the production rates for Comet 1P/Halley derived from the the velocity distribution of the H atoms and the presence of
OH UV data and those derived from H I Lyman-α, both ob- radiation trapping near the nucleus, which are relatively few
432 Comets II

photodissociation of the parent molecule. The lifetime of

the 1D state is about 130 s, while the 1S state lifetime is less
than 1 s. Thus, the three transitions discussed here are ex-
cellent tracers of the distributions of their parents because
they cannot travel far without decaying. Oxygen atoms that
are excited to the 1S state decay to the ground 3P state via
the 1D state 95% of the time, while 5% decay directly to
the ground state emitting lines at 2977 Å and 2958 Å. Thus,
if the green line is present in a cometary spectrum, the red
doublet must also be present, although the red doublet can
be formed without the green line.
The forbidden O lines can be formed via photoprocesses
involving H2O, CO, or CO2 as parents. More complex O-
bearing species such as HCOOH or H2CO are unlikely to be
the parent because they cannot decay fast enough to produce
the observed O(1D) distribution (Festou and Feldman, 1981).
Fig. 2. Hydrogen Lyman-α line profile in Comet C/1996 B2 It is believed that H2O is the dominant, if not the sole, O(1D)
(Hyakutake). The triangles show the observed line profile obtained and O(1S) parent out to distances of 105 km from the nu-
with the GHRS instrument on HST with the small science aper- cleus, beyond which OH becomes the dominant parent. The
ture located at a point 111,000 km sunward of the position of the determination of the parent abundance requires observations
nucleus, which is in the optically thin region of the coma. The of the intensities of the three lines, coupled with accurate
thin line shows the intrinsic emission from the comet at very high understanding of the dissociation rates and branching ratios.
spectral resolution (1 km s–1) as calculated by the model of Combi Measuring the intensities of the three lines accurately
et al. (1998). The thicker line is the model convolved with the requires high spectral resolution to resolve the cometary O
instrument spectral function (4 km s–1 resolution). The emission
lines from telluric O lines and other cometary emissions.
of H in the geocorona is the line at 0 km s–1 to the left of the comet
line, and the comet’s emission is Doppler shifted to the comet’s
The resolution needed to resolve the cometary and telluric
55 km s–1 relative geocentric velocity (from Combi et al., 1998). O lines is dependent on the Doppler shift of the comet with
respect to the Earth. For the red doublet, the O(1D) line is
situated near cometary NH2 emissions, but the strong NH2
lines are generally easy to resolve from the O line when the
(Festou et al., 1979; Combi et al., 1998). Very high spectral spectral resolution is sufficient to resolve the cometary and
resolution has also been obtained using Fabry-Pérot inter- telluric O emissions. The region of the green line is much
ferometry and coudé/echelle spectroscopy to observe the Hα more difficult. Again, the cometary and telluric lines are
line at 6563 Å (Huppler et al., 1975; Scherb, 1981; Brown Doppler shifted apart. However, the region of the green line
and Spinrad, 1993; Combi et al., 1999). is in the middle of the C2 (1,2) P-branch. Only four obser-
Combi et al. (1998) showed Lyman-α line profiles mea- vations of the 5577 Å O(1S) line in cometary spectra have
sured with the GHRS on HST obtained with a spectral sam- been reported: Observations of Comets C/1983 H1 (IRAS-
pling of 4 km s–1. A spectrum obtained 111,000 km on the Araki-Alcock) (Cochran, 1984) and C/1996 B2 (Hyaku-
sunward side of the coma of C/1996 B2 (Hyakutake) was take) (Morrison et al., 1997) relied on high spatial resolu-
just outside the optically thick coma. The profile and a tion in addition to high spectral resolution; observation of
Monte Carlo model analysis shows the signatures of the Comet 1P/Halley (Smith and Schempp, 1989) relied on ex-
various components: 18 km s–1 from H2O dissociation, tremely high spectral resolution plus modeling; and Coch-
8 km s–1 from OH, and the low-velocity line center from ran and Cochran (2001) reported an unequivocal detection
thermalized H atoms as shown in Fig. 2. A radiative trans- of the O(1S) line in spectra of C/1994 S4 (LINEAR) in a
fer calculation of all the HST data by Richter et al. (2000) comet that was severely depleted in C2, making the contami-
showed the detailed effects of multiple scattering of the nation issue go away.
illuminating solar Lyman-α photons and the progressive Cochran and Cochran computed the intensity ratio of the
saturation of the line center at decreasing distances toward red doublet lines and found it to be 3.03 ± 0.14, in excel-
the nucleus of the comet. lent agreement with the ratio predicted by the Einstein A-
values of Storey and Zeippen (2000). Accurate measurement
4.3. O(1D) λ6300 and Other Forbidden Emissions of the ratio of the green line intensity to the sum of the
intensities of the red doublet lines can then be used to dis-
Three forbidden O transitions exist in the optical region criminate between parent species. The values that have been
of the spectrum: the red doublet at 6300.304 and 6363.776 Å reported [0.22–0.34 for IRAS-Araki-Alcock (Cochran,
(1D–3P) and the green line at 5577.339 Å (1S–1D). These 1984), 0.12–0.15 for Hyakutake (Morrison et al., 1997),
transitions are the result of “prompt” emission, i.e., the at- 0.05–0.1 for Halley (Smith and Schempp, 1989), and 0.06 ±
oms are produced directly in the excited 1S or 1D states by 0.01 for LINEAR (Cochran and Cochran, 2001)] all point
 Feldman et al.: Spectroscopy of Fragment Species in the Coma 433

Fig. 3. FUSE spectrum of Comet C/2001 A2 (LINEAR) obtained beginning 2001 July 12.58 UT (from Feldman et al., 2002). Two
of the fluorescently excited H2 lines are identified as well as the CO bands and atomic emissions that lie in this spectral region. A
number of detected features remain unidentified.

to H2O as the dominant parent in the production of the for- low spectral resolution can lead to an underestimate of the
bidden O lines. However, Cochran and Cochran argue, on O(1D) intensity and production rate by about a factor of 2.
the basis of line widths, that H2O cannot be the sole parent Another limitation of using O(1D) as a measure of the
of the O(1D). H2O production is that the branching ratios of the reactions
With the assumption that most of the O(1D) is produced that dissociate H2O are not well determined. Budzien et al.
from the dissociation of H2O, then the line at 6300 Å can (1994) summarized the uncertainties in our knowledge of
be used to measure the H2O production rate. This line is these branching ratios. Since OH is produced approximately
more accessible to most detectors than the OH bands of the 90% of the time, with O produced approximately 10% of
UV, making its observation an important tool for measur- the time, errors in the branching ratio induce a larger un-
ing the H2O production. Enthusiasm for using measure- certainty in our calculation of H2O production rates from
ments of the 6300 Å line must be tempered by an under- O(1D) than from OH. In addition, while all the OH is a
standing of the limitations. First, there is the issue of the daughter of H2O, some of the O(1D) is a daughter of the dis-
blending of the line with both the telluric O line and with sociation of H2O, while some is a product of the subsequent
NH2. In particular, the telluric line is quite variable, so mod- dissociation of OH.
eling its removal when it is blended with the cometary fea-
ture is not easy. High spectral resolution observations of 4.4. Molecular Hydrogen
O(1D) has been used on a number of comets (Magee-Sauer
et al., 1988; Combi and McCrosky, 1991). A far larger set of Feldman et al. (2002) recently reported the FUSE obser-
observations have been obtained at moderate resolution and vation of three P1 lines of the H2 Lyman series that are ex-
the O(1D) intensity has been calculated by modeling the con- cited by the accidental coincidence of the solar Lyman-β
tribution of the telluric O(1D) and the cometary NH2 (Spin- line with the P1 line of the B1Σ+u –X1Σ+g (6,0) band in the
rad, 1982; Fink and Hicks, 1996). Arpigny et al. (1987) in- spectrum of Comet C/2001 A2 (LINEAR), shown in Fig. 3.
vestigated the effects of spectral resolution on the difficulty Similar fluorescence has also been seen in the spectra of
of deblending the O(1D) and NH2 lines and concluded that Jupiter and Mars. Although the strongest of the fluorescent
434 Comets II

Fig. 4. Spectrum of Comet 122P/deVico showing two-thirds of the C2 ∆v = 0 band observed at a resolving power λ/∆λ = 60,000
with the McDonald Observatory 2.7-m 2D-coudé spectrograph. The two panels have different ordinate scalings to better show the
details of the spectra. The bluest lines shown at 4932.059 and 4932.139 Å are C2 (0,0) R1(73), R2(72), and R3(71). Most of the lines
shown in the spectrum are attributable to C2. However, there are some NH2 and unidentified lines mixed throughout this spectrum.

lines appear near 1600 Å, longer-wavelength spectra of D1Σ+u –X1Σ+g, or Mulliken, system has been detected in the
comets from IUE, HST, and sounding rockets have not had UV, despite the fact that the Mulliken ∆v = 0 band’s g-factor
sufficient spectral resolution to unambiguously identify H2 is about 40 times smaller than that of the Swan ∆v = –1 band
in cometary spectra. The determination of the H2 column sequence [see Fig. 2 of A’Hearn (1982)].
density in the field of view depends strongly on the shape In comparison to CN and other cometary molecules,
of the solar Lyman-β line, the rotational temperature and much higher C2 vibration-rotation levels are excited (see
outflow velocity of the H2, and the heliocentric velocity of Fig. 4). Indeed, vibration-rotation levels as high as J = 109
the comet. Feldman et al. demonstrated that the derived have been detected (Cochran and Cochran, 2002). This
column abundance of H2 is consistent with H2O dissocia- high-J distribution occurs because C2 is a homonuclear
tion models but cannot exclude that some of it is produced molecule with no permanent dipole moment so that vibra-
directly from the nucleus (Bar-Nun and Prialnik, 1988) or tional and rotational electric dipole transitions within an
by solar wind sputtering of dirty ice grains (Pirronello et electronic state are forbidden. Thus, the rotational excitation
al., 1983). temperature of the C2 coma would be approximately the
color temperature of the Sun (T = 5800 K) in the absence of
5. CARBON-, NITROGEN-, AND SULFUR- any mechanism for cooling the rotational temperature. This
CONTAINING RADICALS mechanism does exist, however, in the form of interactions
with other electronic states.
5.1. C2 The rotational excitation temperature (Trot) of the coma
can be measured by observing the Swan bands at high spec-
There are two principal band systems of C2 that are tral resolution. Such observations have generally yielded
observed in the optical spectra of comets. These are the Trot ~ 3000 K. Lambert et al. (1990) observed Comet Halley
Swan, or d3Πg–a3Πu, system, and the Phillips, or A1Πu– and found that the C2 gas could not be described by a single
X1Σ+g, system. The Swan system was the first molecule iden- rotational temperature. They found that the lower rotational
tified in a cometary spectrum and is dominant in the green, levels (J < 15) could be fit with Trot ~ 600 K, while higher
orange, and red region of the spectrum; the Phillips bands levels required Trot ~ 3200 K. Indeed, when the contribution
are important in the near-IR and IR. In addition, the C2 of the hotter population is accounted for, the low-J levels
 Feldman et al.: Spectroscopy of Fragment Species in the Coma 435

yield Trot = 190 K. Krishna Swamy (1997) has shown that nence, its parent must have less than 1% of the abundance
these results can be understood in detail by the inclusion of H2O.
of many more transitions in models of the photolysis of C2. Because the violet system is a Σ–Σ transition, only P-
C2 emissions can be detected at large distances from the and R-branches are permitted and J < 20 is generally ob-
nucleus, implying a large scale length for its production. served. This, coupled with the density of absorption features
However, it has long been noted that the distribution in the in the solar spectrum at the wavelength of the ∆v = 0 bands
inner few thousand kilometers of the coma is essentially at 3883 Å, makes it necessary to account for the Swings
constant. This flat distribution is inconsistent with a simple effect when converting observed band flux to column den-
parent/daughter production for C2. Jackson (1976) was the sity. Results of calculations of the change in the g-factor
first to suggest that C2H2 was the grandparent of C2, with with changing heliocentric radial velocity have been given
an intermediate decay of the C2H2 to C2H + H. Using long- by Tatum and Gillespie (1977), Tatum (1984), and others.
slit CCD observations of Comet Halley, O’Dell et al. (1988) The solar spectrum shows strong CN Σ–Σ absorption so that
also concluded that C2 must be the product of the decay of the g-factor reaches a minimum at zero heliocentric radial
two precursors. Using a multigeneration Haser model, they velocity (at perihelion). While the cometary CN violet band
found that the data can be fit with parameters between R1 = does not disappear entirely at perihelion, it becomes quite
12,000 km, R1/R2 = 3, and R2/R3 = 0.8; to R1 = 17,000 km, weak. The red system is generally much more spread over
R1/R2 = 1.5, and R2/R3 = 0.12, where R1, R2, and R3 are the wavelength and does not appear as such an obvious band.
grandparent, parent, and daughter destruction scale lengths, High spectral resolution allows the isotopic features of
respectively. CN to be clearly resolved from the weak, high-order non-
Combi and Fink (1997) further investigated a solution for isotopic features. Thus, studies of CN with high spectral
the flat inner profile of the C2 gas. They also used a three- resolution have been used to derive 13C/12C values that are
generation dissociation model, but theirs differed from that essentially the solar value for several comets (Kleine et al.,
of O’Dell et al. (1988) by the inclusion of ejection velocities 1994, 1995; Lambert and Danks, 1983; Lambert et al.,
resulting from the excess energy of the photodissociations. 1990). High spectral resolution, coupled with high signal/
They found that, as long as the ejection velocities are greater noise, have allowed Arpigny et al. (2003) to determine 15N
than 0.5 km s–1, the excess energy imparted during the vari- 14N in a number of comets. They found a value that is a fac-

ous dissociations will cause a filling in of the “hole” in the tor of 2 higher than the value from the Earth’s atmosphere.
profile, resulting in a profile that is no longer flat in the inner Although the identification of the violet system as CN
coma. They argued that typical heavy molecules produce has been known since the earliest days of comet spectros-
ejection velocities in excess of 1 km s–1, so a three-genera- copy, the identification of the parent is still in doubt. The
tion photodissociation is unlikely the parent process for the Haser (or radial) scale length of the CN parent is on the
production of C2. Instead, they suggest that a CHON grain order of 2 × 10 4 km at 1 AU. A potential parent, HCN, is
halo with a size of 104 km is responsible for the produc- observed in the millimeter portion of the spectrum, but it
tion of X–C2 (X is some unknown species), which in turn is still uncertain whether HCN is a minor parent or a domi-
is photodissociated on a scale of several times 104 km to nant parent of CN. Bockelée-Morvan and Crovisier (1985)
produce the C2. This process can proceed with little or no argued that the CN distribution is inconsistent with HCN
excess energy. as a dominant parent unless the coma expansion velocity
New laboratory data and ab initio calculations (Sorkhabi was much lower than generally assumed. In contrast, di-
et al., 1997) would seem to allow for the original thesis of rect comparison of the distribution of HCN and CN using
Jackson (1976), that the grandparent of C2 is C2H2, while the more recent millimeter observations have shown that there
direct parent is C2H. Sorkhabi et al. (1997) obtained laser- is sufficient HCN to be a dominant parent of CN (Ziurys et
induced fluorescence spectra of C2 (X1Σ+g) radicals produced al., 1999) and that the HCN and CN are distributed simi-
during 1930 Å laser photolysis of C2H2. They used these larly within the coma (Woodney et al., 2002).
observations along with calculations to match the spectrum Festou et al. (1998) asserted that HCN contributes at the
of the C2 Mulliken system in HST observations of Comet percent level to the production of CN. They found that a
C/1996 B2 (Hyakutake). best case for a parent for CN has a lifetime of 3.5 × 10 4 s
at 1 AU with a velocity of 1–2 km s–1. They concluded that
5.2. CN this is consistent with C2N2 as the dominant parent. Bonev
and Komitov (2000) fit the CN scale lengths and concluded
There are two CN electronic band systems that can be that C2N2 is the sole parent for CN.
observed in the optical in cometary spectra. These are the
“violet” system (B2Σ+–X2Σ+) and the “red” system (A2Π– 5.3. C3
X2Σ+). The violet system is one of the most prominent fea-
tures in cometary spectra and is seen in most comets with The first detection of the emission band that we now
heliocentric distances less than 3 AU. It has been detected know to be C3 was in 1881. However, the tentative identifi-
in Comets 1P/Halley and C/1995 O1 (Hale-Bopp) at dis- cation of the band as C3 was not made until 1951 (Douglas,
tances greater than 4 AU and in the Centaur (2060) Chiron 1951). C3 is a relatively unstable molecule, making its study
at 11.26 AU (Bus et al., 1991). Despite its spectral promi- difficult. Until its identification, the band was known sim-
436 Comets II

ply as the “4050-Å Group.” The main part of the band lies since some of the CH lines are coincident with the weaker
between 3900 and 4140 Å with a maximum at 4050 Å and CN lines.
an additional peak, not well defined, at 4300 Å. However,
careful examination of cometary spectra shows lines attrib- 5.5. NH and NH2
utable to this band from ~3350 to 4700 Å.
C3 is a linear, symmetric molecule containing equal-mass The (0,0) A3Πi–X3Σ– band of NH occurs between 3345
nuclei. The band has been identified as an A1Πu–X1Σ+g elec- and 3375 Å. It was first detected in the spectrum of Comet
tronic transition. R-branch bandheads at 4072 and 4260 Å Cunningham (Swings et al., 1941) and is generally the only
can be assigned to the (1,0,0)–(1,0,0) and (0,0,0)–(1,0,0) NH band seen. This band shows an R- and P-branch but
bands respectively. The density of the lines results in a pseudo- the Q-branch is absent or weak. Kim et al. (1989) showed
continuum from C3. For all Σ states of the molecule, every that the spectrum can be explained completely on the basis
second line is missing. In other states, one member of the of pure resonance fluorescence without any collisions.
e/f-parity doublet of each rotational level is missing, al- Emission lines of NH2 have been detected throughout a
though all rotational levels are represented (Tokaryk and region from ~3980 Å to well past 1 µm (Cochran and
Chomiak, 1997). The complexity of the spectrum and the Cochran, 2002). These lines belong to the A2A1–X2B1 elec-
difficulty of exciting C3 in the laboratory have resulted in tronic transition, along with transitions between the high
many missing identifications of lines. In addition, the den- vibronic levels and the ground state of the X2B1 electronic
sity of lines has made it impossible to resolve all the individ- band [e.g., (0,13,0)X2B1–(0,0,0)X2B1]. NH2 is an asymmet-
ual lines. Recently, observations of cometary C3 were used ric top molecule, with a linear upper level and a lower level
to derive a new dipole moment derivative (dµ/dr) of approx- bent at an angle of 103°, making its spectrum quite complex
imately 2.5 Debye Å–1 for this band system (Rousselot et and irregular.
al., 2001). It is widely believed that NH3 is the parent for NH2,
The parent of C3 is unknown. Chemically plausible par- which decays, in turn, into NH. However, until recently,
ents, such as C3H4 and C3H8, are not detected in cometary NH3 had not been detected in cometary spectra. Palmer et
spectra. Either of these would produce C3 in a multigenera- al. (1996) first detected NH3 in the radio spectrum of C/
tional process and many of the photolysis rates for such re- 1996 B2 (Hyakutake) and it has now also been detected in
actions are very uncertain. Observations of the distribution the radio spectrum of C/1995 O1 (Hale-Bopp) (Bird et al.,
of C3 gas in the comae of comets suggests that the parent 1997) and the IR spectrum of 153P/Ikeya-Zhang (Magee-
must have a short scale length, on the order of 3 × 103 km Sauer et al., 2002). Other potential parents include N2H4
(Randall et al., 1992). It is unlikely that the long-chain C and CH3NH2.
molecules seen in the interstellar medium are parents for Prior to the detection of NH3, the chemical reaction path-
C3 since these long-chain C molecules are believed to have way was argued on the basis of the observed scale lengths
alternating single and triple bonds that would more likely of the various species. However, there has been much dis-
break to produce C2 than C3. The photodestruction of C3 agreement on the values relevant to each species. Typically,
results in the production of a C2 molecule and a C atom. the g-factors for NH2 of Tegler and Wyckoff (1989) are used.
Arpigny (1994) pointed out that this g-factor calculation is
5.4. CH off by a factor of 2 because the structure of the NH2 bands
means that a single band when the linear band notation is
The CH (0,0) A2∆–X2Π band has its peak at 4314 Å and used (typical in past cometary work) only samples either
appears in cometary spectra as a weak band. Two factors odd or even Ka lower levels. Cochran and Cochran (2002)
contribute to this weak feature of interest: (1) The oscilla- advocated converting to using the bent band notation adopt-
tor strength is small, ~5 × 10–3; and (2) the lifetime against ed by the physicists. Under that notation, the linearly de-
photodissociation at 1 AU is between 35 and 315 s (Singh noted (0,8,0) Π band is a part of the bent notation (0,3,0)
and Dalgarno, 1987). The former implies that even a very band and the (0,8,0) Φ band is part of the (0,2,0) band. The
weak feature is the result of a significant column density. bent notation bands contain both odd and even Ka lower
The latter means that wherever the CH is detected in the levels. It is generally believed that the parent of NH2 has a
coma, the parent must be close by. Thus, CH can be used relatively short scale length, on the order of ~4 × 103 km
as a tracer of the parent distribution. (Krasnopolsky and Tkachuk, 1991; Fink et al., 1991). The
The probable parent of CH is CH4. Methane will first destruction scale length is a few times 104 km.
decay into CH2 (CH3 is highly unstable) and then into CH. Kawakita et al. (2001b) have derived new g-factors for
The detection of CH in the optical is far simpler than the five of the bands (in the linear notation) and find values
detection of CH4 in the IR so there is a significantly larger smaller than those of Tegler and Wyckoff (1989) by factors
database of CH detections than CH4 detections. of 2.7 to 6.4. Korsun and Jockers (2002) have applied these
The (0,0) B2Σ––X2Π band has also been detected at high g-factors to NH2 filter images and shown that the derived
spectral resolution at 3886 Å. This band cannot be resolved NH2 production rate is consistent with NH3 as the parent.
from CN at lower resolution. It is necessary to be aware of Kim et al. (1989) have calculated NH fluorescence effi-
this band, however, when computing models of 12CN/13CN, ciencies incorporating the Swings effect. Part of the prob-
 Feldman et al.: Spectroscopy of Fragment Species in the Coma 437

lem with defining scale lengths for NH is a paucity of data Further IUE observations and laboratory data led Jackson
coupled with the difficulty of determining the atmospheric et al. (1986) to revise the CS2 lifetime at 1 AU to ~500 s,
extinction at the wavelength of NH. Parent scale lengths and this seemed to be consistent with the limited spatial in-
range from 1–5 × 104 km. Schleicher and Millis (1989) formation available from low-dispersion IUE spectra. How-
argue reasonably convincingly for the longer of these val- ever, high-dispersion spectra of 1P/Halley showed the band
ues. Most datasets are not very sensitive to the destruction shape to be quite different from previously observed com-
scale length used, but it is generally agreed to be about 2 × ets, with the R-branch blueward of the band head much en-
105 km. Feldman et al. (1993) used spectrophotometric spa- hanced over the redward P,Q branches, in contradiction with
tial profiles of OH and NH emission derived from observa- solar fluorescence models. Attempts to model this band with
tions of Comet 1P/Halley made by the Soviet-era ASTRON two components along the spectrograph line of sight, the
satellite to derive the relative NH3 abundance with a nearly first in statistical equilibrium near the nucleus, and the sec-
model-independent analysis. ond in fluorescence equilibrium for distances greater than
All the observations suggest that about 95% of the pho- ~1000 km from the nucleus, have been only partially suc-
todissociations of NH3 produce NH2 and that very little of cessful in reproducing the observations (Prisant and Jack-
the NH comes directly from NH3. Using the various param- son, 1987; Krishna Swamy and Tarafdar, 1993).
eters found in the literature, there is general agreement that In the HST era, spectra of the CS (0,0) band at resolu-
the abundance of NH3 in the nucleus is about 0.5% that of tion comparable to that of the IUE high-dispersion mode
H2O for all comets, if NH3 is the sole parent of NH2 and NH. (∆λ = 0.8 Å) have not been obtained, precluding a resolu-
Recently, Kawakita et al. (2001a) have utilized high- tion of this problem. In one area, though, spatial imaging
resolution NH2 spectra of Comet C/1999 S4 (LINEAR) to with STIS has led to a more reliable estimate of the CS par-
model the ortho-to-para ratio and to derive a spin tempera- ent lifetime of ~1000 s (Feldman et al., 1999).
ture for NH3. They found a temperature of 28 ± 2 K, assum- Another potential source of CS in the coma is OCS, de-
ing that the NH2 arises from pure fluorescence excitation tected in the radio in recent comets in comparable abun-
of NH3. dance to CS2 (see Bockelée-Morvan et al., 2004). However,
the primary dissociation path of OCS is to CO and S (Hueb-
5.6. CS ner et al., 1992) so that the contribution to the CS abun-
dance is minor. Other S-bearing parent molecules identified
Ultraviolet emission from carbon monosulfide (CS) and in the radio are H2S and SO2, the former being the princi-
atomic sulfur was first reported in rocket spectra of Comet pal S species in the cometary ice (see Bockelée-Morvan et
West (C/1976 V1) by Smith et al. (1980). The (0,0) band al., 2004). Kim and A’Hearn (1991, 1992) have given spec-
of the A1Π–X1Σ+ system of CS at 2576 Å is the strongest troscopic limits on the dissociation products SH and SO,
of four bands of this system lying between 2500 and 2700 Å although the latter has been detected in the radio in Comet
and has been detected in nearly all IUE and HST comet Hale-Bopp (Bockelée-Morvan et al., 2000). Finally, we note
spectra. More recently, CS has also been detected in the that Irvine et al. (2000) have reported the detection of NS
radio (Biver et al., 1999). Jackson et al. (1982) analyzed in Comet Hale-Bopp, although its origin remains unknown.
both high- and low-dispersion IUE spectra of Comet Brad-
field (C/1979 Y1), concluding that the likely parent was CS2 6. ATOMIC BUDGET OF THE COMA
with an extremely short photodissociation lifetime of ~100 s
at 1 AU. They also found that the band shape was indica- With the exception of CO and CO2, solar photodisso-
tive of a 70-K rotational temperature, that the production ciation rates are significantly higher than the rates for photo-
rate of the parent was about 0.1% that of water near 1 AU, or solar wind ionization of the principal molecular constitu-
and that this ratio decreased with increasing heliocentric dis- ents of the coma (Huebner et al., 1992). Thus, the end prod-
tance. This latter behavior has been seen in all the comets ucts of the molecular species will be predominantly the
observed by IUE over a significant range of r and also in the constituent atoms, H, O, C, N, and S, and their correspond-
radio observations of Comet Hale-Bopp (C/1995 O1) (Biver ing ions. The neutral atomic species all have their princi-
et al., 1999). Jackson et al. (1982) suggested that CS2 could pal resonance transitions in the vacuum UV in a wavelength
also account for all the observed S I emission at 1814 Å, al- range amenable to spectroscopic observations by IUE and
though it was later shown that H2S was a more important HST (see Table 2). H I Lyman-α observations, both spectro-
source of S than CS2 (Meier and A’Hearn, 1997). Sulfur- scopic and imaging, are discussed in section 4.2 above and
bearing species are discussed in section 4.5 of Bockelée- in Combi et al. (2004). Because of the large scale lengths
Morvan et al. (2004). Jackson et al. (1982), in discussing the against ionization for these species, the atomic coma can
photodissociation of CS2, noted that laboratory measure- extend to millions of kilometers from the nucleus and im-
ments using a source at 1930 Å produced an abundant amount ages in Lyman-α show the atomic hydrogen corona to be
of S(1D) atoms in addition to ground state 3P atoms. Sul- the largest object in the solar system, often attaining a size
fur in the 1D state was detected by its transition at 1667 Å in of ~0.1–0.2 AU.
GHRS spectra of Comet Hyakutake (C/1996 B2) (A’Hearn The resonance transitions of atomic carbon and oxygen
et al., 1999). were first detected in rocket observations of Comet Kohou-
438 Comets II

TABLE 2. Principal resonance transitions presence of many other C-bearing species near the nucleus,
of cometary atoms and ions. many of which were subsequently discovered in later com-
ets. Festou also postulated that the atomic inventory, inde-
Species Transition Wavelength (Å) pendent of the details of the molecular parentage and
HI 2Po –2 S 1216 assuming that all the photons could be collected from the
OI 3 So– 3 P 1302–06 extended coma, would be a strong indicator of cometary
CI 3D o– 3 P 1561 diversity.
3 Po– 3 P 1657 In addition to the resonance multiplet of O I, the inter-
NI 4P–4 So 1134 combination doublet at 1356 Å has been observed in a few
4P–4 So 1200
3P–3 So
coma spectra (Woods et al., 1987; McPhate et al., 1999).
SI 1807–26
Because the g-factor for this transition is so small, the ex-
O II 4P–4 So 834 citation source has been attributed to photoelectrons, analo-
C II 2S–2 Po 1037 gous to the excitation in planetary atmospheres (Cravens
2D–2 Po 1335 and Green, 1978). Electron impact excitation may also con-
N II 3D o– 3 P 1085 tribute to the observed CO Cameron band emission (Weaver
S II 4P–4 So 1250–59 et al., 1994).
Atomic sulfur was first identified in the spectrum of
Comet West by Smith et al. (1980), who also obtained an
objective image of the S I λ1813 multiplet. This emission has
tek (C/1973 E1) (Feldman et al., 1974; Opal et al., 1974), been detected in nearly every comet observed since then by
the latter also providing objective grating images of the C IUE or HST, and most of the observations show the 1807 Å
and O comae. Because of the large heliocentric velocity at component, the transition connecting to the lowest ground-
the time of the observation, the O I λ1302 multiplet was state level, to be saturated. Azoulay and Festou (1986) first
Doppler shifted away from the solar O I line and the ex- treated opacity effects in order to properly extract S produc-
citation was attributed to “Bowen fluorescence” of solar tion rates and concluded that CS2 was insufficient to account
Lyman-β (Feldman et al., 1974). Similarly, C I λ1657 and for the amount of S observed and that OCS was likely the
the CO Fourth Positive bands were shown to be subject to primary parent. Meier and A’Hearn (1997), analyzing a
a large “Swings effect” (Feldman et al., 1976). From similar much larger database of S observations, came to a similar
observations made of Comet West (C/1975 V1), Feldman conclusion but identified the primary parent as H2S, which
and Brune (1976) showed that the C could be accounted had recently been detected in radio observations.
for as the dissociation product of the CO simultaneously Two other S multiplets are occasionally detected in com-
measured. Comet West had an unusually high CO abun- ets that are observed at small heliocentric velocity (<10 km
dance and so it was a surprise when Comet Bradfield (C/ s–1), at 1429 and 1479 Å. These transitions are also opti-
1979 Y1), observed by IUE, showed a large C emission de- cally thick near the nucleus. A particularly nice example
spite a much smaller relative CO production rate (A’Hearn of these emissions is seen in the long-slit spectrum of Comet
and Feldman, 1980). IUE used a much smaller aperture than Hale-Bopp obtained from the rocket experiment of McPhate
had the earlier rocket spectrometers, and Festou (1984) con- et al. (1999) (Fig. 5). This spectrum also shows how the
sidered whether the additional C could be indicative of the relative intensities of the three components of the S I λ1813

Fig. 5. Long-slit spectral image of Comet Hale-Bopp acquired on 1997 April 6.16 UT. The long axis of the slit was oriented along
the Sun-comet line and the slit was offset 20" from the nucleus. The Sun is down in this image. Each pixel is 0.6 Å × 0."8 and sub-
tends 800 km at the comet. The emission features are identified in Fig. 6. From McPhate et al. (1999).
 Feldman et al.: Spectroscopy of Fragment Species in the Coma 439

Fig. 6. Full-slit average spectrum derived from the data of Fig. 5. The top frame identifies the stronger atomic emissions while the
bottom frame, expanded in scale, shows the rich molecular spectrum of CO. The gray line is a modeled optically thin CO Fourth
Positive band spectrum. From McPhate et al. (1999).

multiplet vary with distance from the nucleus, the line ratios (Newall, 1910). For the latter comet, handheld prism ob-
approaching optically thin values at 150,000 km (Fig. 6). servations indicated that the tailward extent of the Na emis-
In contrast to the other atomic species, little is known sion exceeded that of the C2 Swan band for this comet.
about atomic nitrogen in the coma. Its principal resonance Although Na is a minor species in all atmospheres where
transition at 1200 Å has never been detected, presumably it has been detected [Io (Brown and Chaffee, 1974), Mer-
due to the weakness and narrowness of the solar exciting cury (Potter and Morgan, 1985), Moon (Potter and Mor-
lines and its close proximity to the very strong H I Lyman-α gan, 1988)], it has nonetheless been useful because trace
line. Weaver et al. (2002) report the detection of the stron- amounts of Na are easily observed because of the large
gest member of the N I λ1134 multiplet in the FUSE spec- ocillator strength in the D-lines and their placement at the
trum of Comet C/2001 A2 (LINEAR), but this identification peak wavelength of solar radiation.
needs to be confirmed. The curious behavior of Na and its emission results from
the strong interaction with solar radiation. The solar spec-
7. SODIUM IN COMETS NEAR 1 AU trum contains two strong Na absorption lines that modu-
late the fluorescence of Na atoms in the solar system
Recognition of cometary Na D-line emissions at 5890/ depending upon their heliocentric velocity. At 1 AU from
5896 Å dates back to visual observations of Comets C/1882 the Sun, strong fluorescence in the D-lines produces a large
F1 and C/1882 R1 (Levin, 1964) and Comet C/1910 A1 radiation pressure acceleration, which varies from about
440 Comets II

3 cm s–2 for Na atoms at rest with respect to the Sun (and Because of its extremely large overall gas production
seeing the bottom of the solar lines) to more than 50 cm s–2 rate, a spectacularly bright and long Na tail was imaged in
for Na atoms Doppler shifted to the nearby continuum. Comet Hale-Bopp (C/1995 O1) by Cremonese et al. (1997)
The first Na studies were largely confined to Sun-grazing and Wilson et al. (1998). Modeling analysis of these im-
comets, perhaps most notable of which was Comet Ikeya- ages and further spectroscopic observations (Brown et al.,
Seki (C/1965 S1), with perihelion q = 0.04 AU, and for 1998; Rauer et al., 1998; Arpigny et al., 1998) showed that
which Na emission was not seen for heliocentric distances the observed distribution of Na in the tail could be explained
r > 0.6 AU (Bappu and Sivaraman, 1969). Based on ob- by a nucleus or near-nucleus source of Na at a production
servations of this comet by Preston (1967) and Spinrad and rate that is less than 0.3% of what would be expected based
Miner (1968), Huebner (1970) argued that under these on solar abundances of Na compared with O. This is in fact
harsh conditions the intensity of Na D emission could be the same level as the nucleus or near-nucleus source for Na
accounted for by Na atoms embedded within micrometer- identified by Combi et al. (1997) in Comet Halley and seen
sized refractory silicate material having a high latent heat in Comets Bennett and Kohoutek. Therefore, the gaseous
of vaporization. Preston (1967), in particular, noted that a Na seen in non-Sun-grazing comets does not represent the
whole set of metallic species in addition to Na were detected bulk of Na in comets, which is mostly bound to the refrac-
spectroscopically. These emission lines were tabulated by tory component and was seen in the dust mass spectra of
Slaughter (1969). Because of the short photoionization life- 1P/Halley (Jessberger and Kissel, 1991).
time of Na atoms close to the Sun and the substantial tail- Unlike the extended source of Na in Halley, inner coma
ward extent of the Na emission (~103 km), the early studies measurements of Na in Comet Hale-Bopp showed an ex-
of the Sun-grazing comets (Spinrad and Miner, 1968; Hueb- tended source component that appeared to be associated
ner, 1970) equated the tailward extent as being indicative with the asymmetric dust distribution (Brown et al., 1998).
of the lifetimes of parent refractory grains. These studies, Brown et al. found that roughly half the Na was produced
however, neglected the very large radiation pressure accel- from the nucleus source and half from an extended source
eration on Na atoms. In addition, it has since been found that roughly followed the r –2 distribution of the asymmetric
that the photoionization lifetime (Huebner et al., 1992; dust coma and did not resemble either the spatial or velocity
Combi et al., 1997) may be up to three times longer than distribution seen in simultaneously observed H2O+ ions. Ob-
believed at the time. servations of Na in future bright comets are required in order
Observations of Na emission near and beyond 1 AU have to answer the question of the nature of the extended source.
been limited to a few bright, active comets. The Na in Comet
Kohoutek C/1973 E1 (q = 0.18 AU) was seen at least out 8. IONS
to heliocentric distance of 0.47 AU (Delsemme and Combi,
1983). The first interpretation of Na D emission at distances 8.1. Molecular Ions
beyond 1 AU was by Oppenheimer (1980) in Comet West
(C/1975 V1) at 1.4 AU; Oppenheimer concluded that the Photolytic processes and chemical reactions will ionize
Na was trapped in molecules within the volatile ice compo- molecules in the comae of comets and, as a result, various
nent. He reasoned that only with Sun-grazing comets would molecular ions have been detected in cometary spectra. In
the refractory grain component be hot enough to liberate Na, the UV and optical, these include CH+, CO+, CO+2, H2O+,
either in elemental or molecular form. N+2 , and OH+. Ions have now been detected in the radio
Delsemme and Combi (1983) reported that the Na spa- spectrum of Comet C/1995 O1 (Hale-Bopp), including
tial profile in Comet Kohoutek had its brightest pixel at HCO+ (Wright et al., 1998), H3O+, and CO+ (Lis et al.,
the same location as the dust continuum, whereas the other 1999). The ions show a very different distribution in the
gas species (C2, CN, and NH2) were all displaced sunward, coma than do neutrals since the ions are accelerated tailward
suggesting some connection of Na with the dust. Combi et by the solar wind. Thus, the ionic species are often called
al. (1997) reported a detailed model analysis of spatial pro- “tail” species. However, it should be noted that many are
files of Na from long-slit spectra in non-Sun-grazing com- observed relatively close to the nucleus of the comet, a good
ets [Bennett (C/1969 Y1), Kohoutek (C/1973 E1), and 1P/ illustration being obtained from long-slit spectra of CO+ and
Halley] and identified two types of spatial signatures. There CO+2 in Comet 1P/Halley given by Umbach et al. (1998).
was a relatively stable point source of Na, produced directly The predominant processes for the production of ions
from the nucleus or a short-lived parent, as well as an ex- are photodissociation (e.g., H2O + hν → OH+ + H + e) and
tended source seen mainly on the tailward side. The latter photoionization (e.g., H2O + hν → H2O+ + e) (Jackson and
had a larger production rate and varied by factors of a few Donn, 1968). Within the collisional zone (the inner few
compared with the nucleus source on timescales as short thousand kilometers of the coma for moderately bright com-
as a day. They also noted some spatial similarities in Halley ets), ions can be produced by charge exchange with solar
between the extended Na distribution and ion profiles but wind protons, electron impact ionization, charge transfer
not with the dust. This combined with the large variability reactions, and proton transfer reactions.
led them to suggest a possible role for some plasma pro- The transitions of CO+ that are seen in the blue/UV re-
cess for the extended source. gion of the spectrum arise from the first negative bands
 Feldman et al.: Spectroscopy of Fragment Species in the Coma 441

Fig. 7. Spectrum of Comet 153P/Ikeya-Zhang, recorded 15,000 km tailward from the optocenter, illustrating a well-developed ion
tail. The narrow panel for each half of the order is the optocenter spectrum while the wide panel is the tail spectrum. All lines from
two H2O+ bands are marked, along with lines of NH2 and C2 (Phillips). Not all the marked ionic lines are present; only the lower J-
values appear in the spectrum. Comparison of the tail and the optocenter spectra show the increased strength of the ionic lines relative
to the neutrals. The solar continuum has not been removed from either spectrum. This spectrum was obtained with the McDonald
Observatory 2D-coudé at R = 60,000.

(B2Σ–X2Σ) and the comet-tail bands (A 2Π–X2 Σ). The houtek) (Herzberg and Lew, 1974). The electronic transi-
comet-tail bands show two peaks that are due to the Π1/2 tion is A2A1–X2B1 and it is observed from 4000 to 7500 Å;
and Π3/2 branches. Generally, the (2,0) and (3,0) comet-tail a small part of this range is seen in Fig. 7. Wegmann et al.
bands are the strongest bands observed. The comet-tail tran- (1999) have run magnetohydrodynamic and chemical simu-
sitions are responsible for the blue appearance of the ion lations of cometary comae and have concluded that for
tail in color images of comets. small comets, up to 11% of the water molecules are ulti-
The presence of the CO+ bands in cometary spectra has mately ionized. H2O+ occurs in a spectral bandpass that is
led to the belief that CO is generally present at the few per- easily accessible to CCD detectors, so there are many ob-
cent level in cometary nuclei. CO+ emissions are seen in servations of H2O+ in cometary comae. Lutz et al. (1993)
cometary spectra to heliocentric distances greater than 5 AU have calculated fluorescence efficiency factors for six of the
(Cochran and Cochran, 1991). Magnani and A’Hearn bands. H2O+ is isoelectronic to NH2 so Arpigny’s (1994)
(1986) have calculated fluorescence efficiencies for most comment concerning increasing the efficiency factors of
of the comet-tail bands accounting for the Swings effect, NH2 by a factor of 2 also applies to H2O+. Indeed, although
which should be a factor since there are relatively few ex- the standard reference on the H2O+ band (Lew, 1976) used
cited levels and the solar spectrum is dense in the blue. the linear notation, the transitions are more correctly speci-
Another ion that appears prominently in the red part of fied in their bent notation (Cochran and Cochran, 2002).
the spectrum is H2O+. Although it has been observed in Bonev and Jockers (1994) mapped the distribution of
cometary spectra for a long time, it was only identified for H2O+ in Comet C/1989 X1 (Austin). They found a strong
the first time in 1974 in spectra of Comet C/1973 E1 (Ko- asymmetry with a relatively flat distribution tailward and a
442 Comets II

factor of 4 dropoff in the first 104 km sunward. The maxi- promised by the fact that N2 and CO both share the mass 28
mum H2O+ column density was frequently observed to be bin. Therefore, observations of the First Negative (B2Σ+u –
shifted tailward. X1Σ+g) (0,0) band of N+2 at 3914 Å have been used as a proxy
CO+2 emission was first identified in the optical spectrum for studying N2. Such observations require high spectral
of Comet C/1947 S1 (Bester) (Swings and Page, 1950) and resolution in order to isolate the cometary N+2 emission from
in the UV spectrum of Comet C/1975 V1 (West) (Feldman any telluric N+2 emission. They also require a relatively bright
and Brune, 1976). The optical lines arise from the Fox- comet with a well-developed ion tail for observation. The
Duffendack-Barker (A2Πu–X2Πg) electronic band system spatial distribution of any emissions can be used to differ-
and appear in the wavelength range from 3000 to 4000 Å. entiate between telluric and cometary species.
The UV doublet at 2890 Å is from the B2Σu–X2Πg elec- Observations of the appropriate spectral region of the
tronic transition (Festou et al., 1982). Feldman et al. (1986), tails of comets have been made in the past, and examples
using the IUE, noted a strong enhancement of this fea- of comets that show N+2 in their spectra can be found in
ture in a spectrum of Comet 1P/Halley taken at a position Swings and Haser (1956) (e.g., Comet Bester, plate XXIIIa,
150,000 km tailward of the nucleus at a time correspond- and Comet Morehouse, plates VIa and VIb). Cochran et al.
ing to the peak of an optical outburst. This observation sug- (2000) summarized most of the past N+2 observations. These
gested that CO2 may have played a significant role in the observations have not generally been obtained at high spec-
outburst process. tral resolving power. Recently, Cochran and co-workers
Leach (1987) has noted that the CO+2 emission rates are (Cochran et al., 2000; Cochran, 2002) have reported high-
affected by intramolecular coupling between the B2Σu and spectral-resolution, high-signal-to-noise observations of
A2Πu states so that emission from the B2Σu state can occur at three comets that definitely do not show N+2 in their spec-
λ > 3000 Å (this is referred to as “redshifted fluorescence”). tra and that have very tight limits on the quantity of N+2 .
Such bands are detected in cometary spectra along with Do different comets have differing amounts of N2, possibly
some unclassified bands redward of 4000 Å. Excitation effi- related to their place of origin? Is N2 depleted during the
ciencies for some of the transitions can be found in Fox and life of some comets? Are our models that indicate that N
Dalgarno (1979). should be preferentially in N2 rather than NH3 in the solar
Bands of the OH+ A3Π–X3Σ– electronic system cover the nebula in error? Are variations in the quantity of N2 in com-
complete optical bandpass. However, only lines from the ets the result of clathration of the N2 and CO (Iro et al.,
(0,0) and (1,0) bands have been detected (Swings and Page, 2003)? And ultimately, how reliable are the earlier reports
1950; Festou et al., 1982). Lutz et al. (1993) have derived of N+2 in cometary tail spectra? Answers to these important
fluorescence efficiency factors for many bands of OH+, but questions will require more high-spectral-resolution obser-
caution that they are only accurate to ±50% because the vations of comets with a variety of dynamical histories.
Swings effect was not included.
The CH+ lines that are seen in cometary spectra are from 8.3. Atomic Ions
a A1Π–X1Σ transition. Only the low-energy transitions of
the (0,0) band are seen at around 4230 Å. These lines are Table 2 also lists the wavelengths of the resonance transi-
coincident with bands of CH and CO+. Lutz et al. (1993) tions of the principal atomic ions. The C II doublet at 1335 Å
have also calculated g-factors for CH+. As with the OH+, has been detected in several comets, particularly from sound-
they caution that the Swings effect was not included and ing rocket observations made with fairly large fields of view
therefore the fluorescence efficiencies are only good to (Feldman and Brune, 1976; Woods et al., 1987; McPhate
±50%. et al., 1999). It is difficult to identify the source of the emis-
Other molecular ions were detected by the in situ mass sion. Resonance scattering of the solar C II lines would show
spectrometer measurements made at Comet Halley in 1986. a very strong Swings effect. Photoionization of neutral C
These include H3S+, C3H+, and C3H+3, as well as more com- into an excited ion state has an excitation rate ~10 –9 s–1
plex organic ions (Marconi et al., 1990; Eberhardt and atom–1 (Hofmann et al., 1983) and is insufficient to account
Krankowsky, 1995). Attempts to associate some of the uni- for the observed brightness. Perhaps electron impact ion-
dentified visible spectral features with ions such as these ization is responsible as the C II emission is present in the
or with H2S+ must be taken with caution. same spectra as the O I] λ1356 emission, but the excitation
rate is difficult to evaluate quantitatively. C II λ1037 emis-
8.2. The Case of N+2 sion has recently been detected in FUSE spectra (Weaver
et al., 2002).
N2 is the least reactive of all N-bearing species, so study The only other reported atomic ion emission is O II λ834
of N2 is important for understanding cometary N. In addi- from a rocket observation of Comet Hale-Bopp by Stern
tion, conditions in the early solar nebula were such that the et al. (2000). No quantitative information about this mea-
dominant equilibrium species of N should be N2. However, surement is given.
observations of N2 are extremely difficult to obtain. Ground- Despite the large number of spectra covering this wave-
based observations suffer from telluric absorption; interpre- length range from IUE and HST, the S II triplet at 1256 Å
tations of spacecraft flyby mass spectrometer data are com- has never been detected.
 Feldman et al.: Spectroscopy of Fragment Species in the Coma 443

9. OUTLOOK sion from cometary nuclei. Sol. Phys., 10, 496–501.

Bar-Nun A. and Prialnik D. (1988) The possible formation of a
The study of the gaseous content of cometary comae has hydrogen coma around comets at large heliocentric distances.
seen much progress during the past two decades due to both Astrophys. J. Lett., 324, L31–L34.
Bertaux J. L. (1986) The UV bright spot of water vapor in comets.
enhancements in technology, enabling many more species
Astron. Astrophys., 160, L7–L10.
to be observed, and to a better understanding of the physi-
Bertaux J. L., Blamont J. E., and Festou M. (1973) Interpretation
cal processes producing the observed emissions. Spectros- of hydrogen Lyman-alpha observations of Comets Bennett and
copy continues to be a powerful tool that remains ahead of Encke. Astron. Astrophys., 25, 415–430.
the laboratory data needed to identify the still large num- Bird M. K., Huchtmeier W. K., Gensheimer P., Wilson T. L.,
ber of unexplained features seen in high-resolution spectra Janardhan P., and Lemme C. (1997) Radio detection of am-
both in the visible (Cochran and Cochran, 2002) and the monia in comet Hale-Bopp. Astron. Astrophys., 325, L5–L8.
far-UV (Weaver et al., 2002). The large database of obser- Biver N., Bockelée-Morvan D., Colom P., Crovisier J., Germain
vations, dating back more than a century, provides an im- B., Lellouch E., Davies J. K., Dent W. R. F., Moreno R.,
portant tool to assess the chemical and evolutionary divers- Paubert G., Wink J., Despois D., Lis D. C., Mehringer D.,
ity of comets. Benford D., Gardner M., Phillips T. G., Gunnarsson M., Rick-
man H., Winnberg A., Bergman P., Johansson L. E. B., and
Rauer H. (1999) Long-term evolution of the outgassing of
Acknowledgments. P.D.F. wishes to thank the Institut d’Astro-
Comet Hale-Bopp from radio observations. Earth Moon Plan-
physique de Paris for their hospitality while he held a Poste Rouge
ets, 78, 5–11.
from the CNRS during the fall of 2002. This work was partially
Bockelée-Morvan D. and Crovisier J. (1985) Possible parents for
supported by NASA grants NAG5-9003 (A.L.C.), NAG5-8942
the cometary CN radical — Photochemistry and excitation
(M.R.C.), and NAG5-5315 (P.D.F.).
conditions. Astron. Astrophys., 151, 90–100.
Bockelée-Morvan D. and Gérard E. (1984) Radio observations of
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448 Comets II
 Schleicher and Farnham: Photometry and Imaging Using Narrowband Filters 449

Photometry and Imaging of the Coma

with Narrowband Filters
David G. Schleicher
Lowell Observatory

Tony L. Farnham
University of Maryland

The use of narrowband filters to isolate light reflected by cometary grains and emitted by
several gas species permits a wide variety of compositional and morphological studies to be
performed. A brief survey of some of these studies is presented, along with detailed discus-
sions of the techniques, procedures, and methodologies used. In particular, the advantages and
disadvantages of both traditional photoelectric photometers and CCD cameras is explored, and
an update is given regarding the new narrowband comet filter sets produced in recent years.
Some of the unique aspects of narrowband filter reductions are characterized, as are the steps
required in compositional studies. Finally, the most useful aspects of enhancing, measuring, and
analyzing morphological features are investigated in detail.

1. INTRODUCTION AND BACKGROUND decades up to and including C/Kohoutek (1973 XII) are
summarized by Vanysek (1976), while Meisel and Morris
In this chapter, we provide both a brief review and tuto- (1982) briefly review the topics of bulk brightness variations,
rial of the fields of narrowband photometry and narrowband narrowband and IR photometry, and early compositional
imaging of comets. The use of narrowband filters to isolate studies. Photometry in the IR is also the focus of reviews
the light emitted by various molecular species and reflected by Ney (1982) and Hanner and Tokunaga (1991). Polariza-
solar radiation by dust grains in cometary comae has a long tion studies are discussed by Kolokolova et al. (1997),
and productive history, dating back nearly half a century Levasseur-Regourd (1999), and Kolokolova et al. (2004).
(cf. Schmidt and van Woerden, 1957). While photoelectric Some of the physical properties that can be determined
photometers have been used throughout this interval, digi- for the coma include spatial profiles of individual gas spe-
tal array detectors such as charge-coupled devices (CCDs) cies and of the dust, the presence or lack of jets, sporadic
have now largely replaced photometers as the detectors of brightness variations or unusual coma morphology indica-
choice (cf. Jewitt, 1991). In spite of the overwhelming ad- tive of outbursts, periodic brightness variations or jet mo-
vantages CCDs provide in morphological studies, photome- tions caused by nucleus rotation, and the color and polariza-
ters continue to play an important role, particularly in chem- tion of dust grains. Analyses of many of these characteristics
ical abundance studies. of the coma can yield strong constraints on nucleus proper-
Included here are discussions of the techniques, proce- ties, such as rotation period, pole orientation, and the num-
dures, and methodologies used, and a survey of some of ber, location, and size of individual source regions on the
the physical and chemical properties that can be determined surface of the nucleus. For some comets, in which the signal
with these techniques, along with references to numerous from the nucleus is not overwhelmed by that from the coma,
examples. As such, in many respects this chapter is an up- one can also obtain direct measurements of the nucleus.
date to the valuable review by A’Hearn (1983), where the Chemical composition studies that can be performed in-
issues of observational and reduction techniques were first clude the determination of relative abundances of different
summarized. We also include several topics in common with molecular species, and how these vary with heliocentric dis-
the more recent review by Jewitt (1991), in which his focus tance and/or orbital position and from comet to comet, and
was on the types of studies obtainable with CCDs, but to the absolute production rates of water and dust. With the
minimize overlap, our emphasis is on the general topic of application of an appropriate vaporization model, physical
coma morphologies. As we have neither the space nor the properties such as effective active areas and lower limits on
desire to repeat details provided in previous summaries, we the nucleus size can also be computed. Each of these topics
also urge the reader to examine several other excellent re- is discussed in more detail either here or in other chapters
views in addition to those by A’Hearn and by Jewitt. In par- (e.g., Samarasinha et al., 2004; Bockelée-Morvan et al.,
ticular, a discussion of observations obtained in the early 2004; Feldman et al., 2004; Combi et al., 2004; Fulle, 2004).

449
450 Comets II

2. INSTRUMENTATION 100 counts per second within a relatively large photometric

aperture of 1 arcmin. With a conventional photometer, this
Although many early photometric studies, as well as results in a photon statistical uncertainty of about 1% with
many more recent imaging studies, have used wideband less than 2 min of integration. With a CCD, however, the
filters or even no filtration, in most cases the observer is same ~104 photons are spread over ~10 4 pixels. Given the
inevitably left with an ensemble of reflected light from typical brightness fall-off away from the nucleus, a pixel
grains and emitted light from multiple gas species that can- 30 arcsec from the nucleus would, on average, only receive
not readily be disentangled. Exceptions to this generaliza- <0.2 photons during the equivalent exposure time — a value
tion include nucleus studies at large heliocentric distances, similar to or less than the inherent noise level associated
where the coma is either nonexistent or sufficiently faint with the read-out of each pixel. At such low signal levels,
that the nucleus’ signal can be extracted, and dust studies the absolute uncertainties associated with flatfielding also
when an object is known to be gas-poor, or in the near-IR become quite important in determining the level of the
where gas emission is only a minor contaminant. To isolate background sky. It is hoped that the development of truly
individual emission bands or to obtain continuum measure- flat and readnoise-free CCDs will eventually mitigate these
ments in the near-UV to near-IR region of the spectrum, one problems. Although aperture extractions from a CCD frame
must either use narrowband filters or spectroscopic tech- can be performed, obtaining images solely to extract aper-
niques, each of which has numerous strengths and weak- ture photometry of the coma largely defeats the advantages
nesses. Spectroscopic methods (cf. Feldman et al., 2004, of a CCD, and the resulting photometric uncertainties are
and references therein) have the advantage of permitting the always worse than those associated with a simple photom-
observer to directly detect and measure the shape of spec- eter. Other practical concerns involve observing efficiencies,
tral features, simplifying the task of separating emission such as the effort required to obtain good twilight flatfield
lines and bands from the continuum. This is particularly im- measurements for several narrowband filters, and the longer
portant in the case of weak emission features, such as CH, total time required to obtain sets of images of both the
NH2, or [O I], where the contrast with respect to the local comet and sky in each filter, as compared to the time re-
continuum is very low. However, even with a long-slit in- quired with a photometer. As a result of all these issues,
strument or multiple apertures, only a very small fraction narrowband CCD observations have only rarely been cali-
of the total coma is sampled at one time, and the signal-to- brated and continuum subtracted to obtain gas column den-
noise ratio (S/N) per spatial and per spectral resolution ele- sities and abundances (cf. Schulz et al., 1993).
ment drops rapidly as one samples farther from the nucleus For all these reasons, we have found that basic coma
and inner-coma. If sufficient time is available, mapping the abundance measurements are much more readily obtained
coma can greatly improve the spatial coverage. In compari- (and with much better S/N) using conventional photoelec-
son, conventional photometry and imaging can sample a tric photometers. In our own work, we use a new, computer-
much greater portion of the coma at one time, but only for controlled photometer, but with the same EMI 6256 S-11
the stronger emission bands that can be reliably isolated phototube as used with our previous, manually operated
with narrowband filters. And while both spectroscopy and photometer. This tube, with a quartz window, provides good
imaging techniques permit investigations of gross asymme- throughput to wavelengths below the atmospheric cutoff in
tries in the coma, such as sunward-tailward, only imaging the UV and an extremely low dark current when thermo-
readily permits more detailed morphological studies in the electrically cooled, but has essentially no response in the
visible regime, such as those desired when studying dust red and near-IR. A variety of tubes, having a wide range of
and gas jets. However, the steady increase in the size of characteristics, remain available from several manufacturers.
optical fiber bundles for two-dimensional spectroscopy im- For details regarding construction and use of photoelectric
plies that IFU spectroscopy may permit useful morphologi- photometers, we refer the reader to several books on this
cal studies in the future. subject, particularly those by Henden and Kaitchuck (1982),
With the advent of the twenty-first century and improve- Sterken and Manfroid (1992), and Budding (1993).
ments in digital detectors, one might expect that narrowband In contrast, CCD imaging is clearly the appropriate tech-
imaging would have completely superseded the technique nique to employ if the primary goal is to study morphology
of aperture photometry using conventional photoelectric or to extract the signal from the nucleus from that of the
photometers. While in principle this seems reasonable, in surrounding coma, rather than to obtain abundance mea-
practice several issues have necessitated the continued use surements. In addition to advances in quantum efficiency,
of conventional photometers for many types of composi- particularly in the UV, and readout noise suppression, per-
tional studies. The primary limitation of CCD detectors is haps the most important changes in CCD detectors in re-
the inherent level of noise at the per-pixel level due to read- cent years for comet research have been the ever-increasing
out noise and slight variations in bias level. While these format sizes and the decreased overhead associated with
sources of uncertainty are usually quite small (<1 count), readout times. Larger formats directly yield larger fractions
they can still dominate over the cometary signal in many of the coma being measured or may even extend to uncon-
instances. As an example, it is quite common for the meas- taminated sky, while faster readout of the chip permits more
ured count level for OH or NH emission in a moderately filters to be used in a limited interval of time for both stan-
bright comet (10th–12th magnitude) to be on the order of dard star measurements and twilight flats as well as for the
 Schleicher and Farnham: Photometry and Imaging Using Narrowband Filters 451

comet itself. Numerous books detailing the physical charac- servatories as the initial phase of the Lowell comet photom-
teristics of CCD chips and/or observing and reduction tech- etry program (cf. A’Hearn et al., 1979; A’Hearn and Millis,
niques are now available, including those by Jacoby (1990), 1980). A related effort at producing standard filter sets by
Howell (1992, 2000), and Philip et al. (1995). an IAU Commission 15 Working Group resulted in design
recommendations for a nine-filter set. Manufactured for
3. NARROWBAND FILTERS worldwide distribution in time for Comet 1P/Halley’s 1985/
1986 apparition, several dozen sets were produced for pho-
For both historical and practical reasons, the wavelength toelectric photometers and CCD cameras under the auspices
range within which narrowband filters have usually been of the International Halley Watch, and are now known as the
constructed for comet studies has been between about 3000 IHW filters (cf. Osborn et al., 1990; A’Hearn, 1991, Larson
and 7000 Å. The lower end of the range is set by the at- et al., 1991). Representative transmission curves for the
mospheric cutoff, while the upper end is defined by the IHW filters are shown in Fig. 1.
locations of the strongest emission bands for the observ- Since the design of the IHW filters, several dust-poor
able species. For instance, although the CN molecule pro- comets have been observed spectroscopically, and the re-
duces several emission bands between 7000 Å and 1.5 µm, sulting spectra revealed that wings of the C2 and, especially,
each of these bands in the CN red system is much weaker the C3 bands extended considerably further blueward than
than the primary band of the violet system at 3875 Å. Emis- previously assumed, with the result that the IHW continuum
sion studies of comets in the UV (spacebased) and IR have filters at 3650 and 4845 Å suffered from much larger con-
nearly always been conducted using spectroscopic detectors, tamination than originally believed. In fact, for comets with
because the permanently installed filters are seldom useful very low dust-to-gas ratios, such as 2P/Encke, the wing of
for cometary studies (in the UV) or gas emission features C3 completely dominates the measured flux in the 3650-Å
are relatively weak. However, continuum studies in the IR filter. It also became evident that the red continuum filter,
have often made use of standard broadband filters such as centered at 6840 Å, was contaminated by an emission band
J, H, and K. tentatively identified as NH2. Worse, as early as 1990 it was
A total of five neutral gas species produce sufficiently determined that some of the filters in some sets, including
strong emission bands between about 3000 and 7000 Å to CN, were physically degrading, resulting in a decrease in
be easily isolated with narrowband filters. In order of wave- the band transmission and a redward shift of the bandpass
length, these are OH, NH, CN, C3, and C2. Figure 1 shows (cf. Schleicher et al., 1991). This degradation of interfer-
a composite spectrum, identifying the major emission fea- ence filters is unfortunately common, especially for band-
tures. Note that none of these species are assumed to exist passes at wavelengths <4200 Å, because of older manufac-
in these forms in the nucleus, but each is instead at least a turing techniques. By 1996, many observers had reported
daughter species, produced by the dissociation of one or problems with their IHW sets, as they prepared to observe
more parent (or grandparent) species. Appropriate model- Comets Hale-Bopp (1995 O1) and Hyakutake (1996 B2).
ing is therefore required to ultimately derive the nuclear Because of the overwhelming interest in observing Hale-
abundances of the parents. Emission features by other neu- Bopp, NASA agreed to support the production of new sets
tral species, notably CH, NH2, and O, are too weak and/or of narrowband filters in time for Hale-Bopp’s perihelion
the species are too short-lived to remove the underlying con- passage. In taking on the task of designing and calibrating
tinuum sufficiently accurately to produce reliable results in these new sets, we decided to take advantage of improved
most circumstances. Emissions by two ion species, CO+ and manufacturing techniques, resulting in bandpasses being
H2O+, have also been successfully isolated with narrowband “squarer,” i.e., having flatter tops and shorter wings, and
filters. Unfortunately, as a consequence of the long wings filters with greater longevity and almost no variation of the
of the C3 and C2 bands, together with the profusion of weak bandpass with temperature. At the same time, we altered
emission bands from NH2 and other minor species, very few the placement of each of the continuum bandpasses to mini-
locations between 3000 and 7000 Å are completely absent of mize the contaminations that were present in the IHW fil-
emission. This makes it difficult to obtain clean continuum ters, and added an additional continuum point in order to
measurements, and the decontamination of continuum meas- better measure variations in dust reflectivity as a function
urements by gas emission is a significant issue to which we of wavelength. The filter locations for the emission features
will return. were similar to those in the IHW sets, but with slight adjust-
Over the past half-century, numerous investigators have ments to take advantage of the squarer bandpasses and to
had individual filters manufactured to isolate one or more minimize changes in the fractional transmission caused by
of the stronger emission bands, often with accompanying the Swings effect, whereby the shape of the emission feature
continuum filters (cf. Schmidt and van Woerden, 1957; varies with heliocentric velocity and/or distance. Accom-
O’Dell and Osterbrock, 1962; Blamont and Festou, 1974; modations were also made for the shorter f-ratio systems
A’Hearn and Cowan, 1975). Unfortunately, the lack of stan- that are increasingly used with CCD systems. A total of 48
dardization made it difficult to sort out the many discrepan- full or partial sets of these 11 new filters were produced
cies among the results. An initial effort at standardization and distributed, and these have been designated the HB filter
was made in the late 1970s, when 3 sets of up to 10 filters sets, since Hale-Bopp provided the motivation for their con-
were produced for use primarily at Lowell and Perth Ob- struction and was the initial target. The HB bandpasses are
452 Comets II

Fig. 1. Transmission profiles for the HB filters (thick lines) and IHW filters (dotted lines). For comparison, measured comet spectra
illustrate the locations of the different emission bands. The neutral species and continuum regions are depicted by a spectrum of Comet
122P/deVico (spectral resolution = 12 Å) in the three top panels, and a spectrum of Comet 8P/Tuttle (resolution ~40 Å) in the bottom
panel (thin solid lines). Because these comets do not exhibit clear ion bands, the 2–0 band of CO+ from Comet 29P/Schwassmann-
Wachmann 1 (resolution = 12 Å) has been inserted from 4240 to 4265 Å in the second panel and the 0–6–0 band of H2O+ from Comet
Kohoutek 1973 E1 (resolution = 5 Å) has been inserted from 6940 to 7080 Å in the bottom panel (dashed lines). The 122P/deVico
spectrum is courtesy of A. Cochran, and the 8P/Tuttle spectrum, created by S. Larson and J. Johnson, is courtesy of S. Larson. The
CO+ band was extracted from Cochran and Cochran (1991) and Cochran et al. (1991), and the H2O + band was extracted from Wehinger
et al. (1974) and Wyckoff and Wehinger (1976). From Farnham et al. (2000).

presented in Fig. 1 and itemized in Table 1; details of the paritions. Due to a variety of issues, including the timing of
individual filter design criteria and associated issues are the availability of funding and requirements regarding the
available in Farnham et al. (2000). choice of manufacturers, the ESA and NASA efforts pro-
Shortly prior to our efforts to design and produce the HB ceeded mostly independent of one another, with somewhat
filter sets, ESA began a similar effort to produce new filters different design preferences and specifications. A total of
to replace the aging IHW sets. In ESA’s case, the primary 18 sets of these ESA filters for support of the Rosetta mis-
motivation was to observe the Rosetta spacecraft target, sion were produced and distributed. These bandpasses are
Comet 46P/Wirtanen, during its 1996/1997 and future ap- also listed in Table 1. Because most of the HB and ESA
 Schleicher and Farnham: Photometry and Imaging Using Narrowband Filters 453

TABLE 1. Characteristics of new narrowband comet filters. 18 Sco, 16 Cyg A, vB 106, 16 Cyg B, vB 64, and HD 76151
(in order of their colors in the near-UV) — were averaged
Bandpass† (Å)
and adopted as representative solar colors, and these have
Species* HB Sets ESA Sets
been incorporated in the various reduction coefficients.
OH (0–0) 3090/62 3085/75
Therefore, if an investigator uses the equations and coeffi-
NH (0–0) 3362/58 —
UV Continuum 3448/84 — cients listed in Farnham et al. (2000), solar analogs do not
CN (∆v = 0) 3870/62 3870/50 need to be included in the observing program.
C3 (Swings System) 4062/62 4060/70 Unlike solar analogs, flux standards must be observed
CO+ (2–0) 4266/64 — nightly, to determine both the amount of atmospheric ex-
Blue Continuum 4450/67 4430/40
tinction and the instrumental corrections associated with
C2 (∆v = 0) 5141/118 5125/125
Green Continuum 5260/56 — each filter. For the HB filters, a total of 24 stars were se-
NH2 (0,2,0) — 6630/60 lected having spectral types of late-O to late-B and V mag-
H2O+ (0,6,0) 7020/170 — nitudes ranging from 4th to 8th. Besides the obvious need
Red Continuum 7128/58 6840/90 to be nonvariables, relatively hot stars are preferred to mini-
*Emission band designations in parentheses. mize the number of spectral absorption features and to
† Nominal center wavelength and full-width half-maximum (FWHM).
maximize the flux in the UV. The stars are nearly uniformly
distributed near the celestial equator, insuring that some
stars would match the airmass of any comet within 1–2 h
filter sets were intended for use with CCD cameras, several of the comet observations. The brighter flux standards pro-
differently sized filters were produced, ranging from 25 to vide excellent S/N for photometric systems on smaller tele-
100 mm and 25 to 80 mm respectively. scopes, while the fainter stars are suitable for many CCD
A wide variety of issues must be addressed when cali- systems by minimizing the need to defocus the image to
brating a filter set, including the selection and calibration prevent saturation.
of standard stars, the determination of reduction coefficients
for the calculation of absolute fluxes, and, specifically for 4. DATA ACQUISITION AND REDUCTION
comet filters, the determination of nonlinear extinction co-
efficients for the reduction of the OH band measurements, Basic data acquisition and reduction of a night’s obser-
and coefficients for the decontamination of continuum fil- vations follow conventional procedures except for a few
ters and the removal of continuum from the emission bands. notable exceptions unique to cometary data. The first ex-
These are discussed in some detail by A’Hearn (1983) and ception is that observations must often be obtained at high
references therein, and, for the IHW filter sets, in Osborn air mass due to a comet’s proximity to the Sun. This fact,
et al. (1990) and A’Hearn (1991). Because a complete dis- coupled with the number of species that have their primary
cussion of these issues as applied to the new HB filter sets emission bands in the near-UV, implies that precise extinc-
is contained in Farnham et al. (2000), we next provide only tion coefficients must be determined on a nightly basis,
an abbreviated summary; we use the HB filters as an ex- requiring standard star measurements over a range of air-
ample, since the calibration of the ESA filter sets is cur- masses bracketing the airmass range of the comet. Fortu-
rently in progress. nately, because the filters have relatively narrow bandpasses,
The usefulness of a new filter set is entirely dependent no color terms are required in the reductions, except for the
on the availability of suitable standard stars. In the case of OH filter near 3100 Å. In this unique case, extinction varies
comet observations, two types of standards are needed: flux significantly across the bandpass, due to the strong wave-
standards, used to determine atmospheric extinction and to length-dependence of the ozone component of extinction.
convert relative magnitudes to absolute fluxes, and solar Moreover, the resulting curvature of the extinction-airmass
analogs, used to mimic the solar spectrum in determining relation differs with the detailed spectral signature being
the spectral reflectivity of the dust or nucleus and for con- measured, and therefore different reduction coefficients are
tinuum subtraction from the emission bands. For these latter required for flux standards and for comets having differ-
objectives, the key issue is selecting stars that best match the ing gas-to-dust ratios. The appropriate equations and coef-
color of the Sun. Since no star has yet been identified as a ficients for extinction with the HB OH filter are detailed in
true “twin” of the Sun, and there are differences among Farnham et al. (2000).
researchers as to which star most closely matches the Sun, The need to accurately remove contamination by emis-
we measured a dozen known solar analogs using the HB sion bands of the continuum filters in high gas-to-dust ra-
filters and discovered a surprisingly large dispersion in tio comets, and to subtract continuum from emission bands
colors in the near-UV. Because several of these stars are in low gas-to-dust ratio comets, requires sufficiently high
considered close solar analogs, we removed three other stars S/N for whichever filters yield the smallest count levels.
whose colors were most discrepant. We also wanted to This implies that the optimum integration times for each
evenly bracket the Sun’s physical properties, such as tem- filter will not only differ due to the overall brightness of
perature, metallicity, and chromospheric activity, resulting the comet, but also with the relative amounts of gas and
in the removal of two additional stars that skewed the brack- dust. It is therefore highly desirable to reduce the first ob-
ets. Ultimately, colors of seven solar analogs — HD 25680, servations of a new comet rapidly so as to be able to tailor
454 Comets II

subsequent observations. Accurate determinations of the results in improved S/N for a given amount of observing
background sky with each filter are also necessary, and can time. This section is therefore primarily aimed at, but not
be very time-consuming to obtain. Typically, if a comet is restricted to, observations obtained with a conventional pho-
sufficiently bright to enable the use of narrowband filters, tometer system. Of course, many of the following proce-
the coma is likely to cover the entire CCD frame, forcing dures have direct analogs in the analysis of comet spectro-
one to obtain separate sky frames for each filter. It is gen- photometry.
erally sufficient to obtain sky measurements at distances The derived continuum fluxes and emission band fluxes
greater than ~30 arcmin from the nucleus in any direction are usually the final reduced quantities that can be consid-
other than that of the tail, although larger distances are re- ered model-independent. In the typical case of comets with
quired for exceptionally bright or close comets. It is also detectable coma, unlike for point sources, the aperture used
almost always preferable to track at the comet’s rate of for the measurements must be specified for these quanti-
motion across the sky when obtaining either photometry or ties to be meaningful. Usually the observer will also want
imaging of the coma; this capability is more routine now to compute an aperture-independent quantity by applying a
that most telescopes are computer-controlled. suitable model of the coma, after first converting gas emis-
When performing small-aperture extractions from CCD sion band fluxes to the number of molecules required to
images, one must be aware of the effects of changing produce the measured fluxes. This conversion to a molecu-
amounts of flux from the coma and from the nucleus due lar abundance requires the use of the fluorescence efficiency
to seeing variations during the night; otherwise, artificially (L/N or luminosity per molecule when given in units of ergs
produced lightcurve features can result. While these effects per second per molecule, or, equivalently, g-factor when
can be searched for by extracting fluxes from a series of given in units of photons per second per molecule) for the
apertures, compensating for this situation is extremely dif- particular molecular band. While the fluorescence efficien-
ficult unless the effective pointspread function is available cies for comets are generally unchanging for polyatomic
on each frame, and background stars will be trailed unless species due to their large number of populated rotational
the exposures are kept sufficiently short. Decisions regard- levels (except for the r –2 dependence due to the fall-off of
ing appropriate aperture sizes for a conventional photom- solar flux with distance from the Sun), diatomic molecules
eter must be made at the time the observations are acquired. such as OH, NH, and CN display large variations as a func-
Here, some major tradeoffs must be made to (1) avoid back- tion of heliocentric velocity due to the Swings effect (cf.
ground stars, (2) minimize the sky signal, and (3) maximize Arpigny, 1976; Feldman et al., 2004). Appropriate values
the comet signal. With either instrumentation, practical limi- as a function of velocity for OH can be found in Schleicher
tations on integration times are imposed by (1) changing sky and A’Hearn (1988), for NH in Kim et al. (1989) and Meier
brightness (particularly near twilight), (2) total time the et al. (1998), and for CN in Tatum and Gillespie (1977),
comet is available, and (3) the number of filters to be used. Schleicher (1983), and Zucconi and Festou (1985). Note
Compromises must almost always be made; the observer that the latter two CN references also present the variation
should let the specific science goals determine the best ob- of the fluorescence efficiencies as a function of heliocen-
serving procedures on a case-by-case basis. tric distance as well as with velocity, since the number of
Except for the nonlinear extinction associated with the populated rotational levels in CN varies strongly with the
OH filter and already discussed, reductions to filter fluxes available solar flux. In the Lowell photometric program, we
follow standard methods. Thereafter, narrowband reductions currently continue to use the same fluorescence efficiencies
are somewhat unusual, in that the continuum filters often adopted by A’Hearn et al. (1995), and these are summa-
suffer from some contamination from cometary emission rized in Table 2. However, the values for some species, such
bands, the emission filters include underlying continuum, as C3, may change in the future as band oscillator strengths
and the continuum is often reddened with respect to solar are revised or as fluorescence models include more transi-
spectrum. A new iterative technique was developed by Farn- tions and collisional effects.
ham et al. (2000) to deal with these issues when using the The resulting molecular abundances obtained following
HB filters. This procedure uses the measured fluxes in the the application of fluorescence efficiencies can be readily
continuum bands to remove underlying continuum from the converted to column densities, if desired, but for either
C3 and C2 filter fluxes, which can then be used to compute abundances or column densities the size and location of the
the amount of contaminating emission in the continuum aperture or slit must be stated for the result to be useful. In
filters. At each step of the iteration the remaining contami- order to intercompare results obtained with differing aper-
nation is reduced, until essentially pure emission fluxes and tures on a single comet or to intercompare comets, a coma
continuum fluxes are obtained. Again, all relevant equations model (such as the Haser, the Vectorial, or a numerical
and coefficients are provided in Farnham et al. (2000). model such as the Monte Carlo) is applied to extrapolate
the measured column abundance to a total coma abundance.
5. COMPOSITIONAL PHOTOMETRY While there are pros and cons to each specific model (see
Combi et al., 2004, and references therein), in each case a
As previously noted, comet photometry for the purposes few parameters (such as the lifetime, velocity, and/or scale-
of compositional determinations can be made using either length) are used to approximate the spatial distribution of the
a phototube or a CCD as a detector, but the former usually specific gas species in cometary comae. Once a total coma
 Schleicher and Farnham: Photometry and Imaging Using Narrowband Filters 455

TABLE 2. Adopted parameters used in reduction of Lowell narrowband photometry.

Haser Scalelength† Daughter

L/N* Parent Daughter Lifetime†
Species (erg s–1 mol–1 ) Reference (km) (km) (s) Reference
OH (0–0) 1.4–8.3 × 10 –15 Schleicher and A’Hearn (1988) 2.4 × 10 4 1.6 × 105 1.6 × 10 5 Cochran and Schleicher (1993)
NH (0–0) 4.9–7.6 × 10 –14 Kim et al. (1989) 5.0 × 10 4 1.5 × 105 1.5 × 10 5 Randall et al. (1992)
CN (∆v = 0) 2.4–5.0 × 10 –13 Schleicher (1983) 1.3 × 10 4 2.1 × 105 2.1 × 10 5 Randall et al. (1992)
C3 (λ4050) 1.0 × 10 –12 A’Hearn et al. (1985) 2.8 × 10 3 2.7 × 10 4 2.7 × 10 4 Randall et al. (1992)
C2 (∆v = 0) 4.5 × 10 –13 A’Hearn (1982) 2.2 × 10 4 6.6 × 10 4 6.6 × 10 4 Randall et al. (1992)
*All fluorescence efficiencies (L/N; for rH = 1 AU) are scaled by r 2H. L/N for OH, NH, and CN are functions of rH, and L/N for CN is also a function of rH
(see A’Hearn et al., 1995, for details). The CN (0–0) L/N values are multiplied by 1.08 to approximate the contribution of the CN (1–1) band.
†All scale lengths and lifetimes (for rH = 1 AU) are scaled by r–2 H
(see A’Hearn et al., 1995, for details).

abundance is computed, this quantity can be divided by the as the appropriate values for the conversion coefficient for
lifetime of the species (usually controlled by the photodis- each HB continuum filter, are given in Appendix D of Farn-
sociation rate from solar radiation) to compute the produc- ham et al. (2000). Since no knowledge of the grain prop-
tion rate of the species, Q, i.e., the rate at which new mole- erties is required as input to the calculation, the computation
cules (or their parents) must be released from the nucleus of A(θ)fρ from the measured continuum flux is straightfor-
to maintain the observed abundance. Unfortunately, the val- ward, and therefore A(θ)fρ is often used as a proxy of dust
ues for these seemingly fundamental parameters are often production, somewhat analogous to the gas production rates
poorly known, because many of the species are radicals and discussed above. Indeed, the quantity A(θ)fρ varies propor-
therefore difficult to measure in the laboratory. Moreover, tionally to the dust release rate from the nucleus, but also
lifetimes also vary with solar activity, while the amount of inversely proportional to the dust outflow velocity. Unfor-
acceleration of the bulk gas flow varies with collision rates, tunately, the very fact that grain properties are not included
which depend upon the total gas production rate and the in A(θ)fρ means that intercomparisons as a function of time
distance from the nucleus. for a single comet or intercomparisons between comets
To minimize the number of parameters needed when must be made with caution. Simple intercomparisons inher-
intercomparing the composition of comets, the Lowell pro- ently assume that numerous properties of the dust grains
gram generally uses the Haser model, again with the same are constant with time and among comets, such as particle
values for the model parameters as those adopted by size distribution, grain shape and porosity, and outflow ve-
A’Hearn et al. (1995), and these are also summarized in locity. However, since dust grains are initially entrained with
Table 2, along with assumed daughter lifetimes. These par- the gas flow, the resulting bulk dust velocity can vary with
ticular values were based on observed radial profiles ob- total gas production rates. Particle size distributions are
tained over a variety of heliocentric distances, but they do known to differ drastically among comets, and outflow ve-
not work in all circumstances. For instance, in the case of locities also vary with particle size. Grains have also been
Comet Hale-Bopp, the scalelengths must be increased by seen to “fade” as they move away from the nucleus, either
2–3× due to the combination of unusually large gas out- by shrinking in size or darkening as volatiles escape from
flow velocities in this very high production comet along the grains, or by breaking apart (Jewitt and Meech, 1987;
with low solar activity (Schleicher et al., 1999). For these Baum et al., 1992). Therefore, it can be difficult to determine
and other reasons, to the extent possible it is important to whether a particular variation or trend of A(θ)fρ is actually a
observationally verify the validity of the parameters used measure of the rate of release of dust grains from the nu-
in this modeling, such as by directly measuring the radial cleus, or an indication of differing grain properties, as was de-
profiles of each gas species, either by observing with mul- termined in the recent case of Comet 19P/Borrelly (Schlei-
tiple photometer entrance apertures, narrowband imaging, cher et al., 2003).
or longslit spectroscopy. Unfortunately, in practice, this A variety of types of scientific studies that can be per-
testing of the parameters is usually not feasible except with formed from photometric measurements obtained through
relatively bright comets. narrowband filters was itemized in the introduction to this
A method to produce an aperture-independent quantity chapter. We now briefly explore a selected subset of these
utilizing continuum flux measurements of the dust coma topics, primarily drawing on examples from our own work
was introduced by A’Hearn et al. (1984). This quantity, simply because, following the apparition of Comet 1P/
A(θ)fρ, is the product of the bond albedo, A, at a particu- Halley in 1985/1986, very few groups have continued to
lar phase angle, θ, the filling factor, f, and the projected ap- employ this technique. Certainly one of the most basic types
erture radius, ρ, as seen on the sky plane. This product will of studies are those of relative gas and dust production rates
be independent of aperture size if the dust follows a canoni- to determine the relative composition of parent or grand-
cal 1/ρ spatial distribution for outflowing dust, and will be parent species in the nucleus (or, at least, the active source
independent of wavelength if the dust has no color as com- regions on the nucleus). Differences in the abundance ra-
pared to the Sun. The equation to compute A(θ)fρ, as well tios as a comet moves along its orbit can be used to infer
456 Comets II

chemical inhomogeneities in the nucleus (e.g., A’Hearn et brightness variations, such as a comet’s changing heliocen-
al., 1985), while differences among comets can indicate tric distance. A few comets for which phase effects have
either evolutionary effects, such as the strong gas-to-dust been successfully separated from other effects include P/
variation with perihelion distance (A’Hearn et al., 1995), or Stephan-Oterma (Millis et al., 1982), Bowell (1980b)
primordial, such as the large fraction of Jupiter-family com- (A’Hearn et al., 1984), and Halley (Meech and Jewitt, 1987;
ets that are depleted in carbon-chain molecules as shown Schleicher et al., 1998a). The most diagnostic type of re-
in Fig. 2 (A’Hearn et al., 1995). With a sufficiently large mote measurements for dust particles in cometary comae is
database, such as the 85 comets observed by A’Hearn et al. that of polarization. These can usefully constrain physical
(1995), numerous compositional investigations were pos- properties, but are difficult to obtain. Here, again, narrow-
sible on a statistical basis. Of course, other properties, such band filters minimize the contamination otherwise caused
as heliocentric distance-dependencies and possible varia- by gas emission. One research group that has routinely ob-
tions with species, can be determined for well-studied com- tained this type of narrowband measurements is that of
ets such as 1P/Halley (Schleicher et al., 1998a), 2P/Encke Kiselev and Chernova and their associates (cf. Kiselev and
(A’Hearn et al., 1985), 21P/Giacobini-Zinner (Schleicher et Chernova, 1981; Chernova et al., 1993; Kolokolova et al.,
al., 1987), and Hyakutake (1996 B2) (Schleicher and Osip, 2004). Note that narrowband filters have also been occa-
2002). By utilizing a basic water vaporization model (cf. sionally used to obtain polarimetric measurements of mo-
Cowan and A’Hearn, 1979), minimum effective active areas lecular gas emission (cf. Le Borgne et al., 1987; Sen et al.,
on the surface of the nucleus can be computed, yielding a 1989), but the degree of polarization is generally much
minimum effective radius or, if the nucleus size is deter- smaller for gas than for dust and underlying continuum
mined separately, a fractional active area. One of the most must be very accurately removed, making gas polarization
unexpected results from the Lowell photometry program is measurements quite difficult.
the large number of comets having very small (<3%) ac- Finally, periodic variations detected within a photomet-
tive fractions (A’Hearn et al., 1995). ric lightcurve can, of course, be used to determine the rota-
The color of dust grains is primarily an indicator of the tion period of a comet nucleus. While variations due to the
particle size(s), and has limited value in determining other changing cross-section of the nucleus itself are most easily
physical properties of the grains, such as composition or po- interpreted (and are most readily obtained using a CCD),
rosity (cf. Kolokolova et al., 2004). Measurements of phase measured variations of the brightness of the coma can be
effects, particularly at small and large phase angles, are dif- used to infer the number and relative strengths of individual
ficult to obtain because of other, often stronger sources of source regions on the surface of the nucleus. Differences
in lightcurve amplitudes and phase lags among the various
gas species and with the dust can further be used to con-
strain outflow velocities and lifetimes, as in the cases of
Comets 1P/Halley (cf. Millis and Schleicher, 1986), Levy
(1990c) (Schleicher et al., 1991), and Hyakutake (1996 B2)
(Schleicher and Osip, 2002).

6. IMAGING AND COMA MORPHOLOGY

6.1. Morphological Features

Many comets exhibit detailed, well-defined features in

their comae. The presence of these features indicates that
the surfaces of the nuclei of these comets are not uniformly
active, but emit material anisotropically, with at least part
of the material coming from isolated active areas. Some of
the more prominent types of features that are observed in-
clude jets (radial structures produced by isolated active re-
gions, or sources, that emit collimated streams of gas and
Fig. 2. Derived production rate ratios of C2 to CN as a function dust), fans (jet-like structures that tend to be broader and
of the Tisserand invariant with respect to Jupiter, TJ. The C2-to- more diffuse than jets), spirals and arcs (outflowing material
CN ratios are based on each species’ respective ratio to OH. Com- from jets on a rotating nucleus that form archimedean spi-
ets having “typical” composition are those within the horizontal
rals, or partial segments of spirals, respectively), and coma
band ( ), while carbon-chain depleted comets lie below this band
asymmetries (some regions of the coma appear brighter than
( ). One-half of Jupiter-family comets (TJ > 2) are depleted, while
only two non-Jupiter-family comets (TJ < 2) display significant de- others). In addition to providing an explanation for the coma
pletions, and one of these — P/IRAS — oscillates across the TJ = morphology, the existence of isolated source regions also
2 boundary. Statistically, most Jupiter-family comets are believed to provides a natural explanation for a variety of other phe-
have originated in the Kuiper belt, while most other comets should nomena observed in comets, including seasonal variations
have come from the Oort cloud. Based on A’Hearn et al. (1995). in the production rates, nongravitational accelerations of the
 Schleicher and Farnham: Photometry and Imaging Using Narrowband Filters 457

comet’s orbit, and changes in the rotation state of the nu-

cleus. Because isolated source regions can contribute to so
many different aspects of the comet’s activity, it is impor-
tant to determine their characteristics.
To fully understand the role that the active regions play
in the comet’s behavior, properties such as the rotation state
of the nucleus and the location of the sources must also be
known, so that the dust and gas emission can be character-
ized as a function of time. Frequently, models of jet emis-
(a) (b)
sions can be used to reproduce the observed morphology
and infer the relevant properties of the nucleus. Further-
more, in certain situations, it is possible to utilize these de-
rived results to aid other analyses. Potential secondary stud-
ies include searching for compositional inhomogeneities in
the jets (cf. A’Hearn et al., 1986a,b; Lederer et al., 1997;
Festou and Barale, 2000) or constraining more fundamental
characteristics such as the mass and density of the nucleus
(Farnham and Cochran, 2002). Although some of the prop-
erties determined through coma modeling could be found (c) (d)
using other techniques (e.g., lightcurve variations may re-
veal the rotation period), many could otherwise only be Fig. 3. Comparison of radial and azimuthal features, and the dif-
found via spacecraft encounters. This makes the analysis of ferences between dust and gas morphology. (a) Comet Borrelly
the coma morphology an extremely valuable technique for showing purely radial structure (Farnham and Cochran, 2002).
understanding the fundamental qualities of cometary nuclei. (b) CN jets observed in Comet Halley, showing initially radial
The majority of studies involving analysis of a comet’s features with curvature induced by rotation of the nucleus
coma features are performed using images obtained with (A’Hearn et al., 1986a; International Halley Watch, 1995). (c) Dust
broadband or continuum filters. This is likely due to two and (d) CN images of Comet Hale-Bopp, showing azimuthal fea-
factors: The dust coma tends to show clearer, more well- tures and the difference between the structure of the gas and dust
in the coma (Farnham et al., 1999). Features were enhanced by
defined structures than the gas species, and the data reduc-
dividing out a 1/ρ profile from the dust frames and an azimuthal-
tion process is simpler. However, while they have proven
averaged profile from the CN images.
to be very useful, dust images only provide a partial pic-
ture of the overall coma morphology, with gas and ions
adding their own contributions. In most comets, features in
the gas coma tend to be completely overwhelmed by the tional cycle, while the dust shows only two, which might
dust, but narrowband filters can be used to help isolate the suggest inhomogeneities in the nucleus. Finally, Woodney
gas features. Then, as described previously, with careful et al. (2002) used narrowband filter data, in conjunction
calibration the underlying continuum can be removed, leav- with radio measurements of the spatial structure, to explore
ing images of the pure gas coma (Schulz et al., 1993, 2000; the relationship between the HCN and CN.
Farnham et al., 2000). (Similarly, gas contamination can Investigations of the nucleus size and the cometary
be removed from images obtained with narrowband con- plasma environment can both benefit from the use of nar-
tinuum filters to leave the pure dust coma.) The pure gas rowband filters, too. For high gas-to-dust comets, direct
images can then be enhanced or modeled, in the same man- measurements of the nucleus (Lamy et al., 2004) are more
ner as the dust images, to learn about the gas properties and efficient with narrowband filters than broadband ones, be-
to provide additional constraints on the nucleus properties. cause continuum filters exclude the gas contribution and
Studies of the CN coma in Comet Hale-Bopp illustrate the make the nucleus stand out more against the coma. In
potential benefits of utilizing the gas morphology: First, the plasma tail studies, the narrow passbands will isolate CO+
CN forms complete spirals around the nucleus, while only or H2O+ much more efficiently than broadband filters or
partial arcs are seen in the continuum (see Fig. 3), indicating photographic plates, increasing the contrast of the plasma
that the gas production behaves differently from that of the features against the background. Furthermore, with proper
dust (Larson et al., 1997; Farnham et al., 1998b; Mueller calibration, the continuum can be removed from the ion
et al., 1999). Second, the CN spirals expand radially out- images to reveal the features very close to the nucleus. This
ward at about twice the speed of the dust features, which improves the potential for following phenomena such as
is likely due to differences in initial outflow velocities and disconnection events from their earliest stages (Ip, 2004).
accelerations (Schleicher et al., 1999). The fact that the gas Dust, gas, and ion features have been observed and stud-
and dust are not co-spatial indicates that most of the gas is ied in many comets, with recent examples including Halley,
being emitted directly from the nucleus rather than coming Hyakutake, Hale-Bopp, and Borrelly. Although the detailed
from the optically important dust grains in the coma. Third, morphology in each comet is unique, the features can gen-
the CN images clearly show three distinct jets in each rota- erally be classified into two main categories: azimuthal and
458 Comets II

radial (or a combination of the two). Because most of the positions that are being used to constrain models of the
material from a jet expands radially away from the surface, morphology. Another potential problem with enhancing an
the appearance of structures in the coma is strongly depen- image is that various techniques may reveal different types
dent on the geometric viewing conditions and the rotation of features in a given image. Because of this, the interpre-
state of the nucleus. A source at a given latitude will sweep tation of the nature of the feature may be strongly depen-
out a hollow cone centered on the spin axis (or a partial dent on the particular technique as well as on the manner
cone if the source rotates out of sunlight and shuts down in which it was applied. For example, images of Comet
during part of a rotation). When Earth is oriented inside the Hyakutake processed with a 1/ρ removal (discussed below)
cone, features usually appear to be azimuthal — archime- appear to have round blobs of material moving radially out-
dean spirals when the source is continuously illuminated ward, while processing with radial profiles derived from the
and concentric arcs when it turns on and off. If Earth is comet itself reveal that the blobs are actually broad spiral
outside the cone, then the feature may appear to oscillate arcs (cf. Figs. 4b and 4k) (Schleicher et al., 1998b; Schlei-
back and forth, or it may smear together to produce a fan cher and Woodney, 2003). Finally, enhancement of an image
with primarily radial structures [due either to the planetary inherently changes the relative intensities of the different
nebula effect at the edges of the fan or to insufficient spa- regions of the coma. This is a concern in the interpretation
tial resolution (Samarasinha et al., 1999)]. Radial features of the relative brightnesses and strengths of the different
are also produced when the jet is on a slowly rotating nu- sources, as well as in using coma asymmetries to constrain the
cleus (e.g., seeing only the innermost segment of the archi- gas and dust production as a function of solar illumination.
medean spiral, which is nearly radial) or if the active region There are a wide variety of enhancement techniques,
is near the rotation pole, as is the case for Comet 19P/ each of which has its own strengths and drawbacks. Any
Borrelly (Samarasinha and Mueller, 2002; Farnham and technique can be good or bad and no single technique is
Cochran, 2002; Schleicher et al., 2003). ideal for every situation. Thus, it is important for the user
We note that factors other than isolated active regions to experiment with different methods on a variety of data,
can also produce features in the coma. Solar radiation pres- to become familiar with their pros and cons, to understand
sure can act on the dust grains to produce envelopes that the types of data for which specific techniques are most use-
can be mistaken for arcs, while anti-tails and neck-line ful, and to help in recognizing potential problems and arti-
structures can mimic radial structures (Fulle, 2004). How- facts. A number of basic processing methods are discussed
ever, both of these cases are only observed in continuum in Schwarz et al. (1989), Larson and Slaughter (1992), and
images and involve relatively unique circumstances and Farnham and Meech (1994). We review these and introduce
geometric alignments, which can be investigated to avoid additional techniques in the following discussion, and pre-
misinterpretation of the results. Structure in the coma can sent representative enhancements in Fig. 4. As this figure
also result from outflowing material that experiences con- shows, different techniques can produce dramatically dif-
structive interference and density enhancements due to the ferent effects, and it is advisable to utilize several different
topology of the nucleus (Crifo et al., 2004), but this mecha- ones on the same image, so that they complement each other
nism can only produce features that are restricted to the very and act to create an overall portrayal of all aspects of the
innermost coma regions and have a low contrast against the coma. This also provides a cross-check to determine if a
background. Finally, other types of features, such as knots, feature is real or if it was introduced by the processing.
condensations, and kinks, are observed in plasma tails, but Before introducing the different enhancement tech-
these are not addressed in any detail here. niques, we address a few practical notes regarding their
definitions and applications. First, many of the techniques
6.2. Image Enhancement Techniques require the “removal” of a radial profile from the observed
coma. This removal process can be done via either subtrac-
Any comprehensive discussion of the coma morphology, tion or division, with very different results. For example,
gas, dust, or plasma, must inevitably address the topic of subtracting a 1/ρ profile emphasizes features in the inner-
image enhancement techniques, as the two are intimately most coma, while dividing by this same profile suppresses
related. Indeed, many features are overwhelmed by the bulk the innermost coma but dramatically enhances the features
radial brightness fall-off of the coma and only become further out (compare Figs. 4b and 4c). Second, a number
obvious when the image has been processed in some man- of techniques require that a coma profile be created directly
ner (though once the user knows what to look for, the fea- from the comet images themselves. Usually, this involves
tures are usually detectable in the unenhanced image with combining a set of pixels (e.g., all the pixels in a given
appropriate display parameters). Unfortunately, enhancing annulus) to produce a mean value that can then be removed.
an image, by definition, alters the image, and not always For these cases, we tend to utilize the term “averaging” of
in the manner that is expected or desired. Thus, any pro- the pixels, but they can be combined by computing the
cessing technique should be used with caution. Potential mean, median, or mode of the sample. Again, different re-
dangers include introducing artifacts that can be misinter- sults can be obtained in each case. Third, many enhance-
preted as real structures or shifting the apparent positions ments utilize radial and/or azimuthal information from the
of features. Even if these shifts are small (which is not al- original image to generate profiles. For these situations, it
ways the case), they are misleading when they change the is easiest to work with an image that has been unwrapped
 Schleicher and Farnham: Photometry and Imaging Using Narrowband Filters 459

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

( j) (k) (l)

Fig. 4. Comparison of different image enhancement techniques on a common coma image containing three primary features: a broad,
diffuse outer arc, an intermediate-scale inner arc, and a narrow, sharply defined tail. These three examples illustrate the type of fea-
tures revealed by each technique (although different kernel sizes or shifts of different amounts can change the scale of the features that
are revealed). Note that some methods enhance the radial tail, others reveal the azimuthal arcs, and some remove the azimuthal varia-
tions, while in others it is retained. Although dramatically different results are obtained with the different techniques, it is clear that no
single enhancement is ideal for every situation. This emphasizes why multiple techniques should be used to investigate the variety of
potential coma features that may be present. (a) Original image of Comet Hyakutake (Schleicher and Woodney, 2003), displayed with
a logarithmic scale to show the straight narrow tail. (b) 1/ρ profile, divided out. (c) 1/ρ profile, subtracted out (for comparison, to
show how different applications of the same technique can affect the result). (d) Azimuthal-averaged profile divided out. (e) Linear
shift difference with a five-pixel shift in both the vertical and horizontal directions. (f) Rotational shift difference with a 10° rotation.
(g) Laplace filter. (h) Unsharp mask with a three-pixel Gaussian smoothing kernel. (i) Radial gradient filter. (j) Azimuthal renormalization.
(k) Phase-stacked mask. (l) Phase-stacked/azimuthal-averaged profile. Other examples of enhancements (b) and (d) are shown in Fig. 3.
460 Comets II

from the standard rectangular format into a polar format or radially smooth the profile to suppress any arc residuals;
(θ,ρ, where θ is the position angle and ρ is the projected in other cases, using a median rather than an average of the
distance from the nucleus). Using the unwrapped image, it annulus pixels may suffice.
is trivial to extract radial and azimuthal information from 6.2.2. Edge detection techniques. Another type of en-
the rows and columns. The drawback to this process is the hancement is the edge detection technique (EDT), which
need for high-quality unwrapping and rewrapping routines covers a large family of routines. These tend to be very pop-
that conserve flux and do not introduce artifacts. Finally, ular because they are easy to use, require little effort to
we stress the importance of accurately finding the opto- develop, and dramatically increase the contrast of some fea-
center of the coma when using many enhancement tech- tures. The first group of edge detectors includes derivative
niques. Accurate centering, at the fractional pixel level, is routines such a linear shift differencing (Klinglesmith, 1981;
crucial when any kind of profile is removed from the coma Wood and Albrecht, 1981) or rotational shift differencing
or when the image is being unwrapped into polar coordi- (Larson and Sekanina, 1984), where a copy of the image
nates. Similarly, when multiple images are being combined, is shifted or rotated and then subtracted from the original.
it is critical to have them properly registered so the nucleus Features that are revealed in this process are a function of
is in the same position in each frame. For most comets, the the size and direction of the shift, so several applications
central condensation of the continuum provides a suitable should be used to look for features at different spatial scales
reference for the optocenter of both gas and dust images, and in different orientations. A powerful benefit of the rota-
whereas for comets with little or no dust, the nucleus itself tional shift is that a rotation around the optocenter will pro-
is sometimes visible. duce small shifts near the nucleus, where features tend to
The most benign technique available for searching for be small and well-defined, and increasingly larger shifts at
features comes from the display process itself. Displaying larger distances, where the features spread out and become
the image with a log or square root intensity or as a histo- more diffuse. This minimizes the number of applications
gram equalization, and then adjusting the contrast stretch, needed. Another technique, the temporal derivative, uses the
will often reveal a significant amount of detail. This is a ratio of two images obtained at different times to reveal
straightforward method that is available as a standard option changes in the features as a function of time. This technique
on most display packages and tends to work well. Because is frequently used for work with plasma tails where features
there is no manipulation of the data, and hence no way to change rapidly. There are situations where the temporal
introduce artifacts, any features that are seen are likely to derivative can be used over longer timescales (e.g., night to
be real. In addition, once a feature has been identified using night), but the approach should be used cautiously because
another technique, it can usually be detected in the original other factors, including seeing variations and changes in the
image if the display is set correctly. For this reason, it is a viewing geometry, can also affect the appearance of the
good idea to return to the unprocessed image to confirm coma. Next is the color derivative, which, although not an
the existence of any features found using the more aggres- EDT, we include here for completeness. In this method, the
sive enhancement methods. ratio of two images obtained at different wavelengths (usu-
6.2.1. Removal of simple profiles. The most basic level ally from two different continuum filters) shows spatial
of processing uses a simple profile to remove the bulk coma color variations in the coma. This is useful for procedures
shape from the observed image. For the continuum, a logi- such as comparing the particle size information in a jet to
cal first choice is a 1/ρ profile, in which the brightness falls that in the rest of the coma. This derivative should be used
off as the inverse of the projected distance from the nucleus. with care, however, because gas contamination, poor flat
This is the canonical shape of a coma produced by steady- fielding, or residual sky background can produce misleading
state isotropic emission of dust. (An analogous shape for results, and so high-quality, decontaminated data are neces-
gas images would be a Haser model profile.) The resulting sary for accurate results.
image highlights the deviations of the observed coma from The next group of edge-detection enhancements includes
the idealized one. Not only is this an easy enhancement to spatial filters, such as the Laplace filter and other proce-
apply, but it is fairly benign and it makes the interpretation of dures in which a kernel is convolved with the image (e.g.,
the morphology relatively straightforward because the ex- Richards, 1993). It also includes unsharp masking (e.g.,
tracted profile is smooth and its shape is known. A slightly Sekanina, 1978), in which a copy of an image is digitally
more complex technique, based on the same principle, uses smoothed and the lower-resolution version removed from
the observed coma, gas or dust, to create a profile from the the original. These techniques tend to be easy to use and
comet itself. By averaging azimuthally around the opto- are very useful for exploring whether or not features are
center (easily done from the polar format image) a radial present. However, if measurements are to be obtained from
profile that closely matches the shape of the real coma can the processed image, then edge-finding routines should be
be created. The main problem with this technique is that avoided for a number of reasons. First, the enhanced fea-
strong arc-shaped features or bright stars may introduce tures are dependent on the size and shape of the filter that
bumps into the profile, which can then produce artifacts in is applied, which in turn affects the interpretation of the
the enhanced image. To avoid this, it may be necessary to result. When using unsharp masking, for example, smooth-
remove the stars before computing the average profile and/ ing the image with a Gaussian filter produces a result very
 Schleicher and Farnham: Photometry and Imaging Using Narrowband Filters 461

different from what is obtained with a square filter. Sec- rectly compare the results. To avoid this problem, it makes
ond, EDTs are specifically designed to identify edges or sense to enhance the images by removing the same bulk
discontinuities. Thus, positions obtained from an EDT-en- coma shape from each frame. Again, a standard profile (e.g.,
hanced image may not be accurate if the measurements are 1/ρ) can be assumed or one can be created from the comet
intended to represent the center of a feature (as is usually itself. In the latter case, however, the profile should be de-
the case when the positions are used as input for coma rived using all the images in the sequence so that it incor-
models). Third, these techniques are very harsh and remove porates not only spatial variations in the the coma, but tem-
a significant amount of information about the coma, which poral ones as well. This was done in an analysis of the CN
is why they produce high-contrast features. Fourth, this jets in Comet Halley (Schulz and A’Hearn, 1995) in which
same harshness means that EDTs are more prone to intro- a series of images were combined to produce an averaged
ducing artifacts, especially near the nucleus where the bright shape that was then removed from the individual frames.
central peak dominates. Artifacts are also more common in In this same vein, we developed and tested a set of pro-
regions where multiple features overlap and can interact cedures for use in situations where the rotation period is
with the convolution filter in an unpredictable manner. known and is well covered by observations. We found that
6.2.3. Azimuthal renormalization and radial gradient taking a sequence of images, uniformly spaced throughout
filter. We now turn to enhancement techniques that are the rotation sequence, and averaging them together works
somewhat more involved to create or apply. The first of well to create a template for removing the bulk coma. The
these is azimuthal renormalization (A’Hearn et al., 1986a), averaging process smooths out temporal changes in the fea-
in which the coma is divided into a series of annuli and the tures, so that when the template is removed from each im-
pixel intensities in each annulus are rescaled to a common age, any moving features are highlighted. Because the tem-
minimum and maximum. Again, this is a simple procedure plate is created by combining images throughout a rota-
to perform using the polar format image. The result is ef- tional phase, we refer to this technique as the phase-stacked
fective for removing the central peak, although it also re- mask. In essence, this procedure is a straightforward mask
moves much of the relative brightness information. Its removal, which means that it is relatively benign, it is very
strength lies in its usefulness for showing radial features that good for enhancing faint structure, it can be used to enhance
rapidly fade with distance. Another, more-intricate tech- any image obtained throughout the rotation (e.g., it is not
nique that is presently not widely available is the radial gra- restricted to those that were used to create the mask), and
dient spatial filter (S. M. Larson, personal communication, any features that are revealed are not likely to have their
2002). This routine uses the basic principles of a convolu- positions shifted. Like many other techniques that use a
tion filter, but varies the size of the kernel as a function of coma shape derived from the comet itself, most of the in-
the distance from the nucleus. The result has the same ben- tensity information is lost, including any azimuthal asym-
efits as the rotational shift removal, in that the enhancements metries. As is discussed later, these asymmetries can provide
are optimized to reveal small features near the nucleus and important constraints on the coma models, so it may be
increasingly larger features at greater distances, but unlike desirable to retain the information. To avoid removing the
the rotational shift, it enhances azimuthal as well as radial asymmetries, the procedure can be taken a step further by
features (Fig. 4i). computing the average azimuthal profile from the phase-
6.2.4. Image sequences and temporal image enhance- stacked mask, to produce a phase-stacked/azimuthal-aver-
ments. Relating to the following enhancement techniques aged profile. Removal of this profile from the individual
is another tool that can be useful for understanding and images then enhances the features, while still preserving the
interpreting complicated features. Given a sequence of im- original azimuthal asymmetries.
ages uniformly spaced in time, a “movie” of the comet mo- These two phase-averaging techniques, used together,
tions can be created. With these sequences, the evolution have proven to be very useful in analyses of images of
of the coma and the motions of the features can be followed Comets Hale-Bopp and Hyakutake (Farnham et al., 1998b;
more clearly. Furthermore, if the features have a periodic Schleicher and Woodney, 2003). Unfortunately, they have
nature (e.g., consecutive arcs representing successive rota- drawbacks that limit the number of objects on which they
tions of the nucleus) and the viewing geometry varies slowly can be used: They are time-consuming to apply, the comet’s
with respect to the rotation period, then it may be possible rotation period must be known, and multiple images with
to phase images from different rotational cycles to simulate good phase coverage are needed to smooth out the features.
a full rotation. If so, then movies can be created, even if the If good temporal coverage is not available, combining the
comet was only observed for short periods on any given images from different phases may leave residual features
night during an observing run. in the profile that can again introduce artifacts when the
Unfortunately, most standard enhancement techniques template is used to enhance an image (as is the case for any
are not optimally suited for use on a sequence of images. of the temporal-averaged techniques). Fortunately, most of
For example, an unsharp mask can only be applied to the these residual features can be removed from the averaged
individual frames in any sequence, but due to temporal profile by applying a smoothing spline function in the ra-
changes in the features, the shape removed by the mask will dial direction, which minimizes the effect of poor phase
be different for each image. This makes it difficult to di- coverage. Although this may slightly change the shape of
462 Comets II

the coma template, it can still be effectively used to enhance which requires an accurate calibration of the images. Ulti-
the original images to reveal temporal changes in the coma. mately, it may be possible to use the calibrated images to
constrain the models sufficiently well to determine gas and/
6.3. Quantitative Measurements or dust release rates as a function of location on the nucleus.

Once features have been identified in the coma, with or 6.4. Rotation Periods
without the use of enhancements, their qualitative appear-
ance must be converted into quantitative measurements that Many comets exhibit features that are observed to regu-
can be used as constraints for coma models. Depending on larly repeat with time. These repetitious structures are a sig-
the types of features present and the requirements of the nature of the rotation of the nucleus and under the proper
model, different measurements are possible. For predomi- conditions, they can be used to measure the rotation period.
nantly radial features, the position angle (PA) of the feature Repeating features can include concentric arcs, a ray that
is the most useful measurement, although if some curvature oscillates back and forth, or any structure or outburst that
is present, then it may also be necessary to specify at what appears at regular intervals. These manifestations reflect
distance the PA was obtained. Positions of arcs and spirals either the changing production rates as active regions rotate
are usually quantified by measuring the cometocentric dis- into and out of sunlight or the changing direction of the emis-
tance at a number of different PAs. When making these sion as the nucleus spins, and thus can be used to derive the
measurements, the center or brightest point of the jet is the rotation period. Furthermore, regular repetitions in the mor-
preferred reference location, because models are more likely phology suggest that the nucleus is in or near a state of prin-
to reliably reproduce the bright central peak of the jet than cipal axis rotation. (Although long-term precession or com-
its edge. Characterization can also include measurements plex rotation may be present in some comets, they cannot
of other properties, such as the width of the feature, which be addressed if they are not evident in the available obser-
is often quoted as the full-width at half-maximum (FWHM) vations.) There are exceptions to this rule, including Comet
above the background. Although this type of measurement Halley, which exhibits periodic variations, even though it is
can be difficult (and may require additional information if in a state of complex rotation (Belton et al., 1991).
the feature is not symmetric about the center), it provides The most straightforward means of measuring the rota-
valuable information about the dispersion of the material tion period is to use a sequence of images that span a full
in the jets. For the gas species it may also provide informa- rotation of the nucleus, as was done for Comets Halley
tion about the relative velocities of the parent and daughter (Samarasinha et al., 1986; Hoban et al., 1988), Swift-Tuttle
species. (Boehnhardt and Birkle, 1994; Fomenkova et al., 1995),
As with the enhancement procedures, it is useful to uti- Hyakutake (Schleicher et al., 1998b), and Hale-Bopp (Sar-
lize the polar format image, as well as the rectangular im- mecanic et al., 1997; Jorda et al., 1999). The period is sim-
age, for making certain spatial measurements. The polar ply the time that it takes for the feature to reappear in the
format not only provides a different perspective for look- same place it was at the start of the sequence. Unfortunately,
ing at the data (cf. Schwarz et al., 1997; Samarasinha and this requires an observing window that permits good tem-
Mueller, 2002), but PAs and distances are directly measur- poral coverage throughout a full rotation period, which can
able from the rows and columns. Also, whenever possible, be rare for comets. In the examples noted above, Hale-Bopp
measurements should be obtained from multiple images. If was bright enough that distinct features could be seen in
the features are stationary, then the additional measurements infrared measurements obtained during the day; Hyakutake
will improve the uncertainties; if they move, then the addi- passed near Polaris and, for northern hemisphere observ-
tional measurements give positions as a function of time, and ers, was observable all night during its closest approach to
result in a quantitative measure of the motion and thereby Earth; and Halley and Swift-Tuttle have rotation periods that
constrain the projected velocity of the feature. span several days, so coverage over many nights provided
Another form of quantitative measurement that can be sufficient sampling to follow the rotation.
used to constrain models is the brightness of the coma and If the comet is only observable for short periods, then
morphological features. The brightnesses of different jets other methods must be used to derive the rotation period
can be used to find the relative strengths of their sources, from the features. One method is to phase images from night
while the amount of material coming from the active areas to night, as discussed above, to determine how long it takes
can be compared to that in the isotropic background. Using for a feature to repeat. This requires an understanding of
the brightness in this manner requires that, if any image how much a feature moves from one night to the next to
enhancement techniques at all are used, then they must be avoid converging on a false alias of the period, but motions
very benign so that relevant brightness information is not can usually be constrained with observations spanning an
lost. Furthermore, to get a proper comparison of the bright- hour or two. In the case of Comet Hale-Bopp, the motion
ness levels, contributions from undesired species must be of an arc during 2 h of observations was sufficient to show
removed from the images. Thus, not only must continuum that the arc would repeat about twice per day (i.e., the nu-
be removed from the gas images, but also contamination cleus had a rotation period of approximately 12 h, rather
from other gas species (e.g., the wing of C3 in the CN filter), than 24 or 8 if the arc repeated once or three times respec-
 Schleicher and Farnham: Photometry and Imaging Using Narrowband Filters 463

tively). With this constraint, images from several nights but because it is at the pole, it contains no information about
could be utilized to determine a more precise rotation period the rotation period or the direction of spin.
of 11.3 h (Lecacheux et al., 1997; Mannucci and Tozzi, 1997; The fortuitous circumstances regarding Comet Borrelly
Licandro et al., 1998; Farnham et al., 1998a; Warell et al., are unusual, however, and for most comets, more intricate
1999). If temporal coverage is minimal, an alternative, al- models of the coma morphology must be used to extract
though less reliable, method can be used to constrain the the nucleus properties. Many different models, both sim-
rotation period. Using the curvature of a jet and an estimate plistic and intricate, have been introduced to explain the
of the outflow velocity, the spin rate of the nucleus may be morphology observed in cometary comae. Early models in-
found (e.g., Larson and Sekanina, 1984; Watanabe, 1987; voked such concepts as using thermal lags to explain the
Boehnhardt et al., 1992). Unfortunately, a lack of phase cov- projected direction of a sunward fan on a homogeneous ro-
erage means that assumptions must be made about the pro- tating nucleus (Sekanina, 1979) and using the dimensions
jection effects and outflow velocities (or they must be con- of consecutive arcs along with assumed expansion velocities
strained in some independent manner). If the assumptions to compute rotation periods (Whipple, 1982). These early
are not valid, then the results may have significant errors. models produced mixed results at best, with a number of the
Finally, in quoting a rotation period, it should be speci- test cases being proven wrong by subsequent observations
fied as to which type has been determined: sidereal, solar, (Borrelly being one notable case). The next generation of
or synodic. The sidereal rotation period, which is the most models used continuous tracks of jet particles to follow the
desired but not always the one measured, is the time needed features produced by emitted material (Sekanina, 1981;
for the nucleus to rotate once with respect to the stars. The Sekanina and Larson, 1984, 1986; Massonne, 1985) and
solar rotation period is the time it takes for one full rotation showed promising results. More recently, a variety of differ-
with respect to the Sun. Since most morphological features ent types of models have been presented, for reproducing
are directly related to the amount of sunlight illuminating both dust morphology (cf. Sekanina, 1987, 1991; Sekanina
an active region, this is probably the most common type of et al., 1992; Combi, 1994; Sekanina and Boehnhardt, 1997;
period measured from coma morphology. The solar rota- Fulle et al., 1997; Schleicher et al., 1998c; Samarasinha,
tion period is also commonly referred to as the synodic rota- 2000) and gas morphology (cf. Lederer et al., 1997; Festou
tion period, in a manner analogous to that used with planets and Barale, 2000). Most of these recent techniques are
in the solar system. Unfortunately, the term synodic period based on numerical methods or Monte Carlo simulations.
is also often used, particularly in asteroid studies, for the The increase in computing power over the last decade
time needed for one rotation of a body with respect to Earth. has not only made the Monte Carlo-style techniques very
Therefore, it is important to define which type of synodic popular, but they are also very powerful and provide a natu-
period is meant for any particular usage. The differences ral approach for simulating particles emitted from a spin-
between these three periods are usually small, but in some ning nucleus. In addition to the characteristics already dis-
circumstances, they may not be negligible and understand- cussed, a number of fundamental nucleus properties can be
ing exactly what is being measured may be important. For determined from the morphology, including a comprehen-
example, Comet Hyakutake’s solar rotation period was meas- sive depiction of the rotation state and the locations and
ured sufficiently accurately as to be distinguishable from the sizes of the active areas. Secondary parameters can also be
sidereal period determined from Monte Carlo modeling of derived using the results from the primary analysis: With
the dust jets during the comet’s close approach to Earth. an understanding of the spin properties and source locations,
The difference of 0.0004 d between the two periods was projection effects can be computed, allowing true distances
completely consistent with the expected difference, based and velocities to be determined; similarly, thermal lags can
on the model pole orientation and the position of the comet be found when sources remain active, even after they are
in its orbit (Schleicher and Woodney, 2003). no longer illuminated by sunlight; knowledge of the rota-
tion state and production rates (which can be estimated from
6.5. Modeling Morphological Features the solar illumination on the active regions), provides neces-
sary constraints for analyses involving torques and nongravi-
We now turn to methods that are used for inferring addi- tational forces on the nucleus (Samarasinha et al., 2004;
tional properties of the nucleus from the coma morphology. Yeomans et al., 2004); finally, comparisons of models inde-
In certain circumstances, properties can be determined di- pendently derived from the dust and various gas species may
rectly from measurements, without the need for models. An reveal potential composition inhomogeneities, if different
excellent example of this is Comet Borrelly, whose strongest species originate from different source regions. Under typi-
source emits material in a straight jet that is aligned with cal circumstances, only a subset of these properties will be
the nucleus’ spin axis. Given this configuration, the appar- determined for any given comet, with the type and quality
ent position of the jet on different dates can be used to de- of the features governing which results can be derived.
termine the orientation of the rotation pole (Farnham and When using models to analyze a comet’s coma morphol-
Cochran, 2002) [a similar technique was used in an analysis ogy, different researchers are likely to use slightly different
of Hale-Bopp by Licandro et al. (1999)]. It is ironic that the approaches, although the fundamental basis will be similar.
jet can be used to determine so much about the spin axis, The following discussion describes the specific techniques
464 Comets II

and procedures that we have used in our work with various tion of the spin axis and location of the main source have
comets, and although the details may differ somewhat from been constrained, and parameter space has been narrowed,
other researcher’s methods, any model should address es- we can introduce additional parameters (new active regions,
sentially the same issues. In our work, we use a standard radiation pressure, etc.) to model other features and help
Monte Carlo model that is discussed more fully by Schlei- fine tune all the model parameters. This is again done in
cher and Woodney (2003) and Farnham and Schleicher (in stages to allow the effects of each addition to be determined.
preparation, 2004). The routine is presently designed to Given the fact that there will always be at least four free
model the motions of the dust grains and can follow up to parameters (with the potential of many more), any infor-
106 representative particles that are emitted from multiple mation that can be used to help narrow down the param-
active areas at different locations and of different sizes (al- eter space is welcome. Frequently, it is possible to use a
lowing us to model the extended active areas discussed simple inspection of the morphology to limit parameters,
later). The model can also handle radiation pressure and even before detailed modeling begins. For example, the
precession of the nucleus, if necessary. Initial calculations shape of a spiral arc can often be used to set constraints on
are done in the comet’s orbital reference frame, from which the parameters. If the spirals extend completely around the
it is straightforward to determine the orientation of the nucleus, then Earth must lie within the cone swept out by
nucleus, the Sun’s position, and other geometric relation- the active region during a rotation (i.e., the sub-Earth point
ships. For each particle, the routine computes the direction lies at a higher latitude than the active region). In addition,
in which it was emitted and the distance it has traveled the shape of the spiral may define the direction of rotation,
between its emission time and the observation time, which which will naturally eliminate at least half the potential pole
defines its location in cometary coordinates when the comet orientations. Finally, if the spiral appears elongated, then
was observed. After the positions have been computed for the ratio of the short- and long-axis dimensions can pro-
all the particles, the results are then transformed to the plane vide a constraint on the aspect angle of the pole. Similarly,
of the sky coordinates as seen from Earth, and the result radial features can also be used to constrain the parameters.
can be compared to the observed morphology. The nucleus A jet that oscillates back and forth in position angle indi-
properties that can be found from our model include the cates that Earth is outside the cone, and the size of the os-
rotation period; orientation of the spin axis; direction of ro- cillation can be used to set a limit on the latitude of the
tation; locations, sizes, and relative strengths of multiple source. Furthermore, if the feature is continuously visible,
active areas; emission velocities; and the average influence then the center of the oscillation likely represents the pro-
of radiation pressure on the dust grains. jection of the rotation axis on the sky. Even though some
In our application of the model, we start by selecting the parameters can be constrained in this manner, it is a good
most obvious and clearly defined feature in an image and idea to utilize the modeling process to check that the inter-
use it as a guide throughout the early stages of the model- pretation of the features is correct and to make sure that
ing. By initially focusing on only the main feature, we can the excluded areas of parameter space behave as expected.
limit the number of free parameters, which reduces the Another procedure that can be employed in the analysis is
volume of phase space that must be explored. (Typically the incorporation of multiple images throughout the comet’s
only four parameters — right ascension and declination of apparition (e.g., Braustein et al., 1997; Vasundhara and
the pole, the rotation period, and the latitude of the primary Chakraborty, 1999). Tracking the long-term evolution of the
source — are needed to explore the basic morphology; other coma makes it possible to generate a comprehensive model
parameters, such as the longitude of the source and the ejec- for reproducing the general appearance of the coma at any
tion velocity, only control the relative phasing and the scale given time. Furthermore, dramatic changes in the morphol-
of the coma.) Next, we assign a pole orientation and a lo- ogy can act as benchmarks for deriving the locations of the
cation for the main active region and generate a model for active regions. For example, the gradual appearance or dis-
those parameters. Comparing the synthetic image to the appearance of a bright jet can indicate that the subsolar lati-
observed one (specifically, to the positions measured from tude is changing and a source is becoming illuminated or
the images) allows us to adjust the model parameters and losing its illumination. Observations spanning a significant
rerun the model to improve the fit. This process is iterated arc of the orbit may also reveal other factors, such as the
until the model parameters converge to produce a good times at which Earth crosses into or out of the cone swept
match to the observations. As in any multivariable analysis, out by an active area. These types of information can be used
there is always a concern that the parameters are unique and to severely constrain the locations of the source regions,
that other combinations of parameters cannot be combined which in turn simplifies the modeling process.
to produce equally suitable results. Therefore, to avoid miss- We now address a new complication regarding coma
ing any potential solutions, we perform a full grid search models that was introduced during our studies of Comet
of the four main parameters at low resolution. This allows Hale-Bopp and has implications for coma models in gen-
us to map the areas of parameter space where viable models eral. There is an extensive amount of data available for this
exist, and we can then focus on these areas at higher resolu- comet around the time of perihelion and the coma could
tion to converge on the optimum solution. Once the orienta- be studied in detail from March through early May. Exami-
 Schleicher and Farnham: Photometry and Imaging Using Narrowband Filters 465

nation of the arcs in any particular Hale-Bopp image from

this time frame shows primarily circular features (dust arcs
or CN spirals) with little foreshortening in any direction.
The rounded shape suggests that the comet’s spin axis was
pointed in the general direction of Earth, which posed a prob-
lem, because the Earth-comet viewing geometry changed
by about 90° between March and May. In other words, for
the pole to be pointed toward Earth throughout this time
frame, the nucleus would have to be in a state of fast pre-
cession with the pole tracking Earth — a difficult scenario
to accept. The solution to this puzzle was suggested by
Samarasinha (2000), and involves the size of the active re-
gion creating the feature. Normally, jets in a model are
assumed to be narrow, if indeed any width at all is specified.
This simplifies the models, produces well-defined features,
and has been widely accepted because the result usually
reflects the appearance of the observed image. Samarasinha
suggested that the arcs in Comet Hale-Bopp are not pro-
duced by jets only a few degrees wide, but instead are the
result of large active regions, spanning tens of degrees in
latitude and/or longitude. The effect of these broad jets is Fig. 5. Sequence of simulated images showing the effects of
to form a partial shell structure that can mimic the plane- extended active regions on the appearance of the coma. Clock-
tary nebula effect. In a planetary nebula, the spherical shell wise from the upper left, the source regions span angles of 1°,
appears to be circular because the greatest column density 5°, 15°, and 30°, with all other parameters left unchanged. No-
is at the outer edge. Similarly, in Hale-Bopp, the partial tice that for the larger source regions, the arcs are more circular,
giving the appearance that Earth lies very close to the spin axis.
shells are seen as arcs that always appear circular, even
From Samarasinha (2000).
when the aspect angle changes dramatically (Fig. 5). An-
other effect of the extended sources is that they can create
intricate overlapping structures, which naturally reproduce
the appearance of many of the complicated features seen model should reproduce the morphology of the original im-
in Hale-Bopp. age, not the enhanced one. When possible, the model should
The existence of wide jets makes the coma more diffi- be enhanced with the same methods used on the original
cult to model, not only because it introduces more free image to see how well the two really match. This is not
parameters, but also because it makes interpretation of the always practical, especially during the global search of pa-
features more difficult. With an extended source, the exist- rameters, but as the solution converges, the quality of the
ence of a complete spiral around the nucleus is no longer a fit is more critical. Related to this is the principle of deter-
guarantee that Earth lies within the cone formed by the spin- mining how good a fit has actually been obtained. Using a
ning jet. If Earth lies within only a part of the cone pro- mathematical measure of the goodness-of-fit (e.g., a χ2 fit)
duced by the jet, the planetary nebula effect will dominate is usually not practical because quantifying the difference
and full spirals will be observed. Furthermore, as with Hale- between the model and the image can be difficult without
Bopp, the rounded arc appearance no longer provides a resorting to time-consuming measurements. Fortunately,
severe constraint on the aspect angle of the pole. It is clear pattern matching by eye is very effective for this type of
from these examples that the potential for having extended work, especially when the results can be displayed in mul-
active regions introduces ambiguities into the constraints tiple formats. This argues that both the rectangular and polar
that can be set with simple inspection of the coma structure. versions of the model and the image should be compared.
Thus, in any comprehensive analysis, it is wise to investigate Finally, the role that is played by the background material in
the possibility that broad jets are contributing to the coma the coma should be considered. The bulk shape of the coma
morphology, because the differences can have a profound (the component that is usually removed in the enhancement
influence on the model results, as it did for Comet Hale- process) must come from somewhere, with two possible
Bopp. sources being isotropic emission from the nucleus’ surface
Our final discussion addresses various concerns and con- and diffusion of material outward from the isolated sources.
siderations to be aware of when applying these models. Ideally, this component should be included in the model for
First, the uniqueness of the solution is foremost when pre- completeness, but it is not always clear exactly how to in-
senting a result, and a global search of parameter space, clude it or account for it.
although tedious and time consuming, may be necessary to As described here, modeling the structures in cometary
rule out other families of solutions. Next, a comprehensive comae can reveal fundamental properties of the nucleus.
466 Comets II

The results that are obtained are inherently important in and undergo severe testing, with spacecraft encountering sev-
of themselves, but they become even more valuable when eral comets in the near future; these encounters will either
they are used to set constraints on a variety of other comet validate the modeling procedures that are currently in use,
studies. We note a few of these, which are discussed in more or will prompt their reevaluation.
detail in other chapters of this book. First, understanding Finally, narrowband imaging, multiwavelength polariza-
the main jet structures in the coma as a function of time tion studies show promise for better understanding the phys-
helps in interpreting the more intricate effects produced by ical properties of dust grains as they move outward from the
topography and the gas/dust interactions near the nucleus nucleus. They may answer questions about fragmentation
(Crifo et al., 2004). As discussed earlier, the rotation prop- of grains and whether the ambient background of the coma
erties can be used as examples for studies of the rotational is caused by dispersed grains from jets or by a more homo-
dynamics of nuclei (Samarasinha et al., 2004) and, when geneous nucleus component.
the locations of the active regions are included, for research
related to nongravitational forces (Yeomans et al., 2004). Acknowledgments. The authors particularly thank M. A’Hearn,
Information about the sizes and locations of the active ar- A. Cochran, M. Combi, R. Millis, S. Larson, and N. Samarasinha
eas and when they turn on and off provide constraints for for innumerable fruitful conversations regarding aspects of the
studies of normal cometary activity and outbursts (Prialnik contents of this chapter, as well as the referees for many useful
comments and suggestions. We also thank S. Larson for providing
et al., 2004; Boehnhardt, 2004). Finally, the source activity
the radial gradient filter enhancement of the image of Comet Hya-
information and true emission velocities obtained from in-
kutake. This work has been made possible due to grants from the
ner coma models can be used to improve models of the gas National Aeronautics and Space Administration and the National
dynamics (Combi et al., 2004) and models of the comet’s Science Foundation.
dust tail (Fulle, 2004).
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470 Comets II
 Crifo et al.: Nucleus-Coma Structural Relationships 471

Nucleus-Coma Structural Relationships:

Lessons from Physical Models
J. F. Crifo
Centre National de la Recherche Scientifique

M. Fulle
Osservatorio Astronomico

N. I. Kömle
Space Research Institute of the Austrian Academy of Sciences

K. Szego
KFKI Research Institute for Particle and Nuclear Physics
of the Hungarian Academy of Sciences

1. INTRODUCTION Groundbased coma observations typically provide im-

ages and spectra of the gas and dust coma at a spatial resolu-
One of the most frequently advocated incentives for the tion not better than several hundreds of kilometers, and at
study of comets is that the cometary nuclei carry clues about a time resolution sometimes of hours but more typically of
the origin of the solar system. However, cometary obser- days. The overall appearance of the coma is usually simple,
vations almost never deal with the nucleus itself, but with but image enhancement techniques reveal well-defined spa-
its surrounding coma. An essential problem is therefore the tial structures both in the dust and in the gas coma. These
derivation of nuclear properties from coma observations. In structures often repeat themselves in time, quasiperiodically,
this chapter, we do not review the observations, nor the and quasiperiodicity is also often observed in the global
derived nuclear properties. Instead, we focus on the meth- properties of the coma (superimposed upon the secular evo-
ods by which the latter are derived from the former: What lution due to the orbital motion). It has become standard
are they? What are their formal justifications? Are the con- practice to summarize the coma observations by phenom-
clusions derived by these methods reliable? If not, which enological models. Here, as we shall demonstrate at length
alternative methods should be used? in the following sections of this chapter, (1) one assumes
As discussed in detail in the literature (e.g., Weissman, that the coma formed by the real, complicated nuclei is well
1999): (1) comets may have been formed from planetesi- understood after having discussed only the coma formed
mals over a large range of heliocentric distances, includ- by the simplest conceivable nuclei (e.g., spherical in shape,
ing the asteroid belt region, and therefore may differ from emitting spherical dust grains, rotating uniformly, etc.);
one another in composition and structure, in particular in (2) even this simplest possible coma is not self-consistently
volatile to refractory relative abundance; and (2) dynami- modeled using the relevant well-established applied phys-
cal exchanges of material during the formation of the plan- ics methods, but simply “understood” from subjective pos-
etesimals probably mixed materials formed at different dis- tulates (e.g., there exists rotationally-invariant gas and dust
tances from the Sun, so that any cometary nucleus may be ejection patterns, “gas and dust heliocentric dependence
a mixture of materials formed at different temperatures, and velocity laws”, etc.) (see Crifo and Rodionov, 1999). This
therefore may be a complicated object. The shape of the double arbitrariness in analyzing the data is perhaps toler-
nucleus should be expected to be as complicated as aster- able as long as it is only used as a convenient means of
oidal shapes, hence its rotation should not be assumed to summarizing observations, but, otherwise, it raises the ques-
be simple (such as a symmetrical top rotator). Furthermore, tion of whether the “derived” properties capture anything
while the nucleus interior is generally considered as undif- of the real properties of the real nuclei. This question can
ferentiated, such cannot be the case of the external layers — only be answered by taking into consideration realistically
those from which the coma is formed: They are submitted complicated nuclei, and thoroughly computing the structure
to thermal cycling (e.g., Espinasse et al., 1991), cosmic- of the coma they form — i.e., by physical modeling.
ray irradiation (e.g., Strazzulla, 1997), and meteoroid im- The 1986 flyby missions to Comet P/Halley have opened
pacts (Fernández, 1990). This intrinsic complexity suggests a new era. With the advent of observations that resolve the
that the interpretation of coma observations in terms of nu- nucleus and sample the coma on a kilometer scale, a direct
clei properties cannot be trivial. physical description becomes conceivable, i.e., one in which

471
472 Comets II

the complexity of the object is taken into consideration in Section 7 reviews the cases where model and observations
detail. But, in the same manner as radically new observa- are compared. Section 8 then briefly addresses the outer
tional techniques are requested for the flyby observations, coma, again with an emphasis on the validity (or otherwise)
the objectives themselves of the observations and of their of the phenomenological assumptions. Section 9 attempts
interpretation change dramatically. For instance, the tech- to draw a general lesson from the previous sections.
nical success of future orbiting and landing mission itself
requires that the immediate environment of the nucleus be 2. OBSERVED COMA STRUCTURES AND
forecasted with high reliability and with a quick reaction THEIR HEURISTIC INTERPRETATIONS
time from the data acquired from the probes, regardless of
whether or not this gives “clues on the origin of comets.” By “structures,” we mean spatial details in the coma, or
This is a formidable challenge compared to that of interpret- temporal patterns that can be recognized during the comet
ing groundbased cometary observations. motion: Both are related, owing to the nucleus rotation. The
Even when deep-space mission data are at hand, it is not status of interpretation of these structures just before the first
proven that such data allow a thorough understanding of elaborate physical model results appeared was reviewed in
the nucleus: To investigate it involves a so-called “inverse Kömle (1990). Here, we reexamine the former in the light
problem” with an enormous number of unknowns. The only of the latter. As many chapters of this book are dedicated to
known approach to adressing such a problem is statistical coma structures, we will present here only a few representa-
simulation; the statistical properties of a large class of re- tive examples. Many are relative to Comet P/Halley because
alistic (i.e., as complicated as possible) nuclei must be de- it has been the only comet whose full nucleus shape was
rived and compared to the observations. derived from flyby images. (The January 2004 flyby obser-
Both short-term forecasting of a nucleus activity and vations of Comet P/Wild 2 will probably lead to the deri-
statistical estimates of the significance of nucleus and coma vation of the full shape of a second nucleus.) A few other,
observations require advanced physical modeling. We re- most instructive examples are relative to Comets Swift-
view here the few existing efforts that have been done in Tuttle, Hyakutake, and Hale-Bopp. When physical model-
this direction. As deep-space missions to comets are scarce, ing is advocated in support of the interpretation of the struc-
the institutional support of these efforts is quite limited. In tures, we review it carefully. Often, it is possible to point out
such a context, unfortunate habits persist across decades: uncertainties, misinterpretations, and sometimes severe in-
One such habit is to take the phenomenological models for consistencies in the heuristic interpretations or their support-
a true representation of the real objects, as if this did not ing modeling, even before advocating physical model re-
raise any question; another one is to apply the “supposed sults: A critical internal consistency check of the approach is
behavior” of the phenomenological nuclei even to those few sufficient. Advanced physical models are unavoidable, how-
observed nuclei for which the physical approach is possible, ever, to overcome the difficulties, as will be demonstrated.
thereby cancelling all benefits from these unique observa- It is also unavoidable to comment on the terminology
tions. For instance, exactly the same “opinions” are pres- often found in the literature: Words such as “jets,” “shells,”
ently formulated with respect to the Deep Space 1-supplied and “activity” are, as we shall demonstrate, often used ei-
images of Comet P/Borrelly that were formulated 15 years ther without their standard meaning as defined in physics,
ago when the flyby P/Halley images were collected. Un- or sometimes even in conflict with it. In our opinion, this
abashedly, this is often justified by saying that P/Halley is extremely prejudicial.
images “confirmed the anterior analysis.” If this is so, what
are the goals of current and future work on comets? 2.1. Gas Light Curves
The epistemologically correct attitude, which is exactly
the opposite of the practices described above, is to use If one observes a comet with the same spectrophotom-
physical modeling not only for the rare comets with re- eter at intervals of days or fractions of days, the molecular
solved nuclei, but even in the case where observations are emissions are seen to exhibit secular variations related to
crude: By performing numerical simulations of the “opera- changes in heliocentric distance rh, plus, in general, short-
tion” of (1) objects that plausibly represent real comets and term variations. A good example can be found in Millis and
(2) the simple fictitious objects usually considered, one can Schleicher (1986). Some of these fluctuations may be ran-
hope to separate the domain of robustly derived conclusions dom (“bursts”), but more attention is usually given to those
from the domain of unwarranted speculations. that suggest approximate periodicities, because of their un-
The present chapter is organized as follows. In section 2, questionable relation to the nucleus rotation.
we illustrate by a few representative examples the underlying With the exception of the peculiar case of Comet Hale-
assumptions on which heuristic inferences have been made Bopp (see below), such short-term variations are observed
in the cometary literature. Sections 3–5 describe the exist- at small heliocentric distances, where water production is
ing physical models, placing emphasis on their physical dominant. Water molecules emissions from the coma are
significance, not on the mathematical methods. In section 6 rarely observable, so that their production rate Q(t) is usu-
we review the physical model results relative to the near- ally derived from the number N of daughter OH molecules
nucleus coma; special attention is given to whether they present inside the observed coma volume (usually a cylin-
support the assumptions listed in section 2, or otherwise. der). To relate Q(t) to N(t), observers use a trivial analytical
 Crifo et al.: Nucleus-Coma Structural Relationships 473

formula, the “Haser model” (the expression “Haser for- during a much longer period of time than the previous gas
mula” would be more suitable). There are many recognized jets, and exhibited definite periodicity:
weaknesses in this formula. Let us only mention a funda- 1. Long-lasting spiral-shaped jets (A’Hearn et al., 1986),
mental one: The coma must be spherically symmetric and extending out to >6 × 104 km, were evidenced by azimuthal
quasisteady. But the very interpretation of quasiperiodicities enhancement technique; Hoban et al. (1988) concluded
in gas lightcurves, in terms of nucleus rotation, implies that from a dataset collected between April 9 and May 2, 1986,
this is not the case. Due allowance for asphericity of the within 5 × 104 km from the nucleus, that the evolution of
coma is therefore needed. Furthermore, since inside a very the morphology of the jets suggests the existence of a pe-
narrow field of view, molecules are present to very large riod of recurrence of 7.37 d. The current interpretation of
distances (on the order of 105 km), the observational vol- these structures follows the original discussion of A’Hearn
ume filling time is on the order of a day, comparable to et al. (1986): The observed features are not due to local
typical rotation periods; there is “hysteresis,” i.e., a time- fluctuations in the density of a rotationally modulated fluid
dependent model of the coma content must be used. This, CN coma, but are due to parent species moving according
in turn, requires knowing the nucleus rotational state. to quite narrow spiral patterns (with thickness <3000 km
Some authors are careful to point out that their use of at 30,000 km from the nucleus) and with a quite accurate
the Haser formula is only done for convenience, the accu- radial velocity. “In the absence of a confining mechanism
racy of the algorithm being unknown. Our impression is, for the jets the inescapable conclusion is that the jets are
however, that many readers take the Haser-derived Q(t) as composed of dust grains,” small enough to be invisible on
the real variation of the nucleus production rate. For in- white light images.
stance, Julian et al. (2000) and Szego et al. (2001) check 2. Ring-like, expanding “shells” were discovered by
their P/Halley rotation models against such a Q(t). One can visual inspection of the CN images (Schlosser et al., 1986;
therefore question the satisfaction the two groups express Schulz and Schlosser, 1989). These shells (actually asym-
regarding their fits. metrical rings or haloes around the position of the nucleus)
always dominated the outer coma, at a distance greater than
2.2. Comet P/Halley Gas “Jets” and “Shells” 105 km from the nucleus, during the two-month observing
period. Here again, the words “shell” or “ring” designate a
Both groundbased and flyby spacecraft data revealed that localized enhancement of the brightness of a much wider
the gas coma of P/Halley is structured. Clairemidi et al. distribution; furthermore, since it is observed in the emission
(1990) identified OH and NH brightness maxima, which of the nondominant CN molecule, it is uncertain whether
they called “jets,” in the images obtained by the three-chan- it traces a local density enhancement of the whole coma,
nel UV spectrophotometer onboard Vega 2. Two “jets” were or a local variation in CN content. In any case, it would be
seen, one pointing toward the Sun, and another, stronger incorrect to model it as an isolated distribution of gas: There
one nearly perpendicular to the sunward direction in the can be only one global model of the coma, with the require-
image plane. Since we refer here to this widely used term ment that it reproduces the observed localized enhancement.
“jet” for the first time, let us make a brief comment. Ap-
parently, it is used to describe a structured (linear or curved) 2.3. Comet Hyakutake Arcs
brightness enhancement. However, as used in physical gas
dynamics, a neutral gas jet is a region of collimated flow Comet Hyakutake passed unusually close to the Earth on
created by a localized source. It should not necessarily be March 25, 1986. This led to the unique detection, during 10
a region of high brightness; conversely, regions of gas at successive nights, of spectacular arcs of OH, CN, and C2,
rest (shocked gas or stagnation gas) are regions of high centered on the antisunward cometocentric axis (at least in
brightness, and not at all akin to jets. Furthermore, a gas projection), having their apex on it at a variable distance (be-
jet is an isolated system, not the subsystem of anything; it tween 400 and 2000 km) and their convexity toward the Sun
cannot coexist at the same location with another, superim- (reproduced in section 7.1). A detailed account of the obser-
posed flow structure. But in the cometary case, the advo- vations is given in Harris et al. (1997) and in Rodionov et al.
cated “jets” result from image enhancement, and represent (1998). Both groups have interpreted the observations as the
only a tiny fraction of the flow; they are flow details, not at signature of an H2O arc, caused by some secondary H2O
all jets in the gas dynamic sense. This is not only a matter of source. We compare and discuss the approaches in section 7.1.
terminology; it generates considerable confusion, prompt-
ing questions such as “What is the collimation mechanism?” 2.4. Comet Hale-Bopp Spirals
Where there is no collimation, there can be no collimated
gas. In the following we will continue to use the term “jets” Spectacular spirals appear in the large-scale images of
in this manner, but the reader should be careful to remem- Comet Hale-Bopp in March and April 1997 (i.e., shortly
ber that it designates only a localized detail in a large-scale before and after its perihelion pass), for the observed mol-
gas or dust distribution. ecules OH, CN, C2, C3, and NH (Lederer et al., 1997).
Structures with a completely different appearance were These structures are conspicuous after image enhancement,
discovered in P/Halley from groundbased observations of but their real contrast must be high enough, as the authors
the CN distribution. These CN features could be observed state that they can be discerned even in the raw images. On
474 Comets II

April 26, for instance, a single spiral is seen in the cleanest with any other related observation (cometary or not). The
OH and CN images with an arm spacing of roughly 6 × assumption that molecules move in straight lines conflicts
104 km. At an outer coma flow velocity of 1–2 km/s, this with all estimates of the mean free path inside the coma,
corresponds to a periodic modulation of the gas production which is found to be smaller than 1 m near to the nucleus.
rate with period 8–16 h. Lederer (2000) has interpreted Therefore, the inner coma should be modeled as a fluid,
these structures as follows. Parent molecules and fine or- not as a set of non-mutually colliding particles. We return
ganic dust grains are assumed to be ejected from the nucleus to this issue later in the chapter.
along straight lines, partly inside a certain number Nj of
cones rotating rigidly with the nucleus, partly inside the 2.5. Dust Lightcurves
background space outside of the cones. The assumed nu-
cleus rotation period is 11.3 h. Each cone is ascribed a rela- Usually dust coma isophotes are nearly perfect circles,
tive production strength Sj, as is the background space, and and the radial slope of the coma brightness is well approxi-
a width wj. The gas flux in any given dayside direction is mated by a power law vs. the coma radius with index –1.
assumed proportional to its Sj and to the cosine of its angle This led to the definition of the most frequently used tool
to the solar direction. Once this is done, the daughter radi- to characterize the dust activity of a comet: the Aƒρ prod-
cals are computed from a Monte Carlo procedure from the uct (A’Hearn et al., 1995). In interpreting this product, two
distribution of the primary molecules and organic dust, important assumptions are made: (1) the 1/r brightness
following Combi et al. (1993). A satisfactory fit is obtained variation is due to a trivial 1/r2 isotropic dust outflow; and
assuming Nj = 5 cones; the cones and background are as- (2) the dust grain outflow velocity is that applying to spheri-
sumed to produce the same mixture of H2O, HCN, and cal grains ejected from a uniformly sunlit spherical nu-
“parent-of-C2” molecules, save one cone that, allowing for cleus — the “dust ejection velocity law.” We will comment
one-half of the OH in the spirals, is assumed to produce on these assumptions in section 7.
only H2O and grains releasing only OH. The computed total
OH productions from the “jets” represents less than one- 2.6. Large-Scale Coma Dust Structures
half the total comet OH production.
Interferometric radiowave mapping of CO lines in the In the following, we will focus on dust coma structures
same comet on March 11, 1997, slightly before its perihe- that can hopefully be related to the properties of the nucleus
lion (Henry et al., 2002), revealed time-dependent veloc- and of the near-nucleus gas-dust interaction. Presumably,
ity-space structures in the emission. The measurements yield the closer to the surface the structures are, the more suit-
the line profile of the flux in each =1500 km × 1500 km able they will be for this purpose, as several effects perturb
element of the image. The intrinsic line profile of the CO this relation; e.g., solar radiation reprocesses the structures
line is negligible compared to the observed profile widths, because of the dependence, upon grain mass and grain
so the latter are due to the Doppler shifts induced by the composition, of the radiation pressure to solar gravity ratio
CO velocity distribution within the observed coma volume. βs. Also, it is suggested from time to time that dust frag-
Seen at a Sun-comet-observer angle of 45°, the profile usu- mentation is present in the coma.
ally exhibits two peaks approximately symmetrical with Years of intensive groundbased dust coma image pro-
respect to the line center. The ratio of the number of mole- cessing have shown that many dust comas that at a first
cules on both sides of the line center changes smoothly in glance appeared isotropic actually contain faint dust struc-
about 7 h from =1.7 to =0.5, and back to nearly 1.5, sug- tures. Many of these structures strongly suggest the picture
gesting a periodicity similar to that we have noticed above of a rotating inhomogeneous point source. The impression
for the spirals (unfortunately, the CO observation duration is is even stronger if a motion picture of the observations is
not long enough to confirm it). According to the observers, viewed — so strong that one is tempted to forget that these
“this is indicative of a jet” rotating with the nucleus. The structures result from strong image structure enhancement,
authors declare to have obtained good agreement with the hence, as do the gas structures, characterize only a minor
data using “a 3-D model of the coma consisting of an iso- fraction of the whole coma brightness (however, in contrast
tropic contribution plus a conically spiralling jet of opening with the gas, several different dust populations can evolve
angle 30° and having outgassed 30% of the CO in the coma.” independently in the same region, since there are no dust-
The number and positions of the “active regions” postu- dust collisions). We have not found in the literature any
lated to explain the dust spirals, the OH, CN, and C2 spirals, estimate of even approximately how much nucleus dust pro-
and the CO spirals are totally different, which is considered duction these figures represent. In fact, most authors process
as “evidence for chemical heterogeneity in the nucleus” images by means of nonlinear algorithms, hereby losing any
(Lederer and Campins, 2002). quantitative information on the extracted structures.
After reading sections 5 and 6, the readers will have A good review of the classical interpretation of such
enough material at their disposal to form their opinion re- structures was done by Sekanina (1991). A typical example
garding the preceding interpretations. These interpretations of result is Sekanina’s (1981) model of the nucleus of
are usually considered satisfactory because they “fit the Comet P/Swift-Tuttle. First, a trial-and-error procedure
observations.” This widely used argument is not sufficient. searches for recurring jet patterns in order to establish a
It is also required that the interpretation not be in conflict nucleus rotation period. Then the time-dependent orienta-
 Crifo et al.: Nucleus-Coma Structural Relationships 475

tion of the most prominent jets is used to constrain the nu- likely that the gas will diverge over a broad solid angle, and
cleus spin-axis orientation. As all dust of a given type is force the dust to do the same. On the contrary, if the gas
then assumed to move radially from the origin and with a emission is uniform (or nearly so) over the surface, its di-
common velocity V, an “activity map” is built in cometo- vergence should not be great (near-radial flow), hence trace
centric longitude-latitude coordinates. This allows the iden- variations in the dust content will be preserved outward.
tification of so-called “active” and “inactive” areas. The (b) By the same token, one does not see how a βs(V) rela-
wider the jet, the more extended the active area is declared tion derived for a strictly spherically symmetric gas flow
to be. Then, it is assumed that all grains in a jet were ejected would apply to a highly non-uniform and highly time-vary-
at the same time, the curvature of the jet being due to the ing gas flow. (c) If, as likely, the mean direction of gas emis-
dispersion in V and βs between the grains. Assuming that sion from a discrete area is set by the local topography (e.g.,
there exists a simple analytical expression βs = βs(V) relat- a pit), how is it that only sources active in precisely the pos-
ing V to βs, the so-called “dust ejection velocity law,” the tulated radial direction ever manifest themselves? (d) With a
author derives, at each point of the jet axis, a value of βs gas emission confined to transient localized areas, the torque
and a value of V. The double jets that sometimes appear applied by the reaction forces to the nucleus should be max-
(e.g., in Swift-Tuttle) are interpreted in terms of two differ- imized, which renders the assumption of a simple, non-
ent dust chemical species: This shows the ad hoc nature of excited nucleus spin quite uncertain.
the relation between active spots and jets. Finally, conclusion (3) also raises as many questions as
Minor jets not used to constrain the nucleus spin state it answers: What controls the switching on and off of an
or not interpretable in terms of different dust chemistry are active area, if not the Sun?
considered to be produced by ad hoc-defined spots active In most papers, however, these questions are not ad-
only during a time segment adjusted to generate the ob- dressed. In a few, they are raised, but not answered, or
served jet. Thus, while the very use of the word “jet” sug- answered in a velikovskian way, suggesting, e.g., that the
gests a long-lasting phenomenon, it is frequently assumed transient behavior is induced by the “opening and reclosing
that the jet duration is short, sometimes lasting only min- of cracks” in a surface mantle, and so on. But the most
utes. Also, to avoid conflict between different observations, important point is that supporting quantitative physical
an active spot exposed to sunlight is often declared to have modeling results are never presented, as if cometary activity
“deactivated” itself. stood outside the field of physical concepts and methods.
We do not question the fact that the “mechanism” thus This way of “explaining” the coma structure persists today,
offered, if carefully implemented, might give birth to the even though the first physical simulation of cometary activ-
observed dust coma structures. But, in the literature, in par- ity casting a severe shadow on these explanations appeared
ticular in the two preceding references, it is used for reach- 14 years ago (Kitamura, 1990), and has been followed by
ing a much stronger conclusion: The “active area map” the vast body of even more devastating gas dynamic results
derived by this method is explicitly declared to represent described in section 6.
the total activity map of the nucleus. In other words, (1) all
the dust is assumed emitted from the active areas, (2) all 2.7. Near-Nucleus Dust Structures
the gas is assumed to originate from these active areas, and
(3) the emission of the active areas is transient and, for some We use the term near-nucleus dust structures to refer to
of them, occurs only one time. This analysis is often supple- structures observed at a spatial resolution smaller than the
mented by a quantitative estimate of which fraction of the nucleus size. Hence, data of this kind exist only for Comets
nucleus is active: For this evaluation, the active areas are P/Halley, P/Borrelly, and P/Wild 2. In the first case, the re-
assumed to consist of pure ice. Their total extent is found to sults are superbly described in the two-volume report pub-
be typically 5–10% of the nucleus surface. lished by the European Space Agency (Keller et al., 1995;
Conclusion (1) meets with severe objections: Why would Szego et al., 1995). In the two more recent cases, prelimi-
only a small fraction of the dust emitted by an active area nary results have just appeared (Soderblom et al., 2004;
go to the observed “jet,” while most of this dust would go Brownlee et al., 2004). In all three cases, the nucleus was
to the background coma? And how are we sure that this is also imaged. The spatial resolution was smaller (and posi-
really the case? As no analysis is offered for the background tion-dependent) for P/Halley, but the coverage was practi-
coma dust (which makes up most of the dust emission), we cally complete. For P/Borrelly, only part of the sunlit surface
are free to assume that it comes from the whole sunlit area was imaged. The coverage seems to have been nearly com-
of the nucleus. In fact, a much more natural assumption plete for P/Wild 2.
would indeed be that active areas (as derived above) are The main result of the Giotto flyby is a synthetic image
areas where, transiently, a tiny dust flux excess occurs, for obtained by the HMC camera, in which bright dust struc-
any reason. In such a picture, all nuclei are essentially seen tures are seen attached to a restricted part of the nucleus
to emit dust homogeneously. edge (see Fig. 10 in section 7.2). This is typically described
Conclusion (2) also meets with many strong objections. in the following terms: “ . . . distinct jets emanated from
(a) As already pointed out by Whipple (1982), it is arbitrary active spots on the sunward side of the nucleus. Most of
to postulate that a dust-gas mixture can be blown from dis- the elongated and structured nucleus appeared inactive”
crete sources in a narrow collimated way; it is much more (Keller et al., 1994, p. 69). Figure 76 of the same reference
476 Comets II

quantitatively reproduces the gross coma appearance, using 3. PHYSICAL MODELS OF THE
a model described in Knollenberg et al. (1996): The dust NUCLEUS-COMA INTERFACE
distributions from three unequal circular active sources,
placed on a sphere centered on the nucleus, are added. Each It is not possible to build a physical model of the coma
distribution is computed as if the source was isolated on without having a model of at least the outer layers of the
that spherical nucleus. We return to this in section 7.2. nucleus, yielding at each point of the surface algorithms that
After enhancement of the azimuthal gradients of the allow computation of the temperature and gas and dust flux
HMC image, a wealth of fine radial structures appear, which as a function of the solar direction (and distance). We say
the authors called “filaments” (Keller et al., 1994, pp. 83– “algorithms,” because the coma conditions and near-surface
85). A gas dynamical simulation of a process by which a nucleus conditions are mutually coupled and therefore must
narrow pencil of dust could be produced in an uniform am- be computed self-consistently. One example of this coupling
bient coma was developed (Knollenberg, 1994; Keller et al., has long been recognized: The emitted dust can influence
1994); an inactive circular area (100 m size) was assumed the visible and IR irradiation of the surface, hence react on
to exist as a defect inside a uniformly active surface; it was the emission (Salo, 1988; Moreno et al., 2002). Another
computed (not just stated) that a narrow pencil of dust is example, only recently documented, is that both net subli-
formed on its axis due to the convergence toward the axis mation or net condensation are possible, even on the day-
of the surrounding gas and the resulting cross-axis motion side surface, not only in the shadowed areas (Crifo and
of the dust. We return to this explanation in section 7.2. But Rodionov, 2000) but on the sunlit portions as well (Crifo
we may immediately observe that this model result exactly et al., 2003a). Hence, both nucleus interior models and
supports Whipple’s (1982) criticism of the classical active coma models should be unbiased with respect to the value
area concept that we cited in section 2.6: A small-scale of the gas pressure at the surface, as well as with respect to
coma dust density maximum is found (not just assumed) to the sign of the net surface gas flux.
be due to a surface gas-dust production minimum.
Similar azimuthal enhancements were applied to the 3.1. Interface Description
Vega 2 camera images. Here, due to a lower resolution, fila-
ments could not be identified, but more than 10 directions At the present time, there are only indirect inferences
of brightness enhancement were clearly distinguished (see about composition and structure of the nucleus. It seems
pp. 208–228 of Szego et al., 1995). Enough view directions that all authors follow Whipple (1950, 1951), who proposed
were available to conclude that “the jet sources formed a that (1) it is a mixture of the ices of simple molecules and
long linear feature on the nucleus passing across the sub- of refractory dust, probably with a complicated physical
solar point” (Szego et al., 1995, p. 72). texture; (2) its outer, near-surface layers must be radially
Both the Giotto and Vega observations are being reinter- differentiated (the most volatile ices being absent from the
preted by the global physical model described in Rodionov outer layers). Estimating the stability of the various volatiles
et al. (2002). We will discuss some of the results in sec- residing at or just below a nucleus surface, Whipple con-
tion 7.2. cluded that ices of the most volatile molecules (such as CO,
Finally, let us observe two essential differences between CO2, etc.) cannot survive one nucleus perihelion passage;
near-nuclear structures and distant coma structures: this means that in comets approaching the Sun periodically,
1. The near-nucleus dust dynamics are controlled every- these volatile molecules must sublimate at some depth in-
where by the gas interaction, as already established by side the nucleus and then diffuse toward the surface. It has
Whipple (1951). Hence it is unrealistic to claim to under- been postulated sometimes that even H2O ice itself could
stand by means of visual observation the dust motion that is sublimate below a blanket of more or less cohesive dust.
present before clearly stating how the (invisible) gas is con- In all cases, the outer layers must be porous to permit gas
sidered to flow. In fact, when such images are presented to effusion (actually, the voids created by the elimination of
a gas dynamic scientist, the reaction is unvariably that the the volatile species already create porosity). The current
observer is merely seeing plumes (i.e., dust in a gas flow). speculations about comet formation in the early solar sys-
2. Observation of the near-nucleus coma is concomitent tem also suggest that the nucleus as a whole may be a low-
with a determination of the nucleus shape. Therefore, real- density, porous and brittle medium. One of the goals of the
istic three-dimensional models can be devoped. Further- nucleus internal heat transfer models is to offer scenarios
more, Comet P/Halley will return to perihelion in the year for this radial differentiation (see below).
2061, a horizon not totally discouraging for young scien- Little consideration has been given in the cometary liter-
tists, and Comets P/Borrelly and P/Wild 2 will return much ature to the difficult problem of taking into account the sur-
earlier. So, conclusions derived about these comets can be face topography. As already suggested by Whipple (1951),
made under the form of precise predictions. As long as and confirmed by radar backscattering data (Harmon et al.,
physical truth can result only from predictive-corrective 1999), the nucleus surface must be “extremely rough on
iterations, these observations provide the first (and for the scales of meter and larger.” The same must be true at smaller
time being, the only) basis for a true physical study of com- scales, due to dust ejection. Also, the surface is subjected
ets. We return to these observations below. to erosion — roughly 1 m will be lost per perihelion pas-
 Crifo et al.: Nucleus-Coma Structural Relationships 477

sage, which may imply locally stronger depletions. Thus transported to or created at the respective depth. There are
the nucleus’ shape itself evolves both on a global and on a in principle three ways in which the energy can be trans-
local scale. On a timescale of days, the submetric surface ported to a subsurface layer: (1) solid-state heat conduc-
details will change. Keeping these facts in mind, the ques- tion via the solid matrix, composed of connected grains;
tion arises of down to which level of accuracy does it make (2) transport of heat by inward-flowing gases that recon-
sense to describe these surface variations in the frame of a dense in the deeper/colder layers and release their latent heat
numerical model? The answer is difficult and depends upon there; and (3) penetration of the solar radiation into the ice
the goal envisioned. The model of Rodionov et al. (2002) and absorption in the interior instead of at the immediate
was constructed to handle the surface at a spatial resolu- surface; this can only happen if the ice is to a certain ex-
tion ∆ = 50 m, consistent with the Halley imaging data. The tent transparent and the radiation is trapped in the interior
assessment of the Rosetta lander descent parameters re- (solid-state greenhouse effect).
quires a description of the surface such that short-term pre- 3.2.1. Porous ice models. The first thermal models of
dictions of the near-surface coma structure (a few rotation cometary nuclei (published in the 1980s and earlier) as-
periods) are possible. What this means in terms of spatial sumed nuclei to be nonporous ice/dust mixtures. Smolu-
resolution of the surface has not yet been assessed. chowski (1982) was the first to take into account porosity
Given that the nucleus rotates at an angular velocity Ω, and gas flow through the pores. Subsequently, the heat and
if the surface is to be described at the spatial resolution ∆, mass transport in porous, grainy ices was investigated in
for consistency this must be done with a time resolution δt = more detail by several groups (Squyres et al., 1985; Mekler
∆/(ΩR). But should one use a true time-dependent model, et al., 1990; Steiner and Kömle, 1991a). The latter model
or a succession of quasisteady models? was successfully applied to laboratory samples composed
As the near-surface nucleus material is potentially quite of artificially produced grainy ice (Kömle et al., 1991). The
inhomogeneous in all respects (optical properties, volatility, thermal evolution of larger ice/dust samples irradiated un-
porosity, granulometry, etc.), its relatively fast time-depen- der space conditions was described by a similar model
dent illumination will induce both a horizontal and a verti- published by Benkhoff and Spohn (1991). The two latter
cal dispersion of the temperature(s). It is not at all proven models clearly showed that heat transport via the gas phase
that a quasi-steady-state temperature(s) distribution is ever (energy transfer by sublimation/condensation processes)
reached, nor even that local thermal equilibrium prevails. should play a significant role under “cometary” conditions.
That is, there is no proof that, within a surface element ∆ × Otherwise it would be difficult to understand the measured
∆, the various components (ice and minerals, for example) temperature profiles. Another important aspect, studied by
take on the same temperature. Actually this can only be Kossacki et al. (1994), is the influence of grain sintering
expected if they are very intimately mixed and thermally processes on the thermal evolution. Along the lines outlined
well coupled. This problem has been considered to some by these models (which mostly included only water ice)
extent by Kömle and Ulamec (1989), but certainly needs multicomponent models were developed that allowed the
to be reinvestigated in a more general context. The same prediction of the depths of various sublimation fronts as a
unanswered questions apply just below the surface. function of the thermal history if a particular initial com-
The near-surface coma gas adjusts itself to a steady state position were given (Espinasse et al., 1991; Steiner and
extremely fast (typically within seconds), but this is not Kömle, 1991b, 1993; Benkhoff and Huebner, 1995; Kossacki
necessarily the case for the dust: Heavy grains can be ac- et al., 1997). The current state of the art of these models is
celerated to only fractions or small multiples of the nucleus nicely described in the recent review by Capria (2002).
escape velocity (meters per second) and hence they stay in These models brought forward two important facts:
the vicinity of the surface for times comparable to the ro- (1) the possibly strongly reduced heat conduction caused
tation period. Thus, a thorough description of the gas pro- by small grain contact area, as known from lunar regolith;
duction consists of a succession of steady-state maps of the and (2) the heat transported, by the migration of evaporated
mass density, velocity, temperature and of the various spe- molecules along the thermal gradient, by sublimation and
cies’ mole fractions on a reference surface encircling the release of latent heat upon recondensation.
nucleus, at a spatial resolution ∆ on the order of several The basic equations describing this process are the con-
mean free paths (m.f.p.), which is typically fractions of a servation equations for energy (heat transfer equation) and
meter to tens of meters — depending upon local solar ze- mass (continuity equation)
nith angle — near 1 AU from the Sun. For the dust pro-
duction, not only the surface mass distribution gs(m) is ∂T ∂ ∂T ∂T
needed, but the shape distribution hs (clearly out of reach) (1 − ψ)ρici = λ − cgφg − qH (1)
∂t ∂x ∂x ∂x
and a true time-dependent model may be needed as well
for large grains.
∂ρg ∂φg
3.2. Near-Surface Nucleus Interior ψ =− +q (2)
∂t ∂x
Volatiles residing below the surface can escape through
pores and cracks in a rather direct way, if enough heat is in which ψ denotes porosity, ρ specific mass, c specific heat
478 Comets II

content, λ heat conductivity coefficient, φ mass flux, H la- (1) If forward-scattering dust particles are embedded in a
tent heat, q gas mass source term, and the subscripts i and transparent ice layer with a density realistic for comets, very
g refer to the solid and to the gas phase, respectively. dark surfaces (with a few percent albedo only, similar to
While the basic equations used in these various model- that observed for Comet P/Halley in 1986) can be created.
ing approaches are consistent, there are controversial ap- (2) With the same active area given, significantly lower gas
proaches in the formulation of the boundary conditions: production rates result, because the very surface is colder
(1) In all the models noted above, free-molecular outflow than in the case of “surface absorption” of the sunlight.
into vacuum is assumed, i.e., the backflow of molecules Laboratory experiments aimed at investigating this solid-
from the coma toward the surface is neglected. (2) Solu- state greenhouse effect more systematically and evaluating
tion of the continuity equation demands specification of the its significance for comets and other icy solar system bod-
surface pressure and/or surface density of the emitted gas. ies are currently under way (Kaufmann et al., 2002).
Different authors use quite different boundary conditions 3.2.3. Comparative results. The vertical temperature
here, from p = 0 at the surface to p = pS, the ice saturation gradient that develops in the near surface layer of the
pressure. Reduction of the two conservation equations (1) nucleus in response to solar irradiation strongly depends on
and (2) to one single energy equation is only possible if the the structure and composition of these layers:
surface pressure is assumed to be equal to the saturation 1. For a compact, well-sintered dirty ice with little po-
pressure pS. This has been explicitly verified by Steiner et rosity the thermal conductivity is high, close to that of com-
al. (1991). Something more realistic was used in the pact water ice. For long constant irradiation this leads to a
Espinasse et al. (1991) model. However, as a matter of fact, temperature profile close to linear, but not steep, as calcu-
the highly nonequilibrated condition, in which the mol- lated from classical models using the Klinger (1981) for-
ecules are emitted, is not properly accounted for in any of mula for the conductivity of water ice (a weak temperature
the models. For a more detailed discussion of this point, dependence, compared to the exponential temperature de-
see Skorov et al. (2001); this paper, as well as the previous pendence, which characterizes the heat transfer by gas sub-
one (Skorov et al., 1999), provided an important step be- limation/condensation).
yond the previous modeling efforts, by presenting semi- 2. If the ice is porous (open porosity) and composed of
analytical solutions for the kinetic gas flow in tubes of finite grains with low contact area, there will be a steep tempera-
length (assuming that the temperature profile along the ture gradient at the very surface (where the sublimating gas
length of the tube is known) and combining it with a nu- flows outward) and a rather flat temperature profile below,
merical solution of the heat conduction equation. Thus it where the sublimated gas flows inward toward colder re-
is not necessary to specify a separate pressure boundary gions and recondenses there, because the effective thermal
condition at the surface, because the gas outflow from the conductivity of the medium is high.
tube is found directly from the temperature distribution 3. If the ice is covered by a loose dust mantle a few
along the ice tube walls and the associated local sublima- millimeters or centimeters thick, composed of refractory
tion. The approach is similar to that already described in grains, a very steep temperature profile develops across this
Kömle and Dettleff (1991), but with tubes instead of rect- dust mantle, with a temperature drop of 100 K or more. This
angular cracks. is due to the fact that the dust mantle in the low-pressure
3.2.2. Partially transparent porous ice models. A much environment has an extremely low thermal conductivity,
more direct way to heat the subsurface layers of a comet similar to that of lunar regolith. The conductivity of a dust
nucleus exists if the ice is to a certain extent transparent. mantle could be increased by orders of magnitude, if it con-
In this case the solar radiation is not fully absorbed or re- tains organic components that might act as a glue between
flected at the surface, but penetrates icy layers down to a particles and cause some cohesiveness (Kömle et al., 1996).
certain depth. It is then absorbed either by enclosed dust 4. If transparent ice exists as such, it may influence the
particles over a longer distance or by dusty layers with high activity of the surface in various ways. Depending on the
optical thickness in the interior of the ice (see Plate 9). gas permeability of the transparent layer, it may cause sub-
The idea that the ice transparency could play an active surface pressure buildup and violent activity if the gas pres-
role in the thermodynamics of comets and icy satellites is sure exceeds the tensile strength of the crust. A typical fea-
relatively old (Kömle et al., 1990; Brown and Matson, 1987; ture is the existence of a subsurface temperature maximum,
Matson and Brown, 1989). Recently it was reinvestigated as shown in the example below.
by introducing the appropriate source terms into a more An example for the temperature profile that may develop
advanced thermal model (Davidsson and Skorov, 2002a,b) inside transparent ice subject to the solid-state greenhouse
and applied to calculate the gas production rate of Comet effect is shown in Fig. 1. The main feature is that the maxi-
P/Borrelly (Skorov et al., 2002) and to calculate the tem- mum temperature occurs not at the surface, but a few cen-
perature profiles to be expected in artificial ice/dust samples timeters below it. From there the heat is conducted away
(Kaufmann et al., 2002). The conclusions from these new toward the surface. The position and sharpness of this sub-
calculations could modify the currently accepted view of surface temperature maximum depend on the absorption
cometary energy balance and gas production quite signifi- profile as well as on the thermophysical properties of the
cantly. There are two important findings worth mentioning: ice. Higher temperatures could be reached in the case of a
 Crifo et al.: Nucleus-Coma Structural Relationships 479

10% only of P/Halley’s surface is active” is based on such

an unlikely assumption.
Efforts have been made to develop models capable of
handling the geometrical complexity of real nuclei. Enzian
et al. (1997) developed a “2-D 1/2 + t” approach for a
spherical nucleus — in the sense that one-dimensional ther-
mal equations (in the direction perpendicular to the surface)
are solved at each point of the surface. Guttiérrez et al.
(2000, 2001) extended this method to aspherical nuclei and
Rodionov et al. (2002) developed a similar method for com-
plex nuclei having spatial details of size comparable to that
used in their coma model. However, for mathematical trac-
tability, in all these models the nucleus interior physics has
to be simplified to pure heat transfer.

3.3. Near-Surface Dusty Gas

Fig. 1. Typical temperature profiles resulting from one-dimen- The relevant modeling of the first tens of meters above
sional time-dependent models, including the solid-state greenhouse the surface of an active nucleus is the only way to cross-
effect in ice (Kaufmann et al., 2002; based on model by Davidsson correlate the thermal and dynamical evolution of the nu-
and Skorov, 2002a,b). The different curves correspond to various cleus (mass loss, orbital perturbations, angular momentum
penetration depths and surface albedos. changes) and the formation of its gas and dust coma. It is
an unescapable task if one wants to interpret or forecast the
coma structure, orbital evolution, or nucleus rotational state.
low gas permeability, possibly caused by the sintering and Models that, for instance, prescribe “arbitrary boundary
densification processes described before. conditions” at the nucleus to compute the coma structure
3.2.4. Stumbling blocks. The next logical step of the are intrinsically unable to provide any information on its
previously described interior models would be their com- evolution during the nucleus rotation (to interpret coma dust
bination with a near-surface coma model to derive the proper structures, for example.)
gas conditions at the surface. But here, a severe obstacle of Unfortunately, the physical conditions in the near-sur-
most present nucleus models is that they are one-dimen- face gas-dust mixture can only be the subject of specula-
sional (and time dependent), and hence cannot accommodate tion: (1) the statistical properties of the surface topography
the expected complex geometry of the real surface, nor even and composition are unknown; (2) very little information
the smoothed approximation used in the coma models. It is available about the dust; (3) where gas is released by the
is unclear how this could be circumvented in the future. surface, it is not known whether it diffuses from below the
Another consequential limitation of these models is that surface, is sublimated from it, or both; (4) one is free to ad-
they assume that ice and dust share a common temperature vocate more intricate processes such as dust fragmentation,
at the surface (and in the near surface interior). This may sublimation from icy grains, etc. It is hard to believe, how-
be true for very fine dust, but cannot be true for large grains ever, that tiny details of what happens here influence the
(pebbles, boulders). In fact, the laboratory simulations of structure of the observable coma, considering the existence
KOSI have already found evidence of sizable dispersions of efficient smoothing processes inside the gas and dust
in the surface temperature of samples of illuminated ice- coma: pressure for the gas; shape, mass, and compositional
dust mixtures even though only small amounts of fine dust dispersion for the dust. Hence it can be hoped that effective
were used in the experiment (in an unrealistic way) (Lorenz (simplified) models of this region can represent in a roughly
et al., 1995). In reality, surface dust is expected to be warmer correct manner how the nucleus and coma are coupled. Of
than surface ice and will therefore radiate more thermal course, this can also be tested by developing alternative
energy, hence its neglect overestimates the energy available models that allow for different processes.
for sublimation. The models with a surface crust are free 3.3.1. Near-surface conditions in a dust-free case. Ele-
from this criticism, but in general lead to rather small surface mentary calculations show that a surface of pure ice sub-
fluxes. In some models (e.g., Enzian et al., 1997, 1999), a mitted to solar illumination in free space assumes a tempera-
first-order correction is made in the surface energy budget ture below the water triple point, and hence sublimates: It
equation by the introduction of an “icy area fraction” f. We emits molecules according to a half-space centered Max-
come back to this in section 3.3.2. wellian distribution M (0,Tn), where Tn is the surface tem-
Let us notice that most nuclei size estimates assume not perature. The rate Z+ (molecule/m2 s) of the emitted mole-
only that the surface is isothermal, but that it is really pure cules is, very roughly, Z+ = c cos z /LSr 2h, where c is the
sublimating ice with no embedded dust — even in very solar constant, z the solar zenith angle, and LS the subli-
dusty comets. For instance, the often quoted estimation “that mation latent heat. If the gas diffuses from pores, the distri-
480 Comets II

bution is no longer a half-space Maxwellian, but some other because any surface that is smooth enough can be approxi-
function defined by the pores’ geometry and temperature, mated by locally plane-parallel elements. This is done sys-
and Z+ is necessarily of a smaller magnitude than before. tematically in all papers by Crifo and Rodionov cited here-
It is easy to compute that, near rh = 1 AU, the mean free after. The accuracy of this approximation is found to be
path of the molecules emitted from a given point against unexpectedly high (see section 6.3.3.).
collisions with those from the adjacent points is very small In the plane-parallel method, the “surrounding flow”
(typically a fraction of a meter), hence a fluid atmosphere degenerates to the specification of one set (p0, V0, T0): the
is formed. A flow pattern must establish itself inside this gas parameters at the distance where equilibrium flow is
atmosphere, resulting from the complex surface distribution reached. This distance is found to be on the order of several
of Z+. It is the purpose of the coma model to compute this tens of mean free paths. This implies that, for a comet near
flow. Here, two difficulties arise, first mentioned in the Rus- 1 AU, the thickness of the BL will be several meters to sev-
sian literature (see references in Crifo, 1991a), and first eral tens of meters. Obviously, the mathematical smoothing
discussed in detail in Crifo (1987). of a real nucleus surface to ∆ = 50 m makes the plane-par-
The first difficulty is that the velocity distribution of allel approach usable, but it remains to be seen whether this
the molecules returned to the surface is the downward part smoothing is acceptable in itself. The computed structure
M –(V0,T0) of a Maxwellian function with some mean ve- of the BE is found to depend upon one free parameter, in
locity V0 and temperature T0. Let us refer to M +(V0,T0) as accordance with the previously established fact that there is
the corresponding upward part, then the distribution of the no way to predict Z– by consideration of the BL flow only.
emitted molecules must differ substantially from M +(V0,T0), For this free parameter, the initial Mach number
otherwise the net gas flux at the surface would be vanish-
ingly small. Therefore, in the immediate vicinity of the sur- M0 = V0 / γ kBT0 /m
face, the gas is not in an equilibrium regime (which requires
a strict, or moderately distorted Maxwellian shape). This in which kB is Boltzmann’s constant, is usually used. It has
region must therefore be treated by gas kinetic methods been proven from first principles that no solution exists for
(solving the Boltzmann equation, or BE). If this region is M0 > 1 (once more, contrary to some — inaccurate — re-
small, hereby defining a so-called surface boundary layer sults published in the recent cometary literature). Thus, one
(BL), the much more efficient gas dynamic methods will be arrives at relations p0 = p0(Tn,M0) and T0 = T0(Tn,M0) at
used to compute the flow outside of it (section 5). each point of the top of the BL, to be taken as the bound-
The second difficulty is that in a gas, the flow regime ary conditions for computing the coma flow. Only when this
depends upon the conditions holding at all boundaries of flow is computed (see section 5) is M0 known at each point,
the flow. Therefore, the preceding (V0,T0) near any point hence the return flux Z–. This approach is fully described
of the nucleus surface does not depend only upon the local in Rodionov et al. (2002) and references therein.
values of Z+ and Tn, but upon these values at all points of 3.3.2. Near-surface conditions in a dusty case. Perhaps
the surface. From the point of view of nuclear interior pure ice volumes exist in some nuclei, but, in general, one
models, this means that the return flux Z– (recondensed onto expects the ice to be dirty. It follows that only a fraction
the ice) is not proportional to the upward flux Z+ (contrary f = 1/(1 + ℜ) (where ℜ is the relative dust-to-ice mass con-
to what is assumed in many recent cometary papers). In par- tent) of the surface is ice; the rest is dust (e.g., Crifo, 1997).
ticular, there is no “simple” way of predicting whether Z– As already stated, it is not expected that these two constitu-
is smaller or greater than Z+. This is not simply a cosmetic ents assume a common temperature. Furthermore, dust,
argument: Indeed, we shall see in section 6 that very plau- even porous, cannot produce vapor at the rate Z+ of ice. The
sible surface topographies lead to recondensation (instead above picture must therefore be amended. An approximate
of sublimation) over sizable fractions of the sunlit areas of modification of the above model has been proposed by
the nucleus. Crifo and Rodionov (1997a), consisting in writing that the
These two difficulties have been identified for quite some net upward flux is reduced (compared to pure ice) by the
time in the rarefied gas dynamic literature, and continue to factor f. As already stated, this factor is used in many
be the subject of advanced developments (see Cercignani, nucleus models, but unfortunately not in all.
2000, and references therein). The reader is urged to be Since the initial dust velocity is negligibly small, the fact
cautious about the relevance of publications concerning that there is a large dust concentration inside the BL must
these problems that do not refer to the aforementioned liter- still be taken into consideration. Based on the fact that the
ature. The specific problems of integrating the BE over sub- dust density is also large just outside the BL, and that, out-
limating or condensing ice under simple geometries have side of it, exact dusty gas dynamic computations show that
long been solved exactly by analytic methods (e.g., Cercig- the perturbation of the gas is small, Crifo and Rodionov
nani, 1981) or direct Monte Carlo simulations (DSMC) (1997a) assume that this is also true inside the BL. This
(e.g., Abramov, 1984). Notice in passing that for the rea- analysis was done assuming a P/Halley-like dust mass dis-
son given above, solutions can only exist for specific ge- tribution of spherical grains. It is possible that the situation
ometries. Of special interest is the plane-parallel solution, could be different for other dust properties.
 Crifo et al.: Nucleus-Coma Structural Relationships 481

4. PHYSICAL MODELS OF Because Tn scales as the third power of the characteris-

THE NUCLEUS ROTATION tic nucleus size, while the inertia momenta scale as its fifth
power, the angular acceleration due to outgassing scales as
In the same way as it is impossible to build a coma struc- its inverse square. The effect of the torque is therefore ex-
ture model without matching it to a subsurface nucleus pected to be maximum for very small nuclei. Indeed, Crifo
model, neither is it possible to reproduce most of the coma et al. (2003b) have computed the torque and rotation of very
structures, whether directly observed or observed through small (subkilometric) irregular nuclei and found it to induce
lightcurves, without introducing a nucleus rotation model. highly irregular, possibly chaotic rotational motions. On the
This is true even of the near-nucleus structures, which criti- other hand, the effect is modest for Halley-like comets, and
cally depend upon the direction of solar illumination of the must be negligible for very large comets (e.g., Hale-Bopp).
complex nucleus orography.
The nucleus rotation is governed by the equations for an 5. PHYSICAL MODELS OF THE COMA
asymmetric top (Landau and Lifshitz, 1976, section 36), tak-
ing into account the outgassing torque. Differences among By physical model, we mean an approach that tries to
researchers appear when evaluating the net recoil force Fn make full use of the latest available methods in applied
and net torque Tn exerted on a nucleus by its gas and dust physics. Unavoidably, only brief descriptions of these meth-
emission. However, such computations are at the heart of the ods appear in the cometary literature. The reader unfamil-
aerospace industry (rocket motors), so that reliable meth- iar with these methods will first have to get acquainted with
ods of computation exist in that field of study. For pure gas, the proceedings of the Rarefied Gas Dynamics Symposia
both Tn and Fn can be computed by integration over any held every two years. Examples of up-to-date textbooks
closed surface inside the gas flow, as long as mass, momen- covering most topics of interest here are Gombosi (1994)
tum, and energy (MME) are preserved. The best is to choose and Cercignani (2000). For information about fluid dynam-
the top of the BL, where (1) the gas is in fluid regime (hence ics computational methods, see references in Rodionov et al.
the integrals involve only p0, V0, T0) and (2) MME have (2002), and for the Monte Carlo simulation methods, see
been preserved as photochemistry and other effects are not Bird (1994).
yet at play. For dusty gas, the only exact method is the Once methods are available, they must be applied. Here,
nucleus surface integration. However, for a P/Halley-like the cometary medium must be described by selecting nu-
distribution, one can still integrate at the top of the BL, as merical values for all physical properties. This occasionally
stated above, because this kind of dust does not substan- raises difficulties. For instance, collision cross sections
tially perturb the flow inside the BL (in keeping with the between exotic molecules may not be known. However, the
fact that its global momentum is still negligible at this dominant molecules in the coma — H2O, CO, etc. — have
point). been the subject of in-depth studies in the laboratory and
An exact computation of Tn and Fn is possible only for in the industry. Their physical properties (both in the gas
nuclei with a known external shape and surface composi- phase and in the solid phase) are therefore available. Un-
tion. The adoption of an arbitrary external shape when the fortunately, it is not uncommon to find works in which
real shape is unknown is unwarranted. The worst possible fancy numerical values are adopted for these properties. The
practice is to assume a spherical shape, since unrealistic nonexpert reader is therefore advised to check all values
symmetry cancellations occur during the surface integra- against such robust sources as the American Institute of
tions and since, in addition, the strict periodicity of the Physics (AIP) Physics Handbook (last edition in 1972) or
rotation induces a quite atypical quasisteady surface tem- the Chemical Rubber Company (CRC) Press Handbook of
perature distribution. Physics and Chemistry (84th edition in 2003).
Rodionov et al. (2002) have computed Tn and Fn for P/ While a gas molecule is a precisely defined entity, such
Halley using the observed shape, a best-fit rotation mode, is not the case for a “dust grain.” One usually ignores it by
and assuming that the nucleus is uniform in composition. the “simplifying assumptions” that the grains are spherical,
This revealed that that both Tn and Fn vary considerably in but this is unfortunate: Intuition as well as pioneering simu-
magnitude and direction during the nucleus rotation. Belton lations using aspherical grains (Crifo and Rodionov, 1999)
et al. (1991) and Samarashinha and Belton (1995) calcu- indicate that spherical grains have a totally atypical aero-
lated the nongravitational effects on P/Halley nucleus as- dynamical behavior: A flowing-by gas submits them only
suming that the dust jets seen far from the nucleus originate to a drag force, the lift and torque being null. It follows that
from active areas derived by tracing the jets back to the all spherical grains of a given mass starting from a given
surface of an approximating ellipsoid. This is subject to two point follow the same trajectory and have the same final
severe criticisms: (1) The correct shape should have been velocity. Such is not the case for grains having the same
used, and (2) the definition of “surface jets” should have mass, but varying shapes: Their trajectories differ, and their
been done on the basis of fluid dynamics — this is the same final velocities can be spread over orders of magnitude. In
criticism as when discussing Hale-Bopp spirals. We will fact, even the initial orientation of the grain at the surface
return to the rotation of P/Halley in section 7.3. influences their trajectory and final velocity, with some
482 Comets II

shapes and orientations preventing ejection, and others lead- 5.1.1. Gas dynamic approach. The most general form
ing to high velocities. used hitherto in coma studies is the single-fluid Navier-
Not only does it appear mathematically difficult to build Stokes equations (NSE)
a model of a near-nucleus coma with shape-dispersed dust,
but it seems unlikely that one will ever access the needed ∂
ρ + ∇ ⋅ (ρV) = fρ (3)
input parameters of the model, such as the grain shape dis- ∂t
tribution and the distribution of initial orientation of these
grains at the surface. From this point of view, the ultimate ∂
(ρV) + ∇ ⋅ (ρVV) + ∇p − ∇ ⋅ τ − F = fv (4)
goal of cometary dust studies is (to tell the truth) rather ∂t
unclear to us.
∂
(ρh0 − p) − ∇ ⋅ q + ∇ ⋅ (τV) − F ⋅ V = fh (5)
5.1. Gas Coma ∂t

The ultimate description of a coma is the set of distri- where ρ is the total mass density, h0 is the specific enthalpy,
bution functions fi(t, r, vi), defined as the number of par- p is the pressure, q is the heat conduction vector, τ is the
ticle of species i (H2O molecules, CO + ion, spherical olivine second-rank viscous stress tensor, and F the total macro-
grain of radius ai, etc.), having the cometocentric particle scopic force. The vector q can be expressed as a function
velocity vector vi at the cometocentric position (vector) r, of T, and τ can be expressed as a function of T and the par-
per unit volume dr and unit velocity-space volume dvi. tial derivatives of V with respect to the coordinates.
These functions are governed by coupled BEs (see, e.g., In F the radiation pressure force is generally negligible,
Gombosi, 1994; Cercignani, 2000). It is the goal of gas and the nucleus gravity generally neglected, but there would
kinetic methods to solve these BEs. It can be done in ex- be no problem with keeping the latter term in order to deal
ceptionally simple cases by numerical methods; otherwise, with Kuiper belt-sized objects if one wanted to. If the pre-
in principle, DSMC can be used (see Cercignani, 2000). ceding equations are written in a non-Galilean frame, inertia
However, DSMC requires forbidding computational resources forces must be introduced. For instance, if a nucleus-at-
as soon as interparticle collisions become important. For- tached frame is used, it can be shown (Rodionov et al., 2002)
tunately, in this case, solving the BEs is unnecessary because that the Coriolis force 2 V × Ω (where Ω is the nucleus
it is possible to predict the general form of the solution. For angular velocity vector) is the dominant inertia force. It can
instance, in a gas mixture where near-thermal equilibrium also be shown that the ratio of the pressure force |∇p| to
prevails, the fi are exact or nearly exact Maxwellian func- the Coriolis force decreases as 1/r with distance to the nu-
tions of the gas mean mass density ρ, flow velocity V, tem- cleus. In a very large comet with fluid region exceeding
perature T, and species mass concentrations qi. It is therefore 104 km (like Hale-Bopp), at such a distance a plausible Ω =
optimal to solve only fluid equations governing these quan- 10 –5 radian s–1 sets the preceding ratio to about 1/10: In
tities — the objective of gas dynamic methods. Computing other words, the Coriolis force is dominant — an hitherto
the same flow by the two alternative methods, when pos- unnoticed fact. Such may also be the case for less-produc-
sible, is beneficial, providing, in particular, cross-validation tive comets if their nucleus has a higher spin rate. It implies
of the numerical methods. that rotationally induced gas structures are to be expected
It is a fairly difficult task to derive from first principles at large distance.
which method is best suited to deal with a rarefied flow such The “source-sinks” terms fρ, fv, fh at the r.h.s. of these
as the coma gas flow. The discussion is to be based on a equations allow for (1) the fact that the fluid interacts with
comparison between the mean free path and the character- photons, or with particles not belonging to the fluid itself
istic scale L of the flow, as well as between the collision (e.g., dust), and (2) possible inelastic processes that are
times and the timescales of the flow. This comparison must internal to the fluid itself and that affect its momentum and
be done at each point. Additional limitations due to the energy budget. An important example of the first effect is
mathematical methods also come into play; see a concise photodissociation of H2O, and an example of the second
discussion in Rodionov et al. (2002), and more detailed de- effect is partial H2O recondensation into clusters (H2O)n;
velopments in, e.g., Gombosi (1994) and Cercignani (2000). both yield a large fh term, a moderate fρ term, and a negli-
To give an oversimplified summary, when the mean free gible fv term. Another example is cooling through IR emis-
path is much smaller than L , the gas is said to be “in fluid sion. It is not possible to incorporate dust inside the fluid
regime,” fluid equations apply exactly, and DSMC is use- described by the above NSE, because the huge mass differ-
less; when the mean free path is much greater than L , the ence between molecules and dust grains forbids the dust
gas is said to be in “free-molecular” regime; in between, the grains to share a common flow velocity with the gas (and
gas is said to be in “transition regime.” In the two last cases, even a common flow velocity between themselves). Further-
DSMC always applies, and fluid equations may or may not more, in typical coma conditions the grain-grain collisions
provide accurate results; the quality of their solutions must are negligible, so that dust grains do not acquire thermal
be evaluated case by case (see examples in Crifo et al., velocity spread or pressure. The dynamics of the grains
2002a, 2003a). must therefore be treated by separate equations (see below),
 Crifo et al.: Nucleus-Coma Structural Relationships 483

and their interaction with the gas must be represented by For modeling most observed coma gas structures involv-
r.h.s. terms in the NSE. If the grains do not emit or con- ing distances much in excess of 1000 km, the time-depen-
dense gas, there is no fρ term, and the two other terms have dent gas equations must be solved, but looking for a true
little effect on the gas, for a dust mass distribution of the time-dependent solution, not just for the limit for large
kind found in Comet P/Halley (see Gombosi, 1986; Crifo, times. To do this, instead of keeping the nucleus surface pa-
1987). But if the dust is icy, it will condense or emit H2O rameters constant, one must first compute a set of succes-
and release or absorb latent heat, and this may result in sive nucleus surface parameters, forming the boundary
strong perturbations of the gas flow (see Crifo, 1995). condition for the variable t. The solution is a set of succes-
The “source-sinks” terms, whatever their origin, must sive three-dimensional coma structures. Obtaining it is an
themselves be computed by solving so-called “rate equa- enormous undertaking in terms of computer resources. It
tions,” to be solved simultaneously with the above ones. For has been achieved for the first time during the preparation
a review of the forms of r.h.s. terms, see Crifo (1991a) and of this text, and will be described only in forthcoming pub-
Rodionov et al. (2002). lications by Rodionov and Crifo.
For many applications, the Eulerian form of the equa- However, observations involving distances in excess of
tions (EE), simpler because it involves only first-order par- 1000 km may be interpreted by a succession of steady-state
tial derivatives, can be used; this is obtained by setting τ = solutions, if free-molecular conditions are reached before
0 and q = 0. Formally speaking, the relative ranges of valid- or near that distance: In such a case, the extrapolation of
ity of the EE and NSE should be delineated using a dimen- the gas parameters beyond 1000 km is trivial, and is not
sionless rarefaction parameter, the so-called generalized affected by photodissociation. This is, for instance, the case
Knudsen number, defined in Crifo and Rodionov (1997a). of the interesting Comet P/Schwassmann-Wachmann 1 dis-
But comparisons with solutions obtained by DSMC show cussed, e.g., in Crifo et al. (1999), which lends itself to
that the frontiers of these domains also depend upon the velocity-resolved observations.
details of construction of the numerical method of solution Finally, it may happen that the gas reaches, near 1000 km,
(see Crifo et al., 2002a, 2003a). The existing results from transition regime conditions; in such a case, the validity of
such comparisons show that the NSE and even the EE pro- the use of fluid equations becomes uncertain, in particular
vide acceptable solutions over practically the whole day- due to the presence of photodissociation. It is then necessary
side coma of observable comets. Two restrictions are to be to use a time-dependent DSMC, or to validate the use of
made, however: (1) The immediate vicinity of the nucleus fluid equations by comparison with DSMC results.
surface must always be dealt with by gas kinetic methods. 5.1.2. Direct Monte Carlo simulations. In a DSMC
This is a very strong restriction, since only a correct treat- model, the evolution resulting from mutual collisions, of the
ment of this region warrants the obtention of a correct solu- individual velocity components, of the internal energy, and
tion from the EE or NSE “downstream” in the coma. We of the position coordinates of a large number of “weighted”
have discussed this region in section 3.3.1. In all their stud- molecules are monitored. Instead of introducing molecules
ies, Crifo et al. treat this region by an algorithm based on the at the rate Z+, they are introduced at a somewhat reduced
BE, hence they call their solutions “BE-EE” or “BE-NSE”. rate Z/q (q > 1 can be position-dependent). The statistical
(2) In the outer reaches of the coma, where dissociation consequence of the replacement of the extremely large num-
products are dominant, it is presently not known to which ber of real molecules by a much smaller number of simu-
accuracy these equations represent the real situation. This lated molecules is of course taken into account. Space is
is because photodissociation creates the daughter molecules discretized into adjacent cells, and time into a succession
with high velocities relative to the parent velocity; for the of time steps. At each time, the number of mutual collisions
fluid equations to be valid, it is necessary that slowing down of the molecules expected in each cell is evaluated, and the
of these products to the local velocity distribution occurs velocities and internal energies of a corresponding number
within one computational cell. This may not necessarily of randomly selected pairs of molecules are changed using
occur. Unfortunately, comparisons between NSE (or EE) and a binary collision model. During the next time interval, all
DSMC for such cases are not yet available. molecules are moved. The procedure is reiterated until
Finally, let us comment about the presence of the time t steady state is achieved. [For a description of the method,
in the above equations. Given angular speeds Ω = O (3 × see Bird (1994); for an insight into the future of this method,
10–5) radian/s, near-nucleus gas speeds V = O (300) m/s, and see Bird (2001).]
a modest lateral spatial resolution δ = O (0.01) radian, one The DSMC method offers specific advantages: (1) It is
sees that steady-state gas solutions can be used out to dis- valid for any form of the gas velocity distribution function;
tances <(V/Ω)δ = O (1000) km. However, such time-station- and (2) the boundary conditions can always be formulated
ary solutions can be obtained only by solving the time- exactly (for instance, very complicated nucleus surfaces, on
dependent equations — with time-independent boundary any linear scale, can be considered). But, as with any
conditions. The reason for this is associated with the fact method, it can be (and is indeed sometimes) improperly
that the gas flow is in (large) part supersonic; see references implemented. For instance, three mandatory requirements
in Rodionov et al. (2002) for an extensive description of are that (1) the chosen time steps must be much smaller than
the methods of solution. the mean collision time, (2) the typical cell dimension must
484 Comets II

be much smaller than the local mean free path; and (3) the nating from any given subdivision never mutually intersect.
cell dimension must also be smaller than the characteristic We will present illustrative examples of this in sections 6.1
flow scale L . Unfortunately, information that allows the and 6.2.
reader to check whether these conditions are satisfied is not In conclusion, it is possible to compute the dust distri-
always included in the publications. Finally, the method is bution at small distances from the nucleus by a so-called
computationally much less efficient than the solution of “multifluid model” with possibly a very large number of
fluid equations, so it should not be considered to be a sub- fluids. Each fluid will be governed by “zero-temperature
stitute for the latter, but should be used to complement them. EE” with p = T = 0 and h0 = cs Ts (s is the grain type tag,
cs the specific heat, Ts the grain internal temperature). An
5.2. Dust Coma other possibility would be to use a DSMC for the dust,
seeding them inside the precedingly known gas solution (see
If the dust perturbs the gas flow, its distribution must be section 6.2).
computed self-consistently together with the gas equations.
This was done in the old one-dimensional works reviewed, 6. INNER COMA STRUCTURES AS
e.g., by Wallis (1982) and later on by Crifo (1991a), and in REVEALED BY PHYSICAL MODELING
several of the two-dimensional works reviewed in Kömle
(1990) and in the present section 6.2. In most of these works, On the scale of the groundbased data spatial resolution
all the dust mass loss was (unrealistically) assumed to be (hundreds of kilometers at best), the zero-order coma gas
concentrated in single-size small spherical grains. This re- flow is trivial: A point source placed in a near-vacuum can
sulted in a strong perturbation of the gas. But with the mass only provide a radially diverging flow; mass conservation
being spread over a very large range of mass, as was found produces a ∝ (1/Vr2) gas density decrease, the resulting
in Comet P/Halley, this effect disappears (see Gombosi, pressure gradient accelerates the gas velocity, and kinetic
1986; Crifo, 1987). While it is not possible to exclude very energy conservation requires a concomitent gas tempera-
narrow size distributions, this presently seems to be permit- ture decrease; a classical analytic treatment demonstrates
ted, hence one will currently solve first the gas equations that the flow becomes rapidly supersonic (e.g., Wallis,
and then the dust equations. 1982). The flow will ultimately “freeze” at some terminal
Conversely, as the gas density decreases outward, and velocity and temperature when collisions become rare (e.g.,
the gas-dust interaction is a function of at least the square Cercignani, 2000, section 5.9). Innumerable illustrations of
of their relative velocity — which also decreases outward — these effects are described in the gas dynamic literature. The
the acceleration and cooling of the dust by the gas stops at solar wind is formed by a similar process (Parker, 1965).
some distance from the nucleus surface (typically less than Of course, in the cometary case, there are also specific so-
100 km). called “nonadiabatic” effects by which mass, momentum,
Since the “dust velocity” is typically one or several and energy can be input or removed from the flow, thus
order(s) of magnitude smaller than the gas velocity, the altering its structure. For instance, a general gas dynamic
range of validity of steady-state dust distributions is also theorem states that exothermic effects tend to render the
an order of magnitude smaller, i.e., is typically only 100 km. flow sonic: If they occur in a subsonic flow, its Mach num-
Beyond it, standard interplanetary dust modeling techniques ber is increased, and if in a supersonic one, the Mach number
are to be used (see Fulle et al., 1999; Fulle, 2004). These is decreased (possibly strongly enough to generate a shock).
methods are intrinsically time-dependent. Partial recondensation of H2O molecules into molecu-
Here, we will only deal with the modeling of the region lar clusters and large amounts of fine dust may heat the gas.
where the dust-gas interaction is sizable. If possible, it is These effects are limited to the vicinity of the nucleus sur-
appealing to use, for the dust, equations similar to those for face, because the first one is proportional to at least the
the gas. However, the latter express the fact that mass, mo- square of the gas density, and the second one to the square
mentum, and energy are preserved during the many colli- of the gas density. Water photodissociation releases fast H
sions occuring in each elementary volume. For cometary and OH that, by thermalization, heat the gas; this occurs in
dust, collisions are practically absent. Hence the use of fluid a large part of the coma and limits the gas Mach number.
equations seems unwarranted. However, it is correct to write In the old cometary literature (1965–1990), the super-
that the mass, momentum, and energy of a set of co-moving sonic state of most of the coma and the preceding nonadia-
particles are preserved. So, it is possible to group in the same batic effects have been recognized and studied in trivial one-
“fluid” particles that follow everywhere the same trajectory. dimensional geometry [see the review of Crifo (1991a),
Since the aerodynamic acceleration depends upon mass and supplemented by Crifo (1993) and Crifo (1995) for poste-
shape, these particles must have the same mass, shape, and rior developments]. However, an essential implication of the
initial orientation at the surface. This is still not sufficient: supersonic state of the coma was universally overlooked in
One must also make certain that trajectories do not cross that literature: the tendency of the flow to form shock struc-
one another at any point. This leads to subdividing the nu- tures to adjust itself to nontrivial geometrical constraints, or
cleus surface in areas such that dust grain trajectories ema- in reaction to external perturbations. Gas shocks of inter-
 Crifo et al.: Nucleus-Coma Structural Relationships 485

est here can tentatively be divided in two groups: (1) “jet (MCTP) used precedingly by this author and a few others,
jet interactions” (a classical problem in the design of multi- and not discussed here.] Finally, the three methods were
ple thruster rockets); here, two gas flows meet — if one used and compared in Crifo et al. (2002a). In these numer-
only is supersonic, it will form one steady shock; if both ous works, the boundary conditions at the nucleus differ:
are supersonic, two shocks will be formed (e.g., Ni-Imi et In all works except those by Crifo et al., the surface tem-
al., 1992); and (2) internally generated flows; here, the heat perature and H2O flux are prescribed arbitrarily (most often,
deposition effect is strong enough to create a shock transition the surface flux is assumed to be ∝ cos z ); in the works
to subsonic state; in principle, H2O recondensation could by Crifo et al., either a CO flux is prescribed arbitrarily, or
create such shocks. Shocks are the canonical examples of an H2O flux is derived from surface ice sublimation equa-
structures in a nonturbulent fluid. Hence, it is somewhat sur- tions. The greatest difference in these input assumptions
prising that the possible connection between shocks and regards the nightside surface, which is either assumed to
coma structures was only first suggested by Kitamura be inactive, or assumed to produce a uniform background
(1990). However, geometrical constraints and strong nona- flux of gas representing either a very small, or a sizable,
diabatic effects exist in the coma only at a short distance fraction of the total dayside flux.
from the nucleus surface (abundantly illustrated below), a The computed structure of the dayside gas and dust coma
region not accessible to observations except in flyby and is trivial (see Fig. 2) — notice, however, that a “gas velocity”
rendezvous missions. Even then, one essentially observes or a “dust velocity” does not exist; both quantities are po-
dust — not gas — structures, and dust cannot form shocks; sition-dependent. On the contrary, the nightside structure
it is surely not intuitive that near-nucleus dust structures can be extremely complicated, as Fig. 2 indicates. It pro-
trace gas structures, and an understanding requires advanced vides an ideal benchmark to discuss how the gas coma is
simulations of the kind described below. formed, and with which accuracy it can be modeled. This
All presently published physical model results refer to led Crifo et al. (2000) to systematically simulate the range
the near-nucleus coma. However, because of the scarcity of possible nightside conditions by varying the nightside
of space missions to comets, most coma structures observed ice surface temperature, hence the nightside background gas
are located at very large distances from the nucleus. Are production, using a heuristic parameter κ << 1: The ther-
they just the result of the evolution to large distances of the mal flux returned to surface elements in shadow is assumed
near-nucleus structures, or do they result from other struc- to be κc /rh2. Plate 10 shows the results. The ∝ cos z varia-
turing mechanisms? We address this briefly in section 8. tion of surface pressure on the dayside creates a lateral flow
from noon to midnight; in the absence of night background
6.1. Homogeneous, Spherical Nuclei (κ = 0), the nightside surface is a cold trap for the gas.
Therefore the flow from the dayside divides itself into one
“Spherical nuclei” have been considered as the only portion recondensing on the nightside and one portion es-
paradigm for at least a half century of cometary specula- caping in the nightside hemisphere. The division occurs
tions. In fact, isothermal spherical nuclei were assumed, along a flow line terminating on the midnight axis at a point
even though no explicit mention of it was ever made. While where the gas is at rest — a stagnation point. This gas at rest,
this absolutely forbids any comparison with observational as well as the gas reaccelerating upward and downward
data, it is still is a suitable paradigm to test new algorithms from it, form an obstacle for the arriving gas. Information
dedicated to a better physical representation of the coma cannot travel up a supersonic stream, so it cannot “guess”
(e.g., testing new radiative or chemical algorithms in the that there are obstacles ahead of it; it can only undergo a
simplest possible way: one-dimensional equations). Here sudden transition to a subsonic state where information is
we will not deal with such uses; instead, see Crifo (1991a) received from the obstacle. Hence, as visible on the upper
and references therein. left panel of Plate 10, a conical shock is formed in between;
On the other hand, it is not unreasonable for many pur- it is, in fact, a converging-diverging shock (its diverging part
poses to consider that the outer coma is axially symmetric, appears conspicuously on Fig. 2). A very weak nightside
as if produced by a sunlit, slowly rotating spherical nucleus. surface background emission is enough to suppress the con-
This has led to a number of two-dimensional spherical coma densation; the emitted nightside gas is now an obstacle to
models, of variable merit, starting with Krasnobaev (1983) the dayside gas, resulting in the formation of a weak con-
and continuing with Kitamura (1987), Kömle and Ip (1987a,b), verging shock attached to the terminator; inside the shock,
Köröszmezey and Gombosi (1990), Knollenberg (1994), the nightside gas accelerates rather slowly (Plate 10b). At a
Combi (1996), Mueller (1999), Crifo and Rodionov (1997a, somewhat higher background level, fast acceleration of the
1999, 2000), and Crifo et al. (2002a). In most works, EE nightside gas occurs (Plate 10c). The resulting supersonic
were used, but in Kitamura (1987) and Crifo and Rodionov stream interacts with the dayside one via a double shock
(2000), NSE equations were used as well. Combi (1996) structure; in between, sonic gas accelerates slowly outward
used for the first time a DSMC approach. [The DSMC (Plate 10c). Finally, a strong background creates the same
method discussed here should not be confused with the kind of double-shock structure, but now the midnight stream
much less powerful “test particle Monte Carlo method” stays supersonic all the way to infinity (Plate 10d).
486 Comets II

(a) (b)

(c) (d)

(e) (f)
dust trajectory intersection

artificial peak

Fig. 2. Coma around a sublimating homogeneous, spherical nucleus. The Sun is toward +X. (a) H2O number density. (b) H2O ve-
locity. (c) 9-µm-radius dust grain number density. (d) Dust grain velocity. For these computations, the night background emission was
assumed very low (κ = 0.01), so no nightside dust ejection occurred. (e) Trajectories of 2-µm-radius grains originating from various
local times. One can see that, beyond the terminator, the trajectories mutually intersect. (f) Dust density. One can see that density
peaks appear in the region of mutual trajectory crossings. On (e) and (f) (from Mueller, 1999), the night background is higher, and
night dust emission occurs. Mueller (1999) calls the computed peaks “artificial,” which may be misleading (see text).
 Crifo et al.: Nucleus-Coma Structural Relationships 487

(a) (b) interior heat transfer equations would introduce a surface

temperature asymmetry, making the coma fully three-di-
mensional; in this sense, even the spherical, homogeneous
nucleus still remains incompletely modeled today.

6.2. Inhomogeneous Spherical Nuclei

Many decades separated the first heuristic suggestions

that dust structures could be due to nucleus “active areas”
from the first gas dynamic simulations of the effect (Kita-
mura, 1990). Figure 3 shows most inhomogeneous spherical
(c) (d) nuclei submitted to gas dynamic simulations to the present
date.
The first computation was due to Kitamura (1986): One
circular “active spot” defined by a Gaussian variation of the
icy area fraction f = G(z ) is considered at a time when the
Sun is on its axis. This assumption provides computational
simplicity but not optimal significance. The author solved
NSE equations for the gas. Plate 11a shows the gas distribu-
tion for a small spot surrounded by a strong uniform back-
ground: The formation of a conical weak shock (in reality
Fig. 3. Examples of spherical inhomogeneous nuclei treated in a double-shock) appears clearly, matching the source flow
the literature. (a) Kitamura (1990) and Crifo et al. (1995); to the background flow (and transforming the on-axis den-
(b) Kömle and Ip (1987a,b) and Knollenberg (1994); (c) Keller sity maximum quickly into a minimum). Plate 11b shows
et al. (1995); (d) Crifo and Rodionov (1997a). The dark areas are what happens if dust is introduced: Dust density maxima
assumed strongly active, the rest is assumed weakly active, or are formed along the gas conical shock (on an image, the
inactive.
dust would appear as “emanating from two close active re-
gions”).
Knollenberg (1994) revisited the same problem, but as-
sumed another kind of background, ∝ cos z on the day-
In real comets, a substantial night background produc- side, and vanishing in the nightside. He solved EE equations.
tion is expected from the nightside surface (for instance, Plate 11b–d shows the result. One recognizes, on the night-
from CO production, but other molecules are probable as side, the zero-background converging-diverging conical
well, e.g., CO2, HCN, etc.). Therefore the flow structure shock of Fig. 2 — the nightside is not sensitive to details
should resemble that just described, save for the fact that of the dayside gas production. On the dayside, a conical
the molecular composition will differ on the dayside and (double) shock is clearly visible, similar to that in Kitamura
on the nightside. (1986). When dust is introduced — on the dayside only,
The steep gas structures just evidenced (weak shocks) since there is no nightside background — it forms conspicu-
are found to translate themselves into dust structures, due ous enhancement in the vicinity of the gas shocks, for the
to the fact that the dust particles are too heavy to accurately reason already stated.
follow sudden changes in the gas direction: The trajecto- Kömle and Ip (1987a,b) considered a circular ring of
ries of grains originating from both sides of the gas struc- increased activity, with Gaussian profile, superimposed on a
tures, and moving toward it, cross one another, creating a two-step background (i.e., one dayside value and one night-
localized dust density enhancement. This is indeed found side value), with the Sun placed on-axis. Unfortunately, we
by most authors (when not found, inaccurate computational have verified by an unpublished recomputation that, as the
algorithms are to be blamed). For instance, Fig. 2e shows authors suggest in their paper, their computational technique
grain trajectories in the terminator shock region, where the was inaccurate. Therefore, we prefer to comment here on the
gas velocity is about similar to that seen on Plate 10 (lower related (and highly accurate) results of Knollenberg (1994);
right panel). The sudden change in gas direction cannot be see below.
reproduced by the dust; instead, one sees dust trajectories The first paper to explicitly identify as shocks the gas
mutually crossing and a resulting dust density enhancement density enhancements created by surface flux inhomoge-
(Fig. 2f). It is evident that on an image, these enhancements neities was Kitamura (1990). Most importantly, this is also
would be called “jets,” and one can see that such “jets” do the first three-dimensional computation of a coma (EE were
not trace any dust grain trajectory, nor indicate the presence used). Two square spots are placed symmetrically about the
of any active area. noon axis on an inactive background (see Fig. 3a). Figure 4
Further complication in the nightside coma structure shows the results, as recomputed by Crifo et al. (1995). The
would be introduced if one took into consideration a nu- supersonic gas jets from the two sources interact strongly,
cleus rotation: Coupling the gas dynamics to the nucleus forming a V-shaped double-shock structure (in the symme-
488 Comets II

(a) (b)

(c) (d)

Fig. 4. Spherical nucleus with two identical active areas (Kitamura, 1990; Crifo et al., 1995). (a) Isocontours of the gas density;
(b) isocontours of 0.1-µm-radius grain dust density, computed from single-dust-fluid equations. (c) Same, on an enlarged geometrical
scale; (d) same, computed from two-dust-fluids equations.

try plane). [Outside the symmetry plane, the double-shock rect. In more complicated geometries, in the interaction re-
structure is quite complicated in shape, owing particularly gions many different directions of dust motion may exist,
to the square shape of the sources (A. V. Rodionov, unpub- requiring the use of many dust fluids. (This requirement
lished data, 1998).] This is very similar to what is observed should not be confused with that of also using different dust
in multiple thruster rocket motors (e.g., Ni-Imi et al., 1992). fluids if different kinds of dust grains are considered.) This
If dust is introduced in the flow, the result can be seen in quickly becomes unmanageable, and one has to content
Fig. 4d. One can see, once more, that neither the two den- oneself with the indicative one-fluid (per dust type) method,
sity pencils at the edge of the central dust density enhance- or use a DSMC.
ment, nor the enhancement itself, project themselves to the Knollenberg (1994) considered a problem resembling
active spots. The origin of the central enhancement follows that of Kömle and Ip (1987a,b): An active circular spot is
from the fact that the dust emitted by the left spot covers placed on an inactive surface (no background; see Fig. 3b).
the angular sector 75°–>130°, while that emitted from the His computed gas distribution is shown on Plate 12. It was
right spot the sector <50°–105°; this means that in the re- later recomputed by Rodionov and Crifo with strictly iden-
gion 75°–105° at each point there are two different direc- tical (unpublished) results, which we use to display addi-
tions of dust motion. In other words, dust density maxima tional details of the solution. The supersonic gas converging
do not reveal dust trajectories; furthermore, there is noth- from the ring to the axis “interacts with itself,” forming a
ing like a “dust velocity direction” since dust grains moving diverging conical weak shock with apex at a small distance
along distinct directions coexist. Mathematically speaking, over the surface. Below this apex a complicated low-veloc-
two different sets of governing flow equations must be ity (subsonic) region is formed close to the symmetry axis
solved — a so-called “two-fluid model.” This was done in over the inactive surface; it includes a circular stagnation
Crifo et al. (1995) but not in Kitamura (1990). The result line, parallel to the surface and centered on the axis, around
is that the dust density distribution in Kitamura (1990) is which the gas whirls (the flowlines form a torus). Inside
not accurately computed in the interaction region (Fig. 4b). the conical shock, the slow gas is reaccelerated, forming a
However, the position of the density enhancement is cor- “daughter jet.”
 Crifo et al.: Nucleus-Coma Structural Relationships 489

It is to be expected with such a gas flow structure that shocks similar to those discussed above, and illustrate for
all dust trajectories starting from the inner edge of the ac- the first time (owing to the three-dimensional capability of
tive ring are directed toward the axis and mutually inter- the numerical code) the deformation of the near-nucleus
sect there. The vicinity of this axis is thus expected to be a coma with changing solar direction.
region of enhanced density. This is indeed what Knollenberg To conclude this quick overview, let us address the al-
(1994) finds using (appropriately, but without saying it) a ready mentioned configuration proposed in Knollenberg et
Monte Carlo simulation (Plate 12b). This is probably the al. (1996) to account for the gross Halley dust coma ap-
most spectacular confirmation of the basic fact — already pearance during the 1986 Giotto flyby (Fig. 3c). These au-
hinted at by Whipple (1982) — that the vertical of an inac- thors compute the gas and dust distribution from the three
tive spot must be a dust-density maximum. proposed unequal circular active areas as if they were alone
It should be noted that the symmetry that is present in with the Sun on-axis, and then add up the resulting dust
all the preceding solutions is quite artificial: It follows not densities. Instead, Plate 13 shows the gas flow correctly
only from the asumption of a very simple nucleus geom- computed from solving in three dimensions the EE, and the
etry, but also from the equally strong assumptions of (1) so- dust flow computed from a four-fluid model — one fluid
lar illumination along the symmetry axis or (2) absence of for each area, plus one for the background (Crifo and Rodi-
illumination control of the gas production. The first assump- onov, 1998). One sees that the results do not resemble three
tion is not possible because of the nucleus rotation, and the similar structures. First, the difference in solar zenith angle
second would require day-night symmetry in the appearance between the areas results in strong deviations between the
of the coma. gas (and dust) outflow patterns from one another, and from
The results remains that (1) small inactive areas create that of an isolated on-axis illuminated jet; second, the gas
usually coma dust density peaks, not minima, and (2) dust- jets from the three areas interact, forming weak gas shocks
density maxima do not trace only surface production max- and secondary dust-density maxima. But, as we shall see,
ima, but gas shocks as well. there is another, fundamental reason why such a model
Crifo et al. (1995) added to their duplication of Kita- cannot account for Halley’s coma: Halley’s nucleus is any-
mura’s (1990) work the case of three aligned identical thing but spherical, and the outflow from a sphere cannot
sources, with the Sun on the symmetry axis. In such a case, be “pasted by hand” on any aspherical body.
two “secondary” gas jets are formed in between the sources,
and these two gas jets themselves interact at a greater alti- 6.3. Homogeneous, Aspherical Nuclei
tude, to create “second-generation” weak gas shocks. The
dust is not sensitive to these second-generation structures It is evident that cometary nuclei cannot be spherical,
(at least at the moderate production rates considered) be- hence the investigation of aspherical nuclei is the central
cause gas-dust uncoupling has already occurred. Crifo and requirement of cometary activity models. This raises im-
Rodionov (1997a) use the four equal rectangular active mediately the question of down to which scale one wants —
areas shown on Fig. 3d for several directions of solar illu- or can — simulate a nucleus. Figure 5 presents examples
mination. The results, of course, reveal the formation of of shapes that have been subject to investigation to date.

(a) (b) (c)

(d) (e) ( f)

Fig. 5. Examples of aspherical homogeneous nuclei treated in the literature. (a) Triaxial ellipsoid (Crifo et al., 1999; Crifo and Rodionov,
2000); (b) bean-shaped nucleus (Crifo et al., 1997b, 1999); (c) apple-shaped nucleus (Crifo et al., 2003a); (d) top-shaped nucleus
(Crifo et al., 2003a); (e) Muinonen shape (Crifo et al., 2003b); (f) Halley nucleus (Crifo et al., 2002b; Rodionov et al., 2002).
490 Comets II

[To this one should add that Rodionov et al. (2002) have also smooth out such details. For the in situ sampled data,
also studied about 17 different shapes derived from the however, it is evident that surface modeling down to the
Halley shape shown in Fig. 5 by additional and more-se- metric scale will be required.
vere spatial filtering, and that several variants of the so- Not only are real nuclei aspherical, but they cannot be
called “Muinonen shapes” have been studied in Crifo et al. uniformly convex, as with all other small bodies of the solar
(2003b).] One sees that at the present time only relatively system. Common sense indicates that the flow of gas over
smooth shapes have been considered. This is due in part to or near a totally convex object must be much simpler that
mathematical limits, but also partly because the best Halley that around or near an object with concavities. Hence, maxi-
nucleus image resolution was only =50 m. The recent im- mum attention must be paid to the latter.
ages of part of the surface of P/Borrelly (and of most of 6.3.1. Triaxial ellipsoid. A nonspherical, but still con-
the surface of P/Wild 2) reveal that the surface is rich in vex, nucleus can be considered to be merely a variant of
very small topographic features. It may be expected that the the spherical nucleus: Figure 6 shows the case of a triaxial
fine gas structures expected from fine topographic details ellipsoid assumed either to outgas CO in a nearly uniform
will be quickly filtered out by collisional smoothing, mak- way, or to produce H2O through surface sublimation [see
ing the use of a smoothed surface suitable for modeling an a detailed description of the latter in Crifo and Rodionov
imaged coma, given that line-of-sight integration should (2000)]. In the first case, one observes density kinks at the

(a) (b)

(c) (d)

Fig. 6. The coma around an homogeneous triaxial ellipsoidal nucleus. (a) Gas temperature at heliocentric distance of 3 AU. (b) Gas
temperature at heliocentric distance of 1 AU. (c) Gas number density at 3 AU; (d) gas number density at 1 AU. At heliocentric dis-
tance of 3 AU, it is assumed that CO diffuses out with a nearly uniform surface flux; at heliocentric distance of 1 AU, it is assumed
that H2O is sublimated, the Sun being in-plane in the direction of the angular graduation 45°; the nightside background parameter is
κ = 0.0275.
 Crifo et al.: Nucleus-Coma Structural Relationships 491

tips of the ellipsoid, and relatively smooth bulges over the an inclination of the shock structure toward the Sun. The
flatter sides of the nucleus. This is in accordance with the associated enhanced dust-density region is formed, as in the
fact that the local surface radius of curvatures scales the Kitamura (1990) case, by overlap between dust from the
local near-surface flow, as explained in Crifo (1991a). Of two subsolar areas. We will return to this coma below when
course, such kinks will lead to the formation of dust den- discussing the effect of the nucleus rotation.
sity enhancements owing to the trajectory-crossing effect 6.3.3. Apple-shaped nucleus. All preceding results,
described previously. In the second case (solar-driven sub- whether referring to comets near 1 AU from the Sun, or to
limation), the day-to-night pressure difference is enough to larger distances (Crifo and Rodionov, 1997a,b, 1999), were
blow away the kinks at the tips, at least for the adopted obtained from EE equations insensitive to the absolute gas
direction of illumination. As for the general coma layout, density. However, fluid interactions disappear at vanishing
let us observe what turns out (from many yet unpublished gas densities. Crifo et al. (2002a, 2003a) have started to
computations) to be a general behavior: (1) the nightside investigated down to which low levels of gas production
coma is structured around the antisolar axis, and has the the weak shocks computed from EE are real. The method
same complicated patterns as in the spherical case, but dis- used is to compare NSE results with DSMC results. For this
torted; (2) the dayside coma is not structured around the purpose, shapes somewhat simpler than the bean were con-
solar direction, but more around the normal to the flattest sidered, e.g., “apples” and “tops” (cf. Fig. 5). The surprise
area of the surface (minimal curvature), again a consequence was that new effects were discovered during this work —
of the local curvature scaling just mentioned. and now it is not known up to which high level of gas pro-
We may expect that, during the nucleus rotation, in the duction they persist!
case of CO diffusion a nearly invariant density pattern co- Figure 8 shows the flow inside the sunlit cavity of an
rotates, whereas in the case of H2O sublimation, the day- apple-shaped homogeneous icy nucleus with characteristic
to-night density asymmetry will persist, although modulated size =15 km and assumed near the orbit of Jupiter (its com-
by rotation-induced deformations (we return to this in sec- puted total H2O production rate due to sublimation is Q =
tion 6.5). Note that in the CO case there is, however, a sig- 3.3 × 1026 molecules/s). One notices first that this flow is
nificant day-night asymmetry in gas temperature (due to the separated from the external flow (relative to the cavity) by
corresponding surface temperature asymmetry), and there- the separating streamline eB, where B is a stagnation point
fore a significant day-to-night velocity asymmetry (not on the axis, and e is on the surface; this means that no gas
shown). In the H2O case, the temperature (hence velocity) from the cavity escapes to free space! The flow inside the
asymmetry are quite small, due to the temperature buffer- cavity divides itself into two closed cells: one is the trian-
ing effect of the sublimation. gular cell aAc, where a is the bottom of the cavity, A a
6.3.2. Bean-shaped nucleus. As stated earlier, the second stagnation point on the axis, and c a point on the
smooth gas flow possible around smooth, convex nuclei is surface (see Fig. 8c); the second cell is the rectangular cell
impossible around realistic objects, because they have con- cABe (see Fig. 8a). In the first cell, the gas emitted from
cavities; furthermore, in the solar-driven sublimation case, the segment ab (representing 0.06% of Q) is recondensed
the pattern of shadows associated with the concavities sub- on the segment bc, without acceleration to supersonic state.
divides the gas production into “effective” discrete active In the second cell, the gas emitted from de (representing
areas. For these two reasons, even a homogeneous noncon- 0.2% of Q) is recondensed on dc, in part supersonically.
vex nucleus is expected to produce a coma structured by Notice that the two flows inside the two cells rotate in op-
weak gas shocks. The pattern of these shocks will change posite directions, as in convection cells. One additional
during the rotation, following changes in the dayside shadow feature of this fantastic flow structure is the presence of
pattern. With this in mind, Crifo and Rodionov (1997b), for three sonic lines (SL1, SL2, SL3) transverse to the sym-
the first computation of a nonconvex nucleus, designed the metry axis. Note also the broad size of the subsonic region
“bean” shape shown on Fig. 5b. This shape has two planes (shaded on Fig. 8). Thus we see that, even though the cav-
of symmetry, hence an axis of symmetry. [This shape was ity surface is fully illuminated by the Sun, there exists a
also used for two-dimensional + 1/2 heat transfer compu- band db where it condenses the ambient gas; this trapping
tations by Guttiérrez et al. (2000).] Figure 7 shows the gas effect explains why the cavity flow is confined inside the
and dust-number density in three mutually perpendicular cavity, in spite of its wide opening. Such a flow trapping
planes across the nucleus, under solar illumination from a was not observed in the existing “bean” simulations, prob-
direction inside the main symmetry plane. The dust was ably because this cavity has the shape of a saddle, i.e., is
computed from a two-fluid-per-size algorithm. much more widely open to free space. On the other hand, it
There are two maxima of gas production around the two is not yet known whether the effect disappears in the “apple”
subsolar points, and the two associated flows from their at small heliocentric distances, and appears in the “bean”
vicinity interact to form two shock structures (of roughly at very large distances.
hyperbolic shape). For the selected orientation, there is not Note that in the inner cell the Knudsen number Kn = 1
yet partial shadow inside the cavity, but the left flank has (cf. Fig. 8d); also, our approximating BE-NSE approach to
less inclined illumination than the right flank, so there is handle the near-surface conditions, based on nearly plane-
an overall pressure gradient toward the Sun, which induces parallel sublimation or condensation, is here in principle
492 Comets II

(a) (b)

(c) (d)

(e) (f)

Fig. 7. Structure of the gas and dust coma around a bean-shaped nucleus (Crifo and Rodionov, 1999). The top panels show the main
symmetry plane XOY; the Sun direction is in this plane, at the graduation 45°. Bottom panels show the secondary symmetry plane
YOZ and plane XOZ. The lefthand panels show the decimal logarithm of the gas number density; righthand panels show the decimal
logarithm of the dust number density (9.11-µm-radius grains).
 Crifo et al.: Nucleus-Coma Structural Relationships 493

(a)
(b)

(c)
(d)

Fig. 8. Comparison between BE-NSE and DSMC solutions for an apple-shaped nucleus (Crifo et al., 2003a). The Sun direction is
to the right. (a) Flowlines (thin lines with arrows), sonic lines (dashed: DSMC; continuous: BE-NSE), and subsonic regions (shaded).
(b) Log10(gas number density). (c) Flowlines (thin: BE-NSE; thick: DSMC), sonic line SL3, and subsonic region (shaded), on an
enlarged scale. (d) Log10(Knudsen number).

invalidated by the fact that the two effects coexist at neigh- symmetric and the Sun on-axis, so is the dust density, which
boring points. Even so, an impressive good agreement be- thus is obtained by rotating the symmetry plane distribu-
tween the BE-NSE and DSMC solutions is obtained. tion around the symmetry axis; a narrow on-axis centered
Finally, as to the disappearance of weak shocks at very conical pencil of dust is formed (instead of two quasihyper-
small production rates, it was observed in the simulations, bolic surfaces for a “bean”). Of course, this simplified ge-
but this does not mean that structures in the gas density ometry is broken as soon as the Sun leaves that axis.
disappeared: Even in strict free-molecular outflow the gas 6.3.4. Top-shaped nucleus. Figure 9 shows the com-
density is quite uneven, hence dust small enough to be puted gas and dust distributions when the Sun is on the
dragged away will exhibit sharp distribution structures. symmetry axis of a top-shaped homogeneous icy nucleus.
The dust distribution created by the apple-shaped nu- The presence of a partially shadowed cavity creates two
cleus for on-axis illumination of its cavity resembles very separate gas jets whose interaction produces weak shock
much that obtained from the bean shape in its main sym- surfaces (one crosses the circular graduation near 70°, the
metry plane (Fig. 4 of Crifo et al., 1997b), with one no- other near 20°). Then, the dust is thrown into a conical
table difference: Because the “apple” nucleus is rotationally pseudojet in the vicinity of this interaction. The conical
494 Comets II

(a) (b)

Fig. 9. Gas and dust distribution around a top-shaped nucleus. (a) H2O number density (Crifo et al., 2003a); (b) 9.10-µm-radius
dust grain density (A. V. Rodionov, unpublished data, 2003). The Sun is to the right, on the horizontal axis.

geometry will be broken for off-axis illumination. The dust structuring the coma, or whether one is dominant. There is
density shown here was computed from a single-dust fluid at the present time no universal answer to such a question,
approximation, and therefore is only indicative of the cor- in view of its extreme difficulty. Only the case of Halley’s
rect distribution, as discussed previously. nucleus has been studied (Crifo et al., 2002b; Szego et al.,
6.3.5. Realistic shapes. While consideration of simple 2002). The complexity of the gas coma, even assuming
shapes are a must for demonstrating the basic physical pro- Halley’s nucleus to be homogeneous, can be judged on the
cesses at play in the near-nucleus coma, realistic comas can two left gas density panels (b,d) of Plate 14, corresponding
only be produced by consideration of plausible nucleus to two different image planes and solar illumination direc-
shapes. Unfortunately, there exists no bank of cometary tions. Plates 14b,c show the same information if the nucleus
nucleus shapes from which the expression “realistic” could is assumed to have the random distribution of Gaussian cir-
be defined, since only P/Halley’s nucleus shape has been cular active areas of average size comparable to the size of
determined (Keller et al., 1995; Szego et al., 1995, and ref- the topography details, shown on Plate 14a. Unexpectedly,
erences therein). Part of P/Borrelly’s nucleus has been re- the differences are very minor. In particular, most weak
cently imaged, but the whole shape is not known, hence shocks are present in the two cases, at about the same lo-
the computation of the gas flow even assumed to emanate cation. Of course, it is premature to generalize this result
only from that part is impossible. It is hoped that the re- to all conceivable nucleus shapes, inhomogeneity patterns,
cently acquired images of P/Wild 2 will provide the sec- and solar illuminations. Yet we believe that this result is ex-
ond full nucleus shape. At any rate, within the frame of the tremely instructive. It suggests that, at least for P/Halley’s
Rosetta mission definition studies, it is necessary to have a nucleus, only extreme assumptions with respect to the in-
set of “plausible comas” at hand. For that purpose, Crifo homogeneity could significantly manifest themselves in the
et al. (2003b) have considered nuclei having random shapes coma structure. Even though this was not yet computed, it
with the same statistical topographic properties as those of is unlikely that the three-active regions pattern of Plate 11
the imaged asteroids, following Muinonen (1998) and Mui- placed in any manner on Halley’s nucleus will produced
nonen and Lagerros (1998). An example of one such shape anything like the sum of three isolated cylindrical jets. We
is shown in Fig. 5e. Such shapes were also used for thermal will see in section 7.2 how the results of Plate 14 compare
modeling in Guttiérrez et al. (2001). The computed comas with the observations.
are complicated, as is the topography. We will not discuss
them here, but will focus on the equally complicated case 6.5. Influence of the Rotation
of P/Halley’s nucleus, discussed in sections 6.4 and 7.2. on the Coma Structure

6.4. Inhomogeneous, Aspherical Nuclei Plate 15 shows the deformation of the near-nucleus dust
coma around a bean-shaped nucleus with a simple rotational
A real nucleus can be expected to be both complicated motion (no precession or nutation). One sees that the V-
in shape and inhomogeneous in composition. Since both shaped structures rotates, but at a slower rate than the Sun,
effects lead to a structured coma, one does not see on which and with deformation, until disappearance for part of the
basis the observation of structures should be automatically rotation. This is an extreme example, however; for a case
attributed to compositional homogeneity. The question in where the Sun would rotate on a cone with axis tilted to the
fact arises whether these two effects contribute equally to “bean” axis, one can anticipate (based on the result showed
 Crifo et al.: Nucleus-Coma Structural Relationships 495

here) that the V-shape structure will rotate nonuniformly, change its appearance (as shown in Plate 15). If one insists
with deformation, but without disappearing. The important that the observations require a rigidly rotating gas jet, then
point is that the apparent axis of rotation will not be that the gas production should not be due to solar control, and
of the nucleus, and that its apparent angular velocity will therefore there should be no difference in observed activ-
not be its real angular velocity. ity between the day and nightsides of the nucleus, contrary
It is important to notice that the behavior of the near- to observations.
nucleus coma just shown differs from that of the distant 4. Inner coma dust structures are always associated with
coma: The latter is a consequence of the evolution of the the gas structures of the inner coma. The formation of ad-
former during one or several nucleus rotation(s). For the ditional near-nucleus structures due to fluctuations of the
dust, the physical process is the standard collisionless ef- dust concentration in the ice (i.e., a varying dust load in the
fusion in the solar gravity field reduced by radiation pres- gas flow) is possible, but, to interpret observed near nucleus
sure. Hence, from the results shown on Plate 15 one can dust structures, one must first determine which structures
independently compute the outer coma dust distribution at trace gas structures, and only when they have been identi-
any point and time. Such is not the case for the gas coma, fied can the remaining ones be attributed to dust-load in-
as its collective behavior usually extends to very large dis- homogeneities.
tances; one can only compute at once the time-dependent 5. Dust structures resulting from gas structures do not
structure of the whole coma. We return to this in section 8. trace dust grain motions; quite the contrary, they trace dust
trajectory intersections. Their projection to the surface does
6.6. Conclusion: Formation of the not bear any simple relationship to the pattern of dust pro-
Near-Nucleus Coma duction at the surface.
6. Tracing dust grains back to where they left the sur-
The preceding model results are significant enough to face across the gas-dust interaction region raises extreme
draw many robust conclusions concerning the formation of difficulties: One would need to know not only their mass,
the near-nucleus coma. Even though this region is rarely but their shape as well, and even their exact orientation in
observable, it is clearly impossible to accept any paradigm the coma.
concerning the currently observed outer coma that would 7. The impossibility of rotationally invariant near-nu-
violate any of these conclusions, which we summarize now: cleus gas structures implies a similar impossibility for the
1. The essential result is that the near-coma gas outflow near-nucleus dust structures.
is extremely sensitive to the surface topography. Roughly We will return in section 8 to the implications of these
speaking, “hilltops” and high-f areas create supersonic out- conclusions on the formation of outer coma (i.e., very large
flows, “valleys” and low-f regions bounded by high-f ones scale) structures. But first, let us see how the inner coma
create subsonic outflows, but simple rules to “guess” more model results compare to observational data.
precisely what the gas flow pattern is do not seem to ex-
ist — fluid dynamics cannot be guessed. Hence it would 7. MATCHING PHYSICAL MODELS
be physical nonsense to attribute near-nucleus gas structures TO OBSERVATIONAL DATA
(hitherto unobservable) to surface inhomogeneity only.
2. The gas outflow is a global property; there does not 7.1. Hyakutake Arcs
exist any physical mechanism by which some fixed struc-
ture (e.g., a conical jet) could be created at any given place, Figure 10 shows an example of the nightside coma gas
independently from the surrounding environment. Instead arcs observed in Comet Hyakutake. The arcs were also
of coexisting without changing when “placed” on a surface, detected in OH by Harris et al. (1997), but there was no
the structures created in insulation will unescapably be modi- associated dust feature. Both Harris et al. (1997) and
fied when placed in a surrounding environment, be it a back- Rodionov et al. (1998) postulated that the arcs could only
ground emission or some other similar structure. This is be the signature of an unobservable H2O structure formed
independent of how the gas is produced (surface sublima- as a consequence of an auxiliary source of H2O, but their
tion or subsurface diffusion) and independent of its chemi- approach and conclusions differ. The first group uses a
cal composition and production rate. The gas interaction by DSMC method and finds that, assuming a secondary point
definition does not stop at a small distance from the sur- source far from the arc, “they see no shock”; assuming a
face. Hence the paradigm of several simple, noninteracting linear source centered on the shock and aligned on-axis,
structures advocated in most heuristic models of the outer they obtain an arc. Rodionov et al. (1998), recomputing the
coma described previously is physically impossible. first assumption by a NSE method, do find a “viscous”
3. The assumption of one (or even more so, several) double-shock structure, resulting from the interaction be-
rotationally-invariant gas jet structure(s) modulated only in tween the supersonic flow from the main nucleus and that
magnitude by a cos z factor (found in many heuristic in- from the secondary source. The word “viscous” alludes to
terpretations) is physically impossible; if there is such a the fact that, because of the high gas rarefaction, the ca-
solar modulation of the surface gas flux (as is the case for nonical double-shock (visible on Plate 13, left panels) is
solar-driven gas production), then the “jet structure” will smoothed into a single structure. Figure 10 shows the re-
496 Comets II

(a)

(b)

Fig. 10. Hyakutake’s coma on March 26, 1996, after Rodionov et al. (1998). (a) Computed H2O number density (top); Mach num-
ber (center); computed OH number density (bottom); the observed OH arcs are similar to the observed C2 arcs. (b) C2 + dust (top);
dust only (center); C2 only (bottom). Notice the bright spot on the antisolar axis, visible in the center image.
 Crifo et al.: Nucleus-Coma Structural Relationships 497

sult of the computed interaction (assuming a secondary (a)

source representing some 10–20% of the total H2O produc-
tion). This solution is not unique, but it reveals the Hyaku-
take arcs as the first evidence of weak gas shocks in a coma.
Even more importantly, it gives confidence in the validity
of the previously described modeling results, acquired un-
der much denser gas conditions: Near a dayside nucleus
at 1 AU, the gas number density is O (1013) cm–3, while in
the stagnation region of the Hyakutake arcs it is computed
to be O (108) cm–3 only (see Fig. 10). This corresponds to a
Knudsen number O (10–1), quite convenient for the validity
of the NSE approach (see Crifo et al., 2002a, 2003a). The
quoted statement of Harris et al. (1997) that their DSMC
result “does not see a shock” suggests some technical in-
adequacy in the implementation of their DSMC code.

7.2. P/Halley Near-Nucleus Dust Coma

The greatest of all possible challenges to a coma model

was offered by the famous HMC synthetic image of Hal-
ley’s nucleus and its vicinity (Keller et al., 1995, and ref-
erences therein). As stated earlier, this image has been
unanimously — but without any supporting model compu- (b)
tation — interpreted as “visual evidence” that “the activity
is confined to localized regions.” However, “activity” means
surface flux, and we do not “see” dust fluxes on images;
we see dust column densities (more or less proportional to
the local density, near to the surface). But near the surface,
the dust is coupled to the gas. Observing dust in natural
flows (e.g., snow blown on an icy surface, or desert dust
blown by winds) is enlightening here: Dust accumulation
often reveals flow stagnation regions, rather than high flux
regions. There is no intuitive way to reliably infer flux from
density; inferences must be checked by quantitative mod-
eling.
The three-sources-on-a-sphere paradigm of Knollenberg
et al. (1996) described in section 6.2 was offered in sup-
port of the classical interpretation, but we remind the reader
of the weaknesses we have discovered: (1) the interaction
Fig. 11. Interpretation of the near-Halley-nucleus dust coma
between the outflows from the three regions cannot be structures observed by the HMC camera (Crifo et al., 2002b).
neglected, and (2) the control of the outflow by the topog- (a) Azimuthal brightness gradient map derived by Keller et al.
raphy cannot be neglected — it is in all likelihood domi- (1994). (b) 0.91-µm-radius dust grains column density, computed
nant. It is also evident that this model, which assumes a by the present model assuming P/Halley’s nucleus to be strictly
spherical surface, cannot be matched to the central part of homogeneous with f = 0.6.
the HMC images, which resolve a highly aspherical nucleus.
The “filament” map derived by Keller et al. (1995) us-
ing enhancement techniques is reproduced here in Fig. 11a.
Knollenberg et al. (1996) proposed that each filament is the one wanted to state that the gas outflow does not depend
signature of a small-circular-inactive-area, in accordance upon solar illumination, how then could one explain the
with Plate 12. Here again, we must point out the weaknesses vanishing activity observed on the nucleus nightside?
of this explanation: (1) The narrow collimation of the dust Crifo et al. (2002b) have offered a related, but self-con-
pencil obtained requires a strict cylindrical symmetry. This sistent interpretation of the “filament” array. They observe
cannot be achieved by groups of closely positioned spots, that the visible-light HMC images are sensitive to all dust
as would be required; even the symmetry of an isolated spot masses, and it is clear that the dust trajectories depend upon
will be ruined by the irregular topography of the surface their mass; furthermore, nonspherical grains have trajecto-
where it lies. (2) Obviously, the Sun also cannot be placed ries totally different from spherical grains of the same mass.
simultaneously on the axis of many distinct spots. And, if Thus, the simplest bet one should make when looking at
498 Comets II

this map is that one sees the signatures of weak gas shocks, The equations of rotational motion were integrated by
since this signature is due only to the difference in inertia Szego et al. (2001), based on the three nucleus orientations
between dust grains and gas molecules, irrespective of grain indicated by the imaging experiments during the flybys of
size and shape. This signature, being independent from dust Vega 1, Vega 2, and Giotto, with due allowance for the
grain size and shape, can be discovered by “numerical trac- outgassing torque. Assuming a nucleus density 0.5 g/cm3,
ing”: At the laboratory, one would inject calibrated dust the torque is about a 5% large correction term for the equa-
(i.e., single-size, spherical grains) in the flow. Here, we can tions of rotation. Due to this torque, the direction of the
numerically simulate the injection of such calibrated dust. angular momentum vector is changed by ~11° in longitude
Furthermore, a single-fluid dust model can be used, even and 16° in latitude between August 31, 1985, and July 26,
though it does not provide the exact dust density in the 1986, i.e., from 3 AU AP to ~2.8 AU PP. The computed
structures, since it does provide the correct structure posi- rotation exhibits a basic rotation period ~2.2 d about the
tion. Crifo et al. (2002b) consistently computed the over- short axis of the nucleus, modulated by a 7.4-d long pe-
all gas outflow from the whole nucleus surface, using the riod. This model, despite its 7.4-d modulation, does not
nucleus shape derived from the images obtained by the reproduce the basic ~7.4-d periodicity observed in ground-
Vega 1 probe by Szego et al. (1995), and assuming the based observations (lightcurve, recurrence of jet patterns).
nucleus to be (to start with) compositionally homogeneous. Another rotation model has been derived by Belton et
Figure 11b shows the computed dust column density of al. (1991). It exhibits the requested rotation period of ~7.4 d
spherical grains of 0.91-µm radius, computed with a single- (found to be about the long axis of the nucleus). This model,
fluid model. Detailed comparison with the HMC map however, is obtained by flipping the orientation of the
(Fig. 11a) reveals the following: (1) The N1–N2 gradients nucleus during the Vega 1 flyby with respect to the observed
are reproduced with an angular offset of about 20°. (2) All one. This seems to be due to the fact that the authors did
other gradients, in particular U2, U3, U4, N4–N8, and S2, not use the processed Vega 1 images, but only the raw im-
are present in the model computation at the right position. ages, much less constraining.
This result is not significantly changed by changes in dust As already stated, Julian et al. (2000) and Szego et al.
grain size. It is, on the other hand, very sensitive to the nu- (2001) checked their P/Halley rotation models against a Q(t)
cleus orientation — which is not known to better than a few derived from a Haser formula. One can therefore question
degrees, hence the agreement seems surprisingly good. the satisfaction the two groups express regarding their fits.
So, for the first time in the history of cometary data This situation is not satisfactory, and work is in progress
analysis, dust coma structures are reproduced ab initio, i.e., to find a solution for the rotation of the nucleus that satis-
without ad hoc assumptions. The physical meaning of this fies all constraints (and hopefully all groups). It will then
agreement is also clear: The coma structures seen are the be possible to attempt an exact interpretation of P/Halley’s
signatures of gas flow discontinuities induced by the topog- lightcurve.
raphy.
Comparisons of a similar kind (partially published in 7.4. Gas “Velocity Law”
Szego et al., 2002) were made by the same authors with all
Vega 2 images (the Vega 1 images carry little information on In many cometary papers a so-called “Bobrovnikov’s
the near-nucleus coma) with even a more spectacular agree- velocity law” is advocated to evaluate “the coma gas veloc-
ment than that obtained by Giotto — but here, one will no- ity.” Keller (1954) quoted observations (without any tech-
tice that the resolution of the Vega 2 images is somewhat nical details such as the names of the comets that were
lower. observed) of “jets and haloes” by Bobrovnikov that were
later used by Whipple (1982) to derive the above-mentioned
7.3. Gas Lightcurves law. As far as we know, Bobrovnikov himself never pub-
lished such a result, even decades after this report. Indeed,
Gas lightcurves are obtained from summing the emis- this “law” seems to mix up observations of a quite differ-
sion of molecules within a cylinder of radius R (in kilome- ent nature: Anything moving is used. It is in particular quite
ters) (projected in the coma). One can compute that, if the unclear whether the observed motions are due to gas or to
gas velocity is on the order of 1 km/s, and the emission dust. Furthermore, many authors admit that this law (quite
roughly isotropic, about one-third of the molecules were expectedly) is violated by their data. Last, but not least, one
emitted over a time period R (seconds), and two-thirds over can read in Bobrovnikov’s (1931, p. 460) famous report on
a time period of 1 d (case of OH at 1 AU from the Sun). Comet Halley that “the assumption of a constant velocity
Thus, for a real nucleus rotating with a period approxi- of ejection is questionable. Data gathered in Chapter II in-
mately equal to a few days, a 3D + t model of the gas coma dicate rather wide ranges of velocities near the nucleus, from
coupled to a nucleus rotation model should be used to ex- several tenths to several km/sec.” The same statement is
tract a correct Q(t) from the gas lightcurve. At this time, duplicated in the conclusion of the report (p. 581).
we know of no comet for which such a task was done. As evidenced by the model results presented above, there
The best prospect for seeing such a work performed is is nothing like a “gas velocity” in a coma; this velocity varies
Comet Halley, since its complete nucleus shape is known from point to point. This is observationally evident in the
and good lightcurve data are available. high-resolution observations of molecular radiowave emis-
 Crifo et al.: Nucleus-Coma Structural Relationships 499

sions (e.g., Henry et al., 2002). As for the heliocentric de- brightness dependence, the reciprocal statement is incorrect:
pendence, it is straightforward to show that, in the case of Anisotropic dust-ejection patterns are capable of building
subsurface diffusion, the near-nucleus gas velocity is ∝rh–1/4; up an apparently isotropic coma with brightness slopes
in the case of surface sublimation, this dependence is neg- widely dispersed around the value –1, depending on the
ligibly small. For a discussion of outer coma gas velocities, direction of observation (Fulle and Crifo, 1999). Hence,
see Combi et al. (2004). from this point of view, the production rates derived with-
out knowledge of the nucleus shape should be treated with
7.5. Dust “Velocity Law” caution.

In some favorable cases, e.g., the observation of a dust 8. PHYSICAL MODELS OF THE
neckline structure (see Fulle, 2004), it is possible to derive OUTER COMA STRUCTURES
the terminal dust velocity from an analysis of the image
brightness. Most of the time, this is not possible. If one We have seen that (1) steady-state gas and dust solutions
wants to derive a dust mass loss rate from an observed image cease to be valid at distances in excess of typically 1000 km
brightness, it is then necessary to use assumed dust veloci- and 100 km, respectively, and (2) the gas-dust interaction
ties. For this purpose, a “dust velocity law” is often advo- is completed before 100 km, so that the gas and the dust
cated. Many variants of this “law” are circulated, includ- properties can then be computed independently; their outer
ing — as already pointed out in Wallis (1982) — some that coma structures need not bear any similarity. In both cases
are nothing but misprint propagations. Most variants pos- the following are required:
tulate isotropic gas and dust production, and they all as- 1. A physical (time-dependent) model must be used to
sume, quite unrealistically, that both the grains and nucleus compute the evolution of the gas and dust species distribu-
are spherical. An expression summarizing the presently tion with distance to the nucleus. We will not review such
discussed gas dynamic simulations of (nonisotropic) spheri- models in the present chapter. (For the gas in a comet like
cal grain ejection from a spherical nucleus is given in Crifo Hale-Bopp, solving the NSE is one possibility.) The gen-
et al. (1997a). Still, many heuristic parameters are present eral observation is, however, of interest, that this evolution
in this expression, for which different users will unavoidably always involves structure smoothing, as substantiated be-
choose differing numerical values when trying to represent low. Hence the more distant the observed regions, the less
real data. The resulting chaos in dust mass loss rate assess- suitable they are, in principle, for inferring detailed nuclear
ment was already pointed-out in Crifo (1991b) and will properties.
unavoidably persist until the missing information about dust 2. Time-dependent boundary conditions must be speci-
grains is available. fied at the distance where the steady-state solutions cease
More fundamentally, and as stated earlier, one must be to be valid. We discuss in detail these boundary conditions,
careful to remember that dust is an ill-defined concept — because, regardless of the quality of the outer coma model,
or, if one prefers, the properties of real cometary grains are the solution is just as valid as the boundary conditions used
unknown. It is true that large-scale coma structures can be are acceptable.
interpreted under the declared assumption of spherical
grains, but that does not prove that the real grains are spheri- 8.1. Large-Scale Dust Structures
cal. After decoupling from the gas, the grain motion is
controlled by solar radiation pressure and solar gravity. The Plate 13 shows that the evolution of the structures from
two effects do not distinguish the grain shape (a spinning the vicinity of the nucleus to larger distances is very dif-
irregular grain will exhibit an effective radiation pressure ferent for the gas and for the dust. The dust structures are
quite like a spherical one). Hence the success of outer coma quickly “frozen” into a fixed pattern (which changes with
fits gives no clue to what happens inside the gas-dust inter- the rotation phase). The gas structures are not at all frozen.
action region. Unfortunately, the ejection velocity of solids Large-scale dust structures can therefore be considered to
depends critically on their shape and even initial grain orien- be built up by free effusion from an “effective source” that
tation at the surface (see Crifo and Rodionov, 1999), hence is not the nucleus surface, but the terminal gas-dust accel-
the ejection velocity of real cometary grains from a real eration surface. It is perhaps not evident that this effusion
cometary nucleus can simply not be predicted at present, is a smoothing process, because it is a slow one: Smooth-
save in a crude order of magnitude. ing is caused by the fact that, at each point of the distant
coma, dust from all over the terminal surface arrives; only
7.6. Dust Lightcurves the unphysical myth of single-velocity, strictly radial dust
ejection can lead to unique point-to-point dynamical con-
As opposed to the case of the gas, 3D + t outer coma nections between the coma and the surface of the nucleus.
dust models do exist, but to make their use rewarding, nu- Even worse, dust from successive terminal surfaces during
clei shapes are missing. Remembering that dust production a sizable period (weeks) can possibly reach a given point.
rates are derived through the Afρ method, it is easy to show This evidently mixes up the terminal surface pattern.
that, while a spherical nucleus that would eject dust with As shown by Plate 13, this terminal surface has localized
perfect isotropy would build up a dust coma with a 1/r areas of enhanced dust flux, and indeed resembles Seka-
500 Comets II

nina’s (1981, 1991) “nucleus surface activity” maps. Hence, assumptions, and the test repeated. Only if it proves impos-
it is clear that what Sekanina and several other scientists sible to obtain a suitable result in this manner can one start
using the same method determine is, in reality, not a nucleus to introduce ad hoc “active dust.”
surface distribution, but this effective source distribution.
The difference in distances involved — O (100) km — is 9. CONCLUSIONS
much smaller than the spatial resolution in groundbased
coma images. One therefore easily conjectures why the The visionary prediction of Whipple (1950, 1951), that
authors are forced to turn “on” and “off” in an ad hoc way cometary activity is due to the solar-driven surface and
their “active regions”: This is most likely due to their at- subsurface sublimation of a solid nucleus dominantly made
tempt to fit a changing pattern (that at the terminal surface) up of the ices of a few simple molecules and of dust, is still
with a supposedly fixed pattern (assumed to be the nucleus the basis of our efforts to understand comets today. For
surface map). decades, the simple heuristic simplifications he made to
For the nuclei of unknown shape, there is definitely no derive orders of magnitude also remained the basis of most
possibility of passing from such “terminal surface maps” of the interpretations of the observational data. To some
to true “nucleus activity maps.” But for those with a known extent, this can be understood, as it was not possible to
shape (at this time, only P/Halley), this is possible. Work access detailed information about the nucleus and the dust.
in this direction is in progress within the frame of the In- With the implementation of deep-space missions to com-
ternational Space Science Institute “Halley” Team Work. ets, this situation is radically changing. It becomes possible
to picture the cometary nuclei as real solar system objects,
8.2. Large-Scale Gas Structures with their unavoidable extreme complexity. The price to pay
is that, to understand them, the simple heuristic approaches
For the gas, after the initial structuring by weak shocks, must be abandoned in favor of the use of the full arsenal
the persistence of the fluid behavior maintains a very effi- of the modern methods of applied physics. Even before the
cient pressure smoothing (Plate 13). If the expansion was avalanche of data from cometary orbiters is at hand, enor-
adiabatic, this smoothing would stop rapidly as p → 0 when mous efforts should be dedicated to adapting these meth-
T → 0. But the expansion is not at all adiabatic: The gas ods to the difficult problem of inferring properties of a real
pressure continues to be significant because of heating by nucleus from observations of its surrounding gas and dust
fast photodissociation products. Furthermore, the observed coma. We hope that the present chapter has convinced the
daughter species may have a distribution different from that reader that such an undertaking is (1) unavoidable, (2) chal-
of H2O due to partially nonlocal dissociation velocity damp- lenging, and (3) potentially rewarding.
ing. It is therefore quite unlikely that near-nucleus struc-
tures (at least density structures) be maintained far out in a Acknowledgments. This work benefited from many succes-
gas coma. (Velocity structures are, on the other hand, well sive yearly contracts from the French CNES and CNRS agencies,
preserved in supersonic state.) In all likelihood, large-scale from partial support from the Austrian “Fonds zur Foerderung der
“jets,” “shells,” and “spirals” are not the signatures of faint wissenschaft – lichen Forschung” under project P15470, and from
the Hungarian OTKA grant T 32634. The International Space Sci-
details of the gas production, but that of the rotationally
ence Institute in Bern is thanked for having supported an ISSI team
induced fluctuations in the total gas production. In the gov-
meeting dedicated to the work on P/Halley discussed in this chapter.
erning equations, this signature is induced by the Coriolis
force (in a nucleus-attached frame). The production fluctua-
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504 Comets II
 Rodgers et al.: Physical and Chemical Processes in Cometary Comae 505

Physical Processes and Chemical Reactions

in Cometary Comae
S. D. Rodgers and S. B. Charnley
NASA Ames Research Center

W. F. Huebner and D. C. Boice

Southwest Research Institute

A variety of physical and chemical processes are important in the comae of active comets
near the Sun. We review the principal physical processes occurring in the outflowing gas and
dust and their effects on thermodynamics of the coma. We describe the coupling between the
physics and the chemistry and emphasize that any accurate model of the coma must include
both. Chemically, there are a number of mechanisms capable of altering the initial chemical
composition of the gas escaping from the nucleus surface. We assess the importance of these
chemical processes, and discuss several recent models that follow the chemical evolution of
the coma gas. The ultimate aim of most coma studies is to understand the nature of the icy
nucleus, and we briefly review the major obstacles in using coma observations to infer the
nucleus properties.

1. INTRODUCTION concerned chiefly with the collisional coma, i.e., the inner
region where particle collisions affect thermodynamics and
Our knowledge of the composition and structure of com- chemistry of the gas. A rough estimate of the size of the
ets has come primarily from studies of their comae. Astro- collisional coma can be obtained by finding the cometo-
nomical observations of the coma can be made directly centric distance, r, at which the particle mean free path, Λ,
because small dust grains in the coma scatter and reflect equals r. For a Halley-type comet at 1 AU from the Sun,
light much more efficiently than the dark nucleus, and be- this distance is typically several thousand kilometers for
cause the outgassing molecules emit distinct spectral lines neutral-neutral collisions, and up to an order of magnitude
at specific frequencies. Although several space missions larger for ion-molecule collisions, due to the enhanced
have been sent to investigate comets, they have only probed cross-sections for ion-neutral interactions. The size of the
the nucleus indirectly via photographic imaging and low- collisional region is proportional to the total gas production
resolution spectroscopy. Not until the Rosetta mission sends rate, and so will increase as the comet approaches the Sun.
a lander to the nucleus of a comet will we be able to directly One can also loosely define a “molecular coma” within
access the material that resides in the nucleus. In contrast, which most molecules survive against photodissociation.
there exists over a century of data pertaining to observa- Strictly speaking, the size of this region will vary for differ-
tions of cometary comae. It is also interesting to study the ent molecules, since all species have different photodissocia-
coma for its own sake — it provides an environment im- tion lifetimes. For water (and many other species as well),
possible to duplicate on Earth, and can be used as a labo- the lifetime in the solar radiation field at 1 AU is ≈105 s,
ratory to test theories of gas and plasma dynamics and and so for a typical outflow velocity, v, of 1 km s–1 the mo-
photochemistry. Finally, the interaction of the coma with lecular coma will be ~105 km in size. For species such as
the solar wind can provide information on the properties ammonia and formaldehyde that are destroyed more rapidly,
of the solar wind and the interplanetary medium; in fact, the coma will be an order of magnitude smaller, whereas
the existence of the solar wind was first discovered via its more-stable species such as CO and CO2 will survive out to
interaction with cometary comae (Biermann, 1951). 106 km or further. Photodissociation rates are proportional to
the strength of the radiation field, and so molecular comae
1.1. Structure of the Coma will shrink as the comet nears the Sun.
It is important to stress that the coma gas is not gravita-
The coma is the cloud of dust and gas that surrounds tionally bound to the nucleus, and so the coma is a transient
the cometary nucleus. A schematic view of the coma struc- phenomenon. Because sublimation from the nucleus sur-
ture is shown in Fig. 1. The size of the coma depends on face is constantly replenishing the outflowing gas, the coma
how one defines it; for the purposes of this chapter, where can often appear stable and unchanging. However, sudden
we are discussing physical and chemical processes, we are changes in coma brightness and structure are common, with

505
506 Comets II

Fig. 1. Schematic illustration of the coma structure and its major physical regions for a moderate production rate at about 1 AU.
Note the logarithmic distance scale.

features changing rapidly over timescales of several hours. The densities in the inner coma are sufficiently large that
Spatial structures are also seen in many comae, often in both it is reasonable to consider the gaseous coma as a fluid, or
the gas and dust components (although the structure in both more accurately as a mixture of several fluids (neutrals, ions,
may not be the same). Further discussions of these phenom- electrons, as well as different populations of dust grains,
ena appear in Schleicher and Farnham (2004) and Combi and suprathermal photodissociation products; although these
et al. (2004). latter components are not strictly fluids they can typically
The interaction of the solar wind with the coma results be described in terms of hydrodynamic variables, i.e., veloc-
in complex structures in the plasma and magnetic fields (see ity and temperature). Hence, thermodynamic properties of
Neubauer, 1991; Cravens, 1991; Ip, 2004; Lisse et al., 2004). the coma can be calculated from integration of the standard
A bow shock develops in the solar wind on the sunward equations of fluid flow, assuming that the initial conditions
side of the comet; within this region the solar wind “picks at the nucleus surface are known (or can be estimated with
up” slow-moving coma species via charge exchange reac- some degree of accuracy). As the density decreases and Λ
tions. Eventually, as the wind encounters the denser gas in increases, the fluid description becomes less applicable, and
the inner coma it is decelerated, and at the cometopause it a transition to free molecular flow occurs. In this region,
is diverted laterally around the inner coma. The interplane- processes that affect a particular molecule cannot be as-
tary magnetic field also wraps around the comet, which re- sumed to affect the gas as a whole, and the properties of the
sults in a magnetic-field-free cavity surrounding the nucleus. outflowing gas are “frozen in” from the earlier collisional
The existence of this cavity in Comet Halley was demon- regime [see Crifo (1991) for a thorough discussion].
strated by Neubauer et al. (1986). The coma gas also interacts with the entrained dust, and
this affects both the dynamics and chemistry of the coma.
1.2. Physical and Chemical Processes in the Coma For example, gas-dust drag in the very inner coma decel-
erates the outflowing gas to subsonic speeds (Marconi and
Most of the processes that occur in the coma are initi- Mendis, 1983). Chemically, dust grains may account for the
ated by the solar radiation field. Photons at ultraviolet (UV) “extended sources” of some coma molecules, where obser-
wavelengths photodissociate and ionize the original parent vations require that these molecules are injected into the
molecules, producing “second-generation” reactive radicals, coma, rather than released directly from the nucleus (e.g.,
ions, and electrons. These ions and radicals can subse- Festou, 1999). This may result either from delayed subli-
quently react with other species to form “third-generation” mation of low-volatility material from the hotter grains, or
species. Examples include many of the protonated ions de- from the actual breakup of the grains themselves. From
tected by the ion mass spectrometer on the Giotto probe in measurements of the elementary dust composition in Comet
the coma of Comet Halley (Geiss et al., 1991). These pro- Halley it is known that a significant fraction of refractory
cesses are highly exoergic, and so can lead to species in particles consist of organic (CHON) matter (Kissel et al.,
excited states not normally populated at the low tempera- 1986). A variety of complex organics have been proposed
tures in the coma (T ≈ 10–200 K), as can direct absorption to account for this material (Huebner and Boice, 1997). In
of solar photons (fluorescent pumping). Figure 2 illustrates particular, Huebner (1987) proposed that polyoxymethylene
the most important processes occurring in the coma. (POM, the –CH2O– polymer) could account for the ex-
 Rodgers et al.: Physical and Chemical Processes in Cometary Comae 507

Fig. 2. The major radiative, physical, chemical, and thermodynamic processes comets, their coupling, and their interaction between
the various cometary components: nucleus, coma gas, plasma, and dust (Huebner and Benkhoff, 1999).

tended source of formaldehyde in Comet Halley. Other The first simple analytical model of molecular distribu-
macromolecules proposed to be potentially important in the tions in the coma was published by Haser (1957), who
coma include hexamethylenetetramine [HMT, C6H12N4 considered only photodissociation of parent molecules to
(Bernstein et al., 1995)] and polyaminocyanomethylene form daughter and granddaughter molecules. However, as
[PACM, a –C(CN)(NH2)– polymer (Rettig et al., 1992)]. the importance of chemical reactions began to be appreci-
ated in other astrophysical contexts, so it became clear that
1.3. Brief History of Coma Modeling the high-density conditions in the inner coma (n ~ 1013 cm–3
at the nucleus surface) meant that they were also likely to
Prior to the middle of the twentieth century, many spec- be important in comets. Such considerations, together with
troscopic observations of cometary comae revealed the pres- the advent of more powerful computers, led to the develop-
ence of molecular radicals such as C2, C3, CH, CN, NH, ment of detailed chemical models (e.g., Oppenheimer, 1975;
NH2, OH, and a few ions, including CH+, CO+, CO2+, and Giguere and Huebner, 1978; Huebner and Giguere, 1980;
OH+ (e.g., Swings, 1943). In spite of its high abundance, Mitchell et al., 1981; Biermann et al., 1982).
H2O had not been detected but it was postulated to be pres- These early models had many simplifying assumptions,
ent together with CH4, CO2, NH3, and C2N2, consistent with such as constant temperature and velocity profiles. The mod-
the list of observed radicals and ions. Subsequently, Whipple els confirmed that ion-molecule reactions were important
(1950, 1951) postulated the icy conglomerate model for the in the inner coma, particularly proton transfer reactions
comet nucleus based on observations of Comet Encke. followed by dissociative recombination. These models also
508 Comets II

Fig. 3. Comparison of coma temperature profiles predicted by a variety of models. The upper panels show models for which a single
fluid is considered, whereas the bottom panels show results for multifluid models that also include the effects of coma chemistry. In
(a) and (b) the different lines correspond to different assumptions regarding the heating and cooling rates; (c) shows the difference
between the results of hydrodynamic calculations (upper line) compared with Monte Carlo simulations (lower line). In the lower pan-
els Tn, Ti, and Te refer to the temperatures of the neutral, ion, and electron fluids respectively. The different Te profiles in (d) refer to
different assumptions regarding heat transfer from “hot” photoelectrons. In (e), u, N, µ, and B are the velocity (km s–1), number
density (cm–3), mean molecular weight (amu), and magnetic field strength (nT), respectively. References: (a) Marconi and Mendis
(1982); (b) Crovisier (1984); (c) Combi and Smyth (1988); (d) Körösmezey et al. (1987); (e) Schmidt et al. (1988); (f) Rodgers and
Charnley (2002).

showed that the inner region of the coma is opaque to the temperature in the inner coma dropping to around 10 K.
solar UV field, and so accurate chemical models must in- Further out, as photodissociation and photoionization reac-
clude optical depth calculations. Later models included tions become important, the temperatures rise, particularly
additional reactions such as radiative association, electron that of the electrons. It was thus realized that the physics
impact ionization and dissociation, and photodissociative and chemistry are intimately coupled. For example, proton
ionization (e.g., Schmidt et al., 1988). Models have also been transfer reactions are the principal heat source for ions in
developed to account for the extended sources of CO and the inner coma, and the rate of electron recombination re-
H2CO following the breakup of POM in the coma (Boice actions is greatly reduced in the outer coma when the elec-
et al., 1990; Cottin et al., 2001). trons become extremely hot. This led to the development
Subsequent hydrodynamical models of the coma dem- of combined hydrodynamic-chemical models (Huebner,
onstrated that the assumptions of constant velocity and tem- 1985; Körösmezey et al., 1987; Wegmann et al., 1987;
perature were highly unrealistic (e.g., Marconi and Mendis, Rodgers and Charnley, 2002). The agreement between the
1982, 1983, 1986; Gombosi et al., 1985, 1986; Combi and various models is rather good; Fig. 3 presents the tempera-
Smyth, 1988). In particular, adiabatic cooling of the gas as ture profiles calculated by a number of different models.
it initially expands away from the nucleus can lead to the In the remainder of this chapter we shall concentrate on
 Rodgers et al.: Physical and Chemical Processes in Cometary Comae 509

coma chemistry in the hydrodynamic picture, for the MHD 2.2. In Situ Measurement
and Monte Carlo treatments the reader is directed to Ip
(2004) and Combi et al. (2004). Several space missions were sent to rendezvous with
Comet Halley, and mass spectrometry of the coma was
2. OBSERVING THE COMA performed by the Giotto and Vega 1 and 2 probes (e.g.,
Krankowsky et al., 1986). Most recently, in situ analysis of
2.1. Spectroscopy a second comet occurred during the Deep Space 1 flyby of
Comet Borrelly (e.g., Nordholt et al., 2003). Such measure-
The great majority of cometary data is gathered via spec- ments differ from spectroscopic data in that they give infor-
troscopy of the coma, and comes from all accessible regions mation that is local and instantaneous. This has the advan-
of the electromagnetic spectrum. Molecular observations of tage of allowing the structure of the coma to be probed on
coma composition are discussed in detail by Crovisier small scales. For example, the extended sources of CO and
(2004), Feldman et al. (2004), and Bockelée-Morvan et al. H2CO in Comet Halley were discovered by mass spectrom-
(2004). For the purposes of this chapter we note that ob- etry (Eberhardt et al., 1987; Meier et al., 1993). However,
servations of spectral lines give a single globally averaged because the data only yield a single “snapshot” of the state
column density for the number of molecules in a particu- of the coma, one potential pitfall in interpreting these meas-
lar energy level; interpreting this number requires a model urements is that it is difficult to decide whether any anoma-
of the coma. Specifically, one needs to know both n(r) and lies represent previously undiscovered permanent coma fea-
fε(r), where n is the number density and fε is the fraction of tures, or if they are due to transient phenomena.
molecules in energy level ε at cometocentric distance r. This In situ measurements give radial profiles of molecular
distribution must then be convolved with the telescope beam and ionic abundances and gas properties such as density and
profile for the appropriate Earth-comet distance. For parent temperature. Thus, these measurements represent the most
species, it is usually sufficient to assume a Haser distribu- stringent tests of chemical and dynamical models. For ex-
tion for the density, i.e., n ∝ r –2 exp{–r/rphot}, where rphot ample, the importance of proton transfer reactions in the
is the photodissociation scale-length at the appropriate he- inner coma was proved by the results of the Giotto ion mass
liocentric distance. For species formed in the coma the prob- spectrometer (Geiss et al., 1991). The global properties of
lem is more complicated; photodaughters in the outer coma the coma as a whole are best obtained from spectroscopic
can be modeled using the vectorial model of Festou (1981), measurements. In order to obtain the most understanding
or from the results of Monte Carlo calculations (see Combi of the coma, a combination of in situ and global measure-
et al., 2004). Molecules formed via coma chemistry require ments are required, together with detailed modeling.
detailed chemical models to compute their radial density
profiles. 3. COMA-NUCLEUS BOUNDARY
The factor fε is much more difficult to calculate, since it
depends on a number of excitation and deexcitation mecha- A key region is in the vicinity of the nuclear surface,
nisms that operate simultaneously. In the inner coma colli- where the initial chemical and dynamical conditions of the
sions will dominate, and fε will approach the local thermo- outflowing coma are determined. In practice, given the
dynamic equilibrium (LTE) value. Further out, collisions extreme difficulties in accurately calculating the physics and
remain important, but may be too slow to depopulate photo- chemistry in this region, most models of the coma simply
daughters produced in highly excited states. As the elec- assume some set of initial conditions as parameters to be
tron temperature decouples from the neutrals, the collisional input into the model. By comparing the model output with
excitation will be higher for those species with large dipole observations it is hoped that, in addition to understanding
moments that collide more rapidly with electrons (Xie and the processes occurring in the coma, the initial conditions
Mumma, 1992; Biver et al., 1999). Eventually, as all colli- can also be constrained with some degree of accuracy.
sions become unimportant, the excitation will be determined However, because of the complexity of the boundary re-
by the balance between radiative pumping and fluorescent gion, it is naive to assume that the conditions in the very
decay (Bockelée-Morvan and Crovisier, 1987). For lines that inner coma can be easily related to the properties of the
are optically thick, an extra layer of complication is added, nucleus.
in that a full radiative transfer model of the coma must be For example, although the initial chemical composition
employed. If several lines of the same molecule from dif- of the gas is similar to the composition of the nucleus ice,
ferent energy levels can be observed, an estimate of the for some volatile molecules an additional contribution from
globally averaged coma temperature can be obtained (Biver subsurface sublimation fronts may also be important. A
et al., 1999). At radio wavelengths, the spectroscopic reso- thorough discussion of the chemical differentiation and
lution is sufficiently narrow that expansion velocities can stratification in the nucleus appears in Prialnik et al. (2004).
be obtained from line profiles (Bockelée-Morvan et al., The total surface sublimation rate is controlled by the equa-
1990). Again, this value is a global average over the whole tion of energy balance at the nucleus surface, together with
of the coma. a Clausius-Clapeyron-type equation of state of the surface
510 Comets II

ices. For typical cometary parameters, the gas (primarily tions (ODEs) for one-dimensional, steady models. Models
water) production rate is on the order of 1017 mols cm–2 s–1 that considered separate neutral, ion, and electron fluids
at 1 AU (Whipple and Huebner, 1976). found that chemical reactions in the inner coma were an
The dynamics of the circumnuclear boundary region are important heat source, especially for the ions (Körösmezey
also extremely complicated, since the nucleus is likely to et al., 1987).
be heterogeneous on small scales. Sophisticated time-de- Chemically, the simplest models ignore the dynamics,
pendent three-dimensional models are required in order to and assume constant outflow velocities and temperatures
calculate the gas and dust flow in this region, and are dis- (Giguere and Huebner, 1978). Other models take the gas
cussed further in Crifo et al. (2004). These models predict physics into account in some basic fashion, for example,
many interesting features, such as lateral flows and standing by assuming a sudden jump in the electron temperature at
shocks. The possible chemical effects of these features have some arbitrarily chosen radius (Lovell et al., 1999). How-
not yet been investigated, so it is not known whether or not ever, because chemical reaction rates depend on the gas
they may play a role in generating new species. In the re- temperature and density, accurately calculating the chem-
mainder of this chapter we will discuss the chemistry that istry requires an accurate description of the coma dynam-
occurs beyond the boundary region, where the gas flow is ics. In addition, as discussed above, an accurate dynamical
relatively smooth and almost spherically symmetric. We model should include the effect of chemical reactions.
mention the possible chemical processing in the boundary Therefore, the coma chemistry and physics should be solved
layer simply to stress, again, that inferring the properties simultaneously, and a multifluid, dynamical-chemical model
of the nucleus from coma observations is not a simple task. is the minimum necessary to study coma chemistry. Such
The thickness of the boundary layer depends on the gas models were first developed by Körösmezey et al. (1987)
production rate. At large heliocentric distances the rate of (albeit with a limited chemistry) and Schmidt et al. (1988).
gas production is small and the thickness of the boundary In the following section we describe the basic components
layer can be very large. In the extreme case, when the mean of such a model.
free path for collisions between gas molecules approaches A separate category of coma models calculate the gas
infinity, a Maxwellian velocity distribution will never be properties via Monte Carlo techniques (Combi and Smyth,
established and the gas remains in free molecular flow. For a 1988; Hodges, 1990). These models represent the most
comet at 1 AU with a gas production rate of ≈1017 cm–2 s–1 and accurate descriptions of the coma, since they neglect the
T ≈ 100 K, Λ is on the order of 20 cm. Thus, the boundary assumption, common to all hydrodynamic models, that the
layer is on the order of tens of meters on the subsolar side gas behaves as a fluid. However, these models are also
of the nucleus, and will be much larger on the nightside. extremely computationally demanding. Including a detailed
chemistry in these models would be prohibitive. Given the
4. DYNAMICAL-CHEMICAL fairly good agreement between Monte Carlo models and
MODELS OF THE COMA fluid-dynamic treatments in the inner collisional coma, it is
not necessary to use such models when modeling the coma
4.1. Model Classification chemistry.

We begin with a brief review of the different types of 4.2. Simple Multifluid Hydrodynamic Models
models that have been used to model the coma. This is in no
way meant to be an exhaustive list or rigid taxonomy of all Simple, spherically symmetric models, appropriate for
models, but rather to give an idea of the strengths and weak- a steady flow, have previously been employed to investi-
nesses of different approaches, and what level of complexity gate the chemistry of the collisional inner coma (e.g., Hueb-
is feasible and/or necessary. ner, 1985; Wegmann et al., 1987; Schmidt et al., 1988; Konno
The simplest hydrodynamical models of the coma are et al., 1993; Canaves et al., 2002), and we now describe the
steady, spherically symmetric, single-fluid models that cal- key ingredients of such a model; a more detailed descrip-
culate radial profiles of v and T. Such models were first used tion is given in Rodgers and Charnley (2002). In reality, as
to investigate the principal heating and cooling mechanisms we have discussed, cometary comae are not symmetric, and
operating in the coma, and showed that T can vary signifi- rapid temporal variations are observed. Despite this, such
cantly throughout the coma (e.g., Marconi and Mendis, models remain useful since (1) pressure differences in the
1982; Crovisier, 1984; Huebner, 1985) (see Fig. 3). Such very inner coma tend to even out rapidly, leading to fairly
models also serve as the foundation for more complex cal- symmetric spherical outflows in the gas coma (Crifo, 1991);
culations, such as models that are multidimensional (Kita- and (2) the time taken for a particular parcel of gas to reach
mura, 1986), time-dependent (Gombosi et al., 1985), or a distance of 4 × 103 km — roughly corresponding to the
include several fluids (Marconi and Mendis, 1986). In the edge of the collisional regime where bimolecular physical
case of multidimensional or time-dependent models, the and chemical processes cease to significantly affect the
computational demands can be very large, because these gas — is around 1 h. The most important deviations from
calculations involve simultaneously solving large sets of this model occur for the ions and electrons at large cometo-
coupled partial differential equations (PDEs), as opposed centric distances, where the interaction with the solar wind
to a relatively small number of ordinary differential equa- becomes important. In this case, multidimensional models
 Rodgers et al.: Physical and Chemical Processes in Cometary Comae 511

are necessary (Schmidt et al., 1988). Nonetheless, because be derived for dTi/dr and dTe/dr, as well as for the mass
magnetic fields are excluded from the inner coma where density gradient of the plasma. For the plasma, a slight com-
most of the chemistry occurs, the plasma flow in these re- plication arises, since charge conservation and the strength of
gions will trace the near-spherical neutral gas outflow. For the Coulomb force ensures that ne = ni and ve = vi through-
a chemically reacting multicomponent flow we have to out the coma. Therefore, one must solve for the plasma
consider the interaction of the predominately neutral gas and velocity dve/dr by considering the total contributions from
the charged plasma of ions and electrons, and the relatively both ions and electrons. Once the hydrodynamic source
massive dust grains. We also need to treat the suprathermal terms have been defined, and the fluid properties at the
photoproduced hydrogen atoms as an individual component comet surface prescribed, it is possible to numerically inte-
(see section 4.3.3). Here we specifically describe the gas- grate the resulting system of differential equations to obtain
plasma coupling. Assuming a steady, spherically symmet- the coma physical and chemical structure.
ric flow, and neglecting gravitational and magnetic fields, In practice, for steady flows such as these there can exist
the hydrodynamic conservation equations for particle num- mathematical singularities where a fluid encounters a tran-
ber, mass, momentum, and energy for the neutral gas are sonic point, since at these points the denominator in equa-
tion (7) becomes zero. When a dust component is included,
1 d 2
(r nv) = N (1) such a 0/0 singularity is encountered close to the nucleus,
r 2 dr as the expanding neutral gas then has to undergo a subsonic-
supersonic transition. Similarly, further out in the coma,
1 d 2
(r ρv) = M (2) where the electron temperature becomes very high, the
r 2 dr plasma sound speed increases to the point that the plasma
undergoes a supersonic-subsonic transition. For time-depen-
1 d 2 2 dP
(r ρv ) + =F (3) dent flows, where a system of PDEs is solved, singularities
r 2 dr dr do not occur (e.g., Körösmezey et al., 1987; Körösmezey
and Gombosi, 1990). In the case of steady flows, special
numerical techniques, or simplifying approximations, are
1 d 2 ρv2 γ 1
rv + P = G + Fv − Mv2 (4) needed to treat such 0/0 singularities (e.g., Marconi and
r 2 dr 2 γ−1 2 Mendis, 1983, 1986; Gail and Sedlmayr, 1985). It should
be emphasized that, although “simple” by the standards of
where n is the number density, ρ is the mass density, v is recent coma dynamics models (e.g., Combi et al., 2004;
the velocity, P is the pressure, and γ is the ratio of specific Crifo et al., 2004), even steady flow models require a higher
heats. The source terms N, M, F, and G represent, respec- level of sophistication relative to other areas of astrochemical
tively, the net generation rate per unit volume of particles, modeling (as in interstellar clouds or circumstellar enve-
mass, momentum, and thermal energy (heat). It is assumed lopes, for example). Model temperature distributions ob-
that the fluid behaves as an ideal gas. Equation (1) can be tained for a comet similar to Hyakutake at 1 AU are shown
rearranged to give in Fig. 3f.

dns N n dv 2ns 4.3. Heating and Cooling Mechanisms

= s − s − (5)
dr v v dr r
4.3.1. Elastic scattering. Elastic collisions transfer
where the subscript s represents a particular chemical spe- momentum and energy between the three fluids. For ion-
cies. Similarly, the mass conservation equation becomes neutral collisions, if the scattering is assumed to be isotropic
in the center-of-mass frame, the mean amount of thermal
dρ M ρ dv 2ρ energy imparted to the neutrals per collisions can be cal-
= − − (6)
dr v v dr r culated via

After some algebra, one can derive equations for the radial ˆ n(i − n, elastic) =
G
derivatives for the velocity and temperature of the neutral gas
3 (v − ve)2 (9)
2mnmi(mn + mi)2 K(Ti − Tn) + mi n
2 2
dv 1 2γPv
= Fv − (γ − 1)G − Mv2 + (7)
dr ρv − γP
2 r where mn and mi are the masses of the particles involved.
A similar expression holds for the ion fluid heat source term
per collision. The total thermal energy source term due to
dT 2T 1 dv
= + Fv − Mv2 − NkT + (nkT − ρv2) (8) elastic scattering is obtained by summing equation (9) over
dr r nkv dr all collisions. This can be done either by assuming a ge-
neric value for the mean mass of each fluid, or by actively
Each of the three fluids in the coma (neutrals, ion, elec- summing the contributions of the most frequent collisions,
trons) has a distinct temperature, and similar equations can which will involve the ions H3O+, CH3OH+2 , and NH+4 collid-
 512
Comets II

TABLE 1. Thermal energy source terms per reaction, G, for neutral, ion, and electron fluids for different classes of reactions.

Reaction Type Example Gn Gi Ge

Radiative association of neutrals CO + S → OCS –Θn 0 0
m1
Radiative association of ions and neutrals H2O + HCO+ → HCOOH+2 –Θn (m1v2en + Θn − Θi) 0
m3
Neutral-neutral CH4 + CN → HCN + CH3 ∆E 0 0
m4 m3
Ion-neutral NH3 + H3O+ → H2O + NH+4 M(m2v2en + Θi − Θn) + ∆E M(m1v2en − Θi + Θn) + ∆E 0
mT mT
Radiative recombination C+ + e → C + hν m1v2en + Θi –Θi –Θe

Dissociative recombination H3CO+ + e → HCO + 2H m1v2en + Θi + Θe + ∆E –Θi –Θe

Photoionization OH + hν → OH+ + e –Θn m1v2en + Θn ∆E

Photodissociation of neutrals CO2 + hν → CO + O ∆E 0 0

m4 m m3
Photodissociation of ions H2O+ + hν → OH+ + H ∆E + m3v2en + 3 Θi (∆E − Θi) 0
m1 m1 m1
m3 m
Photodissociative ionization (PDI) H2O + hν → OH+ + H + e − Θn m3v2en + 3 Θn ∆E
m1 m1
Electron impact ionization (EII) CH4 + e → CH+4 + 2e –Θn m1v2en + Θn –∆E

Electron impact dissociation (EID) CH4 + e → CH3 + H + e 0 0 –∆E

m is the mass of a species, and subscripts 1–4 refer to those species in the example reactions. mT is the total mass of the reactants, and M is a reduced mass ratio equal to (m1m4 + m2m3)/
mT2. Θn ≡ 3kTn/2, Θi ≡ 3kTi/2, Θe ≡ kTe, v2en ≡ (vn – ve)2/2. ∆E represents the mean exo-/endothermicity of each reaction.
 Rodgers et al.: Physical and Chemical Processes in Cometary Comae 513

ing with H2O, CO, and CO2. In either case, the rate coeffi- 50 can be formed (e.g., Harich et al., 2001). Therefore, the
cient for the collisions must be known; a value equal to the kinetic energy of the Hf atom is likely to be in the range
Langevin value, ~10 –9 cm3 s–1, is typically assumed. Note 1–2 eV, implying a velocity of ≈15–20 km s–1. This has been
that the source term in equation (9) can be considered as a confirmed by observations of numerous comets (Festou et
simplified form of the general expression for reactive ion- al., 1983; McCoy et al., 1992). In addition to being the princi-
molecule collisions (see line 4 in Table 1). pal heating mechanism in the inner coma, these suprather-
For electron-neutral elastic scattering, the most impor- mal atoms may also drive high-energy chemical reactions
tant collision partner is water. Collision rates for e-H2O in this region. This will be discussed in section 5.4.
mixtures were measured by Pack et al. (1962; see also 4.3.4. Chemical reactions. The hydrodynamic source
Körösmezey et al., 1987), and the mean heat transfer per terms due to chemical reactions depends on the reaction type
collision can be obtained from equation (9) with the addi- and the masses and temperatures of the species involved.
tional assumption that the electron mass can be neglected. In order to accurately calculate the effects of chemistry on
Also, because the cross section declines with electron tem- thermodynamics it is necessary to compute the source term
perature, one finds that the mean thermal energy of a col- due to each individual reaction and then multiply this by
liding electron is kTe, not 3kTe/2 (Draine, 1986). The rate the total reaction rate (i.e., reactions cm–3 s–1), and then sum
of energy transfer between ions and electrons was calcu- the total for all reactions. Mass source terms are trivial to
lated by Draine (1980). calculate; e.g., the ionization of water increases the ion fluid
4.3.2. Inelastic scattering. Inelastic collisions can lead mass by 18 amu, and decreases the neutral fluid mass by
to molecules in highly excited states. These will then decay the same amount. Source terms for momentum and energy
with the emission of a photon, and if this photon is able to transfer are not so simple, however. Draine (1986) derived
escape from the coma without being reabsorbed, the energy the expressions appropriate for several of the most common
is lost. Inelastic collisions involving H2O are the most im- reaction types occurring in a multifluid flow and this meth-
portant; water molecules can be excited by collisions with odology can be extended to include all reaction types that
other H2O molecules or with electrons. A semiempirical for- occur in the coma (Rodgers and Charnley, 2002). The result-
mula for the energy loss due to the former was derived by ing heat source terms per reaction, G, are listed in Table 1.
Shimizu (1976). However, radiation trapping in the inner A comparison of the effectiveness of each of the heat-
coma means that the effective cooling rate is much less ing and cooling mechanisms discussed in this section is
(Crovisier, 1984). This can be roughly accounted for by in- shown in Fig. 4.
troducing an optical depth factor (Schmidt et al., 1988). The
energy removed by inelastic e-H2O collisions was calcu- 4.4. Gas-Dust Coupling
lated by Cravens and Körösmezey (1986). Again, accurate
calculations must include the effects of radiation trapping The drag force exerted by the gas on a dust particle de-
in the inner coma. pends on the relative drift velocity between gas and dust,
4.3.3. Thermalization of energetic photoproducts. The vdrift = vg – vd, and can be written
majority of photolytic reactions result in the production of
either atomic or molecular hydrogen, and due to their low CD 2
Fdrag = ndσd ρg v (11)
masses these products also have the largest share of the 2 drift
excess energy of the reaction. Hence, the dominant heat-
ing mechanism in the coma is thermalization of fast H and where nd and σd are the number density and cross section of
H2 particles. It was realized by Ip (1983) that in the outer the dust grains. CD is the drag coefficient, which accounts
coma many of these particles will escape from the coma for the sticking of the molecules on the dust particles, the
before thermalization, thus removing an important energy viscosity of the gas, and the shape of the particle. It also
source for the neutral fluid. A variety of calculations of this depends on the density of the gas. The drag coefficient is
effect have been performed (e.g., Huebner and Keady, 1984; usually expressed in terms of the Reynolds number, Re =
Combi and Smyth, 1988). Although the results are qualita- 2rdρgvdrift/µ, where µ is the viscosity of the gas. For low
tively similar, the radius at which escape becomes impor- Reynolds numbers, the drag coefficient reduces to the Stokes
tant can vary by almost an order of magnitude in different value, CD = 24/Re. A good fit to the drag coefficient over a
models (Crifo, 1991). wide range of Reynolds number was provided by Putnam
The most important reaction forming fast H atoms (here- (1961)
after denoted Hf) is photodissociations of water
24 Re2/3
H2O + hν → OH + Hf (10) CD = 1+ (Re < 1200) (12)
Re 6

The mean excess energy of reaction (10) is 3.4 eV, but as CD = 0 (1200 < Re < 1200) (13)
pointed out by Crovisier (1989), a large fraction of this
energy may go into ro-vibrational excitation of the OH radi- The above discussion applies to gases that can be treated
cal. Laboratory experiments on water photodissociation have as a continuous medium, i.e., Λ is much smaller than the size
shown that OH radicals with rotational energy levels of J > of the dust particle. If this is not the case, Knudsen flow ap-
514 Comets II

dominates for typical dust particles in cometary comae and

dust tails. For larger dust particles, the deceleration due to
gravity must also be taken into account. Equating the drag
force given by equation (11) with the gravitational force
gives the size of the largest particles that can be carried away
by the sublimating gas.
Gas-dust collisions can also heat or cool the colliding
gas particles. The temperature of dust grains is determined
by the energy balance between solar heating, gas-drag heat-
ing, and cooling by reradiation. For a steady flow, the evo-
lution of the dust temperature can be calculated from

dTd
vdCd = Eabs + Edrag − Erad (14)
dr

where Cd is the heat capacity and the terms on the righthand

side refer to the energy sources/sinks mentioned above. In
general, these terms will depend on the shape, size, and
mineralogy of the grains. For example, small grains are
hotter than large grains, and, since they are more absorp-
tive, Fe-bearing silicate grains tend to be hotter than Mg-
rich ones (Harker et al., 2002). The energy transfer between
the gas and dust, Edrag , also affects the gas flow. In general,
this term is calculated from an expression of the form

Edrag = ngσdCH(Tg − Td ) (15)

where CH is the thermal accommodation coefficient. Be-

cause collisions between dust grains are rare, dust grains
are coupled to the gas but not to each other. Therefore, an
accurate description of the dusty coma requires the use of
numerous dust components, each corresponding to a dif-
ferent population of grains with particular properties (e.g.,
size, shape, chemical composition). The acceleration of each
component is obtained from equation (11) and the tempera-
ture from equation (14).

5. COMA CHEMISTRY

5.1. Photochemistry
Fig. 4. Comparison of different heating and cooling mechanisms
for the neutral (n), ion (i), and electron (e) fluids (from Rodgers The principal chemical processes occurring in the coma
and Charnley, 2002). For each process, the total heat source term, are photodissociation and ionization of the parent mol-
G (erg cm–3 s–1), is shown; solid and dashed lines represent heat- ecules. Accurate photodissociation rates are essential in
ing and cooling respectively. Processes considered include chemi- order to model the coma and to interpret observational data.
cal reactions (this also includes photochemistry), loss of fast
Huebner et al. (1992) compiled laboratory and theoretical
hydrogen atoms and molecules, elastic collisions between e-n, i-n,
data on a large number of important coma species; integrat-
and i-e (Coulomb scattering) fluids, and inelastic water-water and
electron-water collisions. ing over the solar spectrum yields photorates appropriate
for both “quiet” and “active” solar photon fluxes. Despite
the gargantuan nature of this undertaking, however, many
gaps in our knowledge remain. Only a handful of species
plies and a correction must be applied to the drag coeffi- have been measured over a large range of wavelengths;
cient by dividing it by a factor [1 + Kn(2.492 + 0.84exp{–1.74/ many important radicals are unstable under laboratory con-
Kn})] ( Friedlander, 1977), where Kn is the Knudsen num- ditions and so are extremely difficult to investigate. In many
ber (the ratio of Λ to the particle size). For a typical comet experiments, although the rates are well determined, the
at 1 AU, Λ ~ 20 cm (see section 3), and so Knudsen flow branching ratios among different sets of possible products
 Rodgers et al.: Physical and Chemical Processes in Cometary Comae 515

Fig. 5. Coma ion chemistry (Schmidt et al., 1988). (a) Relative densities of ionized species in the coma. (b) Cometocentric varia-
tions of important quantities in ion-molecule chemistry. Effective rate coefficients and average surplus energy for photoprocesses [σph
(10 –6 s–1) and eph (102 eV)]; effective rate coefficient for electron recombination and effective cross-section for ion-neutral elastic col-
lisions [αrec (10 –6 cm3 s–1) and Qcol (10 –14 cm2)].

are not well constrained. Thus, laboratory experiments are showed that the resulting rate coefficients can be param-
vital in order to further our understanding of coma chem- eterized in the form
istry (e.g., Jackson et al., 2002).
As the most important species in the coma, the photo-
chemistry of water is of key importance. Due to its impor- 300
k(Tin) = k(300) 1 + β −1 (16)
tance in atmospheric chemistry, water has been studied Tin
extensively in the lab. Details of all the possible product
channels are discussed in Feldman et al. (2004). Here, we
note a couple of important points. First, the dominant dis- where β depends on the dipole moment, µ, polarizability, α,
sociation channel results in OH + H. Studies of OH are and a “locking constant.” Tin is a mass-weighted mean ki-
therefore an excellent proxy for determining the cometary netic temperature of the reactants. β can be calculated from
water production rate (as long as the OH excitation mecha- the expression β = µ/(µ + α), with µ measured in Debye and
nisms are fully understood). The Hf atoms produced in this α in Å3 (Rodgers and Charnley, 2002).
reaction are the principal source of heating in the inner In many ways the chemistry in the coma is analogous
coma, and may also drive a suprathermal chemistry. Second, to the chemistry that occurs in interstellar hot cores. A “pro-
the ionization of water occurs at a rate of ≈3 × 10 –7 s–1 at ton cascade” transfers protons from species with low pro-
1 AU. Hence, for an outflow velocity of 1 km s–1, the frac- ton affinity, i.e., OH (H2O+), to species with larger proton
tional ionization in the coma increases as ne/n(H2O) ~ (r/ affinities, i.e., NH3 (NH+4). Detailed chemical models are
km) × 3 × 10 –7. This gives a rough estimate of the amount necessary to calculate how the ionization is apportioned
of material that can potentially be affected by ion-molecule among different ions, which is essential when interpreting
reactions. in situ ion mass spectrometry data (Geiss et al., 1991).
Many interstellar chemical schemes are lacking in a num-
5.2. Ion-Molecule Reactions ber of important proton transfer reactions, most notably
from methanol to ammonia (Rodgers and Charnley, 2001a).
For molecules with permanent dipole moments, the di- The inclusion of a full set of such reactions is a prerequi-
pole-charge interaction results in an extra attractive force site for an accurate calculation of ionic abundances. Fig-
between the reactants. In this case the rate coefficient can ure 5 shows the degree of ionization and the abundances
be calculated from the average-dipole-orientation theory of of different families of ions in the coma, together with vari-
Su and Bowers (1973). Eberhardt and Krankowsky (1995) ous parameters affecting the plasma chemistry.
516 Comets II

As discussed earlier, the chemistry and hydrodynamics 5.3. Neutral-Neutral Reactions

of the coma are intimately coupled. For example, proton
transfer reactions are exothermic by typically a few electron An alternative source of new species in the coma may
volts (eV). Therefore, the ions formed via these reactions be provided by neutral-neutral reactions. Because photodis-
will have significant energies, and this effect keeps the ions sociation occurs around 100 times faster than photoioniza-
in the inner coma at a warmer temperature than the neutral tion, the abundances of reactive radicals are much larger
fluid (Körösmezey et al., 1987). Also, the rates of many than those of ions. However, many of the subsequent reac-
chemical reactions are temperature dependent. This is most tions will be destructive, with radicals reacting to break
important for dissociative recombination reactions of ions apart parent species they collide with. For example, OH can
and electrons; when the value of Te reaches extremely large react with NH3 and CH4 to reform water and produce NH2
values in the outer coma, such reactions effectively switch and CH3 respectively. A possible exception is the reaction
off, resulting in a larger ionization fraction (see Lovell et al., of CN with hydrocarbons; these reactions typically result in
1999; Bockelée-Morvan et al., 2004, Fig. 1). the replacement of a H atom with the –CN group (Balucani
Despite the importance of ion-molecule reactions in de- et al., 2000). In particular, the reaction with acetylene (C2H2)
termining ionic abundances, it turns out that these reactions will lead to cyanoacetylene (HC3N). Again, however, mod-
are not an efficient source of new, stable neutral molecules. eling shows that the resulting HC3N yields are far less than
For example, Irvine et al. (1998) proposed that proton trans- observed in many comets (Rodgers and Charnley, 2001b).
fer to HCN followed by recombination could account for Neutral-neutral reactions do appear to be important in com-
the HNC seen in Comet Hale-Bopp. However, models that etary sulfur chemistry. Based on our understanding of in-
include a comprehensive ion-molecule chemistry (i.e., in- terstellar chemistry, S-bearing molecules take part in a pre-
volving CH3OH and NH3) show that the amount of HNC dominately neutral chemistry. Canaves et al. (2002, 2004)
actually produced is almost 100 times less than observed have investigated the coma production of several S-bear-
(Rodgers and Charnley, 1998, 2001a). This is illustrated in ing molecules, including NS and CS. They found very good
Fig. 6. Similar calculations on the formation of large organ- agreement with the observed NS abundance in Comet Hale-
ics also show that these species are produced only in small Bopp and that the CS abundance should be approximately
abundances (Rodgers and Charnley, 2001b). A corollary of constant with cometocentric distance.
this is that one can show that the HCOOH, CH3OCHO, and
CH3CN observed in Hale-Bopp (Bockelée-Morvan et al., 5.4. Nonthermal Chemistry
2000) cannot be formed by chemical reactions in the coma.
It has long been recognized that the energetic fragments
produced in photodissociation reactions have the potential
to drive a “suprathermal” chemistry in the coma (e.g., Hueb-
ner et al., 1991; Kissel et al., 1997). However, it was origi-
nally assumed that, in general, these reactions would be
destructive. For example, Hf atoms can react with water to
form H2 and OH. Hence the net effect of such reactions is
simply to increase the quantum yield of OH atoms produced
from photodestruction of water: In addition to the primary
OH daughter, secondary OH radicals will also be produced.
More recent work has focused on the potential of supra-
thermal reactions to affect the coma chemistry in more in-
teresting ways. Rodgers and Charnley (1998, 2001c) looked
at the possibility that Hf atoms could isomerize HCN into
its isomer HNC, thus accounting for the puzzling HNC/
HCN increase seen in several comets as they approach the
Sun (e.g., Irvine et al., 1999; Biver et al., 2002; Rodgers et
al., 2003). They showed that such reactions may be viable
in large, active comets such as Hale-Bopp, but some other
mechanism must account for the HNC production in smaller
comets such as Hyakutake and Ikeya-Zhang (see Fig. 6).
Pierce and A’Hearn (2003) examined the possibility that
Fig. 6. HNC/HCN ratios for a variety of HNC formation mecha-
the reaction of Hf atoms with CO2 could account for the
nisms (Rodgers and Charnley, 2001c). (1) Ion-molecule chemis-
try (curves a–e result from altering model parameters, such as the extended source of CO seen in many comets. However, they
initial HCN abundance, recombination branching ratios, etc.). conclude that this mechanism is an order of magnitude
(2) Isomerization of HCN by Hf atoms. (3) Photodestruction of slower than direct photodissociation of CO2 into CO. It is
an unknown parent. (4) As for (3), but assuming the parent of possible that the coma chemistry of sulfur could be strongly
HNC also has an extended source. affected by Hf atoms since these should readily abstract H
 Rodgers et al.: Physical and Chemical Processes in Cometary Comae 517

atoms from the major parent, H2S. Similarly, more abun- discussed in section 5.2, ion-molecule chemistry cannot
dant coma molecules like H2CO and CH3OH could also be significantly alter the initial abundances of parent molecules
destroyed by Hf atoms. The general applicability of these sublimating from the nucleus, and detailed modeling shows
processes to coma composition remains to be investigated. that parent isotopic ratios are also unaffected (Rodgers and
Other work has looked at the possibility of atoms pro- Charnley, 2002). An important consequence of this result
duced in excited metastable states driving suprathermal is that measurements of isotope ratios can be used to test
reactions. For example, A’Hearn et al. (2000) suggested that putative parent-daughter relationships. For example, al-
S2 may be formed in the coma by the reaction of OCS with though HCN undoubtedly accounts for some fraction of the
atomic sulfur produced in the singlet-D state. More recently, CN observed in the coma, it has long been debated whether
Glinski et al. (2003) showed that the reaction of O(3P) with it can account for all the CN (Festou, 1999). Recent obser-
OH may lead to significant O2 abundances in the inner coma. vations of C15N in Comets LINEAR WM1 and Hale-Bopp
Another class of suprathermal reactions that are likely to by Arpigny et al. (2003) demonstrate that CN is significantly
be important are electron impact reactions. Although pre- enhanced in 15N, by around a factor of 2, as compared with
vious schemes have included these reactions (Boice et al., HCN. Thus, HCN cannot be the sole parent of CN, and if
1986), accurately calculating the rate at which they occur HCN contributes about half the CN, the 15N ratio in the
requires a detailed model of the hot electron energy distribu- additional parent of CN must be even higher. If this parent
tion in the coma (e.g., Wegmann et al., 1999). is the same one that accounts for the extended source of
HNC in comets, then one would also expect to see signifi-
5.5. Dust Fragmentation/Degradation cant 15N enhancements in HNC. Similar observations of
and Extended Sources 13C-bearing isotopomers of C , C , and simple carbon-chain
2 3
molecules (acetylene, ethene, ethane, cyanoacetylene) may
The inability of gas phase chemical reactions to gener- also help to resolve the origin of these radicals.
ate sufficient quantities of particular molecules in the coma As with molecular D/H ratios, the nuclear spin ratios of
means that some other mechanism must be responsible for cometary species reflect the temperatures at which they
the extended sources of these molecules (Festou, 1999). originated, and can be altered in the coma only marginally
Huebner (1987) proposed that destruction of POM in the by proton transfer reactions. Ortho:para ratios (OPRs) have
coma could account for the formaldehyde source, and this been observed in water in several comets (see Bockelée-
was modeled by Boice et al. (1990). Based on their labo- Morvan et al., 2004). Recently, Kawakita et al. (2002) have
ratory studies of POM degradation, Cottin et al. (2000) measured the OPR in NH2; since strict selection rules con-
developed a more detailed model of thermal and photo- strain the OPR in photodaughters as a function of the OPR
degradation of POM in the coma. Matthews and Ludicky in their parents, these observations can be used to probe the
(1986) suggested that HCN polymers may be present in OPR in ammonia. Alternatively, one can turn this argument
comets; degradation of these compounds may be an addi- on its head and say that, if the OPR ratios in NH3 can be
tional source of many small coma molecules (Rettig et al., measured directly, the question of whether NH3 is the sole
1992; Huebner and Boice, 1997), including HNC (Rodgers parent of NH2 can be answered. A similar investigation of
and Charnley, 2001c). Of course, in all these models there the OPR in cometary formaldehyde may provide insights
are a number of free parameters, and it is always possible to into the nature of its extended source.
fit the observed abundances if one adjusts the initial abun-
dance and/or the destruction rate of the mystery parent. 6. SUMMARY
Nevertheless, the models require abundances and destruc-
tion rates that are in agreement with rough theoretical esti- 6.1. Coma Physicochemistry
mates and laboratory measurements. Therefore, although
these models do not prove that dust destruction is respon- In the inner regions of the coma, the outflowing gas
sible for injection of H2CO and HNC into the coma, they behaves as a fluid, and fluid equations can be used to ob-
certainly show that it is plausible. tain a reasonable description of the flow. The gas initially
cools as it expands adiabatically, but is eventually heated
5.6. Isotopic Fractionation and by thermalization of energetic photofragments. The ions are
Nuclear Spin Ratios also heated by exoergic proton transfer reactions. The hy-
drodynamic approximation loses validity in the outer coma,
Deuterium/hydrogen ratios have been observed in two where the density decreases, and many hot photoproducts
coma species (HDO and DCN), 15N/14N ratios in CN and are not thermalized. This is particularly important for elec-
HCN, and 13C/12C ratios in C2, CN, and HCN; see Table 3 trons, and a very hot electron population exists in the outer
in Bockelée-Morvan et al. (2004) for a complete list. In the coma. The chemistry and the physics are intimately coupled,
interstellar medium, proton transfer reactions are efficient and detailed models should include both. The chemistry is
in scrambling the D/H ratios among different species (e.g., initiated by the solar radiation field, which produces reac-
Roberts and Millar, 2000). Hence, we might also expect tive radicals and ions. Subsequent reactions in the coma,
some degree of mixing to occur in the coma. However, as especially proton transfer reactions, result in the production
518 Comets II

of new coma species. However, although chemical reactions cal composition. Interaction of gas jets may result in stand-
are extremely important in determining the relative abun- ing shocks, and the divergence of chemically distinct jets
dances of different ions, they are unable to synthesize signi- may lead to chemical heterogeneity in the outer coma. A
ficant quantities of stable, neutral species. Therefore, unless full understanding of the near-nucleus coma is vital if we
an observed species is an obvious photodaughter, it is prob- are to use observations of the outer coma to infer the prop-
able that it is present in the nuclear ice. Degradation of com- erties of the nucleus. These issues can only be resolved using
plex organic material is likely to contribute to the extended extremely detailed three-dimensional gas-kinetic models;
sources of some molecules, and studies of extended sources some results of the most up-to-date codes are presented in
of molecules may provide insight into the nature of comet- Crifo et al. (2004).
ary CHON material. The energetic photodissociation prod- It appears that ion-molecule chemistry, of the kind that
ucts in the coma may drive a suprathermal chemistry. Studies generates the diversity of molecules seen in the interstellar
of such processes are currently in their infancy. medium, is too slow to produce significant amounts of new
species in the coma. However, the presence of highly ener-
6.2. From Coma Measurements to getic photodissociation products in the coma may allow a
Nucleus Properties suprathermal chemistry to occur. Currently, only a small
number of such reactions have been considered. Fast hy-
Although almost all our information on comets comes drogen atoms could play an important role here. For ex-
from studies of the coma, what we really want to know is ample, many sulfuretted molecules were detected for the
the nature of the cometary nucleus. As stressed in this chap- first time in Comet Hale-Bopp, and it is known that the most
ter, detailed models of the coma are essential in order to important reactions in interstellar sulfur chemistry are neu-
calculate the density profiles and excitation states of coma tral-neutral processes. Hydrogen abstraction from H2S by Hf
molecules. However, even with these models, it is usually could drive some reactions deep in the inner coma, gener-
only possible to derive globally averaged properties in the ating new sulfuretted molecules. Clearly, there may exist
extended coma. In terms of molecular production rates, this many other possible reactions, not included in typical astro-
means that we can derive accurate values for the total gas chemical networks, that can proceed efficiently in the coma.
release rates from the nucleus. However, when using these In particular, the global consequences of nonthermalized
values to understand nucleus properties we encounter two electrons in driving electron impact reactions has not been
important impediments. First, it is now known that gas is studied in sufficient depth.
released not only from the nucleus surface, but also from The origin of the extended sources of certain molecules
subsurface layers (see Prialnik et al., 2004). Therefore, coma are not well known. Fragmentation of dust particles and/or
abundance ratios do not necessarily equal those in the icy macromolecules has been invoked to account for the addi-
nucleus, and models of the evolution of the cometary interior tional sources of some molecules, such as CO, formalde-
are required. Second, the nucleus is likely to be heterogene- hyde, and several small radicals. Encouragingly, laboratory
ous on small scales, and the gas production rate may vary measurements of the properties of the proposed macromole-
dramatically with position (see Crifo et al., 2004). Hence, cules appear to support this hypothesis (Cottin et al., 2000).
the total gas production rate will depend on the sum over the More laboratory work on other possible CHON components
surface of many different regions, so it is not possible to is needed. Despite the fact that they have been seen in com-
simply derive “average” surface properties from the global ets for decades, the origins of radicals such as C2, C3, and
gas production. Again, highly detailed modeling is essential CN are still uncertain. However, measurements of isotopic
to elucidate these issues. ratios in these species and their putative parents may finally
help to resolve this issue. Measurements of the OPR in for-
6.3. Open Questions and Future Directions maldehyde may also help to constrain its source. Interfero-
metric mapping of the coma of Hale-Bopp also appeared
The gas temperatures and velocities measured in situ in to reveal additional extended sources of molecules usually
Comet Halley were in good agreement with coma models. thought to be solely parent species, such as HCN and
It therefore appears that we have a relatively secure under- CH3OH (Blake et al., 1999; Kuan et al., 2003, 2004). The
standing of the physics in the coma. Chemically, the pro- existence of such sources for other parent species would
files and velocities of most parent molecules, as well as of provide evidence that sublimation of volatiles from dust
many simple radicals and atoms, are in broad agreement grains is occurring throughout the coma.
with photodissociation models; nevertheless, many uncer- Given the rate of discovery (Bockelée-Morvan et al.,
tainties remain. We briefly review several of the outstand- 2004), it is likely that many more molecules will be dis-
ing problems. covered in future cometary apparitions, or through the re-
As discussed in section 3, the gas flow immediately analysis of archival data [e.g., the recent detection of ethyl-
above the nucleus surface is extremely complex. The gas ene glycol in Comet Hale-Bopp (Crovisier et al., 2004)].
is not in LTE, and interacts strongly with the entrained dust. Coma chemistry modeling will be necessary to identify the
Small-scale topography and heterogeneity of the nucleus precise source of these molecules. Also, once the relevant
can lead to steep spatial gradients in gas pressure and chemi- laboratory data is available, future molecule discoveries will
 Rodgers et al.: Physical and Chemical Processes in Cometary Comae 519

surely come from the existing large database of unidenti- CN(X2Σ+), with unsaturated hydrocarbons. Astrophys. J., 545,
fied cometary lines (Feldman et al., 2004). It is also probable 892–906.
that many more isotopomers of the principal parent mole- Bernstein M. P., Sandford S. A., Allamandola L. J., Chang S., and
cules will soon be detected. The resulting isotopic ratios will Scharberg M. A. (1995) Organic compounds produced by pho-
tolysis of realistic interstellar and cometary ice analogs contain-
contain important clues about the origins of comets.
ing methanol. Astrophys. J., 454, 327–344.
We have stressed in this chapter the coupling between
Biermann L. (1951) Kometenschweife und solare Korpuskular-
the physics and chemistry in the coma. The chemistry and strahlung. Z. Astrophys., 29, 274–286.
dynamics also strongly influence the excitation of coma Biermann L., Giguere P. T., and Huebner W. F. (1982) A model of
molecules, particularly daughter molecules that will be pro- a comet coma with interstellar molecules in the nucleus. Astron.
duced in excited states, as well as polar molecules that can Astrophys., 108, 221–226.
be excited by collisions with the hot electrons in the outer Biver N. and 13 colleagues (1999) Spectroscopic monitoring of
coma. Therefore, in order to fully understand the observed Comet C/1996 B2 (Hyakutake) with the JCMT and IRAM radio
energy level distributions, combined dynamic-chemistry- telescopes. Astron. J., 118, 1850–1872.
excitation models are required. For example, Reylé and Biver N. and 22 colleagues (2002) The 1995–2002 long-term
Boice (2003) developed such a model for the S2 excitation monitoring of Comet C/1995 O1 (Hale-Bopp) at radio wave-
length. Earth Moon Planets, 90, 5–14.
in the coma. Accurate calculations of the excitation, and its
Bockelée-Morvan D. and Crovisier J. (1987) The 2.7-micron water
spatial variation, are particularly important when interpret-
band of comet P/Halley — Interpretation of observations by an
ing interferometric maps of the coma. excitation model. Astron. Astrophys., 187, 425–430.
In the final analysis, coma chemistry models are only Bockelée-Morvan D., Crovisier J., and Gerard E. (1990) Retriev-
as good as the kinetic data they employ. As discussed in ing the coma gas expansion velocity in P/Halley, Wilson
section 5.1, there are large uncertainties in some of the (1987 VII) and several other comets from the 18-cm OH line
photodissociation and ionization rates used in these mod- shapes. Astron. Astrophys., 238, 382–400.
els. Rate coefficients for bimolecular reactions are typically Bockelée-Morvan D. and 17 colleagues (2000) New molecules
taken from databases developed for modeling interstellar found in comet C/1995 O1 (Hale-Bopp). Investigating the link
clouds [e.g., the UMIST ratefile (Le Teuff et al., 2000)]. between cometary and interstellar material. Astron. Astrophys.,
Although many of the most important reactions in these 353, 1101–1114.
Bockelée-Morvan D., Crovisier J., Mumma M. J., and Weaver
schemes have been measured, there are many others for
H. A. (2004) The composition of cometary volatiles. In
which experimental data is lacking. For the ion-molecule
Comets II (M. C. Festou et al., eds.), this volume. Univ. of Ari-
chemistry in the coma the most important reactions are exo- zona, Tucson.
thermic proton transfer reactions; fortunately, many of these Boice D. C., Huebner W. F., Keady J. J., Schmidt H. U., and
have been measured, or can safely be assumed to occur at Wegmann R. (1986) A model of Comet P/Giacobini-Zinner.
the Langevin collisional rate. Regarding the possible supra- Geophys. Res. Lett., 13, 381–384.
thermal chemistry that may occur in the coma, however, Boice D. C., Huebner W. F., Sablik M. J., and Konno I. (1990)
very few reactions have been measured, and it is likely that Distributed coma sources and the CH4/CO ratio in comet
there are many reactions currently omitted from interstellar Halley. Geophys. Res. Lett., 17, 1813–1816.
reaction schemes that may be important in the coma. With Blake G. A., Qi C., Hogerheijde M. R., Gurwell M. A., and
the exception of POM, the product yields from photodegra- Muhleman D. O. (1999) Sublimation from icy jets as a probe
of the interstellar volatile content of comets. Nature, 398, 213–
dation of proposed CHON constituents are also unknown.
216.
Finally, very few of the rates for collisional excitation have
Canaves M. V., de Almeida A. A., Boice D. C., and Sanzovo G. C.
been measured; most values are simply estimates. (2002) Nitrogen sulfide in Comets Hyakutake (C/1996 B2) and
Hale-Bopp (C/1995 O1). Earth Moon Planets, 90, 335–347.
Acknowledgments. This work was supported by NASA’s Canaves M. V., de Almeida A. A., Boice D. C., and Sanzovo G. C.
Planetary Atmospheres Program through NASA Ames Cooperative (2004) Chemistry of NS and CS in cometary comae. Adv. Space
Agreement NCC2-1412 with the SETI Institute (S.D.R. and S.B.C.) Res., in press.
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 Combi et al.: Gas Dynamics and Kinetics in the Cometary Coma 523

Gas Dynamics and Kinetics in the Cometary Coma:

Theory and Observations
Michael R. Combi
University of Michigan

Walter M. Harris
University of Washington

William H. Smyth
Atmospheric & Environmental Research, Inc.

Our ability to describe the physical state of the expanding coma affects fundamental areas
of cometary study both directly and indirectly. In order to convert measured abundances of gas
species in the coma to gas production rates, models for the distribution and kinematics of gas
species in the coma are required. Conversely, many different types of observations, together with
laboratory data and theory, are still required to determine coma model attributes and parameters.
Accurate relative and absolute gas production rates and their variations with time and from comet
to comet are crucial to our basic understanding of the composition and structure of cometary
nuclei and their place in the solar system. We review the gas dynamics and kinetics of cometary
comae from both theoretical and observational perspectives, which are important for understand-
ing the wide variety of physical conditions that are encountered.

1. INTRODUCTION and N. This description is most applicable for a typical

comet observed in the range of a few tenths to about 2 AU
Gases, primarily water, and entrained dust are liberated from the Sun. For comets much farther away, temperatures
from the icy nucleus by solar heating when a comet is and velocities are smaller and reaction length scales are
within a few astronomical units (AU) of the Sun and form larger. And for comets much closer (Sun-grazers), tempera-
an outflowing cometary atmosphere. The cometary atmo- tures and velocities are much larger and reaction length
sphere, or coma, expands to distances many orders of mag- scales are smaller.
nitude larger than the size of the nucleus itself. Because of Our understanding of the conditions within a few times
the ultimate expansion into vacuum and the very weak grav- the radius of the nucleus results largely from model pre-
ity that affects only the largest dust particles, a Knudsen dictions that are only constrained by the gas fluxes and
layer of a fraction to a few meters in thickness (a few times velocities hundreds of nucleus-radii from the nucleus, and
the molecular collision mean free path) forms near the sur- are determined both by in situ and remote observations.
face where the gas organizes itself into a transient stationary There are not many direct observations about the conditions
thermal layer. The initiation of regular flow transforms this near the surface, beyond the images of 1P/Halley from the
thermal layer into a rapid transonic dusty-gas flow with a Giotto and Vega spacecrafts and those of 19P/Borrelly from
typical scale length of 10–100 m. Expansion and nearly adi- the Deep Space 1 spacecraft, which show only the dust dis-
abatic cooling dominates the flow out to scales of ~100 km tribution. This region is described in detail in Crifo et al.
where the dust becomes decoupled collisionally from the (2004). The photodissociation, photoionization and fast ion-
gas. Here the gas flows with a speed of ~700 m s–1 and has neutral chemical reactions involving ultimately ~100 spe-
a cool temperature of <30 K. The energetic photochemical cies and thousands of reactions forms a complex atmos-
products of solar UV photodissociation then begin to heat phere/ionosphere that is described in detail in Rodgers et
the gas faster than it can cool by adiabatic expansion or IR al. (2004).
radiational cooling, and the gas kinetic temperature and The region of the coma accessible by remote ground-
ultimately the outflow speed increase. Photoionization and based and Earth-orbit-based observations and by direct in
charge impact ionization (~5–10% of the photodissociation situ sampling by spacecraft instrumentations (mostly by
rate) forms a cometary ionosphere on scales of 103–104 km, neutral gas and plasma mass spectrometers) for detailed
which ultimately interacts with the magnetized plasma of study generally covers distances larger than a few hundred
the solar wind forming an ion tail on scales of 105–107 km. kilometers from the nucleus. Remote imaging observations
Also, at large scales of 106–107 km, the neutral coma is of this region have provided information about the projected
broken down into its atomic constituents, such as O, H, C, line-of-sight-integrated distribution of neutral gas and ion

523
524 Comets II

species in two spatial dimensions on the sky plane and 2. FREE-EXPANSION MODELS
sometimes the line-of-sight velocity distribution. Thus re-
mote sensing provides somewhat convoluted, nonunique, 2.1. Eddington to Wallace and Miller
global views of the coma, whereas in situ measurements Fountain Models
have provided some detailed information about neutral gas
and ion densities, velocities, and temperatures, but only for In Eddington’s fountain model the comet is assumed to
a few fleeting threads along a few spacecraft trajectories. be a uniform and isotropic point source of emitters of light
Information about kinetic and rotational temperatures has such that their density (e.g., gas or dust) would fall as the
been obtained by both remote observations and in situ meas- inverse square of the distance from the source, except the
urements. The spectroscopic measurements are discussed emitters are also subject to a uniform acceleration that
in detail in Bockelée-Morvan et al. (2004) (for parent spe- pushes on them from a given direction (presumably from
cies) and Feldman et al. (2004) (for nonparent species). the Sun’s direction). Eddington showed that such a model
It is important to understand the physical state of the defines a paraboloid of revolution along a line parallel to
coma and its variations because it is largely from analyses the acceleration and passing through the point source (the
of observations of various species in the coma that we de- nucleus of the comet) such that
termine the composition of the larger population of com-
v2 v4
ets. Although in the last 20 years IR and radio astronomy x2 + y2 = 2z + (1)
have opened the possibility of directly observing parent gas a a2
species in comets, interpreting these observations is com- where the acceleration, a, is directed in the +z direction, x
plicated by difficult excitation mechanisms, atmospheric and y complete the righthanded Cartesian coordinates, and
extinction (in the IR), and generally weaker signal-to-noise v is the initial uniform outflow speed of the emitting par-
when compared with visible and near-UV measurements of ticles. In this case the density, n, of emitting particles is
daughter species. The interpretations of measurements of determined by two trajectories that cross any given point
daughter species have their own sets of complicating issues within the paraboloid. Later work by Mocknatsche (1938),
regarding production models and kinematics. However, which was independently rediscovered by Fokker (1953)
routine observations of daughter species in the visible re- and later described by Wallace and Miller (1958), showed
mains critically important for the foreseeable future because that the column density, which is what would be observed
they are more sensitive for weak comets and especially for by a remote observer through an optically thin paraboloid
those at large heliocentric distances. This is the only prac- of such particles, N, can be calculated after some algebraic
tical way to characterize the composition and activity of the manipulation for any line-of-sight that passes within the
entire population of comets and to compare with the large projected paraboloid for any angle between the Sun, comet,
base of existent data. Observations of daughter species in and observer to simply be
the visible should also be made and interpreted side-by-side
Q
with IR and radio observations of parent species for brighter N= (2)
comets and those at generally smaller heliocentric distances 4vR
to enable the entire complex picture to be unraveled. where Q is the global particle production rate and R is the
In this chapter we concentrate on those aspects of photo- projected distance on the “sky” plane from the source (i.e.,
chemistry and dynamics that are important for understanding the nucleus). Interestingly, this is the same result as for a
the overall physical state of the coma, and their variations point source without the acceleration. The projected shape
from comet to comet, with changing heliocentric and com- of the paraboloid, of course, depends on the viewing geom-
etocentric distance, and, most importantly, in the region etry. Such a model is still used to understand many basic
sampled by observations, i.e., outside a few hundred kilo- properties of the observed dust distribution in comets.
meters from the nucleus. We also discuss quantitative mod-
els of the coma beginning with the original fountain model 2.2. Haser (1957) Model
of Eddington (1910), which started the heuristic approach
continued by Haser’s (1957) model that in turn later treated Most radiative emissions of gaseous species in comets
the coma as a free expansion problem including produc- in visible light are caused by fluorescence with sunlight
tion and loss processes. From there we move to physics- through an otherwise practically optically thin medium.
based models that treat the energy budget, dynamics, and Early quantitative observations of gas species in the com-
chemistry, leading to hydrodynamics, kinetic and hybrid etary coma indicated that the spatial variation of the ob-
models. These models provide the basis for interpreting and served brightness of some emissions (e.g., C2, CN, etc.)
linking together multiple diagnostic observations of com- deviated from the simple inverse distance relation of a
ets that are becoming increasingly precise. Care must be simple fountain model. It was also realized that most of the
taken in interpreting observations either using complex gas species observed and identified through visible range
models with too many free (and especially unconstrained) spectroscopy were not stable molecules but unstable radi-
parameters, or using simple models with mathematically cals that could be stored in an otherwise icy nucleus but
constrained parameters, where their direct physical mean- were more likely produced in the photodissociation of par-
ing may be simplistic or inaccurate. ent molecules by solar UV radiation. In order to describe
 Combi et al.: Gas Dynamics and Kinetics in the Cometary Coma 525

the kind of expected distribution of an observed gaseous

species in the coma of a comet, one needs to account (po-
tentially) for the creation of that species from a parent spe-
cies and its destruction into some simpler species. An
example would be the production of observed OH by photo-
dissociation of H2O and the subsequent photodissociation
of the OH into O + H.
The quantitative description of this was put forth by
Haser (1957) in a now classic formulation that is still widely
used today. Haser considered the distribution of a second-
ary species (like some cometary radical) being produced by
the photodissociation of some parent molecule and in turn
being destroyed by some photodestruction process. If the
coma is considered to be a spherically symmetric point
source of uniformly outflowing parent molecules, where an
exponential lifetime describes its destruction, then the den-
sity, np, of parents at some distance from the point source,
r, is given by
Q Fig. 1. Family of Haser model profiles of daughter species col-
np(r) = (e−r/γ p)
4πr2v umn densities for different values of the ratio of the scale lengths
plotted as a function of projected distance in units of the daugh-
The density, nd, of a daughter species created by the de- ter scale length. Note that a scale length ratio of infinity (∞) cor-
struction of these parents is given by responds to a parent molecule distribution.

Q γd
nd(r) = (e−r/γ p − e−r/γ d) (3)
4πr v γp − γd
2
2.3. Models with Secondary Product Velocities

where r is the distance from the nucleus, and γp and γd are Of the several simplifying assumptions of Haser’s model
the parent and daughter scale lengths given by the product as most often used, which include spherical symmetry,
of the radial outflow speed, v, and exponential lifetimes of constant outflow velocity, and steady-state gas production,
the parent of the observed species, τp, and that of the ob- one of the basic assumptions is that both the parent and
served daughter species, τd, itself, respectively. The model daughter products undergo purely radial motion. Early re-
is most often used with observed intensity spatial profiles, sults of UV observations of comets indicated that H and
which are typically proportional to the column density pro- OH were produced by photodissociation of water and that
file of the emitting species. Therefore, normally equation (3) this would lead to nonnegligible excess energy, which would
is integrated along the line-of-sight. This can either be per- be distributed in the form of superthermal velocities for the
formed numerically or written in the form of modified Bes- daughter products. The large speeds of the H atoms imply
sel function as done originally by Haser, which yields velocities for the heavier products in the photodissociation
network, namely O and OH, in the range of 1–2 km s–1.
ρ
These are generally larger than the outflow speed of the
ρ
γp γd parent molecules in the coma itself and therefore posed a
Q γd
Nd(ρ) =
2πρv γp − γd ∫ K (y)dy − ∫ K (y)dy
0
0
0
0 (4) serious violation of the assumption of radial outflow for
daughter species in Haser’s model. However, the use of
Haser’s model for interpreting spatial profiles of column
density derived from brightness observations already re-
where ρ is the projected distance from the nucleus through quired either integrals of modified Bessel functions (equa-
which the line-of-sight integration is performed and K0(y) tion (4)) or direct numerical integration of the density
is the modified Bessel function of the first kind. function (equation (3)) itself. The addition of nonradial ejec-
Figure 1 (Combi and Fink, 1997) shows the range of tion of daughter species yields a nonanalytical integral for
the family of column density spatial profiles possible with the density function itself.
Haser’s model. An interesting, but little mentioned, attribute Festou (1981a) and Combi and Delsemme (1980) ad-
of this equation is that the spatial profile shape is the same dressed solving this problem in two different ways. Festou
if the parent and daughter scale lengths are interchanged, (1981a) introduced the vectorial model, which represented
yielding simply an extra factor of the ratio of the two scale a numerical approach to directly solving for the density and
lengths. This means that it is not possible to say whether column density distribution. Combi and Delsemme (1980)
the parent or daughter scale length is the smaller based only introduced Monte Carlo techniques, developed originally
on an observation of the daughter spatial profile. for nuclear reactor particle transport and radiative transfer
526 Comets II

calculations, to simulate the expansion. In their more mod- In order to complete the substitution in the density or col-
ern versions, the vectorial model is faster computationally, umn density expressions for Haser’s model, the effective
but the Monte Carlo technique is directly applicable to even radial velocity, v, in the denominators in the first terms on
more general problems, such as variable outflow velocity, the righthand sides of equations (3) and (4) must be the
aspherical comae, and radiation pressure acceleration of the Haser equivalent daughter expansion velocity vdH, given as
daughter species.
The main effect of the ejection of daughter species on γdH
vdH = vd (8)
observed spatial profiles is that profiles produced are not γd
related to those using Haser’s model with scale lengths sim-
ply given by the velocities × the lifetimes. These more com- 2.4. Three-Generation Haser-like and
plicated models did, however, account for the fact that most Monte Carlo Models
prospective parent molecule lifetimes were actually longer
than the Haser model parent scale length would indicate, Observations of spatial profiles of cometary C2 have
given a reasonable assumption for the parent velocity. often had some difficulty in being interpreted either with a
Combi and Delsemme (1980) also introduced what simple two-generation Haser model or with a model ac-
started as a heuristic geometrical argument for relating the counting for secondary product ejection velocities (see
given velocities and lifetimes that would give a realistic Feldman et al., 2004). The problem is that the innermost
spatial profile with the vectorial model (or Monte Carlo part of the profile has often been seen to be even flatter than
simulation) to a Haser model with some set of Haser scale is possible to be reproduced using any Haser model. A
lengths. This so-called “average random walk model” speci- Haser model that has the flattest inner profile (see Fig. 1)
fies transformations from the actual parent and daughter is one in which the parent and daughter scale lengths are
velocities and lifetimes to the equivalent Haser-model scale equal. Models that allow for secondary product velocities
lengths. Also, like the typically used vectorial model and actually exacerbate the problem, because the effect of iso-
first Monte Carlo models, this assumes the coma is colli- tropic ejection of daughters makes the radial parent scale
sionless for the daughter products. In the case of a highly length seem to be shorter, thus making the profile look like
collisional coma, the ejection velocity will be collisionally Haser models with unequal scale lengths.
quenched; however, in this case, another simplification of Observations of C2 in Comet Halley (O’Dell et al., 1988;
the Haser model, a constant radial outflow speed, will most Wyckoff et al., 1988; Fink et al., 1991) were noteworthy in
certainly be violated. Such was the case for C/1995 O1 showing the flattening of the inner profile. Fink et al. (1991)
Hale-Bopp (Combi, 2002). If vp and ve are the parent out- chose to use the standard two-generation Haser model but
flow and daughter ejection velocities, respectively, and τp fitted models with equal parent and daughter scale lengths.
and τd are the parent and daughter lifetimes, respectively, Wyckoff et al. (1988) suggested that either C2 was produced
then the Haser equivalent parent and daughter scale lengths, as a granddaughter species or by grains instead of simple
γpH and γdH, can be calculated from the following set of photodissociation. These had been suggested much earlier
relationships. If we make the definitions that by both Jackson (1976) and Cochran (1985). O’Dell et al.
vp γp γpH (1988) pursued the granddaughter species idea by perform-
tanδ ≡ µ≡ µH ≡ ing model calculations for a three-generation Haser-type
ve γd γdH model, generalizing the earlier work of Yamamoto (1981)
where γp = vpτp and γd = vdτd, vd = (v2p
+ v2e )1/2 and ve is the and Festou (1981a), who applied a three-generation Haser-
isotropic ejection velocity of the daughter upon production type model to comet-centered, circular aperture observa-
with respect to the original center-of-mass of the parent. The tions.
equations (5)–(7) can be used to go back and forth between The three-generation Haser-type model yields an expres-
the vectorial values and the Haser equivalent scale lengths sion for the column density profile that was given by O’Dell
for a given ratio of the parent outflow to daughter ejection et al. (1988) as
velocity.
Q1
N(ρ) = [AH(β1ρ) + BH(β2ρ) + CH(β3ρ)] (9)
γ2d − γp2 = γ2pH − γ2dH (5) 2πV3ρ

where Q1 is the global production rate of the observed

µ + sinδ
µH = µ (6) (granddaughter) species; V3 is its radial expansion velocity;
1 + µ sinδ and β1, β2, and β3 are the inverse scale lengths of the original
parent, the intermediate daughter, and the observed grand-
or equivalently daughter species, respectively. The quantities A, B, and C are
given as
1/2
sinδ sin2δ β 1β 2 −A(β1 − β3)
µ = (µH − 1) (µH − 1)2 + µH (7) A= B=
2 4 [(β1 − β2)(β1 − β3)] (β2 − β3)
 Combi et al.: Gas Dynamics and Kinetics in the Cometary Coma 527

−B(β1 − β2) one gives the flattest possible inner profile); (2) a Monte
C= Carlo simulation of a three-generation model that is other-
(β1 − β3)
wise similar to that which could be produced using equa-
The function H(x) is given by tion (12) of O’Dell et al. (1988) and could, as they showed,
give a reasonable reproduction of the spatial profile of C2 in
π x
H(x) =
2
− ∫ K (y)dy
0
0 Comet 1P/Halley, (3) a Monte Carlo simulation of a three-
generation model where the ejection velocity of the prod-
where K0(y) is again the zero-order modified Bessel function uct at each dissociation equals half of the parent outflow
of the second kind. velocity; and (4) a similar model but where both ejection
One of the simplifications of this model is the same as velocities are equal to the parent velocity. They also pro-
in the two-generation model of Haser (1957), i.e., that at vided other sets of comparisons. The result was that the
each step the daughter and granddaughter species are as- addition of daughter and granddaughter ejection velocities
sumed to continue to travel in a purely radial direction. causes three-generation models to be unable to produce flat
Combi and Fink (1997) addressed this by using Monte inner profiles, and makes them essentially similar to some
Carlo techniques to explore models that include ejection two-generation Haser or vectorial model with different
velocities for the dissociation product at either or both dis- parameters. Conversely for C2, the results implied that if
sociation steps. This was done for the purpose of putting C2 is a third-generation species, then the total of the ejec-
limits on prospective original parents of observed C2, but tion velocities for each dissociation step had to be less than
would also explain the flat inner profile. Figure 2 shows one about half the parent outflow velocity. In typical photodisso-
of their figures showing comparisons of four otherwise ciations there are 2–4 eV of excess energy that would im-
comparable models: (1) a two-generation Haser model part an ejection velocity of 1 km s–1 or more to the heavier
where the parent and daughter scale lengths are equal (this dissociation product that would contain C2, or C2 itself.

2.5. Grains as Gas Sources

Volatile grains have been suggested as possible sources

for observed species in comets for a long time (see review
by Festou, 1999). The idea regained new interest with the
discovery of CN and C2 jets in Comet 1P/Halley (A’Hearn
et al., 1986) and extended sources for CO and H2CO (Eber-
hardt et al., 1987; Meier et al., 1993; DiSanti et al., 2001),
and from observations of a substantial distributed icy grain
source from C/1996 B2 (Hyakutake) (Harris et al., 1997;
Harmon et al., 1997). Delsemme and Miller (1971) pre-
sented a model calculation for the production of an observed
gas from grains, analogous to the two-generation model of
Haser (1957), except where evaporating grains serve as the
parent of the observed species rather than photodissociat-
ing parent molecules.
This model, however, suffers from the same limitation
as Haser’s model, which is that the observed daughter spe-
cies is restricted to perfectly radial motion. Clearly mole-
cules released from evaporating grains would have some
nonnegligible velocity owing to the temperature of the
grains. The effect would be even more important if the
Fig. 2. Haser and three-generation model spatial profiles with grains were dark organic-rich CHON grains, which are ex-
non-zero daughter ejection speeds. Case 1 from Combi and Fink pected to reach and sublimate at temperatures higher than
(1997) compares a general three-generation dissociation model the blackbody temperature for some given distance from
with ejection speeds at each dissociation. The two ejection speeds the Sun (Lamy and Perrin, 1988). This temperature would
are equal to each other and either equal to the parent outflow generally be much higher than the sublimation temperature
speed, v0, or to half of it. The three-generation radial model is
of water for heliocentric distances less than about 3 AU.
one where there is zero ejection speed for the photodissociation
Combi and Fink (1997) introduced a CHON grain halo
products at either step. The “Best Haser Model” is one where the
daughter and parent scale lengths are equal, which results in the model for gas species that generalizes the icy grain halo
flattest inner profile that is most like the observed inner profile model of Delsemme and Miller (1971) in the same way as
of C2 in Comet 1P/Halley. When the daughter ejection speed is the vectorial (Festou, 1981a) and Monte Carlo (Combi and
nonnegligible, a three-generation model does not produce a flat Delsemme, 1980) models generalized Haser’s model, i.e.,
inner profile. by allowing for isotropic ejection of the daughter species
528 Comets II

TABLE 1. Photochemical branching and exothermic velocities for H2O vapor.

Photodestruction Rate* (10 –6 s–1)

Solar Ultraviolet Product [Branching Ratio]
Wavelength Range Reaction Exothermic Velocities (km s–1) (Quiet Sun) (Active Sun)
1357–1860 Å H2O + hν → H + OH(X2Π) 18.5 (H)† 1.09 (OH)† 4.84 [0.465] 5.36 [0.380]
→ H2 + O(1D) <13.7 (H2) <1.71 (O) 0.05 [0.005] 0.05 [0.004]

1216 Å H2O + hν → H + OH(X2Π) 17.2 (H)† 1.01 (OH)† 3.02 [0.291] 4.53 [0.321]
→ H + OH(A2Σ+) 5 (H)‡ 0.3 (OH)‡ 0.35 [0.033] 0.52 [0.037]
→ H2 + O(1D) <15 (H2)‡ <1.8 (O)‡ 0.43 [0.042] 0.65 [0.046]
→H+O+H <7.4 (2H)§ <0.87 (O)§ 0.52 [0.050] 0.78 [0.055]

984–1357 Å H2O + hν → H + OH(X2Π) <37–27 (H)¶,** <2.2–1.6 (OH)¶,** 0.30 [0.028] 0.45 [0.032]
(excluding 1216 Å) → H + OH(A2Σ+) <25–0 (H)** <1.5–0 (OH)** 0.03 [0.003] 0.05 [0.004]
→ H2 + O(1D) <22–14 (H2)** <2.7–1.7 (O)** 0.04 [0.004] 0.07 [0.005]
→H+O+H <17–0 (2H)** <2.0–0 (O) ** 0.05 [0.005] 0.08 [0.005]

<984 Å H2O + hν → neutral products — — 0.25 [0.024] 0.41 [0.029]

→ ionization products — — 0.52 [0.050] 1.16 [0.082]

Total: 10.40 [1.000] 14.11 [1.000]

* From S. A. Budzien (personal communication, 2003); updated and slightly different than Budzien et al. (1994).
† Average velocity from Crovisier (1989) and similar to Wu and Chen (1993).
‡ Average velocity from Festou (1981b).
§ Determined using the excess energy of 13 kcal mole–1 from Slanger and Black (1982).
¶ Similar to the values of 35–25 (H) and 2.0–1.2 (OH) from Festou (1981b).

** Upper limits determined for the bounding lower and higher (or threshold) wavelengths.

from the radially outflowing parent grains (in this case). The centric distance and radial velocity of the comet as well as
flat inner profiles of cometary C2 have been the main sub- the wavelength-dependent short-term modulations and
jects of three-generation and grain-halo models, and can be longer-term 11-year periodic variations in solar radiation.
reproduced by either three-generation or grain-source mod-
els with appropriate parameters (Combi and Fink, 1997). 3.1. Water Photochemistry

3. WATER-DOMINATED OUTFLOW The photochemistry and photochemical kinetics for H2O

in comets have been studied in detail by a number of in-
Water dominates up to ~90% of the volatile species that vestigators (Huebner and Carpenter, 1979; Openheimer and
outflow from the cometary nucleus within ~3–4 AU from Downey, 1980; Festou, 1981a,b; Huebner, 1985; Krasno-
the Sun. During this outflow, the H2O parent molecule is polsky et al., 1986a,b; Allen et al., 1987; Crovisier, 1989;
destroyed primarily through photodissociation, and to a Huebner et al., 1992; Wu and Chen, 1993; Cochran and
much smaller extent, through photoionization and also dis- Schleicher, 1993; Budzien et al., 1994). The calculated
sociation and ionization interactions with solar wind ions photodestruction rates for different products have become
and electrons. The destruction of H2O creates secondary or more accurately determined with time because of improve-
daughter molecular products, OH and H2, atomic products, ments in cross sections and in the description of the solar
O and H, and various ion species in the inner and outer flux spectrum and its time variations, although a number of
comet coma. The neutral product species are detected re- uncertainties still remain. A summary of the relevant photo-
motely through solar resonance fluorescence for OH and destruction reactions, product exothermic velocities, reac-
H and also through dissociative excitation for O. The disso- tion rates, and branching ratios for H2O is given in Table 1
ciation rates of H2O, OH, and H2 and the imparted exother- and is divided into four wavelength ranges.
mic energy to their daughter products are of fundamental The first wavelength range is bounded above by the ef-
importance in determining the spatial decay rates of these fective onset wavelength at 1860 Å for a nonzero photo-
parent and daughter species in the coma and in determin- absorption cross section, and below by the threshold wave-
ing the basic background density and temperature structure length at 1357 Å for which OH can be produced in excited
for all species in the coma. The photodestruction rates of electronic states. In this first wavelength range, the mea-
H2O, OH, and H2 are variable and depend upon the helio- sured relative branching ratios of the rates for the first and
 Combi et al.: Gas Dynamics and Kinetics in the Cometary Coma 529

second reaction are 0.99 and 0.01 respectively (Stief et al., products [OH(X2Π), OH(A2Σ+), and H2] that determines the
1975), where in the second reaction O(1D) is produced since available excess kinetic energies for the products. Only
the production of O(3P) is spin forbidden. upper limits are therefore given for many of the product
The second wavelength range is only for the large exothermic velocities in Table 1. For different assumptions
Lyman-α peak at 1216 Å in the solar spectrum. For the regarding the product abundances and the configuration of
Lyman-α peak, the measured relative branching ratios of the internal energy of OH, examples are given in Wu and
the rates for the four reactions are 0.70, 0.08, 0.1, and 0.12 Chen (1993) for the velocity distributions of H and OH that
respectively (Slanger and Black, 1982), where the geom- bound their behaviors.
etry and mechanisms for the three-body dissociation in the
fourth reaction are not known (see Wu and Chen, 1993). 3.2. Ion and Electron Impact Water Chemistry
The third wavelength range is from 1357 Å to the thresh-
old wavelength at 984 Å for ionization of water and ex- The solar wind plays a minor role in the destruction of
cludes the solar spectrum contribution of the Lyman-α peak. water compared to photochemistry but plays an important
In the third wavelength range, the relative branching ratios role in the ion chemistry of the coma, which also involves
for the four reactions are not well known and are assumed many other atomic and molecular ions (Häberli et al.,
in Table 1 to be the same as for the Lyman-α wavelength. 1997). A summary of the most relevant solar wind proton
The fourth wavelength range is below the ionization and electron reactions with H2O and the values of the cor-
threshold at 984 Å and includes a contribution from a disso- responding destruction rates is given in Table 2 for a nomi-
ciation cross section with unknown neutral products and a nal solar wind flux of 3 × 108 cm–2 s–1 at 1 AU as reported
contribution from an ionization cross section with a mix of by Budzien et al. (1994). The largest water destruction rate
ionized and not-well-defined neutral products. The cross is for charge exchange with protons, followed by electron
section for photoionization becomes more important than impact ionization, proton impact ionization, proton impact
that for photodissociation below ~875 Å (see Wu and Chen, dissociation, and electron impact dissociation. At 1 AU, the
1993). charge exchange rate is comparable to the photoionization
The H2O photodestruction rates for the four wavelength rate of ~4.1 × 10–7 s–1 for quiet Sun conditions, but is smaller
ranges depend upon an accurate specification of the appro- than the photoionization rate of ~1.04 × 10–6 s–1 for active
priate wavelength-dependent cross sections and the variable Sun conditions (Huebner et al., 1992). These destruction
solar flux. The photodestruction rates adopted in Table 1 are rates are not well established due to uncertainties in cross
for the most recent calculations of S. A. Budzien (personal sections and furthermore vary significantly due to chang-
communication, 2003), which are based upon updated in- ing solar wind conditions upstream of the comet bow shock
formation for the photodissociation cross section in the first and to spatially changing properties of the ion and electron
wavelength range and the solar flux at 1 AU and provide distributions in the cometosheath, outer coma, inner coma,
improved rates that differ only slightly from those calcu- and ion tail. The electron impact rate of 3 × 10 –7 s–1 in
lated earlier by Budzien et al. (1994). Depending upon quiet Table 2 is, for example, a typical value for solar wind elec-
and active Sun conditions, the first wavelength range con- trons in the outer coma, but may be considerably larger,
tributes ~47.0–38.4% of the total photodestruction rate, the ~1 × 10 –6 s–1, for electrons heated in the cometosheath,
Lyman-α solar spectra peak contributes ~41.6–45.9%, the where it may be comparable to the active Sun water pho-
third wavelength range contributes 4.0–4.6%, and the fourth toionization rate, and even larger in the inner coma where
wavelength range contributes 7.4–11.1%. The correspond- stagnation flow and photoelectrons are also present (Cra-
ing branching ratios for the individual reactions in the four vens et al., 1987). The total water destruction rate for the
wavelength intervals are also given and are determined by nominal values in Table 2 is 1.08 × 10–6 s–1. Since this total
the relative branching ratios discussed earlier. The total solar wind destruction rate varies throughout the coma, it is
photodestruction rate of H2O has a value in Table 1 for quiet
and active Sun conditions, respectively, of 1.04 ± 0.123 ×
10–5 s–1 (lifetime ~0.96 × 105 s) and 1.411 ± 0.175 × 10–5 s–1 TABLE 2. Solar wind destruction for H2O vapor.
(lifetime ~0.71 × 105 s).
For the different wavelength ranges in Table 1, the prod- Destruction
uct exothermic velocities depend upon the details of the Reaction Rate (10 –7 s–1)
photochemical kinetics and are distributed nonuniformly in H+ + H2O → H + H2O+ 5.7
discrete velocity groups that are constrained between 0 and → H+ + H2O+ + e 0.75
2.7 km s–1 for O, between 0 and 2.2 km s–1 for OH, between → dissociated neutral products 0.27
0 and 22 km s–1 for H2, and between 0 and 37 km s–1 for
H. The product exothermic velocities and their correspond- e + H2O → H2O+ + e + e ~3 (variable)
ing velocity distributions are generally not well known → dissociated neutral products 1.1
because of the lack of cross sectional information as a func- Destruction rates for a nominal solar wind flux of 3 × 108 cm–2 s–1
tion of wavelength for the internal energy of the molecular from Budzien et al. (1994).
530 Comets II

TABLE 3. Photochemical branching and exothermic velocities for OH.

OH Predissociation Product Exothermic Photodestruction Rate (10 –6 s–1)

Wavelength State Reaction Velocities* (km s–1) (Quiet Sun) (Active Sun)
2160 Å A2Σ+ (v' = 2) OH + hν → O (3P) + H 8 (H) 0.5 (O) 3.0–6.1† 2.5–5.6‡ 3.0–6.1† 2.5–5.6‡
2450 Å A2Σ+ (v' = 3) OH + hν → O (3P) + H 11 (H) 0.7 (O) 0.5† 0.5†
1400–1800 Å 12Σ OH + hν → O (3P) + H 22–26 (H) 1.4–1.6 (O) 1.4† 1.4§ 2.3† 1.58§
1216 Å 12 ∆ OH + hν → O (1D) + H 26.3 (H) 1.6 (O) 0.3† 0.38§ 0.75† 0.57§
1216 Å B2Σ OH + hν → O (1S) + H 17.1 (H) 1.1 (O) 0.05† 0.05§ 0.13† 0.08§
1216 Å 22Π–32Π OH + hν → O (1D) + H 26.3 (H) 1.6 (O) 0.10† 0.24§ 0.25† 0.39§
<1200 Å D2Σ OH + hν → O (3P) + H 22 (H) 1.4 (O) <0.01† — <0.01† —

<958 Å OH + hν → ionized products — — 0.25§ 0.47§

* Product exothermic velocities from van Dishoeck and Dalgarno (1984) with slight updates from Combi (1996).
† Rates from van Dishoeck and Dalgarno (1984).
‡ Combined A2Σ+ (v' = 2 and v' = 3) rate from Schleicher and A’Hearn (1988).
§ Rates from Budzien et al. (1994).

therefore likely to alter the overall water lifetime by some- UV solar flux for these lower wavelengths varies signifi-
what less than 10%. cantly with solar cycle. The product exothermic velocities
are distributed nonuniformly between 8 and 26.3 km s–1 for
3.3. Daughter Product Energetics and H and between 0.5 and 1.6 km s–1 for O. By adding together
Branching Ratios in the Coma the second column entries in Table 3 for the newer rates and
the last row entry rate, the total OH photodestruction rate
The photochemistry and photochemical kinetics for OH then varies with heliocentric velocity from 4.82 to 7.92 ×
have been studied in detail by a number of investigators 10 –6 s–1 (lifetime of 1.26–2.05 × 105 s) for quiet Sun con-
(Schleicher and A’Hearn, 1982, 1988; van Dishoeck and ditions with more typical values of ~5.2–6.3 × 10–6 s–1 (life-
Dalgarno, 1984; Huebner et al., 1992; Budzien et al., 1994). time of ~1.6–1.9 × 105 s) and from 5.59 to 8.69 × 10 –6 s–1
A summary of the relevant OH predissociation states and (lifetime of 1.15–1.79 × 105 s) for active Sun conditions
their corresponding dissociation reactions, product exother- with more typical values of ~6.0–7.1 × 10–6 s–1 (lifetime of
mic velocities, and dissociation rates, as well as OH pho- ~1.4–1.7 × 10 5 s). The OH photodestruction rate (lifetime)
toionization rate, is given in Table 3 and is divided into is then about a factor of 2 smaller (larger) than the photo-
individual contributions for various wavelengths. For the destruction rate (lifetime) for water.
first two wavelengths at 2160 Å and 2450 Å, OH dissoci- The photochemistry and photochemical kinetics for H2,
ates from the A2Σ+ state after absorption of solar radiation a minor dissociative species (5.1–5.5%) of water in Table 1,
during the fluorescence process. The dissociation rates for are summarized in Table 4, as given by Huebner et al.
these two wavelengths do not vary between quiet and ac- (1992). A little more than half the H2 destruction produces
tive solar conditions because at these longer wavelengths two hydrogen atoms with exothermic velocities of 28 km s–1
the solar flux is highly stable. These two contributions to and 6.3–6.5 km s–1, about one-third produces H+2, and some-
the rate, however, vary with heliocentric radial velocity, with what less than 10% produces H + H+. The total H2 photo-
the major contribution from the A2Σ+ (v' = 2) predissocia- destruction rate for all the reactions in Table 4 is 0.146 ×
tion state. For the combined A2Σ+ (v' = 2 and v' = 3) rates, 10 –6 s–1 for quiet Sun conditions and 0.33 × 10–6 s–1 for ac-
this variation is about a factor of 2 with a calculated value tive Sun conditions.
of 3.5–6.6 × 10–6 s–1 and of 2.5–5.6 × 10–6 s–1, respectively,
determined earlier by van Dishoeck and Dalgarno (1984) 3.4. Solar Activity Variations
and more recently by Schleicher and A’Hearn (1988). This
variation is caused because the dissociation that occurs at The primary time variability in the dissociation and ion-
discrete energy levels above the dissociation threshold is ization rates for water and its daughter products noted above
produced by absorption of solar radiation, which has a solar arises from changes that occur in the extreme UV (λ <
radiation-pumping rate that varies with heliocentric radial 1000 Å) and far UV (1000 Å < λ < 2000 Å) fluxes from
velocity through the Swings effect (Jackson, 1980). the Sun. These time variations occur during the 11-year
The dissociation rates for the next five wavelength en- periodic solar cycle because of the variation in the number
tries are produced through direct photodissociation of OH of sunspots that create enhanced extreme UV and far UV
in the 12Σ, 12∆, B2Σ, 22Π–32Π, and D2Σ repulsive states. fluxes from the Sun. The distribution of sunspots on the
These photodissociation rates, as well as that for the <958-Å rotating solar disk also introduces short-term 27-day modu-
wavelength entry for photoionization of OH, are listed for lations of the solar flux, which can be significant compared
quiet and active Sun conditions, since the UV and extreme to quiet Sun conditions. The photochemistry rates sum-
 Combi et al.: Gas Dynamics and Kinetics in the Cometary Coma 531

TABLE 4. Photochemical data for H2.

Product Exothermic Photodestruction Rate (10 –6 s–1)

Reaction Velocities (km s–1) (Quiet Sun) (Active Sun)
H2 + hν → H(1s) + H(1s) 28 (2H) 0.048 0.11
H2 + hν → H(1s) + H(2s,2p) 6.3–6.5 (2H) 0.034 0.082

H2 + hν → H+2 + e — 0.054 0.11

H2 + hν → H + H+ + e — 0.0095 0.028
Product exothermic velocities and rates from Huebner et al. (1992).

marized in Tables 1, 3, and 4 only characterize the basic velocity distribution functions for species p and q, cq is the
changes between the quiet and active Sun conditions and velocity, r is the spatial coordinate, F represents external
thus provide only a basic picture that may be altered sig- forces, crpq is the magnitude of the relative velocity between
nificantly by short-term time variations of the solar radia- particle p and q, Ω is the solid angle, the asterisks (*) indi-
tion that are poorly known for observations of particular cate postcollision particles, the lq subscript refers to the
comets, except for those rare cases where the Sun-comet scattering target particles, and σpq is the total collision cross
line crosses near one of the solar spectrum monitors [e.g., section between species p and q (which can in general be
the Solar and Heliospheric Observatory (SOHO) or Solar velocity dependent). In the collision integral on the right-
Ultraviolet Spectral Irradiance Monitor (SUSIM)]. hand side of the equation, f* represents additions of par-
For convenience, the formulae are given here from Bud- ticles, scattered into the region of velocity space in question,
zien et al. (1994) for the total water photodestruction rate i.e., between c and c + dc, whereas f without the asterisk
(τ tot –1 tot –1
H2O) and the total OH photodestruction rate (τ OH) as a represents scattering out of that region.
function of solar activity indices F10.7 (the 10.7-cm flux), The Boltzmann equation makes neither assumptions nor
its 81-day average, 〈F10.7〉, in solar flux units 10–22 W m–2, any restrictions as to the form of the distribution functions.
the solar He I λ10830 equivalent width in mÅ, the solar Various velocity moment expansions of the integrals over
wind flux 〈nv〉sw in cm–2 s–1, and the heliocentric velocity the distribution functions yield equations of conservation
dependent predissociation rate given in tabular and graphical of mass, momentum, and energy. The assumption of local
form by Schleicher and A’Hearn (1988), [τOH prediss (r)]–1 thermodynamic equilibrium (LTE) and the resulting Max-
well-Boltzmann distribution functions yield the Euler equa-
(τ tot –1
H2O) = 5.868 × 10
–6 + 1.49 × 10 –9 F
10.7 tions for fluid dynamics. The Chapman-Enskog theory is a
+ 2.08 × 10–9 〈F10.7〉 + 9.587 × 10 –8 W10830 perturbation from the Maxwell-Boltzmann distribution,
+ 4.1 × 10 –15 〈nv〉sw (in s–1) which yields the Navier-Stokes equations with viscosity and
heat flux. For the intended purpose of studying tenuous
(τ tot –1
OH) = 1.479 × 10 –6 + 5.8 × 10–10 F10.7 atmospheres and transitions from an LTE fluid to free-flow,
+ 8.1 × 10 –10 〈F10.7〉 + 1.678 × 10–8 W10830 the basic assumptions for these approximations are inher-
+ 3.7 × 10–15 〈nv〉i + [τOH
prediss (r)]–1 (in s–1) ently violated, and therefore a potentially arbitrary form for
the distribution functions remains to be considered.
4. PHYSICS-BASED MODELS Direct analytical or even numerical solutions for the
Boltzmann equation have been done for numbers of ideal-
4.1. Collisional Boltzmann Equation ized simple problems (Fahr and Shizgal, 1981), for reduced
for Rarefied Gases spatial or velocity dimensions, or for specific analytical
forms of the collision integral [see the textbook by Gombosi
The appropriate description for the physical state of any (1994) for an up-to-date treatment of gaskinetic theory].
one of up to s species, p, in a multispecies dilute gas can Even one-dimensional flow problems yield three-dimen-
be described by the Boltzmann equation (Gombosi, 1994), sional distribution functions, one spatial and two velocity.
which is given as For similar reasons the Direct Simulation Monte Carlo
(DSMC) method has also been adopted to treat multidimen-
∂ ∂ ∂ sional, multispecies gas flows for tenuous planetary appli-
(f ) + cp ⋅ (fp) + F ⋅ (f ) =
∂t p ∂r ∂c p cations. In the computational fluid dynamics community,
s + ∞ 4π (10) DSMC is the method of choice for validating such fluid
∑∫ ∫
q = 1 −∞ 0
(f *pf *lq − fpflq)crpqσpqdΩdclq approaches, such as solution of the Navier-Stokes equations
(Bird, 1994). For example, the modelers of shock structures
in one-dimension have typically “resorted” to Monte Carlo
where fp ≡ fp(r ,c,t) and fd ≡ fd(r ,c,t) are the full phase space simulation for numerical experiments.
532 Comets II

4.2. Time-Dependent Hydrodynamics on the individual particle size populations as

N
If one multiplies the Boltzmann equation, alternatively,
by 1, v, and v2 (where v is the gas velocity) and then inte-
F=− ∑F
i−1
i

grates the resulting equations over the vector velocity, the where the size dependent force is given by
resulting equations correspond to conservation laws of mass
3ρi
continuity, momentum, and energy (Gombosi et al., 1986). Fi = pC'Dsi
These equations can be closed and combined with the ideal 4aiρbi
gas law to provide a useful way to understand the trans- where
port and energy of the gas in the coma. The energy and mo- u−v
mentum equations obtained can be manipulated to yield an si =
2kT/m
equation for gas pressure instead of energy. Dust-gas phys-
ics can be added in the form of dust continuity and momen- k is the Boltzmann constant, T is the gas temperature and
tum equations with standard collisional coupling terms that m is the gas mean molecular mass. The accommodation of
assume the gas mean free path is much larger than the dust gas via collisions with hotter dust yields the dust-gas heat
size and that gas molecules accommodate to the dust sur- exchange rate Qgd, which is given as
face temperature upon a collision. Since there is no random
internal energy component for dust particles, no pressure/ N
γ+1
energy equation is required. For detailed derivations see the
papers, for example, by Gombosi et al. (1986) and Crifo et
Qgd =
γ
ρCpu (T rec
i=1
∑
i − Ti)St'i (16)

al. (1995). The coupled system for a single-fluid gas and

multicomponent dust (i.e., dust size distribution) can be Here Cp is the gas heat capacity at constant pressure and
written as the rest of the coefficients can be defined under the assump-
tion of diffusive reflection such that
∂ρ δρ
+ ∇ ⋅ (ρu) = (11) 2 π Ti 2s2 + 1 −s2
∂t δt C'D = + i e i+
3 T s2i π
(17)
∂u 4s4i + 4s2i − 1
ρ + ρ(u ⋅ ∇)u + ∇p = −F (12) erf(si)
∂t 2s3i

1 ∂p 1 γ −1 2
+ (u ⋅ ∇)p +
i = 1+
Trec
λ − 1 ∂t γ−1 s R' T (18)
(13) γ +1 i i
γ
p(∇ ⋅ u) = −Qgd + Qph − QIR
γ−1
1 e−s2i 1
2si + + 2s2i + 2 − erf(si)
∂ρi δρ si π s2i
+ ∇ ⋅ (ρiui) = i i = 1, …, N (14) R'i = (19)
∂t δt e−s2i 1
si + s2i + erf(si)
∂v π 2
ρi i + ρi(vi ⋅ ∇)vi = Fi i = …, N (15)
∂t

e−s2i 1 1
where ρ is the gas mass density, u is the gas velocity, p is St'i = + 1+ erf(si) (20)
the gas pressure, and vi and ρi are the velocity and mass 8si π 8 2s2i
density for dust particles of radius ai. The righthand sides of
all the equations contain the various source terms. The term Finally, ρd is the bulk mass density of dust particles of
δρ radius ai, T is the gas temperature, and Ti is the dust tem-
perature, assumed in equilibrium with solar radiation. A
δt
temperature-dependent value can be used for Cp to account
is the gas production source rate, and for some of the effects of divergence from LTE, especially
δρi at low temperature, where all internal degrees of freedom
are not available. Otherwise the other intermediate quanti-
δt
ties are si, the relative Mach number between gas and dust;
is the dust production source rate for particles of radius, ai. C'D, the dust-gas drag coefficient; Tirec, the recovery tempera-
F is the gas-dust drag force, which is related to the forces ture; R'i, the heat transfer function; and St',i the Stanton
 Combi et al.: Gas Dynamics and Kinetics in the Cometary Coma 533

number. Most of the dust-gas drag physics comes from the optically thick in some lines, and that the rotational tem-
formulation by Finson and Probstein (1968) with later cor- perature comes out of equilibrium with the gas kinetic tem-
rections discussed by Wallis (1982), Kitamura (1986), and perature with increasing distance from the nucleus. The
Körösmezey and Gombosi (1990). optical depth is normally handled with an escape probabil-
ity based on the estimate of Huebner and Keady (1983).
4.3. One-Dimensional Spherical An approximate kinetic to rotational energy transfer rate has
Steady-State Equations been incorporated into effective cooling rates by Crovisier
(1984, 1989). The kinetic simulations by Combi (1996) ex-
The general three-dimensional time-dependent Euler equa- plicitly include a microphysical description of internal rota-
tions of hydrodynamics can be reduced to a steady-state tion energy, which indicates that the earlier approximations
one-dimensional version, which is very useful for under- are generally reasonable.
standing the basic physical state of the outflowing coma.
Again, a detailed description of the derivation was given 4.4. Hybrid Kinetic/Fluid Models
in the review paper by Gombosi et al. (1986). These are
For typical comets over a wide range of gas production
rates and heliocentric distances, the photochemical heating
Qm
ρ= (21) rate is not simple to calculate because the coma gas is not
4πur2 in local thermodynamic equilibrium. As discussed in detail
in a previous section of this chapter, water photodissocia-
du dp
ρu =− −F (22) tion reactions provide the bulk of excess energy for the
dr dr coma, with the main dissociation branch
dvi
ρivi = Fi (23) H2O + hν → H + OH + Energy (25)
dr
providing most of the energy. Because there is excess en-
ergy after overcoming the chemical bond energy on the
1 d u2 γ p
ρur2 + = S − L + Qgd (24) order of 2 eV for this reaction and the products H and OH
2
r dr 2 γ −1ρ must conserve both energy and momentum, so 17/18 of the
energy is imparted to the H atom, producing it with an
Assuming the normal ideal gas law excess velocity of ~17.5 km s–1. The OH radical, on the
ρkT other hand, has an excess velocity of 1.05 km s–1. Typically
p= in modeling energy balance and transport in a planetary
m
atmosphere, the gas densities are large enough that one can
the above system of equations can be solved from an initial normally assume that all the photodissociative heating en-
boundary condition, e.g., at or near the surface of the nu- ergy happens locally, so the heating rate is just given as the
cleus. The main difficulty in implementing the steady-state sum of the products of the local species gas density, the
version of the hydrodynamic equations is if one specifies the excess energy per dissociation, and the dissociation rate. In
inner boundary at or so close to the surface of the (spheri- a comet coma the region where the gas density is large
cal) nucleus that the gas is subsonic, in which case the tran- enough for local photochemical heating efficiency to be
sonic transition is an undefined point. This has been ad- 100% depends on the overall gas production rate and the
dressed either using a shooting method (Marconi and Mendis, expansion velocity of the coma. In addition, because of the
1983), or by using the approach of Gombosi et al. (1985), dominant ~1/r2 fall-off of the density, the decrease of photo-
which solves explicitly for the conditions at or just above chemical heating efficiency is gradual compared to a plane-
the sonic point, normally only meters above the surface of tary atmosphere with an exponential scale height variation in
a spherical nucleus with radius of typically a few kilometers. density. It therefore is not possible to define, strictly speak-
In this case Fi is purely radial and the same dust-gas drag ing, a collision zone size for the heating caused by hot
force as used in the time-dependent equations (11)–(15). superthermal H atoms.
In this case, Q in equation (21) is the simple molecular Ip (1983) first addressed the issue of photochemical
gas production rate, u is the radial gas velocity, S is the heating efficiency for the superthermal H atoms and derived
photochemical heating rate, L is the IR cooling rate. Other an analytical estimate. Huebner and Keady (1983) devel-
variables are consistent with the definitions in the previous oped an escape probability formalism to treat the escaping
section of this chapter. The IR cooling rate has been esti- superthermal H atoms, and Marconi and Mendis (1983)
mated a number of ways over the last three decades, first treated two populations of H atoms: a superthermal com-
heuristically by Shimizu (1976) and then more explicitly by ponent and a thermal one to deal with the photochemical
Crovisier (1984, 1989), Crifo et al. (1989), and Combi heating efficiency. Combi (1987) and Bockelée-Morvan and
(1996). Complicating effects are that water densities are Crovisier (1987) performed Monte Carlo calculations for
large enough in the inner coma for the IR radiation to be individual superthermal H atoms and modified the photo-
534 Comets II

chemical heating rate using the accumulated collisional

energy transfer. Generally the heating efficiency increases
with larger gas production rates (Fig. 3) because of in-
creased gas densities and at smaller heliocentric distance
(Figs. 4 and 5) because of increased photodissociation rates.
Figure 6 shows results by Ip (1989) for hybrid kinetic/fluid
calculations of outflow speeds in Comet 1P/Halleycompared
with measurements of propagating CN shells. These results
are consistent with otherwise similar comparisons of differ-
ent datasets by Combi (1989).
The complementary part of this approach is to predict
the distribution of observed daughter species given a real-
istic physical description of the inner “parent” coma and
the nonequilibrium collisional processes that alter the ve-
locity distribution function of the daughter species. This was
first done by Kitamura et al. (1985) for hydrogen assum-
ing a constant velocity point source parent coma. A gen-
eral time-dependent, three-dimensional approach was taken
by Combi and Smyth (1988a,b), whereby the parent coma
was described by a time-variable hybrid/kinetic calculation
and applied to explain the type of empirical H-atom veloc-
ity distribution found by Meier et al. (1976) for observa-
tions of the shape of the Lyman-α coma of Comet Kohoutek
for two very different sets of conditions. It has been suc-

Fig. 4. Radial velocity and gas kinetic temperatures in Comet

1996 B2 (Hyakutake) from models by Combi et al. (1999a). Helio-
centric distance varies from 0.94 to 0.71 AU. The production rates
for the dates beginning with March 30 are 2.0, 2.2, 2.7, and 4.0 ×
1029 s–1.

cessfully applied to a number of comets since then, includ-

ing 1P/Halley by Smyth et al. (1991) and the very extreme
case of C/1995 O1 (Hale-Bopp) by Combi et al. (2000). As
shown in Feldman et al. (2004), in addition to being able
to reproduce the spatial morphology of the coma, which is
sensitive to the velocity distribution because of the large
solar radiation pressure acceleration on H atoms, it was
applied directly to Goddard High Resolution Spectrograph
(GHRS)/Hubble Space Telescope (HST)-measured Doppler
line profiles of H Lyman-α in Comet C/1996 B2 (Hyaku-
Fig. 3. The effect of coma gas production rate on radial veloc-
ity and kinetic temperature in the coma. Model calculations by take) by Combi et al. (1998) and subsequently included in a
Bockelée-Morvan and Crovisier (1987) from top to bottom for gas full-wavelength-dependent radiative transfer calculation by
production rates of 1027, 1028, 1029, and 1030 s–1. The dashed Richter et al. (2000). The approach was also generalized
portions of the lines correspond to the outer nonfluid region of for heavy species and applied to OH by Combi et al. (1993);
the coma. O(1D) and NH2 by Smyth et al. (1995); C2, CN, NH2, and
 Combi et al.: Gas Dynamics and Kinetics in the Cometary Coma 535

initial assumed description for the distribution function of

the gas that serves as a background for test particles of the
same gases. In this particular case water molecules are
emitted from the model nucleus and dissociation products
(OH, H, O, etc.) are produced in a random but physically
fair fashion. Collision probabilities are calculated between
the test particles and current version of the background
distribution functions for all species, and the test particles
are scattered as necessary. A new background distribution
is accumulated (or partially accumulated) from the state of
the test particles in each iteration, which then serves as a
new background. The premise is that once the background
distribution and the test particle distribution converge to the
same state, then that state describes the steady-state solu-
tion for the gas. Xie and Mumma (1996a,b) updated some of
the statistical algorithms from the original model of Hodges,
improving the sampling of velocities for collision pairs and
including a more accurate description of the IR rotational
cooling by water molecules.
A DSMC model proceeds by following the detailed mol-
ecular motions of many molecules (thousands to millions)
simultaneously, including their responses to imposed fields
(e.g., gravity, or E and B fields in the case of charged parti-
Fig. 5. Model radial velocity and gas kinetic temperatures in cles), binary collisions, and chemistry. The assumption of bi-
Comet Kohoutek by Combi and Smyth (1988b) for large produc- nary collisions is quite good for a dilute gas and basically re-
tion rate and small heliocentric distance. quires that the gas density be such that the distance between
molecules is much larger than the molecular size. Quite
dense gases, for instance, the standard density at the surface
of Earth, which is in the realm of hydrodynamics, easily
satisfy this condition.
A DSMC model is inherently time dependent and can
address a wider range of problems than TP methods. Steady-
state situations are achieved by running a simulation for a
long enough time given steady-state initial and boundary
conditions. Therefore, the final state does not depend per se
on the initial state provided the system is given an adequate
time to relax. The initial state could start at some given state,
or a vacuum. In terms of computational resources the inher-
ently steady-state iterative TP approach requires less mem-
ory than a steady-state version of a DSMC; however, both
must sample a similar number of individual particles over
a similar time with similar time steps in order to model a
real physical system with similar statistical accuracy. There-
fore, the total number of computations between the two
methods should be roughly equivalent.
Fig. 6. Model-data comparison of expansion velocity of CN A DSMC model begins by setting the initial state of a
shells in Comet 1P/Halley by Ip (1989). certain number of molecules of all species in question
throughout the simulation volume. Various boundary con-
ditions from which new particles are introduced into the
O(1D) by Combi et al. (1999a); and then to NH2 by Tegler simulation volume must be defined and characterized. The
et al. (1992) and Kawakita and Watanabe (1998). simulation is divided into small time steps, ∆tS, which must
be small enough so that only a small fraction (<0.1) of
4.5. Kinetic Models particles in any volume of space will collide over that time,
and so that the forces (accelerations) yield small enough
The first fully kinetic model for the water-dominated velocity changes, thereby allowing some finite-difference
cometary coma that included a fairly complete description formulation to follow the particle trajectories. Higher-order
of the physics was presented by Hodges (1990). This cal- schemes can also be used for this purpose if the timescale
culation was of the test particle (TP) type. It starts with an for trajectory variations owing to outside forces (e.g., grav-
536 Comets II

ity, or electromagnetic) is much smaller than the collision

timescale. Furthermore, each spatial cell can have its own
collision time step, so that useless collision testing need not
be performed when the densities are quite low. This clearly
occurs high enough in an atmosphere or far enough away
from the nucleus in a cometary coma, and means that col-
lisions that occur more frequently in regions of high den-
sity can be sampled as often as necessary.
There are clear advantages to kinetic DSMC methods in
being able to treat a whole range of non-LTE processes as
well as multiple species. At the same time there are serious
computational penalties, so particle kinetic methods are not
meant to be substitutes for all other modeling techniques
in all applications: Clearly simple models such as Haser
or vectorial and hydrodynamics approaches, such as Euler
and Navier-Stokes, are highly useful.
A very useful application of DSMC to an expanding
comet atmosphere was to understand the time-dependent
effects of the dynamics of the expanding atmosphere of
Comet 1P/Halley (Combi, 1996). Figure 7 shows a plot of
the measured outflow speed of the heavy molecules in the
coma as measured by the neutral mass spectrometer on the
Giotto spacecraft (Lämmerzahl et al., 1987) compared with
time-dependent DSMC model calculations. Shown are the
time variations of the dependence of the radial outflow
speed on distance from the nucleus owing to the variation
in the water production rate at the nucleus. The model uses
a time-variable production rate at the nucleus derived from
the photometric lightcurve of Schleicher et al. (1990) us-
ing an analysis of spatial profiles of a number of species
by Combi and Fink (1993), which is also shown. When the
production rate is large, the gas densities are high and col-
lisional thermalization of the superthermal H atoms is effi-
cient. This causes an increase in the photochemical heating Fig. 7. Time-dependent DSMC model calculation for Comet 1P/
that drives an increase in the outflow speeds. Therefore, the Halley around the time of the Giotto encounter. In the top plot
radial outflow speeds corresponding to peaks in the light- results are shown for maximum, minimum, and Giotto flyby
curve are noticeably larger than those during the troughs. phases of the lightcurve. Time variations were adopted from the
For the factor of 3–4 in production rate variation in Halley, photometry of Schleicher et al. (1990), and are shown in the plot
this turned out to be a fairly sensitive change, especially below. The seven-day periodic gas production variation leads to
when the timescale for large production rate changes is 25% variations of the outflow speed.
comparable to the timescale of transit of gas across the
coma. As shown by the appropriate lightcurve for the phase
of the Giotto measurements, the model predicts the meas- find that outside the most collisionally thick region of the
ured velocities. As shown, if the comet had been at a dif- coma, where the Euler equations are valid, there is a re-
ferent phase of the variation (only a day or so earlier or gion where the Navier-Stokes equations provide a reason-
later), a measurably different velocity profile would have able calculation of the coma density and velocity flow field,
been obtained. as verified in numerical experiments with DSMC. However,
Skorov and collaborators have used DSMC to explore as mentioned above, the very near-nucleus region is dis-
the Knudsen layer at the nucleus surface/coma boundary cussed in Crifo et al. (2004). In the larger “observable”
(Skorov and Rickman, 1998; Markiewicz et al., 1998) and coma, which we address in this chapter, not only are the
the porous upper layers of the surface of the nucleus itself Euler equations not valid, but also DSMC is very useful to
(Skorov et al., 2001). More recently, Crifo and collabora- model simultaneously multiple species, including photo-
tors (Crifo et al., 2002, 2003) have been comparing calcu- chemical products that are far from any Maxwellian or
lations using DSMC and solutions of the Euler equations slightly skewed Maxwellian distribution assumed for Navier
and Navier-Stokes equations formulation of hydrodynam- Stokes. Here, DSMC is the only currently developed viable
ics for a dusty-gas coma in the vicinity of the nucleus. They alternative.
 Combi et al.: Gas Dynamics and Kinetics in the Cometary Coma 537

4.6. A CO-Dominated Coma eter. Such large temperatures lead to large outflow veloci-
ties at a few nucleus-radii in the range of 0.65–0.75 km s–1
The observed examples of CO-dominated comae are for or more. Accounting for the expected temperature differ-
comets at large heliocentric distances, like Comets 29P/ ences between 3 and 6 AU does not explain the factor-of-2
Schwassmann-Wachmann 1 and 1995 O1 (Hale-Bopp). smaller observed speed in Hale-Bopp. So, at least for the
Biver et al. (1999a) found that the coma of Comet Hale- case of Hale-Bopp, their surface temperature model is too
Bopp underwent a transition from CO-dominated to H2O- hot, but the basic physics of the flow velocity is otherwise
dominated at a heliocentric distance of about 3 AU both reasonable. Clearly, the CO reservoir temperature from Hale-
before and after perihelion. There were velocity resolved Bopp was less than the expected surface temperature. This
millimeter-radio observations of CO, CH3OH, and H2CO either says something important about the surface tempera-
in Hale-Bopp when the comet was at a heliocentric distance ture for these comets at 6 AU or more likely about the tem-
of 6 AU (Jewitt et al., 1996; Womack et al., 1997) and the perature accommodation for CO gas effusing through the
coma was CO-dominated. The CO emission indicates pri- upper porous layers.
marily sunward-directed velocities of 0.3–0.4 km s–1 that
are much larger than would be expected for an exposed 5. SPATIAL AND VELOCITY
sublimated CO-ice surface, which is 25 K when emitted into MEASUREMENTS: OBSERVATIONAL
a vacuum (Yamamota, 1985). On the other hand, emissions TECHNIQUES AND MODELS
from CH3OH and H2CO indicate a more isotropic ejection
that possibly points to an extended source by photodisso- The methods used to study the composition and struc-
ciation of parent molecules and/or sublimation from icy ture of comet comae are beginning to reach the point where
grains. The most reasonable explanation is that CO is likely gas production rates, energy balance, chemistry, velocity
released from the dayside of the nucleus when the subsur- structures, radial distributions, temporal-spatial variability,
face thermal wave causes the dominant H2O ice to undergo and the interaction of the coma with solar wind are all ac-
a phase transition from crystalline to amorphous ice, which cessible at some level with remote sensing, although the
happens at about 125 K (Prialnik et al., 2004). At such a inversion of data to physical parameters continues to require
temperature, CO would be released from the ice below the model interpretation and coordinated complementary ob-
surface and could diffuse through porous upper layers of servations. Maturation of these techniques has been both
the nucleus surface. A temperature of 125 K is consistent technical and physical. The widespread use of linear, high-
with the observed velocity. dynamic-range detectors has improved sensitivity and pho-
There has been little theoretical work done on the pos- tometric accuracy in the visible, while advances in digital
sible conditions in the coma of a comet that is dominated quantum efficiency and array size have combined with
by CO. Ip (1983) computed a photochemical/hydrodynamic larger telescope apertures to increase the absolute sensitiv-
model for a CO-dominated comet at a heliocentric distance ity limit and angular scale over which comets are studied.
of 1 AU, conditions which, we know now in hindsight, are Substantial improvements in UV, IR, and radio instrument
unlikely to occur. Observations of comets to date would capabilities have made accessible many minor species, ther-
indicate that any comet at a heliocentric distance of 1 AU mal diagnostic bands, and faint or previously undetectable
would be water-dominated. The model assumes that the gas emissions from parent species and their atomic end states,
is released from the surface at the vapor-pressure-equilib- while new developments in interferometric, high-resolution,
rium sublimation temperature of CO ice, which is 40 K. The and integral-field (multipoint) spectroscopic techniques
photochemical heating effects of CO at 6 AU are negligible have opened up the study of fine structure and the low-
compared with the model at 1 AU because of the increase velocity (<1 km/s) characteristics in different regions of the
of the CO lifetime by a factor of 36, and this is compounded coma. Finally, our ability to monitor the variable elements
by a production rate for Hale-Bopp that was only a few × of the solar UV spectrum that drive photochemistry has
1028 molecules s–1, and the fact that CO is a reasonably improved our ability to validate theoretical rate calculations
efficient at cooling in the IR (Chin and Weaver, 1984). This and to separate the linked variables of velocity and lifetime
would result in any energetic photodissociation products in expansion models.
(hot superthermal C and O atoms) to be emitted well out- To take full advantage of these improved observational
side the collision zone for this comet. capabilities requires corresponding improvements in our
More recently, Crifo et al. (1999) presented results of understanding of how photolysis, branching ratios, and fluo-
aspherical models for CO-dominated comae of Comets 29P/ rescence efficiencies of a chemical species affect its role
Schwassmann-Wachmann 1 and 46P/Wirtanen. They as- and evolution in the coma, and of how the detailed struc-
sumed that CO diffuses through the surface of a comet at a ture of the coma affects the convergence of measurement,
heliocentric distance of 3 AU, which reaches the local equilib- models, and their relationship to actual conditions. In this
rium temperature of a blackbody with values ranging from section we describe the most widely used techniques for
230 K at the subsolar point to 41–73 K on the nightside de- remote sensing of the evolution of the H2O coma, with an
pending on the value of a surface recondensation param- emphasis on spatial distributions, photometric measure-
538 Comets II

ments, and spectroscopic study of line shapes and Doppler radians; ∆ is the geocentric distance (cm); τx is the photo-
shifts [see Feldman et al. (2004) for an expanded discus- chemical lifetime of species X in seconds; Ix is the field-
sion of spectroscopy]. We emphasize observation and mod- averaged brightness in Rayleighs; and gx is the fluorescence
eling of the evolution of water and its daughters in the efficiency (photons s–1). In a model inversion of resonance
applied examples; however, it should be clear how these line photometric data we are limited by the precision of our
techniques and their limitations are applicable to other coma knowledge of lifetime and fluorescence efficiency. In the
species. Each of these techniques is specialized to the de- case of metastable prompt emissions, a single photon is
sired feature (radial distribution, velocity profile, total pro- produced, which simplifies the relationship such that the
duction rate) or spatial scale (inner vs. outer coma) under production rate follows directly from the brightness (Schultz
study, or is either instrumentally [e.g., Far Ultraviolet Spec- et al., 1993)
troscopic Explorer (FUSE)] or physically (e.g., quenched
radio or metastable emissions) limited to specific regions Qx = 4π∆2ΩIx (27)
of the coma. Such focus means that a detailed understand-
ing is rarely achieved with an isolated observation, and we with the parent production rate following from the chemi-
discuss the value and challenges of a synergistic, coordi- cal branching ratio to the metastable species. The accuracy
nated observational approach for modeling the full dynamic of metastable photometry is similarly limited, in this case
and photochemical evolution of the coma. by our knowledge of the formation rate from its parent(s)
and the contribution of loss/production mechanisms that are
5.1. Remote Sensing of the Spatial, Thermal, important in the inner coma. Neither relationship accounts
and Velocity Properties of Cometary Water for potential complications such as collisional or chemical
quenching, opacity to solar photolyzing or scattering radia-
The observational strategies used to study the H2O coma tion, or Swings/Greenstein g-factor variation (irrelevant for
spatially, photometrically, and in velocity space can be bro- metastable emissions), all of which introduce uncertainties
ken down into five areas: (1) aperture summation (wide and that must be addressed in the model interpretation. Even
narrow field); (2) one- and two-dimensional mapping (nar- when these ancillary factors are correctly addressed, the
row bandpass imaging, spectro-imaging, multiplexed spec- resulting photometric measurement will represent a time-
troscopy); (3) velocity-resolved imaging (interferometric averaged production rate for the period of travel across the
data cube studies); (4) aperture-summed line-shape mea- aperture for the slowest-velocity component of the target
surements (high-resolution/étendue spectroscopy); and species.
(5) temperature sensing. Each of these techniques provide a To derive production rates when the FOV is less than
distinct diagnostic of a given species such as total produc- the diameter of the scale length, the above relationships
tion rate, spatial distribution, temporal variance, tempera- must be adjusted by an aperture correction (AC) term that
ture, or velocity distribution, all on spatial scales ranging accounts for emission beyond the edge of the aperture. The
from the extreme inner coma (102–103 km) to the diffuse value of AC is determinable using model estimates of the
outer coma and ion tail (105–107 km). The results neces- scale lengths (γx ~ vxτx) of the species under study and its
sarily reflect the target diagnostic of the observation in the parent using either simple spherical expansion (Haser-type)
coma/tail region where the information is sought, which or streaming particle (vectorial or Monte Carlo) models, or
limits the scope of a model interpretation. observationally by comparing the models to the total sig-
5.1.1. Aperture summation. Being essentially the case nal obtained by moving apertures (Oliversen et al., 2002)
of zero-dimensional imaging, aperture summation is used to different locations in the coma or using apertures of dif-
to detect faint or low surface brightness features, multiple ferent angular sizes. Coarse scale-length estimates are rela-
lines of a single molecular band, and/or to provide the high- tively straightforward for species (e.g., OH) in simple radial
est possible photometric accuracy on a single coma com- outflow assuming a static, symmetric quasithermal veloc-
ponent. The measurements are done either with a combina- ity relationship such as the vr ~ 0.85 RH–0.5 (where vr and
tion of narrow bandpass target-continuum filter image sub- RH are the outflow velocity and heliocentric distance) of
traction (Schleicher et al., 1998; Kiselev and Velichko, 1999; Budzien et al. (1994). However, a precise scale-length meas-
Grün et al., 2001) or spectrophotometrically (Schultz et al., urement is far more complicated if there are substantial non-
1993; Oliversen et al., 2002). In addition to providing high thermal components, e.g., for H (Richter et al., 2000), if
photometric accuracy, aperture summation is a useful tool there is significant acceleration across the coma (Harris et
for obtaining production rates. This is particularly power- al., 2002; Combi et al., 1999b; Bockelée-Morvan et al.,
ful for the case of wide-field measurements that sample the 1990), temporal variability in gas production, or an ex-
entire scale length of a given species. For fluorescence, such tended source region. At the low end of aperture size, where
measurements invert directly to production rate requiring only the inner coma is sampled [e.g., FUSE (Feldman et
only knowledge of the transition g-factor and lifetime via al., 2002) or the CSHELL spectrometer on the IRTF (Dello
Russo et al., 2000)], the above complications become more
Qx = 106IxΩ∆2/(gxτx) (26) significant, while other unresolvable factors, including
quenching, collisional chemistry (Komitov, 1989), accelera-
where Ω is the solid angle of the field of view (FOV) in tions, and/or asymmetries (spatial and temporal) in gas pro-
 Combi et al.: Gas Dynamics and Kinetics in the Cometary Coma 539

duction further confuse the interpretation. For observations eling the radial shape with spherical expansion or stream-
of parent species with apertures that are small compared ing particle models that require some additional knowledge
with the molecular scale length, one can use the relation of the outflow velocity distribution and/or chemical lifetime.
that is identical to equation (2) where the number of mol- In the case where the detectable dynamic range of the im-
ecules can be extracted knowing only the outflow velocity. age extends from the inner coma to the edge of the target
5.1.2. One- and two-dimensional spatial imaging. Spa- species scale length, a photometrically derived production
tial maps of the coma are obtained using interferometric rate can be combined with radial data to put constraints on
imaging in the radio, spectroscopic imaging in the visible, the production rate and velocity distribution (Harris et al.,
fiberoptically multiplexed or image-sliced spectral tech- 2002) and hence constrain the uniqueness of the model fit.
niques, long-slit imaging spectroscopy (low to high reso- However, if the usable (above detection threshold) FOV is
lution), and narrow bandpass filter images targeting specific less than the scale length of the species under study, a com-
neutral species, ions, and dust continuum points (see Schlei- bination of photometry and model is required. Since spatial
cher and Farnham, 2004). After the removal of sky, con- mapping does not provide velocity information (fiber-op-
tinuum, and detector background the resulting data provides tically multiplexed and image sliced spectral maps are an
a snapshot of the radial, azimuthal, and temporal structure exception), the same limitations on velocity estimates hold
of a coma species. Spatial data cube spectroimages of dif- for imaging studies that are encountered in aperture pho-
ferent lines in thermally diagnostic molecular rotational tometry and the accuracy of the production rate will depend
bands can also be used to track the evolving thermal prop- on the precision of the estimate.
erties of the coma. Such two-dimensional measurements are 5.1.3. Velocity-resolved aperture photometry. An accu-
of immense value for model analysis as they contain records rate measurement of the velocity distribution for a coma
of gas production variability, extended source distributions, species is critical to a detailed understanding of its spatial
radial column density profiles, scale-length information, and distribution, chemistry, temperature, and evolution, particu-
local temperature, although they do come at the expense larly when using detailed models that are capable of ad-
of photometric accuracy in the lower surface brightness dressing multiple component, accelerating, and/or nonradial
outer coma. line profiles (e.g., DSMC or hydrodynamic models). Me-
Long-slit spectra provide single-dimensional spatial maps dium resolution enables the detection of Doppler-broadened
of brightness with radial distance from the nucleus. These or -shifted components of emission lines (e.g., Larson et
spectra are most useful for measuring radial profiles of sev- al., 1987), but it is generally not sufficient for resolving the
eral species at low spectral resolution and providing velocity expansion velocities (1–10 km/s) of most coma species. The
dispersion, Doppler shifts, and line ratios in a single mole- very high spectral resolution (R >> 105) needed to detect low-
cule at medium/high resolution. As with two-dimensional velocity flows is problematic for narrow-aperture grating-
imaging, slit spectroscopy is less effective in the outer coma type spectrographs, because the required combination of
where the surface brightness of the emissions is low. To ex- high signal to noise and high spectral resolution is difficult
tract radial information from the faint, diffuse outer coma, to achieve for the low surface brightness emissions that de-
a spatial summing technique can be applied to a two-di- scribe the coma and ion tail beyond the immediate vicinity
mensional image that collapses the azimuthal dimension of of the nucleus. Aperture-summation techniques provide far
a spectrally filtered image into a single averaged profile of greater étendue and thus sensitivity to diffuse emissions such
brightness as a function of distance from the nucleus (i.e., a as those in comet comae, and radio frequency measurements
ring sum). Azimuthally averaged data provides much greater of OH and other molecular radicals (e.g., CO, HCN, H2O)
sensitivity to the radial profile in the outer coma, where the have emerged as an effective technique for detection of out-
shape is strongly dependent on the outflow velocity distribu- flow velocity signatures as small as 0.1–1 km/s (Bockelée
tion. However, averaging blurs spatial and temporal structure Morvan et al., 1990; Biver et al., 1999a; Colom et al., 1999).
in azimuthal averages and leaves the resulting profile under- Fabry-Pérot and spatial heterodyne spectroscopic (SHS)
constrained, which can make it difficult to obtain a unique or interferometers have been used to study expansions from
consistent model interpretation. Ideally, a hybrid approach atomic species, primarily H (Morgenthaler et al., 2002) and
to spectroimaging data is applied, where spatial information O(1D) (Smyth et al., 1995) at velocity resolutions of up to
on the underlying structures of the coma, including diurnal 1 km/s. H Lyman-α absorption cells (Bertaux et al., 1984)
variances, temporal changes in overall production, vectored have also proven effective for measuring the velocity struc-
flows, jets, temperature, and secondary sources, are retained ture of coma hydrogen at subkilometer-per-second resolu-
in the high surface brightness regions of the coma, while the tions, albeit with substantial temporal averaging as the comet
more diffuse regions are summed to increase signal to noise. velocity must change with respect to the instrument to sam-
This greatly increases the amount of information available ple the full line shape. These observations all share the com-
for model analysis, resulting in a more detailed picture of mon limitation that they average velocities over large areas
coma structure. of the coma.
Inversion of a one-dimensional or two-dimensional spa- As a precision photometric technique, velocity-resolved
tial dataset to production rate can be achieved in two ways, aperture summation is directly invertible to production rate,
either by summing all the photons in the FOV as an effec- subject to the same caveats described above. Because these
tive aperture and using equations (26) and (27), or by mod- measurements average all the velocity structures that are
540 Comets II

detectable in the aperture, acceleration in active comets This makes it useful only for species with substantial non-
(Colom et al., 1999) or changes in the velocity distribution thermal velocity components (e.g., H2O+ or H) or where mul-
due to radial-distance dependent photochemistry (i.e., H) tiple, spectrally separated lines must be ratioed (e.g., for
(Richter et al., 2000; Combi et al., 1998; Morgenthaler et temperature or equilibrium-state measurements).
al., 2002) are mixed both azimuthally and radially in the Multiplexed spectroscopy is a powerful, hybrid technique
measured line profile and can only be partially separated that combines the spectral range, resolution, and étendue
with model analysis. An additional complication arises in limitation of an echelle spectrograph with the two-dimen-
the form of quenching in the inner coma that can render sional coverage of an interferometric image. Tunable multi-
the velocity structure inner coma undetectable for some plexing spectrometers place multiple (~100) feeds at differ-
water daughter species, including OH (Schloerb, 1988) and ent locations over the FOV (Anderson, 1999), providing
O(1D) (Festou and Feldman, 1981; Smyth et al., 1995; Mor- maps of velocity at discrete points over a wide area of the
genthaler et al., 2001). While the effect of quenching on coma. Fixed multiplex arrays consist of multiple feeds cover-
the inversion to production rate can be compensated for with ing a single FOV. In each case, the separate feeds are di-
correction factors, the measured velocities are isolated to rected to points along a long-slit axis of an imaging echelle
the regions beyond the quenching radius. This is not a prob- spectrograph. The inputs tend to be small (approximately
lem for weak comets where the aperture is much larger than few arcseconds in diameter) and cannot be co-added easily.
the quenching radius and the OH velocity is largely invari- This limits their sensitivity to low surface brightness emis-
ant, but can be severe for very active comets such as Hale- sions in the coma. Their resolution depends on the configu-
Bopp where substantial acceleration occurs in the quenched ration of the bench spectrograph used (103 < R < 104).
regions (Colom et al., 1999, Harris et al., 2002). 5.1.5. Thermal measurements in the coma. A meas-
5.1.4. Velocity-resolved spectroimaging. Spatially dis- ured temperature in the coma depends on the species ob-
crete velocity data can be obtained from velocity-resolved served, its formation pathway, and the collision rate both
interferometric (data cube) imaging, one dimensional spatial in the inner coma and at the location where the measure-
SHS, or long-slit or spatially multiplexed echelle spectros- ment is taken. Such measurements thus provide an impor-
copy. Long-slit [e.g., Combi et al. (1999a) at R = 200,000] tant constraint on gas-kinetic models and a link from them
and SHS [e.g., Harlander et al. (2002) at R = 40,000] tech- to the physical properties of the nucleus and surrounding
niques are both limited to a single dimension, but have volatile-rich material. Remote sensing measurements are
demonstrated the very high intrinsic resolution necessary able to provide kinetic temperatures for a number of coma
to resolve the low expansion velocity coma neutrals. Of the species, including the primary parent species CO (e.g.,
two, SHS offers much higher intrinsic étendue, can be tuned DiSanti et al., 2001; Biver et al., 2002; Feldman et al., 2002;
to very high (R >> 105) resolution, and is better suited for Brooke et al., 2003) and H2O (e.g., Mumma et al., 1986;
observations of the outer coma or very diffuse emissions, Crovisier et al., 1997). Owing to the absence of molecular
due to the fact that the instrument collapses the dimension bands for these species in the visible, the bulk of thermal
orthogonal to the spatial direction into the interferogram. remote sensing is done in the IR and at radio frequencies,
This single-dimensional summing improves s/n as with although Feldman et al. (2002) have recently demonstrated
aperture summation, but spatially averaging only one di- that the kinetic temperature of CO can be obtained with
mension, leaving radial data in the other. Echelle spectra FUSE observations of the 0–0 band at 1080 Å.
sample smaller regions and thus probe the velocity struc- Mumma et al. (1986) first reported on measurements of
ture at discrete locations where the surface brightness of the the spin temperature of water in the coma of 1P/Halley,
emission is high. This offers a more constrained measure- obtaining a value of ~40 K from the ortho-para (O-P) ratio
ment for model analysis, but at the expense of s/n. Echelles of lines, which are assumed to be fixed at the long-term
are more easily tuned than SHS instruments, and they have average solid-state temperature before evaporation, in the
much greater flexibility in the selection of bandpass, often ν3 band at 2.65 µm. Similar measurements of the H2O ki-
covering broad ranges of wavelength. netic temperature have been performed since, using the same
Data cube images are typically obtained interferometri- and different bands (e.g., Crovisier et al., 1997) as well as
cally (such as a Fabry-Pérot) using a tunable filter bandpass for O-P ratio of different coma species [e.g., NH3 (Kawakita
and stepped in wavelength across a target emission feature et al., 2001)] with comparable results.
or features (Morgenthaler et al., 2001). The resulting im- Rotational diagram derivations similar to those made in
age arrays have the velocity or line ratio distribution for the interstellar medium have also been used to derive kinetic
every spatial element (radial and azimuthal) in the FOV and temperatures in comets by looking at the ratios of different
are very useful for identifying vectored flows, temperature rovibrational lines in a diagnostic band. These derivations
variations, acceleration, and signatures of secondary or produce results similar to the O-P measurements where they
extended sources. Their limitation comes from the fact that have been compared directly [e.g., H2O from 1P/Halley by
they collapse the full free spectral range of the interferom- Bockelée-Morvan (1987)] and have proven effective for ob-
eter into image space, and they are generally much lower taining temperatures from several species including CH3OH
in spectral resolution (R ≤ 104) in this mode than if the same (Bockelée-Morvan et al., 1994), H2S (Biver et al., 2002),
instrument is used as a line-resolved aperture photometer. and CO (Biver et al., 2002; Feldman et al., 2002). In par-
 Combi et al.: Gas Dynamics and Kinetics in the Cometary Coma 541

ticular, Biver et al. (2002) reported a combined study of cule must be derived or verified by using a comet as an
all three of these as a function of heliocentric distance for astrophysical laboratory. In addition, the primary observ-
Comet C/1995 O1 (Hale-Bopp). In addition to demonstrat- ing factors that complicate the use of its NUV emission
ing consistent thermal properties between these species, features as a diagnostic include variable atmospheric attenu-
they show results extending from 1 to 8 AU. While Hale- ation of ~2.2 magnitudes/airmass (Farnham et al., 2000)
Bopp was an extreme high case for comet activity, their when observed from the ground, and a complex Swings-
results demonstrate that temperature measurements are pos- Greenstein sensitivity in the g-factors of individual lines of
sible for many comets over the full range of their activity the unresolved 0–0 band (Schleicher and A’Hearn, 1988).
cycle, which will enable more detailed study of the gas ki- The 18-cm OH radio emissions are strongly quenched
netic evolution of the coma. (Schloerb, 1988), which restricts the sensitivity of the mea-
surement to the outer coma, an effect that becomes acute
5.2. Measurements of Water and its for active comets such as Hale-Bopp where the quenching
Photochemical Products region exceeded 105 km (Schloerb et al., 1999; Colom et
al., 1999). Finally, there is strong photochemical sensitiv-
Water itself has no visible band signature and is diffi- ity to variable UV emissions in the solar spectrum in its
cult to observe in general. Even as new techniques evolved production and loss rates and its excitation from OH. Con-
that enable direct mapping of the water coma in the IR siderable effort has been expended toward addressing all
(Mumma et al., 1986; Crovisier et al., 1997; Dello Russo these complicating factors, which has greatly improved the
et al., 2000) and radio (Lecacheaux et al., 2003), the most convergence between the different techniques used to study
common method of study continues to be observing the this species.
evolution of the daughter and granddaughter species of its OH is observed using a combination of aperture photom-
photochemistry. The primary channels of this are given in etry, both for radio and NUV emissions, velocity-resolved
Tables 1 and 2 above, with the distributions of H, H2, meta- measurements (Fig. 8) in the radio (Colom et al., 1999;
stable O(1D), OH, and H2O+ being the major products of Bockelée-Morvan et al., 1990; Crovisier et al., 2002), and
interest. Each species provides different elements of the spatial maps in the NUV (Harris et al., 1997, 2002). OH
water evolution picture that depend on the observational and has been also observed in the IR by way of fluorescent and
modeling methods (described above) that are used to ex- prompt emissions in the 3-µm region (Brooke et al., 1996;
amine them. Here we describe most common observational Crovisier et al., 1997; Mumma et al., 2001). Both the 0–0
approaches to each water daughter and discuss where they band and the 1–0 band at 2850 Å are also observed from
are useful for characterizing the coma with respect to vari- spacebased platforms (Weaver et al., 1999). However, sys-
ous model approaches.
5.2.1. OH diagnostics. OH is the most commonly stud-
ied of the water daughters, with ground-detectable signatures
in the NUV [the 0–0 band is the highest contrast emission
feature on groundbased spectra; see Fig. 1 in Feldman et al.
(2004)], radio (18 cm), and IR (Crovisier et al., 1997) that
contain complementary information about its production
rate, velocity structure, and spatial distribution in the coma.
OH is formed almost exclusively from water dissociation,
which makes it the most easily inverted back to a parent
(water) production rate. Indeed, given the single formation
path of OH and the relative difficulty of observing water
directly (see Bockelée-Morvan et al., 2004), OH has gen-
erally been the most effective proxy for water production
with the least ambiguity in its interpretation, especially for
comets that are not productive and in the range of 1 AU
(or less) from the Sun. For this reason the large database
of International Ultraviolet Explorer (IUE) and HST obser-
vations (see Feldman et al., 2004) is particularly useful for
a hard calibration for the water production rate in comets. Fig. 8. OH emission at 18 cm from Comet 1P/Halley obtained
with the Nançay radio telescope (3.5 × 19 arcmin beam) and us-
The complexities of OH photochemistry and interpreta-
ing aperture summation is fit using the trapezoid method to de-
tion are described in more detail above and in Feldman et al.
termine the outflow velocity of the coma (from Bockelée-Morvan
(2004); however, to summarize, the primary issues are a et al., 1990). In the lower left image, the sharp peak of the fitted
lack of knowledge of basic characteristics and observational line is indicative of a case where vparent ~ vejection ~ 1000 m s–1.
difficulties. OH is difficult to isolate in a laboratory setting The upper two profiles are matched with flat-topped fits consis-
(e.g., Nee and Lee, 1985), which requires a somewhat cir- tent with expansion of ~500 m/s, while in the lower right a higher,
cular study of this species where the properties of the mole- asymmetric expansion rate is obtained.
542 Comets II

tematic spacebased observations of OH ended with the tios to the multiple formation pathways are known for the
deactivation of the IUE in 1996. Following the work of conditions of the observation. The H coma is the most ex-
Scheicher and A’Hearn (1988) it has been possible to correct tended structure in comets, with observable emissions out
for g-factor and scale-length variability for the NUV fluores- to more than 107 km from the nucleus (Combi et al., 2000).
cent bands. The inversions of photometric and spectrophoto- Compared to the other water daughters, the H velocity
metric measurements of OH to obtain water production distribution is completely dominated by its nonthermal ele-
rates with the use of spherical expansion models for the ments, with H2O and OH photochemistry contributing from
radial distribution (Schleicher et al., 1998; Kupperman, 4 to 24 km/s in excess velocity. The bulk velocity distribu-
1999; Harris et al., 2002) are generally consistent with other tion of H is also affected by collisions, which partially ther-
estimates of water production. Schloerb (1988) has devel- malize the energetic neutral H population in the inner coma,
oped a formulism for addressing quenching of radio emis- especially in very active comets (Morgenthaler et al., 2001).
sions that is comparably robust, while Bockelée-Morvan et In addition, radiation pressure modifies the distribution with
al. (1990) have developed a line-fitting technique (the “trap- an antisunward acceleration that becomes significant in the
ezoid method”; Fig. 8) for determining the average radial outer coma. The net result is that the velocity distribution is
outflow velocity in radio-band OH emissions from beyond highly dependent on the region of the coma being sampled,
the edge of the quenching region. This also puts some con- the optical depth of the inner coma to solar UV radiation
straints on the OH ejection velocity, which is sometimes (both for photochemistry and resonance scattering), the total
slightly discrepant with that expected from photochemical gas production rate, any short-term gas production rate vari-
analysis (Table 1). However, these might be explained by ability, and the comet heliocentric velocity (for both Swings
uncertainties in the photochemical data as well as simplifi- and Greenstein effects). Modeling of the distribution from
cations in the models, which treat the coma as spherically the inner coma of several comets (Combi and Smyth,
symmetric, collisionless flow and having a constant uniform 1988a,b; Smyth et al., 1991; Combi et al., 1998; Richter et
outflow velocity for parent species. al., 2000) nominally verifies the theoretical estimates of the
The major limiting factor with remote sensing of OH is velocity and its variation with heliocentric and cometocen-
the relatively large number of independent unknowns that tric distances for a variety of activity level comets.
must be relied upon to model an isolated observation, with The observational challenges to the study of H in com-
each technique requiring different approximations (azi- ets include the requirement for observations above the at-
muthal-temporal averaging, reduced outer or inner coma mosphere to detect H Lyman-α or H Lyman-β, the need for
sensitivity, lack of velocity data, etc.). As a result it is dif- measurements over multiple FOV, and strong telluric and
ficult to reconcile model results from different measure- galactic backgrounds at Hα. The primary diagnostics are
ments to within the relative precision of the measurements resonantly scattered H Lyman-α at 1216 Å and cascade Hα
(Schleicher et al., 1998). This nonconvergence is most ef- emission at 6562 Å. Detection of both dates back to the C/
fectively dealt with through the use of coordinated measure- 1973 E1 (Kohoutek) apparition, with a dataset that includes
ments (see below) that act to constrain the individual uncer- most active comets since then (Huppler et al., 1975; Keller
tainties of each observation, such as a lack of velocity data et al., 1975; Drake et al., 1976; Scherb, 1981). In recent
in NUV images/photometry and a lack of spatial informa- years and until the introduction of the SOHO/SWAN in-
tion and the inner coma distribution in radio observations strument, H observations of comets were mainly accom-
(Harris et al., 2002; Colom et al., 1999). Future technical plished using variable width and line-resolved aperture
developments in high étendue/spectral resolution measure- photometry with interference techniques on medium to large
ments of diffuse emissions in the outer coma (Harlander spatial scale (Morgenthaler et al., 2002) or echelle spec-
et al., 2002) and long-slit echelle spectroscopy of the indi- troscopy near the nucleus (Richter et al., 2000; Feldman et
vidual lines of the 0–0 band (Combi et al., 1999a) will al., 2004). SOHO/SWAN has added the ability to image the
improve the accuracy of the interpretation. It should be full H coma (Fig. 9) and even the shadow cast by the coma
noted, however, that the divergence of techniques is small on the background interplanetary medium. Because of the
relative to other species, and that QOH rarely varies by more high energies and velocities involved in the formation of
than 50% between them unless there is considerable unde- H, the contributions from the various dissociation pathways
tected (by one measurement relative to another, e.g., narrow can be seen in the H Lyman-α line shape with intermediate
vs. wide field) spatial and/or temporal variation in gas pro- (R > 104) resolution instruments, which increases the range
duction, or a difference in the underlying assumptions (e.g., of techniques and available instrumentation for the study
outflow velocity or g-factor) used. of this feature.
5.2.2. Hydrogen diagnostics. Hydrogen arguably pro- H line-profiles can be compared with detailed models,
vides the greatest physical information on the chemistry of albeit typically as azimuthal and radial averages over the
water, the structure of the coma, and temporal variability instrument FOV, to determine the contributions from dif-
in gas production; however, its long scale length necessi- ferent dissociation pathways both as a function of location
tates multiple observations on different spatial scales to fully in the coma and as a function of overall gas production.
characterize its evolution. Atomic H is derived largely from Figure 9 compares the model simulations of the velocity
water and OH dissociation, which makes it possible to de- distribution for Comet Hale-Bopp (Combi et al., 2000) when
rive a production rate directly, assuming the branching ra- the comet was at its most active near perihelion (0.9 AU),
 Combi et al.: Gas Dynamics and Kinetics in the Cometary Coma 543

and three months earlier (1.7 AU), when the production rate
was much lower and the dissociation rates much lower. Near
perihelion a large fraction of the highest-speed H atoms are
thermalized to much lower velocities than at 1.7 AU where
the distribution was not changed much. The effects of ther-
malization are directly evident in the perihelion Hα line-
profile measurements of Morgenthaler et al. (2002). As
discussed earlier, this slowing of the H atoms in Hale-Bopp
is matched by a corresponding increase in the outflow speed
of the heavy species, to which the kinetic energy is being
transferred. Both Harris et al. (2002) and Colom et al.
(1999) see clear evidence of this effect in the velocity struc-
ture of OH near Hale-Bopp’s perihelion. The shape of the
coma at perihelion, as shown in Fig. 9c and as observed
with the SWAN instrument on SOHO, is also sensitive to
the velocity distribution as first pointed out by Keller and
Meier (1976).
The calculation of the water production rates (or any
species for that matter), from either fast species like H or
slower heavier species like OH or water, is very sensitive
to our knowledge of the velocity distribution, unless the full
scale length is observed (see equation (26)). This compli-
cation is substantially magnified by the multiple, radially
dependent components of the H velocity distribution and
by the large spatial extent of the H coma. At present we
are able to sample spectrally only small, discrete subsets
of the coma in the UV (H Lyman-α) or large azimuthally
and radially averaged areas at moderate signal to noise
(Morgenthaler et al., 2002). Improvements in interferomet-
ric instrument capabilities in the FUV (Stephan et al., 2001)
and visible offer the promise of additional spatial informa-
tion and increased spectral resolution for future comets.
Other new diagnostics, including observations in the deep
FUV (H Lyman-β) from FUSE (Feldman et al., 2002),
measurements of Hβ emission from Comet C/1996 B2
(Hyakutake) (Scherb et al., 1996), and the planned STE-
REO (SOHO follow-up) mission, suggest a greater capa-
bility to map the structure of the H coma in future comets.
5.2.3. O(1D) diagnostics. Oxygen in the metastable 1D
state is a byproduct of H2O, OH, and CO photochemistry
that is produced at different rates across the coma. Relax-
ation of O(1D) produces a single photon ~110 s after its
formation, meaning that its brightness inverts directly to its
combined parent production rate without any supplemen-
tal knowledge of g-factors via equation (27) above. Only
Fig. 9. Model for the SOHO SWAN observations of the H the various parent lifetimes and chemical branching ratios
Lyman-α coma of Comet 1995 O1 (Hale-Bopp); (a) and (b) show are required to complete the inversion, and, if the full O
the H-atom velocity distribution upon photochemical production coma is sampled, the lifetime dependence disappears as
(thin) and after Monte Carlo model calculation (thick) of thermal- well. Its short lifetime of the metastable state offers an
ization in an expanding water-dominated coma. (a) Conditions on additional advantage, because the locations of formation
the day of perihelion (April 1, 1997) when the comet was at a and emission are nearly co-local. Thus, the radial distribu-
heliocentric distance of 0.91 AU and the water production rate was
tion of O(1D) is a radial map of the site of photochemistry
1.02 × 1031 s–1. (b) Conditions on January 1, 1997 when these
in the coma that is useful for detailed modeling of chemi-
values were 1.75 AU and 2.2 × 1030 s–1 respectively. (c) The
model-data comparison for the H coma at perihelion on April 1 cal rates, source distributions, and the relative density ratio
when collisional thermalization was the largest and the resulting of H2O and CO.
coma is the most distorted from spherical symmetry. The shape Observations of O(1D) do have significant complications
of the coma is formed by the balance between solar radiation as a proxy for H2O and OH photochemistry that are addres-
pressure acceleration and the velocity distribution function. sable to a large degree. Observationally, these complications
544 Comets II

Fig. 10. Two types of multiport spectroscopy and their application to Comet Hale-Bopp are shown (from Morgenthaler et al., 2001).
At left is a sample distribution using the Hydra spectrograph on the WIYN telescope. Here a set of 100 fibers are placed at pro-
grammed positions over a 1° FOV with a minimum separation of 40 arcsec. The array design shown is optimized for the study of
radially distributed emission, with the individual fibers feeding a bench spectrograph mounted below the telescope pier. At center is a
schematic of DensePak, a tight grouping of 100 fibers covering a region equal the minimum spacing in the Hydra array. At right is an
example of observation of O(1D) from Hale-Bopp using DensePak in the inner coma and Hydra for more remote locations.

photochemistry that can be partially correctable with obser-

vations of C(1D) (see below) (Oliversen et al., 2002), un-
certainty in the branching ratios from OH under different
levels of solar activity (van Dishoeck et al., 1984; Huebner
et al., 1992; Morgenthaler et al., 2001), UV opacity effects
on chemical rates, and the role of collisional quenching and
chemistry of O(1D) in the inner coma (Glinsky et al., 2003;
Komitov, 1989). To compensate for the observational effects,
O(1D) is now routinely observed using high-spectral-reso-
lution (R > 15000) techniques including long-slit echelle
spectroscopy (Fink and Hicks, 1996), multiplexed echelle
spectroscopy (Fig. 10) (Anderson, 1999), interferometric
data cube imaging (Fig. 11), and aperture summed line
measurements (Fig. 12). The recent detection of fluores-
cence of metastable O I (D1-D1) by FUSE (Feldman et al.,
2002) offers a potential new diagnostic that is comparable
to the C(1D) line (see below).
As noted above, the integrated brightness of O(1D) is
invertable to a production rate with equation (27) and from
there to QH2O from the branching ratios of OH and H2O
photochemistry. The radial and azimuthal distribution of the
Fig. 11. A single 1° field image slice of the O(1D) coma of Hale-
Bopp is shown after subtraction of continuum. This image was ob- emission traces both the expansion of the coma and the rate
tained using the WHαM instrument at Kitt Peak (from Morgen- of collisional and chemical quenching in the inner coma.
thaler et al., 2001). Overlaid is the location of fiber rings from Because it maps directly to chemistry, O(1D) images also
the Hydra instrument using the array shown in Fig. 8. reveal extended sources and regions of increased velocity
(Morgenthaler et al., 2002). The O(1D) outflow velocity
retains the value of its parents (~1–2 km/s) plus fixed iso-
include substantial telluric O(1D) nightglow, spectral sepa- tropic speed component of about 1.6 or 1.5 km/s from the
ration of O I and nearby NH2 and H2O + coma lines (see photochemical excess energy from H2O and OH, respec-
Feldman et al., 2004), and the low contrast of the emission tively. This requires high resolution (R < 105) to detect. This
over bright dust scattered continuum emission. Physical was achieved for 1P/Halley in 1986, with a Fabry-Pérot
complications include an unknown contribution from CO interferometer tuned to R = 1.9 × 105 (Fig. 12), although it
 Combi et al.: Gas Dynamics and Kinetics in the Cometary Coma 545

required the averaging of a substantial FOV to obtain ac-

ceptable s/n on the line-shape. The Halley profiles were fit
successfully using the Monte-Carlo particle trajectory model
of Combi et al. (1993) and were used to validate the model-
predicted magnitude of expansion velocity and its increase
with increasing gas production (Smyth et al., 1995). Obser-
vations of a similar resolution were made of the inner coma
O(1D) distribution with a high-resolution echelle spectrom-
eter of Comet C/1996 B2 (Hyakutake). These were also in
agreement with model predictions for conditions interme-
diate between the two Halley cases (Combi et al., 1999a).
Continued development of very-high-resolution interfero-
metric techniques and sensitive high-resolution echelle in-
struments will make such observational programs routine
for comets of moderate to high activity, while the further
development of FUSE band technology may provide a com-
plementary diagnostic that will provide useful results for
weaker comets.
5.2.4. Infrared and radio observations of H2O. A miss-
ing key to the observational study of water dynamical and
photochemical evolution is measurement of the properties
of the parent species. This has been historically difficult both
because of the lack of transitions in the FUV-visible band
and because of strong attenuation of IR and radio bands
by telluric water. Over the past two decades considerable
progress has been made in finding ways around the tellu-
ric problem by moving to spacebased observatories or by
observing within the various windows where atmospheric
absorption is not so severe. Comets can sometimes be ob-
served at large enough geocentric velocity in order to Dop-
pler shift the cometary feature away from terrestrial absorp-
tion features. These improvements offer considerable prom-
ise that spacebased aperture photometry of water in the
radio will become routine, while IR measurements (both
ground- and spacebased) will contribute both the tempera-
ture and radial distribution of water. Together they will fill
an important observational niche in our study of coma ki-
netics. The issue of observations of H2O, and parent mole-
cules in general, is covered in detail in Bockelée-Morvan
et al. (2004).
Unambiguous detection of water in the inner coma first
came from 1P/Halley via the Kuiper Airborne Observatory
(KAO) (Mumma et al., 1986) and the IKS instrument on
the Vega spacecraft (Combes et al., 1986), both of which
directly detected emission lines from the ν 3 band near
2.65 µm. In addition to providing a direct measurement of
H2O, the KAO data were used to derive both the nuclear
spin temperature (Tspin) (Mumma et al., 1987) and the ro-
Fig. 12. Aperture-summed O(1D) emission from 1P/Halley is tational temperature (Trot) (Bockelée-Morvan and Crovisier,
displayed at the top showing the clean separation of comet and 1987) of the lines, which sample the formation history and
airglow O(1D) signatures from each other and cometary NH2
the current state of water in the coma respectively. The spin
emission. These were obtained using a Fabry-Pérot interferom-
temperature derived from the ortho-para ratio on the dif-
eter in ring mode. Inspection of the comet and telluric line shapes
shows the broadening in the Halley outflow. The lower panels ferent detected lines of the ν3 band is set at the creation of
show that this broadening is consistent with the magnitude of the H2O molecule by either photochemistry or direct evapo-
coma outflow predicted by model calculations to be broader at ration from ice on the nucleus and thus directly ties to that
smaller (middle panel) heliocentric distances and more narrow at event. The results from 1P/Halley (Northo/Npara = 2.66 ± 0.13
larger (bottom panel) distances (Smyth et al., 1995). indicating Tspin = 32 K +5, –2) were consistent with the
546 Comets II

predicted temperature at the surface of Halley’s nucleus at solve the ~1 km s–1 bulk flow of water, which can now be
aphelion. Inversion of rotational state population to tem- compared with similar measurements of other water daugh-
perature is less straightforward because the H2O molecules ters (H and OH) over similar FOV and used to model the
are IR pumped and strongly non-LTE, with a varying rate complex kinetics of the coma in the active comets detect-
of neutral-neutral and neutral-electron collisions playing a able with these techniques.
significant role in the level population. Within these limi-
tations, the rotational temperatures derived (Trot ~60 K for 5.3. Water Diagnostics in the Far-Ultraviolet (Far
the March 1986 KAO data) suggest that the kinetic tem- Ultraviolet Spectroscopic Explorer) Bandpass
perature, as also reproduced in hybrid/gas-dynamic mod-
els (Combi, 1989), is also similarly low in the region of the The launch of FUSE opened a new chapter in comet
coma sampled. studies by enabling direct observation of new diagnostics
An area where considerable progress has been made is of water production and chemistry in the FUV. To date,
in the inversion of H2O brightness to QH2O and its spatial FUSE has been used to observe long-period Comets C/
and temporal variance. Weaver et al. (1987) derived QH2O 1999 T1 (McNaught-Hartley), C/2000 WM1 (LINEAR),
from the same ν3 KAO data used to derive Tspin and Trot, and C/2001 A2 (LINEAR) (Feldman et al., 2002; Weaver
obtaining results similar to OH, but with far greater vari- et al., 2002). In addition to putting new limits on the abun-
ability on both short and long timescales. They attributed dance fraction of highly volatile species such as Ar (Weaver
the short-term effects to a parent species sensitivity to et al., 2002) and CO (Feldman et al., 2002), several diag-
nucleus activity that had previously been identified in CS nostic features identified with water photochemistry have
(McFadden et al., 1987), but could not fully account for been observed. These include the H2 Lyman band lines at
the longer-term discrepancies. Finally, while they lacked the 1071.6, 1118.6, and 1166.8 Å, H Lyman-β and other lines of
spectral resolution to sample the velocity structure of the the Lyman series, O I multiplets at 989, 1027, and 1040 Å,
ν3 lines directly, Larson et al. (1987) showed that gas pro- fluorescence from the metastable O I(1D) state at 1152 Å
duction asymmetry provides a signature of outflow in the [analogous to the more commonly studied C(1D) emission
form of a Doppler term in the lines. Their post-perihelion line at 1931 Å (Tozzi et al., 1998)] (Feldman et al., 2002),
measurements showed considerable variation from canoni- and the possible detection of charge exchange (between
cal assumptions of water outflow consistent with collisional coma neutrals and the high ionization state component of the
heating in active comets that was subsequently shown more solar wind) cascade lines of O IV at 1031.93 and 1037.62 Å
dramatically in C/1995 O1 (Hale-Bopp) (Harris et al., 2002). (Weaver et al., 2002).
Subsequent observations of water production and tem- The utility of these new diagnostics is still being evalu-
perature using this ν3 band and rotational lines near 180 µm ated; however, it is promising that the two objects observed
have been made with the Infrared Space Observatory (ISO) to date have been intrinsically weak gas producers that
satellite (Crovisier et al., 1997) with results similar to those would yield poor results with many of the other techniques
of the KAO and IKS IR spectrometer onboard in the Giotto described above. Detection of H2 is significant in that it
spacecraft. In addition, Dello Russo et al. (2000) has used provides a new diagnostic of the poorly studied branching
the CSHELL instrument at NASA IRTF to demonstrate a rate to that daughter from water. H2 is also produced with
method for groundbased detection of water in nonresonance a substantial excess velocity (Table 2) and has a long life-
fluorescence “hot-bands” that are not absorbed by the atmos- time against photodissociation (Table 4), a combination that
phere. These were first confirmed in Comet 1P/Halley (e.g., means that, while H2 is a minor inner coma constituent, it
Weaver et al., 1987.) Unlike other studies, the CSHELL is a dominant molecule in the outer coma. Feldman et al.
measurements are spatially resolved over the small aper- (2002) suggest that the O(1D–0D) resonance is being stimu-
ture of the instrument, providing the first radial maps of the lated by an unknown process rather than fluorescing in the
inner coma water distribution and an opportunity to apply comet inner coma. This result is somewhat enigmatic, con-
production models to identify both collisional effects and sidering that fluorescence is the dominant source of C(1D)
the presence of an extended source. in the coma despite having a lower energy of transition than
Progress in the study of line-resolved aperture photom- O(1D). Whether the O(1D) results for the three comets stud-
etry of the water band at 557 GHz, which are available only ied is typical or an anomaly brought about by the unique
from space platforms, has proven very useful for deriving circumstances of the FUSE observations (e.g., aperture,
QH2O and VH2O from the line shape. This emission was first solar cycle, low intrinsic production rates) will require a
detected from Comet C/1991 H1 (Lee) using the Submilli- larger dataset and close theoretical scrutiny to determine.
meter Wave Astronomy Satellite (SWAS) (Neufeld et al., The major limitations for working in the FUV bandpass
2000), and subsequently from Comets C/2001 A2 (LIN- are the availability of observing time, only moderately high
EAR), 19P/Borrelly, C/2000 WM1 (LINEAR), and 153P/ spectral resolution, high sky background noise, the rela-
2002 C1 (Ikeya-Zhang) with the Odin satellite. The radio tively low level of solar FUV flux, and the 30" × 30" angu-
measurements suffer from the same large area summation lar extent of its aperture, which combine to limit observa-
as those used to examine other species; however, they share tions to the inner coma. In this regard FUSE has similar
their primary strength, velocity sensitivity. The Odin instru- limitations to IUE in the 1980s and 1990s. As in this earlier
mental resolution is sufficiently high (80 m/s) to fully re- case, the advent of larger aperture and more flexible instru-
 Combi et al.: Gas Dynamics and Kinetics in the Cometary Coma 547

ments will improve our ability to monitor these important locity (Colom et al., 1999) and inner coma HCN velocity
new features. (Biver et al., 1999a) with the radial distribution of emis-
sion from OH to map out the acceleration across the coma
5.4. The Relationship of Other of C/1995 O1 (Hale-Bopp). The magnitude and variation
Coma Species to Water of these velocity measurements, both with distance from
the nucleus and overall with heliocentric distance, are also
Water is the dominant volatile component of comet nu- in reasonable agreement with models for the expansion of
clei, and therefore its state and evolution are both relevant the coma (Combi et al., 1999b), even for the extreme physi-
to developing an understanding of other coma species, some cal state of Hale-Bopp.
of which have reciprocal effects on the water coma. The 5.4.2. Characterization secondary sources. Of the pri-
above descriptions reveal several weaknesses in the diag- mary neutral water species only H2O itself and OH have
nostics suite used to determine the characteristics of the no significant contribution from other sources. Of the oth-
water coma, and one technique to address this is to com- ers, O I has the largest nonwater component, in this case
bine studies of water with other coma constituents that fill from a combination of CO and CO2. The precision of model
these observational voids. The detailed physics of the other interpretation of O(1D) will depend on the precision by
coma species is dealt with in other chapters of this book, which the CO- and H2O-derived components are separated
and our goal here is to illustrate only how a coordinated or by our knowledge of the CO/H2O ratio, which varies
observing-modeling approach between them and water will substantially among comets and with heliocentric distance.
increase our understanding of each. While coordinated The size of the CO/CO2 contribution can be dominant in the
observations of multiple species provide benefits for under- outer solar system, where water outgassing is suppressed,
standing many other properties of the coma, including its but even where water dominates, the addition of CO/CO2-
thermal properties and the interaction of the solar wind, we derived O [particularly O(1D)] is significant. The role of
will briefly touch here on two examples (the velocity struc- CO/CO2 is further complicated by the fact that the rate of
ture of the inner coma and the role of secondary sources formation of O(1D) differs between the two species and with
of water daughter species) where the above techniques pro- respect to both pathways in water. Indeed, O(1D), derived
vide an incomplete picture and observational solutions us- from CO (as a daughter) and CO2 (as a granddaughter),
ing other species have been identified. most likely dominates over the OH contribution in the outer
5.4.1. Velocity structure. The low velocity of most coma due to the longer lifetime of CO (Tozzi et al., 1998;
coma constituents (in particular, H2O, OH, and O for water) Harris et al., 1999). This would be even further compli-
requires extremely high spectral resolution (R > 105) to cated by a substantial fraction of CO coming from an ex-
measure. Unfortunately, the most common technique used to tended source of another parent like H2CO (DiSanti et al.,
achieve such high resolution in the visible and UV (echelle 2001). Moreover, the ratios of CO : CO2, CO/H2O, and
spectroscopy) has a correspondingly small étendue that CO2 : H2O vary substantially between comets, with no ob-
samples only small regions with fairly low sensitivity. Inter- vious predictive trend yet identified (Weaver et al., 1994;
ferometric techniques (Stephan et al., 2001; Watchorn et al., Feldman et al., 1997; see also Bockelée-Morvan et al.,
2001; Morgenthaler et al., 2002) that co-add large FOV at 2004). Thus, to account for the contribution of these spe-
high spectral resolution in the visible and UV have consider- cies to the O(1D) brightness and spatial distribution, it is
able future promise in this area; however, the most mature necessary to study diagnostics of both CO and CO2 chem-
techniques exist in the radio. Unfortunately, the primary istry. The most direct method is to study C(1D), the meta-
water diagnostic in the radio (OH at 18 cm) is strongly stable analog to O(1D) that is formed in the same process
quenched in the inner coma, which is its the most dynami- from CO (Huebner et al., 1992; Tozzi et al., 1998). From
cally active region for active comets. To get around this QC(1D) it is possible to separate the CO and OH contributions
problem it is possible to use other, less-quenched OH [e.g., directly over any simultaneously observed FOV.
IR (Crovisier et al., 1997)] emission features or other spe- There are two diagnostics for C(1D): fluorescence from
cies to study this region and combine the results to com- the 1D state at 1931 Å and direct detection of the C(1D)
plete the dynamical picture. Several such features exist and decay at 9828/9850 Å. The former is accessible only from
are in common use to determine the velocity within ~103– space and has typically been studied only over small FOV
104 km of the nucleus (Biver et al., 1999b). One commonly (Feldman et al., 1997), which limits its usefulness for a full
observed emission that is useful for such comparative work coma correction. Direct observation of the NIR decay lines
is the J = 1–0 line of HCN (Schloerb et al., 1987; Biver et holds more promise, because it is both directly analogous
al., 1999b), which is detectable close to the nucleus at to the O I visible line and observable from the ground. This
subkilometers per second velocity resolution and therefore feature is faint compared to O(1D), has high background
useful in coordination with OH to measure velocity in the contamination, and falls near a telluric OH absorption. It
inner and outer coma. Models of the outflow (Combi, 1989) has only been detected in two comets, first an unpublished
similar to those shown in Figs. 3–6 reproduced the secular detection from 1P/Halley by Münch et al. (1986), and more
variation (with heliocentric distance) of the HCN line width recently from Fabry-Pérot interferometric observations of
seen by Schloerb et al. (1987). Harris et al. (2002) com- C/1995 O1 Hale-Bopp (Oliversen et al., 2002). The Hale-
bined published measurements of the outer coma OH ve- Bopp detection provides the first quantitative estimates of
548 Comets II

the role of C(1D) in the inner and outer coma and identi- allowed parameter space of the converged model for the
fies how future development of the interferometric tech- coma (Combi et al., 2000; Morgenthaler et al., 2001; Har-
nique will improve our ability to study this diagnostic. ris et al., 2002). The caveat to this is that the capability to
perform the required observations is widely distributed and
6. OUTSTANDING ISSUES AND FUTURE is typically organized only for high-profile apparitions (e.g.,
STUDIES OF COMA STRUCTURE 1P/Halley, C/1995 O1 Hale-Bopp, C/1996 B2 Hyakutake).
AND EXPANSION The results of these campaigns suggest that an improvement
in our understanding of both the role of water in the coma
There is currently no single diagnostic signature of wa- and in the physical parameters that describe its evolution
ter that provides a complete description of its spatial, ve- would result from a consistent organized effort targeting a
locity, temporal, and production rate evolution in the coma. larger sample of comets covering a wider range of activity
Inferring such detail from any one observation therefore and evolution.
requires either an estimate or approximation of the unknown
quantities (usually from observed characteristics of earlier Acknowledgments. M.R.C. acknowledges support from grant
comets) or model derivation of them. As the quality of re- NAG5-13239 from the NASA Planetary Atmospheres program.
mote sensing data has improved, the limiting factor in in-
terpretation has shifted from the instrumental regime to the
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Shimizu M. (1976) The structure of cometary atmospheres. Astro- 1995 O1 (Hale-Bopp). Astron. J., 114, 2789–2795.
phys. Space Sci., 40, 149–155. Wu C. Y. R. and Chen F. Z. (1993) Velocity distributions of hydro-
Skorov Y. V. and Rickman H. (1999) Gas flow and dust accelera- gen atoms and hydroxyl radicals produced through solar pho-
tion in a cometary Knudsen layer. Planet. Space Sci., 47, 935– todissociation of water. J. Geophys. Res., 98, 7415–7435.
949. Wyckoff S., Tegler S., Wehinger P. A., Spinrad H., and Belton
Skorov Y., Kömle N. I., Keller H. U., Kargle G., and Markiewicz M. J. S. (1988) Abundances in Comet Halley at the time of the
W. J. (2001) A model of heat and mass transfer in a porous spacecraft encounters. Astrophys. J., 325, 927–938.
cometary nucleus based on a kinetic treatment of mass flow. Xie X. and Mumma M. J. (1996a) Monte Carlo simulation of
Icarus, 153, 180–196. cometary atmospheres: Application to Comet P/Halley at the
Slanger T. G and Black G. (1982) Photodissociation channels at time of the Giotto spacecraft encounter. I. Isotropic model.
1216 Å for H2O, NH3, and CH4. J. Chem. Phys., 77, 2432– Astrophys. J., 464, 442–456.
2437. Xie X. and Mumma M. J. (1996b) Monte Carlo simulation of
Smyth W. H., Combi M. R., and Stewart A. I. F. (1991) Analysis cometary atmospheres: Application to Comet P/Halley at the
of the Pioneer Venus Lyman-α image of the hydrogen coma time of the Giotto spacecraft encounter. II. Axisymmetric
of Comet P/Halley. Science, 253, 1008–1010. model. Astrophys. J., 464, 457–475.
Smyth W. H., Combi M. R., Roesler F. L., and Scherb F. (1995) Yamamota T. (1981) On the photochemical formation of CN, C2
Observations and analysis of O( 1D) and NH2 line profiles for and C3 radicals in cometary comae. Moon and Planets, 24,
the coma of Comet P/Halley. Astrophys. J., 440, 349–360. 453–463.
Stephan S. G., Chakrabarti S., Vickers J., Cook T., and Cotton D. Yamamota T. (1985) Formation environment of cometary nuclei
(2001) Interplanetary H Ly-α: Observations from a sounding in the primordial solar nebula. Astron. Astrophys., 142, 31–36.
rocket. Astrophys. J., 559, 491–500.
PART VI:
DUST AND PLASMA
 Hanner and Bradley: Composition of Cometary Dust 555

Composition and Mineralogy of Cometary Dust

Martha S. Hanner
Jet Propulsion Laboratory/California Institute of Technology

John P. Bradley
Lawrence Livermore Laboratory

Cometary dust is an unequilibrated, heterogeneous mixture of crystalline and glassy silicate

minerals, organic refractory material, and other constituents such as iron sulfide and possibly
minor amounts of iron oxides. Carbon is enriched relative to CI chondrites; some of the C is
in an organic phase. The silicates are Mg-rich, while iron is distributed in silicates, sulfides, and
FeNi metal. Infrared spectra of silicate emission features in Comet Hale-Bopp have led to iden-
tification of the minerals forsterite and enstatite. The strong similarity of all known cometary
dust properties to the anhydrous chondritic aggregate class of interplanetary dust particles (IDPs)
argues that comets are the source of these IDPs. High D/H ratios in organic refractory material
in these IDPs as well as the physical and chemical structure of glassy silicate grains suggests a
presolar origin for at least some components of cometary dust.

1. INTRODUCTION and ESA’s Giotto probe each carried an impact ionization

time of flight mass spectrometer to measure the elemental
Comets contain some of the least-altered material sur- composition of the dust (Kissel et al., 1986a,b). The com-
viving from the early solar nebula. Cometary dust may con- position was recorded for about 5000 particles in the mass
tain both presolar particulates and solar nebula condensates. range 10 –16–10 –11 g, sampled over tens of thousands of ki-
Their structure and mineralogy may hold important clues lometers in the coma along the three trajectories.
about the chemical and physical processes in the early solar The sampled particles divide into three main types: mass
system. Radial gradients in the temperature and chemical spectra dominated by the major rock-forming elements, Mg,
composition of the solar nebula and the extent of mixing of Si, Ca, Fe; mass spectra consisting primarily of the light
material between the warm inner regions and cold outer re- elements H,C,N,O, the “CHON” particles; and mixed spec-
gions of the nebula at the epoch of comet formation should tra containing both the rock and CHON elements. If one
be evident today as differences in dust properties among defines mixed particles as having a ratio of C to rock-form-
comets related to their place of origin. ing elements between 0.1 and 10, then ~50% of the par-
The extensive infrared spectroscopy of Comet Hale- ticles are mixed and ~25% are rock and CHON respectively
Bopp, from the ground and from ESA’s Infrared Space Ob- (Fomenkova et al., 1992). At some level, however, the
servatory, has led to a revolution in our understanding of CHON and rocky material are mixed down to the finest
the silicate mineralogy in comets. In parallel, the past de- submicrometer scale in all particles (Lawler and Brownlee,
cade has seen extrodinary advances in the analysis of inter- 1992). The bulk abundances of the major rock-forming
planetary dust particles (IDPs), leading to the discovery of elements appear to be solar (chondritic) within a factor of
eroded, glassy silicates of likely interstellar origin and iso- ~2 (Jessberger et al., 1988; Jessberger, 1999). (Conversion
topic anomalies in silicate and carbonaceous components of the mass spectra to relative elemental abundances de-
also pointing toward a possible presolar origin. pends on the ion yields, which are uncertain by at least a
This chapter summarizes our present knowledge of the factor of 2, because the instrument could not be calibrated
composition and mineralogy of cometary dust based on in at the high flyby speed of ~70 km/s.) The C abundance is
situ sampling during the spacecraft encounters with Comet roughly 10 times that of the primitive CI chondrites.
1P/Halley in 1986, Earth-based remote sensing via infrared The rocky material displays a wide range in Fe/Mg abun-
spectroscopy, and laboratory analysis of captured IDPs of dance, but a narrow range in Si/Mg (Lawler et al., 1989).
probable cometary origin. Magnesium-rich (Fe-poor) silicates comprise at least 40%
and perhaps ≥60% of the rocky particles (Jessberger, 1999).
2. IN SITU SAMPLING Iron is present in other minerals including metals (1–2%),
iron sulfides (~10%), and possibly iron oxide (≤1%) (Schulze
The most direct means of determining the composition of et al., 1997).
cometary dust is by in situ sampling or analysis of returned The CHON spectra are evidence for an organic refrac-
samples. To date, in situ sampling has been carried out for tory component in the cometary dust. Significant cluster-
just one comet, 1P/Halley. The two Soviet Vega spacecraft ing of subgroups (e.g., spectra dominated by [H, C], [H,

555
556 Comets II

C, O], etc.) indicate variable composition of the organic 4.0

refractory material (Fomenkova et al., 1994).

10.55
3.5

10.0

11.2

11.9
9.2
Isotopic ratios were found to be solar, within the meas-

Relative Emissivity
urement uncertainties, with the exception of 12C/13C (Jess- 3.0
Hale-Bopp
berger, 1999). While low ratios (13C enrichment) were judged March 26
2.5 T = 440 K
to be uncertain due to noise of uncertain origin, Jessberger
(1999) reported that definite 12C enrichments, up to 12C/13C ~ 2.0
Halley x 3
5000, were identified, indicative of presolar nucleosynthe- Jan. 16, 1986
sis products. 1.5 T = 360 K

1.0
3. SPECTROSCOPY OF
COMETARY SILICATES 0.5
8 9 10 11 12 13

Wavelength (µm)
Small silicate grains in the cometary dust coma will
produce an emission feature near 10 µm due to stretching
vibrations in Si–O bonds. Additional bending mode vibra- Fig. 1. The 10-µm silicate emission feature in Hale-Bopp at r =
tions occur between 16 and 35 µm. The wavelengths and 0.92 AU (dots) and 1P/Halley at r = 0.79 AU from Campins and
shapes of these features are diagnostic of the mineral com- Ryan (1989) (line). Each spectrum has been divided by a Planck
position. The 10-µm feature lies within the 8–13-µm atmos- function for the temperature shown and the Halley spectrum has
pheric “window,” allowing groundbased observations. been multiplied by 3. The spectral peaks in the Hale-Bopp spec-
trum are marked. From Hanner et al. (1999).
Although some 20-µm observations can also be made from
the ground, the full 16–35-µm region is best studied from
above the atmosphere.
Low-resolution (R ~ 50–100), 8–13-µm spectra now ex- cometary spectra is characteristic of amorphous olivine
ist for a number of comets. Several comets display strong (Stephens and Russell, 1979); crystalline olivine has a sec-
structured silicate emission with total flux/continuum at ondary peak at 10 µm as well.
10 µm >1.5. These include long-period comets Bradfield The 9.2-µm feature, first recognized in Hale-Bopp, is a
(1987 XXIX = C/1987 P1) (Hanner et al., 1990, 1994a), signature of pyroxene ([Mg,Fe] SiO3). A peak wavelength
Levy (1990 XX = C/1990 K1) (Lynch et al., 1992), Hya- of 9.2 µm corresponds to amorphous, Mg-rich pyroxene
kutake (C/1996 B2), and Hale-Bopp (C/1995 O1) (Hanner (Stephens and Russell, 1979; Dorschner et al., 1995). Crys-
et al., 1999; Wooden et al., 1999; Hayward et al., 2000); talline pyroxenes generate more variety in their spectra
new comet Mueller (1994 I = C/1993 A1) (Hanner et al., (Sandford and Walker, 1985; Jaeger et al., 1998). Peaks at
1994b); and 1P/Halley (Bregman et al., 1987; Campins and 10–11 µm contribute to the width of the cometary feature
Ryan, 1989). and the structure near 10.5 µm. A peak near 9.3 µm is gen-
By far the strongest silicate emission was seen in Hale- erally present in crystalline pyroxenes as well.
Bopp. This comet was also unusual in displaying a strong A remarkable 16–45-µm spectrum of Comet Hale-Bopp
silicate feature even at 4.6 AU preperihelion (Crovisier et at r = 2.9 AU, shown in Fig. 2, was acquired with the short-
al., 1996; Grün et al., 2001). Near-perihelion, groundbased wavelength spectrometer (SWS) on ESA’s Infrared Space
spectra were obtained by several groups; all spectra show Observatory (Crovisier et al., 1997, 2000). Five peaks are
similar structure (see Hanner et al., 1999, for a review). A clearly visible, corresponding in every case to laboratory
typical spectrum is presented in Fig. 1. The observed fluxes spectra of crystalline forsterite (Mg-olivine) (Koike et al.,
have been divided by a blackbody fitted at 8 and 12.5– 1993). Minor spectral structure is attributed to crystalline
13 µm. There are three main peaks, at 9.2, 10.0, and enstatite (Mg-pyroxene) (Wooden et al., 1999; Crovisier et
11.2 µm, and minor structure at 11.9 and 10.5 µm. The al., 2000). This result is significant in indicating that the
spectral shape is very similar to that in P/Halley and the silicates are Mg-rich, in agreement with the elemental com-
other comets cited above. position detected in P/Halley’s coma.
The 11.2-µm peak is attributed to crystalline olivine These spectra contrast with airborne spectra of Comet
([Mg,Fe]2 SiO4), based on the good spectral match with the P/Halley, the only other complete 20–30-µm spectra of a
measured spectral emissivity of Mg-rich olivine (Stephens comet. A 16–30-µm spectrum at r = 1.3 AU (spectral reso-
and Russell, 1979; Koike et al., 1993). The 11.9-µm shoul- lution 0.2 µm) displays a sharp peak at 28.4 µm, but only
der is also due to crystalline olivine. If all the silicates have weak features at 23.8 and 19.6 µm (Herter et al., 1987).
similar temperatures, then only a small fraction (15–20%) Twenty- to 35-µm spectra with 0.5–1-µm resolution, taken
of the silicate material needs to be in the form of crystal- at 1.2-AU preperihelion and 1.4-AU postperihelion, show
line olivine to produce the observed peak (Hanner et al., only weak excess above the continuum at 24 and 33 µm
1994a); the mass absorption coefficient of olivine near (Glaccum et al., 1987). This result is puzzling. Although
11.2 µm is a factor of 3–10 times that of glassy silicates the strength of the 10-µm silicate feature was quite vari-
(Day, 1976, 1981). The broader 10-µm maximum in the able from day to day, an 11.2-µm olivine peak was clearly
 Hanner and Bradley: Composition of Cometary Dust 557

200

Comet
Model
BB1
BB2
150 Cry Ol
Cry o-Pyr
Am Pyr
Flux (Jy)

100

50

0
10 20 30 40

Wavelength (µm)

Fig. 2. ISO SWS spectrum of Comet Hale-Bopp at r = 2.8 AU, degraded to R = 500, compared with a five-component dust model:
280 K blackbody (BB1); 165 K blackbody (BB2); forsterite (Cry Ol 22%); orthopyroxene (Cry o-Pyr 8%); and amorphous pyroxene
(Am Pyr 70%). From Crovisier et al. (2000).

visible as part of a strong 10-µm feature on the same day all the silicate grains would have sufficient thermal contact
as the 1.2-AU airborne spectrum (Bregman et al., 1987). with absorbing material to be warm, regardless of their Mg/
Viewing restrictions on solar elongation angle prevented Fe content. They concluded that glassy pyroxenes were the
SWS observations when Hale-Bopp was near 1 AU, so we most abundant component (>40%) and that crystalline oli-
do not know how the 16–35-µm spectrum evolved as the vine comprised ≤20% of the small silicate grains.
grains were heated. However, an SWS spectrum acquired Harker et al. (2002) modeled the combined 8–13-µm
at 3.9-AU postperihelion still displayed the major forsterite spectra, IR photometry, and SWS spectra from October
peaks (Crovisier et al., 2000). 1996 (r = 2.8 AU); the extended wavelength baseline en-
To produce a strong emission feature, silicate particles abled them to restrict the temperatures for the various amor-
must have radii on the order of 1 µm or smaller. Larger phous and crystalline silicate components (tied to their Mg/
particles will display a feature only if they are very porous Fe abundance ratios). They introduced porosity of the C and
aggregates and the individual constituent grains are micro- amorphous silicate particles (modeled with effective me-
meter-sized or smaller. dium theory) by adopting the fractal dimension, D, as one
Spectral models to match the Hale-Bopp spectra with a of the model parameters. By comparing their best-fit model
mixture of silicate minerals have been presented by Brucato at r = 2.8 AU with the 1997 8–13-µm spectra and photom-
et al. (1999), Colangeli et al. (1999), Galdemard et al. etry, they concluded that the size distribution steepened and
(1999), Hayward et al. (2000), Wooden et al. (1999, 2000), fractal dimension decreased as the comet approached peri-
and Harker et al. (2002). Wooden et al. (1999, 2000) pro- helion. Crystalline silicates constituted about 30% by mass
posed that the observed changes in spectral shape with of the small dust grains in the coma at all epochs.
heliocentric distance can be explained by temperature dif- In summary, the observed spectral features imply a com-
ferences between more-transparent (cooler) Mg-rich pyrox- plex mineralogy for the cometary silicates, including both
ene grains and less-transparent (warmer) olivine grains. In amorphous and crystalline grains of pyroxene and olivine
their model, the cooler crystalline pyroxenes comprise the composition. This mineralogy is consistent with the chon-
major fraction of small silicate grains (~90%), and these dritic aggregate IDPs, described in the next section.
grains produce the enhanced 9.3-µm feature near perihe- Not all comets display strong 10-µm emission features.
lion. Hayward et al. (2000) assumed in their modeling that The spectra of four new comets discussed in Hanner et al.
558 Comets II

(1994a) are puzzling; each has a unique spectrum that is

not yet understood. For example, an extremely broad emis-
sion feature was present in Wilson (1987 VII = C/1986 P1)
(Lynch et al., 1989), suggesting a very amorphous silicate
material. It is possible that we are witnessing the effect of
cosmic-ray damage to the outermost layer of the nucleus
over the lifetime of the Oort cloud.
No strong 10-µm emission feature has yet been seen in
a short-period comet. Broad emission features about 20%
above a black-body continuum were present in spectra of
Comets 4P/Faye and 19P/Borrelly (Hanner et al., 1996) and
103P/Hartley 2 (Crovisier et al., 2000). Filter photometry
of 81P/Wild 2 revealed a feature about 25% above the con-
tinuum; no spectrum exists (Hanner and Hayward, 2003).
The ratio of the flux in a narrow 10.4-µm filter to the flux
in a broad 10-µm (N) filter indicated some silicate emis-
sion in Comets P/Encke, P/Stephan-Oterma, and P/Tuttle
(Campins et al., 1982). Gehrz et al. (1989) did not detect Fig. 3. Secondary electron micrograph of a chondritic porous
silicate emission in P/Encke near perihelion in 1987. Other (CP) interplanetary dust particle. Bar is 1 µm in length. The frag-
short-period comets with 10-µm filter photometry show no ile microstucture and high porosity of this particle are consistent
feature at the 10% level. The absence of strong silicate with a cometary origin. The submicrometer-sized grains are mainly
emission in the short-period comets could be explained GEMS and carbonaceous material. The angular, micrometer-sized
components include single crystals of forsterite, enstatite, and FeNi
either by a difference in the composition between Oort
sulfides.
cloud and Kuiper belt comets or by a lower abundance of
submicrometer-sized particles. Short-period comets gener-
ally have been outgassing during many orbits in the inner
solar system and the smaller or more fluffy particles may The major form of noncrystalline silicates in the chon-
have been preferentially expelled over time. Thus, a lower dritic aggregate IDPs are the glass with embedded metal
abundance of isolated small grains or very fluffy aggregates and sulfides (GEMS). These are submicrometer-sized glassy
of small grains in the coma is the simplest explanation for Mg-silicate grains with embedded nanometer FeNi and Fe
the lack of a strong silicate feature, although compositional sulfide crystals (Bradley, 1994). The GEMS show evidence
differences cannot be ruled out. of exposure to large doses of ionizing radiation (e.g., Demyk
et al., 2001, Carrez et al., 2002), such as eroded surfaces,
4. INTERPLANETARY DUST PARTICLES O enrichment, gradients in Mg/Si ratio decreasing outward
FROM COMETS from the center, and formation of reduced FeNi metal,
pointing to exposure in the interstellar medium prior to their
The submicrometer grain size, high Mg/Fe ratio, and mix incorporation into comets. Some GEMS contain heavily
of crystalline and noncrystalline olivine and pyroxenes in etched relict mineral grains of sulfides or Mg-rich silicate
the cometary dust have no counterpart in any meteoritic crystals. The physical and chemical properties of GEMS are
material, with the exception of the anhydrous chondritic similar to those inferred for interstellar grains.
aggregate IDPs. These are fine-grained heterogeneous ag- Infrared spectra of GEMs-rich IDP samples (thin sec-
gregates having chondritic abundances of the major rock- tions containing GEMS and silicate crystals) resemble the
forming elements; they comprise a major fraction of the cometary silicate spectra, while spectra of individual GEMS
IDPs captured in the stratosphere (Fig. 3). Typical grain reveal a single broad peak near 9.3 µm (glassy pyroxene)
sizes within the aggregates are 0.1–0.5 µm; micrometer- or 9.8 µm (glassy olivine) (Bradley et al., 1999). The peak
sized crystals of forsterite and enstatite are also present wavelength, width, and long-wavelength asymmetry of the
(Bradley et al., 1992). These aggregate IDPs are thought 9.8-µm peak are similar to the interstellar silicate feature,
to originate from comets, based on their porous structure, such as that of the Trapezium.
small grain size, high C content, and relatively high atmo- Detection of nonsolar isotopic abundances in GEMS
spheric entry speeds. Measured He release temperatures would constitute strong evidence for an interstellar origin.
indicate that many of these IDPs entered the atmosphere at GEMS are frequently embedded in a carbonaceous mate-
speeds >16 km/s, consistent with cometary orbits (Nier and rial that displays high D/H ratios and 15N enrichment (Keller
Schlutter, 1993). The match between the mineral identifi- et al., 2000). A bulk O-isotopic measurement of a GEMS-
cations in the Hale-Bopp spectra and the silicates seen in rich IDP yielded the highest “whole-rock” 16O enrichment
the IDPs strengthens the link between comets and this class yet measured in any chondritic object (Engrand et al.,
of IDPs. Thus, the composition and structure of the porous 1999); silicates are the main carrier of O. NanoSIMS tech-
aggregate IDPs can be used to augment our understanding niques are now reaching the sensitivity to allow isotopic
of the composition and origin of cometary dust. measurements on individual submicrometer-sized grains in
 Hanner and Bradley: Composition of Cometary Dust 559

IDPs. In early results utilizing nanoSIMS, two GEMS with tified component of the dust in Comet Halley sampled dur-
nonsolar O-isotopic ratios have been detected (Messenger ing the spacecraft encounters (Schulze et al., 1997).
et al., 2003).
The crystalline silicates found in chondritic porous IDPs 5. ORIGINS OF COMETARY DUST
are primarily the Mg-rich minerals forsterite and enstatite.
This mineralogy is consistent with the 8–35-µm spectrum It is clear from the in situ and remote observations of
of Hale-Bopp and the in situ Halley elemental composition comets and the analysis of probable cometary IDPs that
data. Grain sizes range from ~0.05 to 5 µm although most cometary dust is an unequilibrated, heterogeneous mixture
are 0.1–0.75 µm in diameter. Some enstatite whiskers, rods, of minerals, including both high- and low-temperature con-
and platelets have unusual growth patterns, such as axial densates. These various components do not necessarily
screw dislocations, that indicate direct vapor phase conden- share a common origin. Temperatures in the solar nebula
sation from a hot gas (Bradley et al., 1983). Some low-Fe, beyond 5 AU, where the comet nuclei accreted, were never
Mn-enriched (LIME) enstatite and forsterite grains contain higher than about 160 K, too low for significant processing
up to 5 wt.% MnO, in contrast to the majority of pyroxenes of dust particles (Boss, 1994, 1998, 2004). Thus interstel-
and olivines in meteorites, which contain <0.5 wt.% MnO lar grains present in the outer solar nebula could have been
(Klock et al., 1989). The high Mn content is further evi- preserved in comets. Material that condensed within the
dence of direct condensation from a gas. At least one sub- solar nebula also may have accreted into the comet nuclei.
micrometer forsterite grain with 17O enrichment, indicating The glassy silicate grains (GEMS) described in section 4
a circumstellar origin, has been identified (Messenger et al., appear to constitute the major fraction of the noncrystal-
2003). line silicates in cometary IDPs and the evidence is quite
The chondritic aggregate IDPs have a high bulk C con- strong that these are interstellar grains, based on their mor-
tent, 2–3 times higher on average than the primitive CI me- phology, physical and chemical structure, and inferred high
teorites. Thomas et al. (1993) measured a range of 1– radiation dosage. They are often embedded in an organic
47 wt% C in 100 anhydrous IDPs; in a few cases, C was C material with nonsolar D/H and 15N/14N isotopic ratios.
the most abundant element by volume. The C is distributed The GEMS must have formed at comparatively low tem-
throughout the IDP as a matrix surrounding the mineral peratures and were never heated sufficiently to anneal. Thus,
grains, but not necessarily as mantles on the grains. Much noncrystalline cometary silicates may be predominantly of
of the C is in an organic phase, evident from X-ray absorp- interstellar origin.
tion edge spectroscopy and C-H stretch absorption features The origin of the crystalline silicates in comets is more
in the 3-µm region (Clemett et al., 1993; Flynn et al., 1999, complex. Crystalline silicate grains can form by direct con-
2000). C = O functional groups have been identified from densation from a hot gas at T = 1200–1400 K, followed by
the absorption edge spectroscopy (Flynn et al., 2001). These slow cooling, or by annealing of amorphous silicates at
results are qualitatively consistent with the nature of the temperatures around 1000 K or higher (Hallenbeck et al.,
CHON particles detected by the dust analysis instrument 1998, 2000; Brucato et al., 2002; Koike and Tsuchiyama,
on the Halley space probes (Fomenkova et al., 1994). Car- 1992; Fabian et al., 2000). While the enstatite whiskers and
bon-rich IDPs show a red reflectance spectrum, similar to rods occasionally seen in aggregate IDPs have growth pat-
red, dark outer solar system material (Bradley et al., 1996; terns indicating direct vapor phase condensation, other crys-
Keller and Messenger, 1997). talline grains in IDPs have no distinctive structure to dis-
Nonsolar isotopic enrichments of D/H and 15N/14N have tinguish between direct condensation or annealing. The Mg
been detected in C-rich IDPs. In particles where further crystalline minerals forsterite and enstatite are predicted
analysis has been carried out, the D and 15N anomalies are from thermodynamic models to be the first to condense in
associated with an organic carrier (e.g., Aleon et al., 2002). a hot gas at 1200–1400 K and only react with Fe at lower
These isotopic enrichments are attributed to mass fraction- temperatures. Thus, direct condensation is a natural expla-
ation during low-temperature ion-molecular reactions in nation for the preponderence of Mg-silicates in comet dust.
cold, dense interstellar molecular clouds. In some cases, the Grain condensation or annealing could have occurred in
measured D/H ratio approaches that observed in molecular the hot inner solar nebula. Disk midplane temperatures
clouds (Messenger, 2000). High D/H ratios, roughly twice ≥1000 K were reached inside about 1 AU, depending on the
the terrestrial value and 10 times the protosolar value, have mass infall rate (Boss, 1998; Chick and Cassen, 1997). Dur-
been observed in gas phase cometary H2O and HCN (Meier ing the early high mass accretion phase (mass infall rate
and Owen, 1999). Iron-nickel sulfide grains are the major ≥10 –6 M yr –1), this hot region could have extended to 3–
carrier of S in the chondritic aggregate IDPs. The sulfide 4 AU (Bell et al., 2000). However, the crystalline grains must
mineralogy is significantly different from that in primitive be transported out to the region where the comets formed at
chondritic meteorites (Dai and Bradley, 2001). Keller et al. 5–50 AU, and the extent of radial mixing of dust is uncer-
(2002) have proposed that sulfides are responsible for a tain. Bockelée-Morvan et al. (2002) have shown that turbu-
broad λ ~ 23-µm feature detected around young and old stars lent diffusion in the solar nebula could be an efficient proc-
by ISO. Laboratory spectra of pyrrhotite grains from IDPs ess to transport the crystalline grains from the inner nebula
display a broad Fe-S stretch feature centered at ~23.5 µm, to the region of comet formation in timescales of a few
similar to the circumstellar feature. Iron sulfide was an iden- 104 yr. This process is efficient as long as the grains remain
560 Comets II

coupled to the gas, i.e., as long as they remain small. The Herbig Ae/Be stars that are precursors of β Pictoris systems
timescales for grain coagulation and growth are uncertain, (Waelkens et al., 1996) does one find the spectral peaks of
but could be short enough to compete with radial transport. crystalline olivine. For example, the ISO spectrum of the
Alternatively, Harker and Desch (2002) have proposed late-stage Herbig Ae/Be star HD100546 is very similar to
that small silicate grains in the solar nebula could have been that of Comet Hale-Bopp (Malfait et al., 1998). These sys-
thermally annealed by passing shock waves, provided that tems are thought to have developed a population of com-
the ambient gas density was high enough to heat the grains ets that are the source of the dust (e.g., Weissman, 1984;
briefly above 1200 K. The relation between the amount of Grady et al., 1997).
heating and the degree of crystallinity is based on laboratory Grain destruction in the ISM is an efficient process.
annealing experiments of Hallenbeck et al. (1998, 2000). Thus, if the comet grains formed in circumstellar outflows
This mechanism would be effective out to about 10 AU; at from evolved stars, one has to understand how they survived
larger heliocentric distances the gas density would be too destruction in the ISM and why their spectral signatures are
low to generate sufficient grain heating. not seen in the ISM or young stellar objects.
More study is needed, however, to understand the de- Kemper et al. (2001) have produced radiative transfer
tails of the annealing process and whether crystals with the models to study the visibility of crystalline silicates in mid-
observed mineralogy and morphology could be produced. infrared spectra of circumstellar dust. Because pure crys-
If GEMS are representative of the amorphous silicate par- talline Mg-silicates are very transparent at visible and near-
ticles present in the solar nebula, one would expect the IR wavelengths, they will be colder than Fe-containing
annealed crystals to retain the FeNi nanoparticles present amorphous silicates in optically thin regions where grains
in the GEMS, and these are not seen. Moreover, the GEMS are heated by exposure to visible/near-IR stellar radiation.
are confined to a narrow size range (0.1–0.5 µm), whereas Kemper et al. showed that, indeed, a considerable fraction
some of the enstatite and olivine crystals in the chondritic of forsterite and enstatite could be present in such environ-
aggregate IDPs are micrometer-sized. The conditions of ments without their spectral signatures being visible in emis-
formation of silicate glasses and crystals are extensively sion above the radiation from the warmer dust components.
documented in a vast body of literature on geochemical These results should make us cautious about concluding that
thermodynamics and igneous and metamorphic petrology. crystalline silicates are absent in cases where they may sim-
Although the temperature and pressure regimes are well ply be “hidden” by their cold temperatures, a point also
outside those of low-temperature annealing, the underlying discussed by Wooden et al. (2000).
thermodynamic constraints are relevant. Anomalous isotopic enrichments could constitute strong
If a large fraction of cometary dust consists of solar evidence for an interstellar origin of cometary dust mate-
system condensates, then radial gradients in the tempera- rial. As described in section 4, analysis techniques have now
ture, composition, and extent of mixing within the solar reached the point where isotopic measurements can be made
nebula should be evident today as differences in the dust for individual grains in IDPs, and the first O-isotopic meas-
chemistry and mineralogy among comets formed in differ- urements provide tantalizing hints that a few grains do pos-
ent regions. For example, if the olivine condensed in the sess nonsolar O-isotopic ratios. However, it is not at all clear
hot inner solar nebula and was transported outward or if that silicate grains formed in the interstellar medium would
olivine was created in situ by passing shock waves, then have anomalous isotopic abundances. Their compositions
one would expect to see a difference in olivine abundance may well have been homogenized to an average close to
between Oort cloud comets that formed in the region of the solar abundances.
giant planets and Kuiper belt comets that formed beyond Greenberg (1982) proposed that interstellar silicate
30 AU. To date, no strong 11.2-µm olivine peak has been grains possess organic refractory mantles as a result of UV
detected in a Kuiper belt comet; however, the cause may photoprocessing in the diffuse interstellar medium follow-
be a lack of disaggregated small grains in the coma rather ing deposition of icy mantles in cold molecular clouds.
than a lack of silicates. A possible, but weak, 11.2-µm peak These submicrometer core/mantle grains, perhaps with an
may be present in the relatively weak silicate features ob- additional icy mantle, were subsequently agglomerated and
served in Comets P/Borrelly (Hanner et al., 1996) and P/ incorporated into comets. A mass of the organic refractory
Hartley 2 (Crovisier et al., 2000). material comparable to the mass of the silicates satisfied
Could the crystalline silicates have a presolar origin? cosmic abundances; in fact, it was argued that organic re-
Silicate grains are known to condense in O-rich envelopes fractory mantles are a necessary repository of C to account
around evolved stars. Spectral peaks of the Mg-silicates for its cosmic abundance. The detection of high D enrich-
forsterite and enstatite are clearly present in the ISO spec- ments in the organic refractory material in chondritic IDPs
tra of some evolved stars (Waters et al., 1996; Molster et lends strong support to a presolar origin for the organic
al., 2002). Yet signatures of crystalline silicates are absent refractory material. The high D/H material often surrounds
in spectra of the diffuse interstellar medium (ISM) or mo- GEMS and other mineral grains, suggesting that these em-
lecular clouds. Moreover, the spectra of most young stellar bedded grains are presolar as well, although the material is
objects show no evidence of crystalline grains. Only in de- more clumpy and irregular rather than a uniform core/man-
bris disks around young main-sequence objects such as tle morphology. However, the distinction between a popu-
β Pictoris (Knacke et al., 1993) and in certain late-stage lation of GEMS with carbonaceous mantles and a popula-
 Hanner and Bradley: Composition of Cometary Dust 561

tion of GEMS within a carbonaceous matrix is difficult to line and amorphous (or glassy) form and include the min-
discern in the electron microscope. Organic refractory eralogy of both olivine and pyroxene. The crystalline sili-
grains have not been detected spectroscopically in comets. cates are primarily the Mg-rich minerals forsterite and ensta-
An emission feature at 3.4 µm first detected in P/Halley, but tite, as is the case for circumstellar dust around evolved
also seen in other comets, was initially attributed to organic stars. Carbon is present in approximately cosmic abundance,
refractory grains. However, the discovery of methanol in much of it in an organic refractory component.
comets and analysis of its infrared bands led to the conclu- We have discussed why the chondritic porous aggregate
sion that the 3.4-µm feature is due to gas phase methanol IDPs are probably from comets. Analysis of their proper-
and other gaseous species (Bockelée-Morvan et al., 1995; ties complements and substantiates the conclusions drawn
DiSanti et al., 1995). For further discussion concerning the from the spectroscopy and from the in situ measurements
origin of cometary grains, see Wooden (2002). during the 1986 Halley spacecraft encounters. In particular,
IDP analysis confirms that much of the carbonaceous ma-
6. FUTURE DIRECTIONS terial is in an organic phase, and the detection of high D/H
ratios implies that at least some of this material is presolar.
The past decade has witnessed significant advances in The D-rich material often surrounds GEMS and other min-
our understanding of the chemistry and mineralogy of eral grains, suggesting that these embedded grains are of
cometary dust. However, questions remain about the nature presolar origin as well. GEMS are the predominant form of
of the refractory organic material, the differing dust prop- noncrystalline silicates. These particles appear to have ex-
erties among comets, and the origins of the various dust perienced high radiation dosage in a presolar environment.
components. The various types of silicate particles do not necessar-
The next decade should bring further advances in our ily have a common origin. While the GEMS are of likely
knowledge of the composition and origin of cometary dust, presolar origin, the origin(s) of the crystalline silicates is
including the first comet dust sample return. NASA’s Star- unclear. If formed as high-temperature condensates or by
dust mission, launched in 1999, will collect a dust sample annealing in the inner solar nebula, radial transport must
from Comet 81P/Wild 2 in January 2004 and return it to have been more efficient during the planetesimal accretion
Earth in January 2006. Coupled with the newest analysis phase than some models predict. It is possible that grains
tools, the sample will yield isotopic abundance ratios for were annealed by transient heating from passing shock
individual particles, as well as the chemistry and mineral- waves in the solar nebula at r ≤ 10 AU. However, the size
ogy of the silicates and other refractory dust components range and composition of the crystalline silicates in porous
from a comet that probably originated in the Kuiper belt. aggregate IDPs are not consistent with what one would
ESA’s ambitious Rosetta mission, now scheduled for expect for annealed GEMS. In either case, one would ex-
launch in 2004, will rendezvous with a short-period comet. pect crystalline silicates to be less abundant — or absent
Rosetta carries several instruments to measure the dust mass entirely — in the Kuiper belt comets that formed beyond
distribution, composition, and structure, as the spacecraft 30 AU.
travels with the comet from aphelion to perihelion (Schwehm If the crystalline silicates were already present in the
and Schulz, 1999). cloud from which the solar nebula formed, then one needs
The midinfrared spectra of Comet Hale-Bopp and astro- to explain why their spectral signatures are not seen in in-
nomical sources from ISO demonstrated the value of 8– terstellar dust or in young stellar objects. The very cold
45-µm spectroscopy for determining dust composition. temperatures of “clean” Mg-rich silicates is one possible
SIRTF, the Space Infrared Telescope Facility, and SOFIA, explanation why their spectral features are not seen in emis-
the Stratospheric Observatory for Infrared Astronomy, will sion. Isotopic measurements of individual silicate grains in
allow a number of comets to be observed in this important IDPs and returned comet samples with nanoSIMS tech-
spectral region. The detection of crystalline silicates in niques may help to clarify their origin.
Kuiper belt comets would be particularly significant in Although the chondritic aggregate IDPs have given us
showing that crystalline silicate particles were spread extremely interesting insight into the nature of probable
throughout the solar nebula. cometary dust, we do not know the specific source of an
Finally, improved sensitivity of laboratory techniques for individual IDP, nor the selection effects between comet
compositional analysis of microscopic samples, such as the ejection and Earth capture. Thus comet dust sample return
nanoSIMS, will offer the opportunity for elemental and iso- and in situ analysis are very important. In the next decade,
topic abundances to be investigated in individual submicro- we can look forward to the Stardust sample return from the
meter-sized grains in IDPs and returned cometary samples. short-period Comet 81P/Wild 2 in January 2006 and the
encounter of ESA’s Rosetta mission with a short-period
7. CONCLUSIONS comet in 2011–2013.
Acknowledgments. The research of M.S.H. was carried out
In situ sampling of Comet Halley dust, remote infrared at the Jet Propulsion Laboratory, California Institute of Technol-
spectroscopy, and IDP analyses yield a consistent picture ogy, under contract with the National Aeronautics and Space
of the composition of cometary dust. Silicates constitute the Administration. J.P.B. acknowledges support from NASA grants
most abundant material; they are present in both crystal- NAG5-7450 and NAG5-9797.
562 Comets II

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 Fulle: Motion of Cometary Dust 565

Motion of Cometary Dust

Marco Fulle
Istituto Nazionale di Astrofisica–Osservatorio Astronomico di Trieste

On timescales of days to months, the motion of cometary dust is mainly affected by solar
radiation pressure, which determines dust dynamics according to the particle-scattering cross-
section. Within this scenario, the motion of the dust creates structures referred to as dust tails.
Tail photometry, depending on the dust cross-section, allows us to infer from model runs the
best available outputs to describe fundamental dust parameters: mass loss rate, ejection veloc-
ity from the coma, and size distribution. Only models that incorporate these parameters, each
strictly linked to all the others, can provide self-consistent estimates for each of them. After
many applications of available tail models, we must conclude that comets release dust with
mass dominated by the largest ejected boulders. Moreover, an unexpected prediction can be
made: The coma brightness may be dominated by light scattered by meter-sized boulders. This
prediction, if confirmed by future observations, will require substantial revisions of most of
the dust coma models in use today, all of which are based on the common assumption that
coma light comes from grains with sizes close to the observation wavelength.

1. HISTORICAL OVERVIEW a particular type of antitails (anti-neck-lines) that lie in the

sector opposite that where most tails are possible. These are
While ices sublimate on the nucleus surface, the dust em- much shorter than usual tails, not exceeding 106 km in length
bedded in them is freed and dragged out by the expanding (section 7.1).
gas. The dust motion then depends on the three-dimensional The first tail model that fit the observations well was de-
nucleus topography and on the complex three-dimensional veloped by Friedrich W. Bessel (1784–1846) and later re-
gas-dust interaction that takes place close to the nucleus fined by Fjodor A. Bredichin (1831–1904). Bredichin intro-
surface. Information on such processes has never been avail- duced the notion of synchrones and syndynes (Fig. 1). Both
able to modelers. Dust coma shapes depend heavily on the authors assumed that a repulsive force, inversely propor-
details of these boundary conditions, and coma models tional to the squared Sun-comet distance, was acting on the
cannot disentangle the effect of dust parameters on coma material composing the tails. According to this hypothesis,
shapes from those due to the unknown boundary conditions. the tail particle is subjected to a total force equal to the solar
On the contrary, dust tails are usually structureless, suggest- gravity times a factor µ characterizing the tail particle. When
ing that the dust has lost the memory of the details of the this repulsive force is equal to the solar gravity, i.e., when
boundary conditions. Moreover, solar radiation pressure acts µ = 0, the tail particle assumes a uniform straight motion.
like a mass spectrometer, putting dust particles of different When µ < 0, the tail particle moves on a hyperbola with
masses in different space positions: This allows models to the convexity directed toward the Sun. When 0 < µ < 1, the
evaluate how dust parameters affect tail shapes, making tail tail particle behaves as if the Sun were lighter, so that its
models powerful tools to describe dust in comets. motion is slower than that of the comet nucleus and its orbit
A dust tail is a broad structure that originates from the is external relative to that of the comet nucleus. This model
comet head and can reach lengths on the order of 104 km explained why cometary tails always lie in the comet or-
in most cases and up to 108 km in the most spectacular cases bital plane sector outside of the comet orbit and behind the
(Plate 16). When we consider the comet orbital path and the comet nucleus. Svante Arrhenius (1859–1927) proposed the
straight line going from the Sun to the comet nucleus (the solar radiation pressure as a candidate for Bessel’s repul-
radius vector), we divide the comet orbital plane in four sec- sive force. The computations of Karl Schwarzschild (1873–
tors (Fig. 1). All cometary tails lie in the sector outside the 1916) and Peter J. W. Debye (1884–1966) established that
comet orbit and behind the comet nucleus. When we project the β = 1 – µ parameter is inversely proportional to the di-
these four sectors of the comet orbital plane onto the sky, ameter of the dust particle (assuming it to be a sphere) and
they may be strongly deformed by the observation perspec- equal to 1 for dust diameters close to 1 µm.
tive, especially when Earth is close to the comet orbital Let us consider the comet nucleus moving along its orbit
plane. In these latter cases, the sector where tails may be and ejecting dust particles with exactly zero ejection veloc-
seen can be a complete sky halfplane and the appearance of ity. Particles all ejected at the same time and characterized
a perspective antitail is then possible, which although seen by any µ value will be distributed at a later observation time
to roughly point to the Sun, is always external to the comet on a line referred to as “synchrone.” Changing the ejection
orbit. A few years ago, Pansecchi et al. (1987) discovered time, we obtain a family of synchrones, each characterized

565
566 Comets II

2. DUST TAILS: PHOTOMETRIC THEORY

The dust dynamics depend on the β = 1 – µ parameter

3E Qpr CprQpr
β =1− µ = = (1)
8πcGM ρdd ρdd

where E is the mean solar radiation, c the light speed, Qpr

the scattering efficiency for radiation pressure, G the gravi-
tational constant, M the solar mass, ρd the dust bulk den-
sity and d the diameter of the dust grains, assumed here to be
spherical in shape. Here we use the terms dust grain or dust
particle to refer to every solid object that escapes a comet
nucleus. The resulting value of Cpr = 1.19 × 10–3 kg m–2.
For the β values most common in dust tails, d >> 1 µm and
Qpr ≈ 1 (Burns et al., 1979), so that the most uncertain
parameter is the dust bulk density. As a consequence, it is
convenient to express all size-dependent quantities as func-
Fig. 1. Synchrone-syndyne network for Comet Hale-Bopp tions of ρdd. The flux of photons I (measured in Jy sr –1)
1995O1 on 3 January 1998, when a neck-line was observed during
received from a dust tail is
the Earth crossing of the comet orbital plane (Fig. 2). The Sun was
located exactly toward the –y direction and the phase angle of the
comet at the observation was φ = 14.4°. The image plane corre- I(x, y) = BD(x, y) =
sponds to the comet orbital plane; the Earth direction is toward to ∞ (2)
the bottom right, forming an angle φ with the –y axis. The dotted
line is the comet elliptical orbit, which, together with the y axis,
∫ ∫
B
−∞ 0
H(x, y, t, 1 − µ)N(t)σ (t, 1 − µ)dtd(1 − µ)

divides the plane in the four sectors discussed in section 1. The where x,y are the sky coordinates, H the sky surface den-
continuous lines are syndynes characterized by the parameter β = sity of dust grains coming from dust tail models, N(t) the
1 – µ = 1, 0.3, 0.1, 0.03, 0.01, 0.003, 0.001, and 0.0003, rotating dust number loss rate, to the observation time, σ the cross-
clockwise from that closest to the +y direction, respectively. The section of a grain, B the flux of photons in thermal or op-
dashed lines are synchrones characterized by the ejection times tical bandwidths (measured in Jy sr–1) received from a grain
250, 200, 100, 0, –100, –200, and –300 d with respect to perihe-
of unit cross-section, and D the dimensionless sky surface
lion, rotating clockwise from the closest one to the +y direction
density weighted by the dust cross-section observed in the
respectively. The three-dotted-and-dashed line is the neck-line axis,
approximately corresponding to the synchrone ejected 43.8 d be- tail: If we are observing optical fluxes, then we are dealing
fore perihelion. Because of the Earth position, it is evident that with scattering cross-sections; if we are observing IR fluxes
the neck-line was observed as a spike pointing toward the antisolar coming from grains with sizes much larger than IR wave-
direction (Fig. 2); its prolongation in the –x direction was observed lengths, then we are dealing with emitting cross-sections.
as a bright spikelike real antitail (Fig. 2). Since we have

π 2 π (ρdd)2
σ(d) = d = (3)
by its ejection time. Synchrones can be approximated by 4 4 ρ2d
radial lines, all diverging from the comet nucleus. Con-
versely, particles characterized by the same µ value ejected
π (ρ d)3
at any time will be distributed at a later observation time on M(d) = N ρd d (4)
a line referred to as “syndyne.” Changing the µ value, we 6 ρ3d
obtain a family of syndynes, each characterized by its µ
value. Syndynes can be approximated by spirals tangent to the relation between the dust mass loss rate M and the flux
the prolonged radius vector, the Sun-comet nucleus vector. I received from the tail is independent of ρd
In this model, only one synchrone and one syndyne pass
in each point of the tail. It is thus possible to derive the 3 to ∞
ejection time and the µ value at each point of the tail. The I(x, y) =
2
B ∫ ∫−∞ 0
H(x, y, t, 1 − µ)
synchrone-syndyne model predicts that dust tails are two- (5)
(ρdd)2
dimensional structures lying in the comet orbital plane. Tail M(t, 1 − µ) dtd(1 − µ)
observations made when Earth crosses the comet orbital (ρdd)3
plane (Pansecchi et al., 1987) have shown that dust tails
are thick, i.e., three-dimensional structures. which makes dust tail models a powerful tool to infer the
 Fulle: Motion of Cometary Dust 567

mass loss rate of cometary dust. Equation (5) shows that mal IR or millimeter data
the relationship between dust mass loss rate and tail bright-
ness depends on the second and third momenta of the differ-
4Sν (x, y, T)
ential dust size distribution (DSD). Since the dust dynamics k= (11)
depend on the β = 1 – µ quantity, it is convenient to express πD(x, y)Bν (T)
the DSD in terms of (ρdd) weighted by the dust cross-sec-
tion observed in the tail. Thus, we define the dimension- so that k is now independent of the dust albedo, depending
less “β-distribution” only on the dust temperature T, usually much better known
than the albedo. Here, Bν(T) is the Planck function at tem-
perature T and Sν(x,y,T) is the flux received from a dust
(ρdd)2g(t,ρdd)d(ρdd)
f (t, 1 − µ)d(1 − µ) = ∞
(6) tail in a thermal IR or millimeter wavelength. If the dust
∫ 0
(ρdd)2g(t,ρdd)d(ρdd) grains have very aspherical shapes, with very different
cross-sections along each space coordinate (e.g., noodles,
long cylinders or flat disks), then it becomes impossible to
g(t,ρdd)d(ρdd) = k(1 – µ)2f(t,1 – µ)d(1 – µ) (7) compute any dust dynamics (Crifo and Rodionov, 1999).
If dust grains are not spherical but still compact, then the
where k is a dimensionless constant depending on the quan- numerical values of Cpr and k change, while equations (1),
tity B defined in equation (2). If the DSD g(t,ρdd) is a power (2), (6), (7), (8), and (9) remain identical (where now d is
law vs. (ρdd) with index α, then f(t,1 – µ) is a power law the mean grain size), along with equations (3), (4), and (5)
vs. (1 – µ) with index –α – 4. Dust tail models provide the after we change only the factors π4 , π6 , and 32 respectively.
quantity F(t,1 – µ), which is expressed in m2 s–1 Therefore, thermal IR or millimeter tail data provide the
most reliable information on dust mass loss rates and DSDs
CprQpr 2 in comets. In fact, the outputs of IR tail models are com-
F(t, 1 − µ) = N(t)f (t, 1 − µ) (8) pletely independent of the dust shape (provided the grains
ρd are compact), bulk density, and albedo (i.e., the most un-
certain parameters in cometary dust modeling). Moreover,
so that the dust mass loss rate given by equation (4) be- parallel IR and optical observations made at the same time
comes can provide unique estimates of the size and time depen-
dency of the dust albedo.
π ∞ F(t, 1 − µ)
M(t) =
6
kCprQpr ∫
0 1− µ
d(1 − µ) (9) 3. TWO-DIMENSIONAL MODELS

If we assume that dust, after having been dragged out by

Values of dimensionless quantity k depend on the actual the expanding gas, is ejected from the coma at zero velocity
techniques used to observe the dust tail. In the case of op- with respect to the nucleus, then the resulting two-dimen-
tical photographic or CCD data, it becomes sional model depends only on the quantity F given by equa-
tion (8). Within this model, the dust tail is a thin dust layer
2 lying in the comet orbital plane. The dust tail brightness D
4 γr 10 0.4[ m − m( x,y)]
k= (10) is simply proportional to F multiplied by the determinant
Ap(φ) 1 AU D(x, y) of the Jacobian between the (x,y) frame and the syndyne-
synchrone network defined in section 1. Then equation (5)
where γ = 206265 arcsec; r the Sun-comet distance at ob- is directly invertible, easily providing the quantity F, from
servation; m(x,y) the dust tail brightness expressed in mag which we can infer the dust mass loss rate by equation (9)
arcsec–2; m the Sun magnitude in the bandwidth of tail ob- and the DSD by means of the normalization of F vs. β and
servations; D(x,y) the dimensionless tail brightness defined then by equation (7). Following such a direct approach, the
in equation (2); and Ap(φ) is the geometric albedo times the DSD of short-period Comets 2P/Encke and 6P/d’Arrest was
phase function at observation [an isotropic body diffusing obtained (Sekanina and Schuster, 1978). The DSD power
all the received radiation uniformly in all directions has Ap = 14 index was always α < –4. In this case, both the brightness
(Hanner et al., 1981)]. CCD data provide much better ob- and the mass mainly depend on the micrometer-sized grains
servational constraints to models, because they have a well- observed in the tail. If α > –3, both the mass and brightness
calibrated photometric response, unlike photographic plates. depend on the largest ejected grains. Brightness and mass
Moreover, the much higher sensitivity of CCDs allows us become decoupled if –4 < α < –3, in which case the dust
to use interferential filters to avoid emissions from ions and mass depends on the largest ejected grains, while the bright-
gases, which usually pollute the wide bandwidths (e.g., John- ness depends on the micrometer-sized grains.
son filters) used in astrophotography. However, CCD data Since the observed brightness fixes the number of mi-
also provide dust mass loss rates that are dependent on the crometer-sized grains observed in the comet if α < –3, the
poorly known dust albedo. Conversely, in the case of ther- DSD index in practice only affects the number of unob-
568 Comets II

TABLE 1. Dust size distributions in comets.

Comet βmin βmax α(t) αm

2P/Encke 6 × 10 –6 0.02 –4.8 < α < –2.8 –3.6 ± 0.3
6P/D’Arrest 1 × 10 –5 0.06 –5.0 < α < –3.5 –3.8 ± 0.1
10P/Tempel2 2 × 10 –5 0.03 –4.8 < α < –3.4
26P/Grigg-Skjellerup 6 × 10 –5 0.06 –4.0 < α < –3.0
29P/SW1 4 × 10 –5 0.2 –4.0 < α < –3.0 –3.3 ± 0.3
46P/Wirtanen 1 × 10 –4 0.2 –4.1 < α < –3.0
65P/Gunn 1 × 10 –4 0.2 –4.3 < α < –3.0
67P/Churyumov-Gerasimenko 6 × 10 –6 0.03 –5.5 < α < –3.2 –3.4 ± 0.2
P/Swift-Tuttle 6 × 10 –5 0.2 –5.0 < α < –3.0 –3.3 ± 0.2
2060 Chiron 2 × 10 –4 1.0 –4.5 < α < –3.0 –3.2 ± 0.1
Seki-Lines 1962III 1 × 10 –4 0.1 –5.0 < α < –4.0 –4.1 ± 0.6
Kohoutek 1973XII 1 × 10 –4 0.2 –5.0 < α < –3.0 –3.3 ± 0.4
Wilson 1987VII 2 × 10 –5 0.1 –3.8 < α < –2.8 –3.0 ± 0.1
Bradfield 1987XXIX 1 × 10 –4 0.6 –4.2 < α < –3.0 –3.2 ± 0.2
Liller 1988V 1 × 10 –5 0.06 –4.3 < α < –3.3 –3.5 ± 0.2
Austin 1990V 1 × 10 –5 0.1 –4.5 < α < –2.8 –3.0 ± 0.2
Levy 1990XX 6 × 10 –5 0.4 –5.0 < α < –3.0 –3.2 ± 0.1
Hyakutake 1996B2 4 × 10 –4 1.0 –4.7 < α < –3.0 –3.6 ± 0.2
Hale-Bopp 1995O1 2 × 10 –3 1.0 –4.2 < α < –3.2 –3.6 ± 0.1
Time-dependent [α(t)] and time-averaged (αm) DSD power index evaluated for various comets within
a β range (defined by βmin and βmax) by means of the inverse tail model (adapted from Fulle, 1999).

served large grains, which may dominate the ejected mass shown that the correct explanation for these spikes requires
if α > –4 as well. Therefore, Sekanina and Schuster (1978) a model more elaborate than the two-dimensional syndyne-
correctly concluded that the index they found (α = –4.2) synchrone model.
implied that the number of ejected large grains was negli- After we have shown that the two-dimensional tail model
gible, and this assumption was adopted to design the Euro- has no physical basis, we must also show that the predic-
pean Space Agency’s Giotto mission to 1P/Halley. The im- tions of this two-dimensional model are systematically dif-
pact of Giotto with a grain of 1 g at the flyby implied that ferent from those of a correct three-dimensional model ap-
the actual probability of such an impact was underestimated plied to the same data. This was done, and in fact the DSD
by at least a factor of 100. Since the size ratio between 1-g power index resulted in α ≈ –3.7 for Comet 2P/Encke and
grains and those dominating the brightness of Comets 2P/ Comet 6P/d’Arrest (Fulle, 1990) (Table 1). The fact that the
Encke and 6P/d’Arrest was 104, the real α value should dust mass in 2P/Encke is strongly dominated by the largest
have been α > –3.7. We should conclude either that the dust ejected grains was further confirmed by applying the same
population of 1P/Halley is very different from that of 2P/ three-dimensional model to independent IR thermal data
Encke or 6P/d’Arrest, or that the two-dimensional model provided by the ISO probe [α = –3.2; Epifani et al. (2001)].
has intrinsic severe shortcomings. These results show that two-dimensional models and all
Observations when Earth crosses the comet orbital plane, related outputs should be ignored in the future, as they are
and hydrodynamic models describing the dust-gas interac- unable to provide useful constraints on the derived cometary
tion in the coma, both point out that the assumption of zero dust properties.
dust ejection velocity is nonphysical. Let us recall that this
approximation is also useless for the so-called perspective 4. THREE-DIMENSIONAL MODELS
antitails, which are sometimes composed of dust released at
very large heliocentric distances. In this latter case, the likely Finson and Probstein (1968) showed that the unrealistic
very low dust velocity is balanced by the very long time two-dimensional synchrone-syndyne models can be con-
interval existing between ejection of the dust and observa- verted into realistic three-dimensional models when we
tion. Since the thickness of the tail is roughly given by such associate a synchronic tube to each synchrone, whose width
a time interval times the dust velocity, it is impossible to is given by the dust ejection velocity at the synchrone time,
obtain a dust tail that can be well approximated by a two- or a syndynamic tube to each syndyne, whose width is given
dimensional model based on synchrones and syndynes. This by the dust ejection velocity of the syndyne β value. In the
is also true for apparently thin antitails observed, e.g., in synchronic approach, they analytically computed the dimen-
Comet Arend-Roland 1957III: Kimura and Liu (1977) have sionless sky surface density of a synchronic tube
 Fulle: Motion of Cometary Dust 569

where H is the kernel matrix provided by the dust tail model

F(t, 1 − µ)dt
dD (x, y, t) = (12) defined in equation (2), F (solution vector defined in equa-
2(to − t)v(t, 1 − µ) d(1ds− µ) tion (8)) is the output of the inversion of equation (14), D is
the dust tail dimensionless sky surface density (data vector
so that the brightness of the whole tail is simply proportional defined in equation (2)), and R is a regularizing constraint
to the numerical time integral of equation (12). Equation (12) to drop noise and negative values in solution F. The inverse
is derived from an analytical integration that is correct if the Monte Carlo approach was applied to tens of dust tails: The
following condition (named by Finson and Probstein, al- results regarding the DSD (Table 1) and the dust mass loss
though quite improperly, hypersonic) is satisfied rate will be discussed in sections 5 and 6. In general, dust
ejection velocities show time and size dependencies more
(t − t)v(t, 1 − µ) complex than predicted by one-dimensional coma models
ds
>> o (13) of dust-gas interaction. In particular, the velocity of large
d(1 − µ) 1−µ grains relative to that of small ones seems higher than ex-
pected. This result was confirmed by independent tail mod-
This usually happens in the outermost dust tail only. In els that left free such a parameter (Waniak, 1992, 1994).
equations (12) and (13), s is the parametric coordinate along This points out that dust-gas interaction must be treated by
the synchrone and v(t,1 – µ) the dust ejection velocity. In three-dimensional coma models to predict reliable dust ejec-
equation (12), the synchronic (or syndynamic) tubes are tion velocities. In most cases the accuracy of the fit of the
assumed to have circular sections, because the dust tail is observed tail brightness did not change after varying the
supposedly built up by dust shells that keep their spherical assumed dust ejection anisotropy. This fact confirms that
expanding shape over time if significant tidal effects due tail shapes have lost memory of the details of the unknown
to the solar gravity are neglected. The spherical shell as- boundary conditions of the three-dimensional gas drag oc-
sumption implies that the dust ejection is isotropic, another curring in the inner coma.
strong approximation. When the numerical integration of Other Monte Carlo dust tail models were developed that
equation (12) is performed, the fit of the tail brightness data followed other approaches (e.g., Waniak, 1994; Lisse et al.,
is performed by trial and error, so we cannot ensure the 1998). Equation (2) allows us to fit more details of the input
uniqueness of the obtained dust loss rate, ejection velocity, tail data by means of a time- and size-dependent dust-scat-
and size distribution. All these approximations make the tering cross-section [i.e., by f(t,1 – µ)]. If the DSD is as-
Finson-Probstein model a first-order model that is unable sumed to be time-independent to stabilize the model out-
to give realistic estimates of the dust parameters. Fulle puts, then it may become impossible to perfectly fit the tail
(1987, 1989) developed an inverse Monte Carlo dust tail data. The assumption of a time-independent DSD is com-
model by taking into account all the improvements intro- monly made: Lisse et al. (1998) analyzed dust tails at mil-
duced by Kimura and Liu (1977) and avoiding all the limi- limeter wavelengths (COBE satellite data) with a poor
tations and approximations of the Finson-Probstein model: spatial resolution (20 arcmin), so that rough assumptions on
(1) It computes the rigorous heliocentric Keplerian orbits DSD [f(1 – µ) = (1 – µ)–1 implying α = –3] allowed them
of millions of sampling dust grains, so that the spherical to fit the input images. Waniak (1994), adopting a constant
shell approximation is avoided. (2) It performs both the size α ≈ –3, improved the tail fit of Comet Wilson 1987VII by
and time integral by means of numerical methods, so that means of a detailed dust ejection pattern. However, the fact
the condition imposed by equation (13) is avoided. In this that this pattern ejects dust mainly on the nucleus nightside
way, it can fit not only the external tail, but also the inner may indicate that temporal variations of the DSD are likely
one, as close as desired to the dust coma, where the largest responsible for the shape of dust tails.
grains usually reside. (3) It takes into account anisotropic
dust ejections. (4) It provides for each dust size a dust ejec- 5. DUST SIZE DISTRIBUTION IN COMETS
tion velocity from the coma that is the mean value of a wide
velocity distribution (Fulle, 1992); this is consistent with The dust size distribution (DSD) plays a crucial role
the predictions of three-dimensional dust-gas interaction when we describe the behavior of dust particles in comets.
models in the inner coma (Crifo and Rodionov, 1999). (5) It For instance, it is widely believed that in dust comae we
avoids the trial-and-error procedure typical of the original mainly see grains with sizes close to the observation wave-
Finson-Probstein model, by means of an inverse ill-posed length. It is easy to conclude (see equation (15) in section
problem theory. In this way, the uniqueness of the results 6.1) that the coma brightness depends on the size of the
(impossible to establish in the original Finson-Probstein largest ejected particle if α > u – 3, where u is the power
approach) is recovered in the least-squares-fit sense. index vs. (ρdd) of the dust velocity. The assumptions (α =
Within the inverse Monte Carlo dust tail model, the dust –3.0 and u = –0.5) made by Lisse et al. (1998) imply that,
ejection velocity, loss rate, and size distribution are obtained if α > –3.5, then the dust coma brightness at optical wave-
through minimization of the function lengths is dominated by the contribution from the largest
ejected boulders. Since dynamical models in comae of
(HF – D)2 + (RF)2 = min (14) micrometer-sized grains or of meter-sized boulders are quite
570 Comets II

different, it is crucial to understand which dust is observed. flux too) depends on the size of the largest ejected boulders;
The total mass of the dust depends on the size of the largest and (3) the DGR is >1 for particle sizes larger than 1 cm.
or the smallest ejected grains according to the actual DSD: All available results confirm that the mass of dust ejected
It is fundamental to define the size range to which the pub- from comets is dominated by the largest boulders. Radar
lished results are related, although this is usually not done. observations (Harmon et al., 1989) operating at centimeter
For usual α > –4, the dust mass diverges if we allow it to wavelengths and coma observations at millimeter wave-
reach the nucleus size. It is impossible to compare dust lengths provide first-quality constraints to this conclusion,
masses without knowing which largest boulder size they because they directly observe grains close in size to the
refer to. observation wavelength if α < –3.5, while they observe dust
We applied the inverse tail model to tens of cometary larger than the observation wavelength if α >> –3.5. Obser-
dust tails, which always resulted in dust grains ranging in vations of P/Swift-Tuttle (Jewitt, 1996) and C/Hyakutake
size between 1 µm and about 1 cm (Table 1). The DSD 1996B2 (Jewitt and Matthews, 1997) at millimeter wave-
often showed large temporal changes: Since most output lengths provided loss mass rates 7 and 10 times higher, re-
instabilities affect the DSD time-dependency, in section 6.2 spectively, than predicted by tail models (Fulle et al., 1994,
we will pay special attention to testing the correctness of 1997). Observations at millimeter wavelengths therefore
this model output. The time-averaged DSD is much more suggest that α was higher than α = –3.3 and α = –3.6 re-
stable: In almost all comets it was characterized by an index spectively (Table 1). We must conclude that the dust coma
α ≈ –3.5. This index is typical of a population of collisionally brightness of these two comets was dominated at all obser-
evolved bodies (Dohnanyi, 1972): Should this index value vation wavelengths by the largest ejected boulders if index
be further confirmed, it would suggest that we do not ob- u is –0.5 (this value is predicted by one-dimensional dust-
serve in comets the pristine dust population of the presolar gas-drag models in the inner coma).
nebula. The α = –3.5 value is the most critical for models Is a power law a proper function to describe the DSD?
aimed to fit the brightness and/or the time evolution of coma This assumption is usually adopted by direct tail modelers
features, like jets or spirals. In fact, if α = –3.5 and u = –0.5 only (e.g., Lisse et al., 1998). Inverse tail models do not
[this value is provided by one-dimensional models of dust- assume that the DSD is a power law; they leave it com-
gas interaction at d > 1 µm (Crifo, 1991)], then a correct pletely free, sampling the DSD in β-bins. Then, the output
computation of the brightness of every feature observed in describing the DSD is fit by a power law to offer an easily
a dust coma must take into account grains of every size, understandable DSD. Sometimes, the direct f(t,1 – µ) output
from submicrometers up to tens of meters. Also, these large was provided (e.g., Fulle et al., 1998). In any case, no DSD
boulders, when present in a dust coma, provide a significant data are determined accurately enough to require more than
fraction of the observed brightness if α = –3.5 and u = –0.5. a power law in order to fit them: A power-law DSD is con-
While it is possible to come up with a theory of dust tails sistent with the DID fluence measured at 1P/Halley, which
that can separate the dependency of the numerous dust pa- is not a power law of the dust size (Fulle et al., 2000). Other
rameters required to interpret the data, this becomes impos- functions were suggested to describe the DSD of cometary
sible in models of dust comae. dust. Hanner (1984) proposed a more complex function,
An important dataset providing DSD in comets is given which becomes a simple power law at the largest sizes (d >
by the only available in situ data we have so far: the results 1 mm), and drops rapidly to zero at submicrometer grains.
of the DID experiment on Giotto (McDonnell et al., 1991) This function was used to fit the IR photometry and spec-
during the 1P/Halley flyby. The power index fitting the DSD tra of comets. These observations are unable to detect sub-
at the nucleus, traced back from the DID fluence in terms micrometer grains, and thereby provide a typical example of
of purely radial expansion, is α ≈ –3.7 for dust masses “absence of evidence” interpreted as “evidence of absence.”
between 10 –14 and 10–3 kg. This slope is also consistent with In fact, Giotto showed that in 1P/Halley, submicrometer
the impact of the 1-g grain that damaged the probe itself. grains were more abundant than larger ones (McDonnell et
This example shows how models crucially affect the inter- al., 1991). This is probably true for all comets: Many au-
pretation of the dust data. The fit of the same data by means thors pointed out that every DSD discussed in this review is
of a rigorous dust dynamical model changed the results consistent with all available IR spectra (Crifo, 1987; Green-
completely (Fulle et al., 2000). The DID fluence was found berg and Li, 1999). Dust tail models and in situ data pro-
to be consistent with any –2.5 < α < –3.0, strongly support- vide much better constraints to the DSD than IR spectra,
ing the possibility considered by Lisse et al. (1998), that and show that a power law defined within a precise size
the coma brightness is dominated by meter-sized boulders. interval is the best approach for describing the DSD in
The same model also inferred the dust-to-gas ratio (3 < comets, avoiding misleading conclusions suggested by more
DGR < 40 for dust masses up to 1 g) and the dust geometric complex and underconstrained size functions.
albedo (0.01 < Ap < 0.15) by means of the Optical Probing It would seem obvious that a comet is defined as “dusty”
Experiment data (Levasseur-Regourd et al., 1999), with a according to its dust-to-gas ratio. In other words, we would
correlation between Ap and ρd (ρd = 2500 Ap kg m–3). Tail like to find that the higher the index α, the higher the re-
models and DID experiments agree with these conclusions: leased dust mass, and the more “dusty” the comet. This is
(1) α >> –4; (2) the dust mass (we cannot exclude the light not the case. Usually, a comet is said to be “dusty” when
 Fulle: Motion of Cometary Dust 571

spectral features in its IR spectrum or high polarization are is commonly related to the water loss rate to obtain incor-
observed. However, it is hard to relate these observed char- rect (at least from a physical point of view) dimensional
acteristics to the actual released dust mass. In particular, ratios. It is obvious that comets with a higher Afρ can eject
when the silicate feature at 10 µm is strong (Lisse, 2002), or less dust mass: This depends on the DSD and dust velocity.
when the highest polarization is higher than 20% (Levasseur- Moreover, the time evolution of Afρ can be unrelated to the
Regourd et al., 1996), the comet is then recognized as loss rate time evolution, depending on time changes of the
“dusty.” Both these features refer to the actual population DSD and velocity. Afρ is a high-quality constraint for physi-
of micrometer-sized grains, which we have seen to be a cal models of comae and tails, but nothing more.
minor component of the total released mass. If the DSD has
a turning point at some size larger than 10 µm, where at 6.2. Dust Size Distribution Time Variability
smaller sizes α becomes larger than 1P/Halley’s index, then
the relative production of micrometer-sized grains drops So far, only inverse dust tail models take into account
compared to 1P/Halley. In this case, the comet is defined as the possibility that dust is ejected from the cometary nucleus
less “dusty” than 1P/Halley, even though its α from milli- with a DSD that may change in time. Despite the high or
meters to meters may be much higher, with a much higher low probability that this really happens in comets, it is sur-
released dust mass. prising that most models describing dust in comets adopt
time-independent DSDs, because most papers on cometary
6. CONSTRAINTS TO THE OUTPUTS dust invoke dust fragmentation to explain the observations.
OF THREE-DIMENSIONAL It is obvious that dust fragmentation implies a time evolu-
TAIL MODELS tion of the DSD, and a model that takes into account a time-
dependent DSD is more general than others that only take
6.1. ρ
Dust Coma Equivalent Size Afρ dust fragmentation into account. So far, no consistent models
of dust fragmentation were developed (Crifo, 1995). Combi
The model outputs F and v can be compared to the ob- (1994) developed a direct dust tail model with fragmentation
served dust coma brightness. This is usually measured by that was based on consistent fits of both the dust coma and
means of the Afρ quantity (A’Hearn et al., 1984) tail. Many tests performed by means of the inverse tail model
that adopted numerous u values showed that such a con-
γr
2
10 0.4[ m − m( x,y)] sistent fit to both the dust coma and the tail simply requires
Afρ(t) = 2π –0.5 << u < –0.1. Fulle et al. (1993) showed that dust frag-
1 AU D(x, y)
(15) mentation is a possible (not unique) explanation of –0.5 <<
∞ F(t, 1 − µ)
∫ d(1 − µ) u < –0.1.
0 v(t, 1 − µ) While inverse dust tail models can provide a stable time-
averaged DSD, the time-dependent DSD is affected by re-
where all the quantities are defined in section 2. Afρ is re- sidual instability. It is not easy to establish if large and sys-
lated to the total dust cross-section Σ observed inside the tematic changes of the DSD are real or simply due to output
observation field of radius ρ (in meters projected at the instability. The most elegant solution is to find independent
comet) centered exactly on the comet nucleus observations that suggest systematic changes of the ejected
dust population in agreement with the time-evolution of the
DSD provided by inverse tail models. These models applied
πρ
Σ= Afρ (16) to C/Hyakutake 1996B2 provided an α value that dropped
4Ap(φ) suddenly from a roughly constant value α = –3 to α = –4
in mid April 1996 (Fulle et al., 1997), in perfect agreement
We note that equation (15) is completely parameter-free: with the time evolution of IR spectra; no silicate feature was
Given the outputs F and v of the tail model, there is no way detected before a strong 10-µm line appeared around mid
to adjust the tail model to fit the observed Afρ values. How- April (Mason et al., 1998). This IR spectral evolution was
ever, the integral of equation (15) can be computed on a interpreted in terms of dust fragmentation exposing small
finite β range, while Afρ is measured observing all the silicate cores to the Sun’s radiation; such cores were em-
ejected dust sizes in the dust coma. Therefore, if the size bedded in large carbonaceous matrices before mid April.
range adopted to compute equation (15) loses dust sizes The inverse tail model applied both to optical data (Fulle,
reflecting a significant light fraction in the coma, then tail 1990) and to IR thermal data (Epifani et al., 2001) collected
models can provide only a lower limit of the actually ob- during two different perihelion passages of Comet 2P/Encke
served Afρ. In any case, Afρ computed by means of equa- provided a similar drop from α = –3 to α = –4 during the
tion (15) was always consistent with that observed (Fulle first three weeks after perihelion. This coincidence has al-
et al., 1998; Fulle, 2000). ready forced us to exclude the possibility that this DSD
Equations (9) and (15) point out that Afρ has little to do time-evolution is due to output instability. Moreover, these
with the dust mass loss rate. Nevertheless, it is commonly three weeks match exactly the seasonal night cycle of the
referred to as the dust loss rate, despite its dimensions, and most active nucleus hemisphere suggested by Sekanina
572 Comets II

(1988) to explain the comet photometry and coma shape grains (usually months), these ellipses may reach huge di-
evolution of 2P/Encke. mensions, up to 10 6 km: When the Earth crossed the orbit
plane of Comets Bennett, 1P/Halley, Austin and Hale-Bopp,
7. FINE STRUCTURES IN TAILS the half of the ellipse inside the comet orbit was seen as a
bright spike pointing to the Sun, which was in fact a real
7.1. Neck-Lines (nonperspective) antitail. Since these real antitails are com-

In several cases, dust tails retain the memory of the dust

ejection over more than half the comet orbit; during such
long periods of time the tidal effects of solar gravity be-
come significant. Kimura and Liu (1977) pointed out that
the dust motion is heliocentric, so that at ejection a dust
grain can be considered as occurring at the first node of its
heliocentric orbit. Every heliocentric orbit has its second
node 180° away from the first, where the dust grain orbit
must necessarily cross the comet orbit again. When we con-
sider a Finson-Probstein dust shell, all these grains, ejected
at the same time, will have their second orbital node at ap-
proximately the same time, i.e., 180° away in orbital anom-
aly, where the spherical dust shell will collapse into a two-
dimensional ellipse contained in the comet orbital plane, a
shape far removed from a sphere. When we consider a col-
lapsed synchronic tube, we obtain a two-dimensional struc-
ture, referred to as the “neck-line” by the discoverers
(Kimura and Liu, 1977). When Earth crosses the comet
orbit, the neck-line appears on the sky as a straight line
much brighter than the surrounding dust tail, because all
the synchronic tube is collapsed in an infinitesimal sky area
(Fig. 2). By means of the neck-line model, Kimura and Liu
fit perfectly the perspective antitail of Comet Arend Roland
1957III, which appeared as a bright spike many millions
of kilometers long and pointing toward the Sun, thus avoid-
ing unrealistic explanations based on dust ejected at zero
velocity from the parent coma.
Neck-lines were observed in the Great Comet 1910 I and
in Comets Arend-Roland 1957III, Bennett 1970II, 1P/
Halley 1986III, Austin 1990V, Levy 1990XX, and Hale-
Bopp 1995O1. It must be pointed out that neck-lines can
appear only after perihelion of comets orbiting in open orb-
its (hyperbolic or parabolic), a fact rigorously verified by
all the registered apparitions. In the case of periodic comets,
dust ejected after perihelion could also form a neck-line
before the next perihelion passage. However, this was never
observed and seems improbable, because planetary pertur-
bations in short-period comets, and stellar ones in long-pe-
riod comets, can perturb the dust orbits enough to prevent
the formation of a neck-line after periods of many years.
Due to the particular perspective conditions, in Comets
Arend-Roland and Levy the neck-line appeared as a per-
spective antitail (it is probable that all observed antitails
were in fact neck-lines). In all other comets, it appeared
Fig. 2. Neck-line observed in Comet Hale-Bopp 1995O1 on
superimposed to the main dust tail as a bright and straight
5 January 1998 with the ESO 1-m Schmidt Telescope. The origi-
linear feature. Since a neck-line is built up by the collapse nal image was filtered (unsharp masking) to enhance the spike
of the dust shells into two-dimensional ellipses, the ellipses features: the real antitail pointing toward the Sun (bottom) and
composed of the largest grains, approximately centered on the neck-line pointing in the opposite direction. ESO Press Photo
the comet nucleus, are placed half out of the comet orbit 05a/98, courtesy of the European Southern Observatory (observer
and half inside of it. Due to the long travel time of the dust Guido Pizarro).
 Fulle: Motion of Cometary Dust 573

posed of the largest grains ever observed in dust tails, neck- is assumed to be zero, in contradiction with all available
line observations provide unique information on the ejec- information on the dust dynamics. For striae models, in
tion velocity and size distribution of grains larger than particular, which are very sensitive to the β value of the
centimeter-sized. parent grain, this assumption might significantly affect the
Fulle and Sedmak (1988) have obtained analytical mod- results. The β value of the parent is easily obtained by the
els of neck-lines, so that the neck-line photometry provides stria origin in a two-dimensional model, while many dif-
the β distribution and the dust ejection velocity at the ejec- ferent β values are consistent with the stria origin in a three-
tion time t of the neck-line. The Keplerian dynamics of the dimensional model. Sekanina and Farrell (1980) showed
grains in space allow us to compute the geometric neck- that the submicrometer-sized fragments observed in the
line parameters a and b (related to the major and minor axes striae of Comet West 1976VI had a β very similar to their
respectively of the ellipses composing the neck-line) and s much larger parents. This result would imply that the par-
(the parametric coordinate along the neck-line axis x) de- ents must be very elongated chains of submicrometer-sized
fined in Fulle and Sedmak (1988). If the velocity condition grains. However, this also implies that the drag by gas on
these chains was correspondingly high (both gas drag and
v(1 – µ) << (1 – µ)sa (17) radiation pressure depend on the parent cross-section):
These chains must have been ejected from the coma exactly
is satisfied, then the dimensionless sky surface density in at the gas velocity, so that they would have been diluted
the neck-line is over huge 106-km-sized shells. The origin of the striae con-
strains neither the fragmentation time nor the β value of the
parent grain.
D(x, y) =

F(t, 1 − µ) ax b2y2 (18) 7.3. Sodium Tail

1 + erf exp −
sv(1 − µ) v(1 − µ) v2 (1 − µ)
Although spectroscopic observations suggested the pres-
ence of tail extensions of the well-known neutral sodium
From equation (18), it is apparent that the neck-line width coma of Comets 1910I and Arend-Roland 1957III, the first
along the y axis provides a direct measurement of the β de- clear images of a huge sodium tail 107 km long, well sepa-
pendency of the dust velocity at centimeter sizes. These are rated in the sky from classical dust and plasma tails, were
the only available direct observations of such a dependency, obtained during the 1997 passage of Comet Hale-Bopp
which is in agreement with the results of three-dimensional 1995O1 (Cremonese et al., 1997). The images were taken
inverse dust tail models: –0.5 << u < –0.1. The obtained β by means of interference filters centered on the sodium D
distributions confirm that most of the dust mass is released lines at 589 nm, and the tail did not appear in simultaneous
in the form of the largest ejected grains. images taken on the H2O+ line, showing a well-developed
ion tail. The sodium tail appeared as a straight linear fea-
7.2. Striae ture located between the ion tail and the prolonged radius
vector. Simultaneous spectroscopic observations permitted
In the brightest comets (e.g., Great Comet 1910I, Comets measurement of the radial velocity of the neutral sodium
Mrkos 1957V, West 1976VI, Hale-Bopp 1995O1), the usu- atoms along the tail. The result was that a syndyne of β =
ally structureless dust tail exhibits detailed substructures of 82 best fit both the sodium tail axis orientation and the radial
two kinds, namely synchronic bands and striae. The syn- velocities along the tail. This was the first time that the β
chronic bands are streamers pointing to the comet nucleus, parameter was best constrained by means of radial velocity
with the axis well fit by synchrones. There is general agree- measurements. The sodium neutral atoms lighten because
ment that they are due to time changes of the dust loss rate of fluorescence: Absorbed UV solar photons spend their
or of the DSD, so that the dust cross-section is larger in the energy to put the external sodium electrons in the most ex-
synchronic bands than outside. On the contrary, the striae ternal orbitals. Since the solar photons are absorbed by the
do not point to the comet nucleus (Plate 17), and they are sodium atoms, their momentum is necessarily transferred
neither fit by synchrones nor by syndynes. There is general to the sodium atoms, so that
agreement that striae are due to instantaneous fragmentation
of larger parents, so that the striae are synchrones not origi-
hg(1 AU)2
nating from the comet nucleus, but from the tail point where β= (19)
the parent was located at the time of fragmentation. This λGM m
explains well the orientation of the striae, which always
point between the comet nucleus and the Sun. where h is the Planck constant, g the number of solar pho-
Usually, the interpretations of bands and striae are per- tons captured in the unit time by a sodium atom at 1 AU
formed using two-dimensional synchrone-syndyne models, (or photon scattering efficiency in the sodium D lines), λ
so that the available quantitative results may be affected by the wavelength of the sodium D lines, and m the tail par-
significant errors. The dust ejection velocity from the coma ticle mass. In perfect agreement with the theoretical com-
574 Comets II

putations, the observed β = 82 provides g = 15 s–1 when we number of free parameters and that are able to provide the
assume the atomic sodium mass for m. Therefore, the so- largest number of dust parameters after data fits have been
dium tail is composed of sodium atoms and not of sodium obtained. Inverse dust tail models appear today as the most
molecules. The sodium atoms in space have a short lifetime, powerful tools we have to interpret groundbased (or Earth-
mainly due to photoionization. The sodium tail brightness orbiting satellite-based) data, because they only require as-
along its axis x provides an unique measurement of the sumptions on the dust grain shapes, their scattering effi-
sodium lifetime τ. Since the sodium tail axis can be best ciency, and albedo. Moreover, when thermal tail data are
approximated by a syndyne, the whole sodium tail can be available, a comparison between outputs of tail models and
modeled by means of a syndynamic tube, whose photomet- optical coma photometry can provide an estimate of the
ric equation was computed by Finson and Probstein (1968). average albedo of the dust. When high-quality data on both
When we consider the sodium lifetime against photoion- the IR and optical dust tails become available, inverse dust
ization, the sky surface density of sodium atoms is tail models will provide unique information on the tempo-
ral and grain-size dependencies of the dust albedo. Dust tail
t o − t ( x) models predict the temporal evolution of the dust coma
N exp − τ
δ(x,y) = (20) brightness, to be compared with the observations of the Afρ
2v[to − t(x)]w(x) parameter: This independent constraint allows one to es-
tablish that the dust environment deduced from modeling
where N is the sodium loss rate, v the sodium ejection ve- the IR and optical tail properties is indeed valid.
locity (related to the sodium tail width), w the sodium radial Information on the velocity imparted to the dust grains
velocity projected on the sky, and t the time of sodium ejec- by the expanding gas is required to constrain three-dimen-
tion (w and t are provided by syndyne computations). Equa- sional model predictions for the gas dynamics in cometary
tion (20) perfectly fits the observed brightness on the tail comae; only dust tail models can provide estimates of the
axis x when we assume τ = 1.7 × 105 s at 1 AU. This lifetime temporal and grain-size dependencies of the dust velocity.
is three times larger than the value assumed in comet and Information on the grain-size distribution is required by all
planetary atmospheric models, as it was already suggested models aimed at fitting the brightness of dust coma features.
by laboratory measurements by Huebner et al. (1992). As a consequence, only inverse dust tail models can provide
estimates of the time-dependent grain-size distribution. Cos-
8. CONCLUSIONS mogonic and evolutionary models of comet nuclei require
a good knowledge of the dust to gas ratio at the nucleus;
Modeling the properties of the dust particles ejected from only dust tail models can provide dust mass loss estimates
comets is one of the most formidable tasks in cometary that are not severely biased by assumptions of the related
physics, as we have little or no information about numerous grain-size distribution. When high-quality data on all the
parameters describing these dust grains. Quantities such as parameters required to describe cometary dust grains be-
albedo, bulk density, radiation-scattering properties, shape, come available, probably provided by future rendezvous
and grain spin are far from completely determined. There missions to comets, complete and detailed models of the
are other quantities either related to the dust sources dis- dust environment of comets will become possible. It is only
persed on the nucleus surface or describing the dust-gas in- then that one will be able to validly describe what space
teraction in the coma, such as the dust velocity relative to probes will face when meeting their targets. Only coordi-
the comet nucleus, the loss rate, and the particle size dis- nated efforts among all modelers, taking into account the
tribution, that are absolutely required by any realistic model unique information that inverse tail models can provide, will
that describes the dust environment of comets. It is impos- enable the attainment of such an ambitious goal.
sible to obtain observational evidence that allows the infer-
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576 Comets II
 Kolokolova et al.: Physical Properties of Cometary Dust 577

Physical Properties of Cometary Dust from

Light Scattering and Thermal Emission
Ludmilla Kolokolova
University of Florida

Martha S. Hanner
Jet Propulsion Laboratory/California Institute of Technology

Anny-Chantal Levasseur-Regourd
Aéronomie CNRS-IPSL, Université Paris

Bo Å. S. Gustafson
University of Florida

This chapter explores how physical properties of cometary dust (size distribution, compo-
sition, and grain structure) can be obtained from characteristics of the electromagnetic radia-
tion that the dust scatters and emits. We summarize results of angular and spectral observations
of brightness and polarization in continuum as well as thermal emission studies. We review
methods to calculate light scattering starting with solutions to Maxwell’s equations as well as
approximations and specific techniques used for the interpretation of cometary data. Laboratory
experiments on light scattering and their results are also reviewed. We discuss constraints on
physical properties of cometary dust based on the results of theoretical and experimental simula-
tions. At the present, optical and thermal infrared observations equally support two models of
cometary dust: (1) irregular polydisperse particles with a predominance of submicrometer parti-
cles, or (2) porous aggregates of submicrometer particles. In both models the dust should contain
silicates and some absorbing material. Comparison with the results obtained by other than light-
scattering methods can provide further constraints.

1. INTRODUCTION which regularities have been found in the variation of these

parameters with phase angle, heliocentric distance and
The main technique to reveal properties of cometary dust within the coma (section 2). Then we describe theoretical
from groundbased observations is to study characteristics light-scattering techniques developed to solve the inverse
of the light it scatters and emits. Such a study can include problem, whereby dust physical characteristics are extracted
dynamical properties of the dust particles, presuming that from the characteristics of the light it scatters and emits
the spatial distribution of the dust resulted from the dust (section 3). Since the concentration of the dust particles in
interaction with gravitation and radiation. However, the pri- cometary coma at cometocentric distances corresponding
mary way is to study the scattered light or emitted thermal to the resolvable scale in the observations is sufficiently low,
infrared radiation to search for signatures typical of spe- the particles can be considered to be independent scatter-
cific particles. The main focus of this chapter is a review ers. This means that the intensity of the light (and its other
of methods in the interpretation and the extraction of the Stokes parameters, see below) scattered by a collection of
data on the size distribution, composition, and structure of dust particles is equal to the sums of the intensity (or re-
cometary dust (hereafter referred to as physical properties) spective Stokes parameters) of the light scattered by all the
from the observed angular and spectral characteristics of particles individually. We therefore consider the methods
the brightness and polarization of scattered and emitted light developed to describe the light scattering by single particles,
(hereafter referred to as observational characteristics). We indicating how light-scattering characteristics depend on the
will not detail here observational techniques (for this, see, particle shape, size, composition, and structure. In section 3
e.g., the review by Jockers, 1999), but will mainly concen- we also show how the application of these techniques to
trate on the results of the observations and methods of their the observational data leads to the current views on the
interpretation. physical properties of cometary dust. Section 4 compares
We review how observational characteristics such as the our knowledge about cometary dust obtained using light-
dust color, albedo, polarization, etc., can be estimated from scattering methods with results obtained using other tech-
visual, near-infrared, and mid-infrared observations and niques and outlines future research.

577
578 Comets II

2. OBSERVATIONAL DATA

2.1. Brightness Characteristics of

Scattered Light

The most straightforward way to characterize cometary

dust is to study how much light it scatters and absorbs and
how this depends on the geometry of observations, mainly
determined by the phase angle, α (the Sun–comet–Earth
angle). The efficiency of scattering and absorption is usu-
ally characterized by the albedo and geometrical character-
ization of the scattering by the angular scattering function.
These characteristics, as well as spectral dependence of the
scattered light, expressed through the dust colors, are con-
sidered below.
2.1.1. Albedo. Single-scattering albedo is defined in
the most general way as the ratio of the energy scattered in Fig. 1. Dependence of albedo on the phase angle. The data are
all directions to the total energy removed from the incident from (0) Mason et al. (2001); (1) Mason et al. (1998); (2)–
beam by an isolated particle (van de Hulst, 1957; Hanner (7) Gehrz and Ney (1992); (8) Grynko and Jockers (2003). The
et al., 1981). This definition includes all components (dif- solid line represents the least-squares fit to the data for Comets
fracted, refracted, reflected) of the scattered radiation and C/1975 V1 West and C/1980 Y1 Bradfield and is interpolated to
smoothly connect to the backscattering data for Comet P/Stephan-
can be applied to small particles where the diffracted ra-
Oterma (Millis et al., 1982) normalized at the angle α = 30°.
diation is spread over a wide angular range and cannot
readily be separated. In practice, this definition is not very
useful when analyzing cometary dust, because it requires
knowledge of the radiation scattered at all directions. Gehrz observed to increase by 50% in Comet P/Halley’s coma dur-
and Ney (1992) compared the scattered energy to the ab- ing episodes of strong jet activity (Tokunaga et al., 1986).
sorbed energy reradiated in the infrared to derive an albedo Difference in albedo may result from different composi-
at the phase angle of observation. This method was used tion, particle size, shape, or internal structure. For example,
by a number of observers, and the results are summarized Mason et al. (2001) found that high albedo of the dust in
in Fig. 1. The albedo estimates thus obtained for dust in Comet Hale-Bopp is consistent with the domination of small
different comets should be compared at the same phase particles in the grain population (see also section 3.4.1).
angle since the radiation scattered in the direction of obser- There may be several components of the dust, with differing
vation depends on the relative positions of the Sun, Earth, albedos and temperatures, and the average albedo may not
and comet. Using such an approach, Mason et al. (2001) represent the actual albedo of any of the components. How-
found the albedo of the dust in Comet C/1995 O1 Hale-Bopp ever, the low average albedo rules out a large population of
to be roughly 50% higher than that of P/Halley at α ~ 40°. cold, bright grains that contribute to the scattered light but
A few maps of albedo obtained so far by combining visi- not to the thermal emission.
ble light and thermal infrared images demonstrate increas- 2.1.2. Angular scattering function. The angular scat-
ing albedo with the distance from the nucleus (Hammel et tering function indicates how the intensity of the scattered
al., 1987; Hayward et al., 1988). light is changing with phase angle. Since a comet can be
The geometric albedo of a particle, Ap, is defined as the observed at only one phase angle on a given date, the an-
ratio of the energy scattered at α = 0° to that scattered by a gular scattering function has to be acquired by observing a
white Lambert disk of the same geometric cross section comet over time as the Sun–Earth–comet geometry changes.
(Hanner et al., 1981). Since comets are rarely observed at Thus this function of individual cometary dust particles is
α = 0°, it is convenient to define Ap(α) as the product of difficult to determine, because the observed brightness de-
the geometric albedo and the normalized scattering func- pends not only on the physical properties of the dust, but
tion at the angle α. Hanner and Newburn (1989) presented also on its amount, and the total cross section of dust in
a plot of Ap(α) in the J bandpass (1.2 µm) for 10 comets. the coma contributing to the scattered light intensity does
The total dust cross section within the field of view was not remain constant over time. Two methods have been used
determined by fitting a dust emission model to the thermal to normalize the observed intensity.
spectral energy distribution, and then applying the total One method is to assume that the ratio of the dust to gas
cross section to the scattered intensity to derive an average production rates remains constant over time, and to normal-
albedo. The resulting Ap are typically very low, close to ize the scattered light intensity to the gas production rate.
0.025 at α = 35°–80° and about 0.05 at α near zero. There Millis et al. (1982) derived the angular scattering function
is some indication that Ap is higher for comets beyond 3 AU for the dusty Comet P/Stephan-Oterma by normalizing the
(see Fig. 3 in Hanner and Newburn, 1989). The albedo was scattered intensity to the C2 production rate. The scattering
 Kolokolova et al.: Physical Properties of Cometary Dust 579

function was a factor of 2 higher at 3°–4° than at 30°, cor-

responding to a slope of ~0.02 mag/°. Meech and Jewitt
(1987) determined a linear slope of 0.02–0.035 mag/° for
four comets observed at α = 0°–25°. They saw no evidence
of an opposition surge larger than 20% in P/Halley within
1.4°–9°. More detailed data by Schleicher et al. (1998) show
an evident curvature of the scattering function for P/Halley
that can be represented by a quadratic fit.
Another method is to compare the measured scattered
light to the measured thermal emission from the same vol-
ume in the coma, with the assumption that the emitting
properties of the dust remain constant. This method was
described above as the means for extracting an albedo for
the dust. The method has been applied to a number of com-
ets (see Fig. 1) and yields a relatively flat scattering func-
tion from 35° to 80° (Tokunaga et al., 1986; Hanner and
Newburn, 1989; Gehrz and Ney, 1992). Two comets have Fig. 2. Color as a function of heliocentric distance: J–H (+), H–
been observed at large phase angles 120°< α < 150° using K ( ), and B–R (×) colors are by Jewitt and Meech (1986); B–R
this method, and they display strong forward scattering (Ney colors ( ) are by Kolokolova et al. (1997) ( for Comet P/Halley).
and Merrill, 1976; Ney, 1982; Gehrz and Ney, 1992). Thus Color is measured in ∆m/∆λ (mag/µm) and the solar color is sub-
we can characterize a typical angular scattering function for tracted. The data cover the range of the phase angles 0°–110°.
cometary dust as possessing a distinct forward-scattering
surge, a rather gentle backscattering peak, and a flat shape
at medium phase angles (Fig. 1). K color was less red in comets observed at R > 3 AU, while
2.1.3. Color. The dust color indicates trends in the the J–H color showed no trend with heliocentric distance.
wavelength dependence of the light scattered by the dust. The B–R color shows no dependence on heliocentric dis-
Traditionally the color of cometary dust was determined tance although Schleicher and Osip (2002) found that the
through measurements of the comet magnitude m in two color m0.4845–m0.3650 for Comet Hyakutake (1996 B2) got
different continuum filters, e.g., blue (B, ~0.4–0.45 µm) and redder with increasing heliocentric distance within 0.6–
red (R, ~0.64–0.68 µm), and was expressed as CB–R = mblue– 1.9 AU. No color dependence on phase angle was found in
mred. This color was a unitless characteristic expressed as the visible or near-infrared.
the logarithm of the ratio of intensities in two filters. Al- Decrease in the near-infrared colors was recorded at peri-
though this definition is still used, spectrophotometry of ods of enhanced comet activity in Comet P/Halley (Toku-
comets resulted in the definition of color as the spectral gra- naga et al., 1986; Morris and Hanner, 1993) A more red
dient of reflectivity, usually measured in % per 0.1 µm with color in the visible was associated with strong jet activity
an indication of the range of wavelength it was measured in. in Comet P/Halley (Hoban et al., 1989), but the spiral struc-
The determination of cometary dust colors requires use tures in Comet Hale-Bopp had less red color (Jockers et al.,
of continuum bands that are truly free of gas contamina- 1999). Less red and even blue color was associated with
tion [see discussion on gas-contamination influence on the outburst in Comet C/1999 S4 LINEAR during its disruption
colors in A’Hearn et al. (1995)]. This tends to make colors (Bonev et al., 2002). Although no regular dependence on
obtained using filters less trustworthy than those obtained the field of view was found, a smooth change in color was
using spectrophotometry to target gas-free spectral regions. observed in the central part of the coma of some comets,
The exception is near-infrared colors that are considered to including Hale-Bopp (Jockers et al., 1999; Laffont et al.,
be free from gas contamination and thus more reliable, al- 1999; Kolokolova et al., 2001a).
though thermal emission from the warm dust will contribute
to the K (2.2 µm) bandpass for comets within 1 AU of the 2.2. Polarization from Cometary Dust
Sun. We summarize the data for B–R color in the visible
and J–H and H–K color in the near-infrared in Fig. 2. The light scattered by particles is usually polarized, i.e.,
The scattered light is generally redder than the Sun; the its electromagnetic wave has a preferential plane of oscil-
reflectivity gradient decreases with wavelength from 5–18% lation. The degree of linear polarization (P, hereafter called
per 0.1 µm at wavelengths 0.35–0.65 µm to 0–2% per polarization) is defined as
0.1 µm at 1.6–2.2 µm (Jewitt and Meech, 1986). Hartmann
et al. (1982) and Hartmann and Cruikshank (1984) found P = (I⊥ – I||)/(I⊥ + I||)
that the near-infrared dust colors depend on heliocentric
distance. However, data by Jewitt and Meech (1986) and where I⊥ and I|| are the intensity components perpendicular
Tokunaga et al. (1986) demonstrate no heliocentric depen- and parallel to the scattering plane. For randomly oriented
dence. Hanner and Newburn (1989) noted that only the H– particles the electromagnetic wave predominantly oscillates
580 Comets II

either perpendicular (by convention positive polarization) or

parallel (by convention negative polarization) to the scatter-
ing plane.
The convenience of polarization is that it is already a
normalized characteristic of the scattered light, whereas the
brightness, I = I⊥ + I||, depends upon the distances to the
Sun and observer, and the spatial distribution of the dust
particles. Polarization variations within a coma relate to
changes in the dust physical properties, and different po-
larization observed for different comets or in features (jets,
shells, etc.) indicates a diversity of dust particles. For a given
type of cometary dust particles, the polarization mainly de-
pends on the phase angle α and wavelength λ.
2.2.1. Angular dependence. The changing geometry of
the comet and observer with respect to the Sun defines a
polarization phase curve. Small phase angles can be ex-
plored for distant comets, while α > 90° can only be reached
at R < 1 AU. Most of the available polarization observations Fig. 3. Polarization in the narrow-band red filter vs. phase angle:
have been performed within the heliocentric distances 0.5– (×) comets with low maximum in polarization, (+) comets with
2 AU using groundbased instruments, although large phase higher maximum, ( ) Comet C/1995 O1 Hale-Bopp, ( ) Comet
angles were studied using the Solar and Heliospheric Ob- C/1999 S4 LINEAR at disruption.
servatory (SOHO) C3 coronagraph (Jockers et al., 2002).
The data, which represent an average value of the polar-
ization on the projected coma, are obtained either by aper-
ture polarimetry (e.g., Dollfus et al., 1988; Kiselev and divide into three classes corresponding to different maxima
Velichko, 1999) or deduced from the integrated flux of the in polarization (Fig. 3): (1) comets with a low maximum,
polarized brightness images (e.g., Renard et al., 1996; about 10–15% depending on the wavelength; (2) comets
Kiselev et al., 2000; Hadamcik and Levasseur-Regourd, with a higher maximum, about 25–30% depending on the
2003). The (real or virtual) diaphragm is centered on the wavelength; and (3) Comet C/1995 O1 Hale-Bopp, whose
center of brightness, which corresponds to the nucleus. Its polarization is distinctively higher, although it was not ob-
aperture, in terms of projected distance on the cometary served for α > 48°.
coma, needs to be large enough to include the coma fea- Numerous observations obtained by Dollfus et al. (1988)
tures that may alter the global polarization. It is usually for P/Halley showed that the polarization at a given phase
found that, once the aperture is sufficiently large, the re- angle and wavelength does not vary with heliocentric dis-
sulting polarization of the comet does not change with in- tance. Some transient increases in polarization were found
creasing aperture. correlated with cometary outbursts. Similarly, the polariza-
The phase dependence of polarization, which has been tion of Comet Hale-Bopp obtained at small phase angles
documented so far in the range 0.3°–122°, is smooth and (large heliocentric distances) was consistent with that ob-
similar to that of atmosphereless solar system bodies. All tained closer to the Sun, but increased after outbursts events
comets show a shallow branch of negative polarization at (Ganesh et al., 1998; Manset and Bastien, 2000). Observa-
the backscattering region, first observed by Kieselev and tions of Comet C/1999 S4 LINEAR during its near-perihelion
Chernova (1978), that inverts to positive polarization at α0 ~ disruption (Kiselev et al., 2002; Hadamcik and Levasseur-
21° with a slope at inversion h ~ 0.2–0.4%/°, and a posi- Regourd, 2003) indicated an increase in polarization of about
tive branch with a broad maximum near 90°–100°. The data 4%, a value comparable with what had been noticed dur-
may be fitted by a typically fifth-order polynomial or trigo- ing the P/Halley outbursts.
nometric function, e.g., as suggested by Lumme and Muino- 2.2.2. Spectral dependence. The data have been re-
nen (1993), P(α) ~ (sinα)a(cosα/2)bsin(α – α0). These func- trieved in the ultraviolet, visible, and near-infrared domains
tions cannot be used for extrapolation but only within the to avoid any contribution from the thermal emission. Nar-
phase angle range where well-distributed data points are row-band cometary filters are now available at 0.3449,
available. 0.4453, 0.5259, and 0.7133 µm (Farnham et al., 2000).
While the minimum polarization is typically –2% (Mukai However, observers often need to make a trade-off between
et al., 1991; Chernova et al., 1993; Levasseur-Regourd et al., narrow filters that remove gaseous emissions and wider fil-
1996), a significant dispersion is noticed for α > 30°–40°. ters that improve the signal-to-noise ratio. It is highly advis-
Once the data are separated in different wavelength ranges, able to analyze spectra of the observed comet and estimate
the dispersion on the positive branch is reduced, and Pλ(α) the contribution of some faint molecular lines to allow for
for a variety of comets can be compared (see Levasseur- the depolarizing effect of molecular emissions when cal-
Regourd et al., 1996, and references therein). Comets tend to culating the dust polarization (Le Borgne and Crovisier,
 Kolokolova et al.: Physical Properties of Cometary Dust 581

1987; Dollfus and Suchail, 1987; Kiselev et al., 2001). large phase angles was observed only for Comet P/Giacobini-
Spectropolarimetric cometary data remain rare, and so far Zinner (Kiselev et al., 2000). Polarimetric color of variable
their resolution is not better than the resolution provided sign was observed for Comet C/1999 S4 LINEAR during
by narrowband cometary filters (Myers and Nordsieck, its disruption (Kiselev et al., 2002).
1984). 2.2.3. Variations within the coma. A coma whose op-
It was noticed for P/Halley (Dollfus et al., 1988) and tical thickness exceeds 0.1 was found so far only for Comet
later confirmed for other comets (Chernova et al., 1993; Hale-Bopp and only at distances closer than 1000 km from
also Kolokolova and Jockers, 1997, and references therein) the nucleus (Fernández, 2002). Thus, except for possibly
that the polarization usually increases with increasing wave- the very innermost coma where multiple scattering might
length, at least in the visible domain, and the increase grows take place, a change in the polarization with the distance
for greater values of the polarization. from the nucleus indicates an evolution in the physical prop-
If polarization data are available for two wavelengths, erties of the particles ejected from the nucleus. Polarization
the spectral gradient of polarization is defined as polarimet- images of P/Halley (Eaton et al., 1988; Sen et al., 1990),
ric color, ∆P/∆λ = [P(λ2) – P(λ1)]/[λ2 – λ1]. C/1990 K1 Levy (Renard et al., 1992), 109P/Swift-Tuttle
The polarimetric color changes with the phase angle (Eaton et al., 1995), 47P/Ashbrook-Jackson (Renard et al.,
(Chernova et al., 1993; Kolokolova and Jockers, 1997) from 1996), and C/1995 O1 Hale-Bopp (Hadamcik et al., 1999;
zero and even negative values to gradually increasing posi- Jockers et al., 1999; Kolokolova et al., 2001a); variable-
tive values at α > 50°. Figure 4 summarizes systematic aperture polarimetry of P/Halley (Dollfus et al., 1988); and
multiwavelength observations of polarization, performed for high-resolution in situ observations with the Optical Probe
Comets Halley and Hale-Bopp. Within α = 25°–60° the po- Experiment (OPE) onboard the Giotto spacecraft (Renard
larization increases with the wavelength in the visible et al., 1996; Levasseur-Regourd et al., 1999) revealed a re-
domain; the gradient seems to decrease in the near-infra- gion in the innermost coma characterized by a lower polari-
red [Fig. 4; see also Hadamcik and Levasseur-Regourd zation. Comet Hale-Bopp could be observed at phase angles
(2003)]. For α ~ 50°, the polarimetric color is about 9%/ ranging from about 7° to 48°. The low polarization region
µm for Halley and 14%/µm for Hale-Bopp (Levasseur- in Comet Hale-Bopp has been monitored within this phase-
Regourd and Hadamcik, 2003), which agrees with the value angle range (Hadamcik and Levasseur-Regourd, 2003). It
11%/µm at 45° obtained by Kiselev and Velichko (1999). showed highly negative values of polarization at small phase
The polarimetric gradient for Comet Hale-Bopp is higher angles, e.g., –5% at α = 8°, whereas a typical value should
than for other comets but its sign and phase-angle trend are be –0.5%. The low negative values of polarization, noticed
typical for comets, whereas asteroids and other atmosphere- at the cometocentric distances less than 2000 km, could not
less bodies usually have negative polarimetric color (e.g., be explained by multiple scattering but is most likely due
Mukai et al., 1997). So far a negative polarimetric color at to the physical properties of the local dust grains.

Fig. 4. Wavelength dependence of polarization for (a) Comet Hale-Bopp [data from Furusho et al. (1999), Ganesh et al. (1998),
Hadamcik et al. (1999), Jockers et al. (1999), Jones and Gehrz (2000), Kiselev and Velichko (1999), Manset and Bastien (2000)] and
(b) Comet Halley [data from Bastien et al. (1986), Brooke et al. (1987), Dollfus and Suchail (1987), Le Borgne et al. (1987), Mukai
et al. (1987), Sen et al. (1990)] for phase angles 40° (bottom curve) and 50°.
582 Comets II

A further proof of different physical properties of the (Dollfus and Suchail, 1987; Metz and Haefner, 1987; Rosen-
dust near the nucleus is its negative polarimetric color ob- bush et al., 1999; Manset and Bastien, 2000; Rosenbush and
served in situ (OPE/Giotto) (Levasseur-Regourd et al., 1999) Shakhovskoj, 2002).
and a smaller polarimetric color in the innermost coma sus- The existence of the faint circular polarization, variations
pected for Comet Hale-Bopp (Jockers et al., 1999). Some in the plane of polarization, and nonzero polarization ob-
comets do not show lower polarization [e.g., C/1989 X1 served at forward-scattering direction during stellar occul-
(Eaton et al., 1992), C/2001 A2 (Rosenbush et al., 2002)] tations (Rosenbush et al., 1994) may be indications of
in the innermost coma, possibly hidden by highly polarized aligned elongated or optically anisotropic particles in comet-
dust jets or, as Kiselev et al. (2001) suggest, resulted from ary atmospheres.
strong gas contamination.
Aperture polarimetry with an offset of the center, as well 2.3. Dust Thermal Emission
as cuts through polarization images, may be used to study
the variation of the polarization with the cometocentric dis- Thermal data provide two types of results that are sen-
tance. The increase within the jets and decrease in the inner- sitive to the physical properties of the particles: the ther-
most coma are clearly visible on such graphs, and some mal spectral energy distribution (SED) and the detection of
differences may be noticed between the sunward and anti- spectral features (e.g., the silicate feature at 10 µm and 16–
sunward side. Although the data are line-of-sight integrated, 30 µm). In addition, the ratio of the thermal energy to the
they emphasize the temporal evolution in the physical prop- scattered energy provides a measure of albedo, as described
erties of the dust particles ejected from the nucleus. Except previously.
for the above-mentioned features, the polarization decreased Thermal emission from the dust in the coma results from
gradually within 5000–8000 km from the nucleus for C/ absorption of the solar radiation followed by its reemission.
1996 B2 Hyakutake and C/1996 Q1 Tabur (Kolokolova et al., The thermal radiation from a single grain depends upon its
2001a) and increased for P/Halley (Levasseur-Regourd et al., temperature, T, and wavelength-dependent emissivity, ε
1999) and Hale-Bopp (Kolokolova et al., 2001a), accom-
panied by similar trends in the B–R color. F(λ) = (r/∆)2ε (r,λ)πB(λ,T) (1)
The polarization images often reveal elongated fan-
shaped structures with polarization higher than in the sur- where r is some specific dimension of the particle, e.g., its
rounding coma. They generally correspond to bright jet-like radius, ∆ the geocentric distance, and B(λ,T) the Planck
features on the brightness images. This effect has been function for grain of temperature T. The observed SED from
noticed for quite a few comets, e.g., 1P/Halley (Eaton et al., the ensemble of grains in a coma having differing tempera-
1988), C/1990 K1 Levy (Renard et al., 1992), 109P/Swift- tures and wavelength-dependent emissivities generally is
Tuttle (Eaton et al., 1995), 47P/Ashbrook-Jackson (Renard similar to (but broader than) a blackbody curve (Fig. 5). The
et al., 1996), or C/1996 B2 Hyakutake (Tozzi et al., 1997). SED can be characterized by a single temperature (the color
The case of the bright and active Comet Hale-Bopp is most temperature, Tc) over a defined wavelength interval, but it
documented; straight jets at large heliocentric distances are is important to remember that the color temperature is not
seen to evolve in arcs or shells around perihelion passage the physical temperature of the grains.
(see, e.g., Hadamcik et al., 1999; Jockers et al., 1999; The physical temperature of a particle in the solar radia-
Furusho et al., 1999). Such conspicuous features could be tion field depends strongly on the latent heat of sublima-
produced by an alignment of elongated particles or by tion and sublimation rate of any material that may be sub-
freshly ejected dust particles different from the particles in limating, but once the sublimation has ceased and thermal
the regular coma. equilibrium is established, the temperature depends on the
2.2.4. Plane of polarization and circular polarization. balance between the solar energy absorbed at visual wave-
The plane of polarization is in almost all cases perpendicular lengths and the energy radiated in the infrared. For a particle
or parallel to the scattering plane, indicating randomly ori- of arbitrary shape we may write the energy balance equation
ented particles. However, some variations by a few degrees
may be noticed with changing aperture size (Manset and R–2 ∫ Cabs(r,m,λ)S(λ)dλ = ζ ∫ πB(λ,T)Cabs(r,m,λ)dλ (2)
Bastien, 2000). Deviations in the polarization plane were no-
ticed for Comet P/Halley near the inversion angle (Beskrov- where S(λ) is the solar flux at 1 AU, R is the heliocentric
naya et al., 1987); they were mapped by Dollfus and Suchail distance in AU, and the factor ζ is the ratio of the total ra-
(1987). Changes in the polarization plane often accompany diating area to the exposed area. This ratio is equal to 4 for
the polarization variations at the outburst activity and were spheres and any convex particle averaged over random ori-
registered in Comets 29P/Schwassmann-Wachmann 1 entations (van de Hulst, 1957, section 8.41). The crucial
(Kiselev and Chernova, 1979), P/Halley (Dollfus et al., parameter in equation (2) is Cabs(r,m,λ), the absorption cross
1988), C/1990 K1 Levy (Rosenbush et al., 1994), and C/ section, which depends on grain size, morphology, and opti-
2001 A2 LINEAR (Rosenbush et al., 2002). For Comets cal constants. By Kirchoff’s law, Cabs(r,m,λ) is equal to the
Halley, Hale-Bopp, and S4 LINEAR, the circular polariza- emissivity, ε (r,λ), times the emitting area. We assume that
tion was estimated and found to be nonzero but below 2% the coma is optically thin (no attenuation of sunlight and no
 Kolokolova et al.: Physical Properties of Cometary Dust 583

body temperature and a drop in the average grain emissiv-

ity at 60 and 100 µm, indicating that the flux contribution
at 60 and 100 µm was primarily from particle sizes smaller
than the wavelength (see section 3.1). Continuum emission
at submillimeter wavelengths has been measured for sev-
eral comets including Hale-Bopp (Jewitt and Luu, 1990,
1992; Jewitt and Matthews, 1997, 1999), indicating the
presence of millimeter-sized particles.
In addition to the smoothly varying infrared continuum
emission, broad spectral features attributed to small silicate
grains are seen in some comets near 10 µm (Fig. 5) and
18 µm. The strength of the features depends upon grain size
and temperature (Hanner et al., 1987). The 16–45-µm spec-
tra of Hale-Bopp recorded by the Short Wavelength Spec-
trometer (SWS) onboard the ISO satellite (Crovisier et al.,
Fig. 5. Spectral energy distribution for Comet Hale-Bopp (Wil- 1997) displayed five distinct spectral peaks that correspond
liams et al., 1997). The left curve is the solar spectrum, the right to laboratory features of crystalline Mg-olivine (forsterite)
curve is the continuum fit to the sum of a 5800 K blackbody com- (see Hanner and Bradley, 2004). Not all comets display a
ponent due to scattered solar radiation and a 475 K blackbody due strong 10-µm silicate feature (Hanner et al., 1994; Hanner
to thermal emission. The heavy solid line shows the silicate fea- and Bradley, 2004). In particular, the feature tends to be
ture observed with the HIFOGS (High-efficiency Infrared Faint
weak (~20% above the continuum) or absent entirely in
Object Grating Spectrometer). Although Comet Hale-Bopp was
Jupiter-family comets (e.g., Hanner et al., 1996; Li and
not a typical comet, the figure provides an illustration of the main
characteristics of cometary dust thermal emission. Greenberg, 1998a).

2.4. Correlations Among Scattering and

heating by other grains) and that sublimation is negligible. Emitting Observational Characteristics
The observed color temperature can be compared with the
SED predicted from equations (1)–(2) for grains of various It has been well established that the observable scatter-
sizes and optical properties in order to infer the physical ing parameters of cometary dust tend to correlate. These
characteristics of the cometary dust. correlations can provide insight into the relative importance
The 3–20-µm thermal SED has been observed for many of particle size, composition, and structure on the observ-
comets over the past three decades, with improving pre- able scattering properties.
cision. P/Halley was monitored regularly at R < 2.8 AU We have already noted that comets divide into some
(Tokunaga et al., 1986, 1988; Gehrz and Ney, 1992) and classes, based upon their maximum polarization (Fig. 3).
Hale-Bopp was observed from the ground and from Earth The high Pmax comets are mostly comets with a strong dust
orbit at 0.9–4.9 AU (Mason et al., 2001; Grün et al., 2001; continuum, while the low Pmax comets are comets with a
Hanner et al., 1999; Wooden et al., 1999; Hayward et al., weak dust continuum (Chernova et al., 1993). Comets ex-
2000). The 5–18-µm color temperature is typically 5–25% hibiting higher polarization generally display a stronger
higher than a perfect blackbody at the same heliocentric silicate feature (Levasseur-Regourd et al., 1996), indicating
distance that can be calculated as T = 280 * R–0.5. that small silicate particles have a major influence on Pmax
Comets display a heliocentric dependence, T ~ R–0.5; in (see section 3.1). The strength of the silicate feature also
the case of P/Halley the 8–20-µm color temperature varied correlates with higher color temperature and stronger flux
as T = 315.5 * R–0.5 (Tokunaga et al., 1988). The comets at 3–5 µm (Gehrz and Ney, 1992), both indicators of hot,
with the strongest dust emission, such as P/Halley and Hale- submicrometer-sized absorbing grains (see section 3.1.1).
Bopp, display a higher color temperature at 3.5–8 µm than The fact that the B–R, J–H, and H–K colors do not cor-
at 8–20 µm (Tokunaga et al., 1988; Williams et al., 1997). relate, e.g., show different tendencies with the heliocentric
Thermal emission observations in the far-infrared and distance or with the distance from the nucleus, supports the
submillimeter spectral regions can potentially provide in- idea that the changes in the colors cannot be explained by
formation about the larger particles in the coma (see sec- simple change of particle size or smooth change in the
tion 3.1). Far-infrared observations at λ < 200 µm have been optical constants. A smooth simultaneous change in B–R
acquired by the InfraRed Astronomical Satellite (IRAS), color and polarization was observed in the innermost coma
Cosmic Background Explorer (COBE), and Infrared Space of some comets (Kolokolova et al., 2001a), indicating a
Observatory (ISO) satellites. The Diffuse InfraRed Back- smooth change in some dust properties that occurs as dust
ground Experiment (DIRBE) instrument on COBE meas- is moving out of the nucleus.
ured the SED from 3.5 to 100 µm for three comets (Lisse Hanner (2002, 2003) summarized the correlations and
et al., 1994, 1998). Among these, only Comet Levy (C/1990 compared the scattering properties in Comets P/Halley and
K1) had a color temperature 10% higher than the black- Hale-Bopp: The dust in Hale-Bopp displayed higher po-
584 Comets II

larization at comparable α, redder polarimetric color, higher The scattering matrix F is defined by the particle prop-
albedo, stronger silicate feature, higher infrared color tem- erties, thus the inverse problem can be solved if the ele-
perature compared to the blackbody temperature, and higher ments of the scattering matrix, obtained from observations,
3–5-µm thermal emission. can be also found from a theory that describes scattering
by particles, i.e., most rigorously, from Maxwell’s equa-
2.5. Summary tions. To determine all 16 elements of the matrix F one must
obtain four independent combinations of vectors I0 and I,
The observational characteristics of cometary dust are but since sunlight is incoherent and essentially unpolarized,
extremely variable and depend on phase angle, heliocen- this is usually not possible from astronomical observations.
tric distance, and position within the coma, especially as- In practice, one therefore fits only the two upper-left ele-
sociated with comet activity (jets, fans, etc.). The most ments, or equivalently the intensity and polarization. While
complex characteristic is the brightness that depends on the the intensity or brightness is plagued by sensitivity to varia-
spatial distribution of dust particles, and thus to a large tions in the particle number density, the polarization is a ratio
extent is affected by temporary variations in dust produc- of intensities and is therefore independent of the amount
tion rate. Parameters, formed as ratios of brightness such of dust. These observational constraints make it even more
as color, polarization, and albedo, are more suitable for important to fit all available observations and to extend the
studying physical properties of the dust grains. However, observations to as broad a range of phase angles as possible
measured using aperture instruments, they demonstrate av- and wavelengths as well as thermal emission spectra. This
erage characteristics related to a mixture of particles of a still cannot guarantee the uniqueness of the solution, espe-
variety of properties and can vary due to comet activity. cially as the dominating grains in a mixture of grain types
Coma images obtained in narrowband continuum filters pro- can vary strongly both with wavelength and with scatter-
vide the most adequate source of information about prop- ing angle. Therefore some authors emphasize the impor-
erties of cometary dust. tance in finding a solution that also adheres to limitations
The general regularities found in observational charac- set by, for example, cosmic abundances (Greenberg and
teristics of cometary dust that may be used as a basis for Hage, 1990) and constraints from the dynamics of the par-
studying physical properties of the dust particles are listed ticles (Gustafson, 1994). However, in this chapter we focus
later in this chapter (see Table 2). Variability of these char- on constraints from optical and infrared observations.
acteristics within the coma, correlations between them, and For electromagnetic waves propagating in a homoge-
exceptions to the listed rules are also an interesting subject neous medium, characterized by its complex refractive in-
for light-scattering modeling. dex m = n + iκ, Maxwell’s equations can be reduced to

3. LIGHT-SCATTERING THEORETICAL curl H = ikm2E

(3)
AND EXPERIMENTAL METHODS curl E = –ikH

Study of cometary dust using its interaction with solar Since the magnetic vector H can be expressed through
radiation is a typical example of remote sensing that usu- the electrical vector E, equation (3) can be further reduced
ally is associated with the scattering inverse problem. The to one so-called Helmholtz equation
sought quantities define a set of particle parameters such
as size, shape, and composition (refractive index) from the ∇2E + k2E = 0 (4)
scattering/emission data; the set can include the parameters
of more than one type of particle. The rigorous way to solve The electromagnetic vector E is related to the Stokes pa-
the inverse problem would be: rameters through the values of its two complex perpendicu-
• to measure the characteristics of the scattered light (in- lar amplitudes E|| and E⊥ and their conjugates as (van de
tensity, I; degree of linear polarization, P; position of Hulst, 1957; Bohren and Huffman, 1983)
the plane of polarization, defined by the angle θ; de-
gree of circular polarization, V) at a given wavelength, I = E|| |E*|| + E⊥ E*⊥
λ, and given phase angle, α; Q= E|| E*|| – E⊥ E*⊥
• to calculate the Stokes vector I = (I, Q, U, V) of the U= E|| E*⊥ + E⊥ E*||
scattered light whose components are related to the V= i (E|| E*⊥ – E⊥ E*)||
observed characteristics as I = I, P = (Q 2 + U 2 ) / I ,
tan(2θ) = Q/U, V = V/I; In principal, a complete solution to the problem can be
• from the Stokes vectors of the scattered and incident achieved if we consider equation (4) outside the particle,
light, I and I0, determine elements of the scattering where the electromagnetic field is a superposition of inci-
matrix F through (I, Q, U, V) = F/(kR)2 * (I0, Q0, U0, dent and scattered fields, and inside the particle (internal
V0), where R is the distance between the detector and field), and apply the boundary conditions. The boundary
the scatterer and k is the wave number in empty space conditions (van de Hulst, 1957, section 9.13) mean that any
equal to k = 2π/λ. tangential and normal components of E are continuous
 Kolokolova et al.: Physical Properties of Cometary Dust 585

across the two materials at the particle boundary. Thus to color, or temperature. However, the calculations for spheres
solve the problem we need to know the shape of the bound- can be used in a qualitative manner to narrow the range of
ary, i.e., the particle shape. The particle shape means a cometary grain parameters, as illustrated by the use of three-
mathematically sharp boundary between a particle interior dimensional or color-contour graphics of the type shown in
and empty space. We therefore tend to distinguish between Fig. 6 (see also numerous examples in Hansen and Travis,
particle shape and structure (surface and internal). Avail- 1974; Mishchenko and Travis, 1994; Mishchenko et al.,
able solutions are specific to classes of particle shapes, e.g., 2002). From Fig. 6 one can see that light scattering from
spheres, cylinders, and spheroids. These are usually for cometary dust is not dominated by particles much smaller
homogeneous and isotropic internal structures, although than the optical wavelengths, since for such particles polari-
solutions for some anisotropic or inhomogeneous structures zation is always positive with very high maximum polariza-
have been derived for some specific shapes. tion at α = 90°. Also, cometary dust cannot be represented
by an ensemble of monodisperse spherical or quasispherical
3.1. Light Scattering by Homogeneous particles of medium size (1 < x < 20) since their light-scat-
Spherical Particles (Mie Theory) tering characteristics experience the oscillating behavior
seen even in Fig. 6 (although the oscillations are smoothed
Mie theory [attributed to Mie (1908); credit is also usu- by the size distribution). Note also that for spherical par-
ally given to earlier works by Clebsch, Lorentz, Debye, and ticles, strong color dependence on the phase angle is seen
others (see Kerker, 1969)] accurately predicts the scattering for all sizes and the polarimetric color is mainly negative.
by any homogeneous and isotropic sphere. It solves equa- The contour graphics and a more quantitative approach
tion (4) in spherical coordinates (H, θ, ϕ) using the separa- based on statistical multifactor analysis (Kolokolova et al.,
tion of variables technique, i.e., presenting the electromag- 1997) can be used to estimate influence of dust properties
netic wave E as on observational characteristics. As a result of such an
analysis, the reason for the trends observed within the coma
E = E(H,θ,ϕ)e = Φ(ϕ)Θ(θ)R(H)e and correlations between light-scattering parameters can be
found. For example, such an approach (Kolokolova et al.,
where vector e indicates the direction of oscillations. This 2001a) showed that the correlation between color and po-
gives E in the form of a sum of products of trigonometric larization observed in the innermost coma of Comets Tabur,
and spherical Bessel functions and associated Legendre Hyakutake, and Hale-Bopp cannot be a result of changing
polynomials with the size parameter x = kr (where r is the particle size, but is more likely an indication of changing
particle radius) and refractive index of the particle in the composition.
argument. In practice, one has to take care with the numeri- For certain applications, we might expect that arbitrarily
cal code in order to not degrade the accuracy for very small shaped, randomly oriented particles can be approximated
or very large particles. Detailed discussion on Mie solution by equal-volume, equal-projected-area, or, in the case of
can be found in van de Hulst (1957) and Bohren and Huff- convex particles, equal-surface-area spheres. They appear
man (1983). The latter book also contains a simple but effi- appropriate when some specific term dominates the scat-
cient Mie code. A modern code is available from M. Mish- tering. For example, we might expect scattering in the for-
chenko at ftp://ftp.giss.nasa.gov/pub/crmim/spher.f. ward domain (large phase angles) to be dominated by dif-
Even when the shape and structure of the particle is as fraction, which is strongly dependent on the particle size
simple as that of a homogeneous sphere, the complexity of since only the particle cross section enters calculations of
the solution does not allow the scattering properties of a the diffraction pattern (van de Hulst, 1957, section 3.3). De-
particle to be expressed through a simple analytical func- pending on the absorption of the particle material at some
tion of the size and refractive index. The numerically de- particle sizes, the transmitted light starts reducing the mag-
rived solutions are also generally found to not be unique nitude of the forward-scattering peak but does not strongly
to one combination of particle size and refractive index. The affect the angular distribution of the intensity. In particu-
problem of uniqueness is more acute if the observations lar, the angle of the first minimum in intensity counted from
cover only a limited range of phase angles. Thus the inverse the direction of backscattering seems to be a good size in-
problem is often solved indirectly using analysis of the dicator even for aggregated particles (Zerull et al., 1993).
qualitative light-scattering behavior and incorporating other Scattering by particles of size x << 1 is proportional to
empirical constraints on particle properties. the square of their polarizability (see section 3.2) and there-
Use of Mie theory has helped exclude spherical and fore to their volume squared (van de Hulst, 1957, section
homogeneous particles as the main component of cometary 6.11) so that equal volume particles in random orientation
dust. Even if some specific size distribution and refractive scatter identically. For the other extreme of large convex
index could fit some observations (e.g., polarization) at particles in the geometric optics regime van de Hulst (1957,
some wavelengths (see examples in Mukai et al., 1987), the section 8.42) showed that the scattering caused by reflec-
same characteristics of spherical particles could not provide tion from randomly oriented particles is identical with the
a reasonable fit over a broad range of wavelengths and to scattering by a sphere of the same material and surface area.
other observational parameters, e.g., scattering function, He also showed that such particles have the same geometri-
586 Comets II

Fig. 6. Top panel: Intensity and polarization of scattered light vs. phase angle and effective size parameter xeff for spheres of the
refractive index m = 1.55 + i0.005. The particle size distribution has the form n(x) = x–3 and is determined by its cross-sectional-area-
weighted mean size parameter xeff, and the width of the size distribution defined by the effective variance veff = 0.05 (for details see
Mishchenko and Travis, 1994). Bottom panel: Same for color and polarimetric color but instead of size parameter the effective size of
particle varies at the fixed wavelengths of 0.45 and 0.65 µm. Darker colors indicate smaller values.
 Kolokolova et al.: Physical Properties of Cometary Dust 587

cal cross section as the sphere. The approximations work wavelengths greater than about 10 times their size. They
better the closer the particle shape is to spherical. For ex- heat up until the energy radiated at the shorter infrared
ample, an error in the absorption cross section is less than wavelengths (roughly 3–8 µm for comets at 0.5–3 AU from
5% for a spheroid of the axes ratio a : b = 1.4 regardless of the Sun) balances the absorbed energy. In fact, for small
the particle size, but can exceed 15% for a spheroid with absorbing grains, their size controls their temperature, re-
the axes ratio a : b = 2 at x = 1 (Mishchenko et al., 1996). gardless of their specific composition (Hanner, 1983).
Important limitations can be high porosity of the particles In contrast to carbon grains, silicate grains radiate effi-
(Henning and Stognienko, 1993) or the presence of sharp ciently in the infrared because of the resonance in their
edges (Yanamandra-Fisher and Hanner, 1998). optical constants near 10 and 20 µm; the amount of absorp-
3.1.1. Use of Mie theory to estimate grain emissivity at tion at visual wavelengths controls their temperature. The
thermal infrared wavelengths. As we will see below, the absorption at visual wavelengths depends strongly on the
thermal emission by cometary dust comes mainly from Fe content of the silicates (Dorschner et al., 1995). Pure
submicrometer particles. Therefore the equal-volume-sphere Mg-rich silicates have very low absorption; the imaginary
representation provides a good estimate for the absorption part of the refractive index κ ~ 0.0003 at 0.5 µm for a glass
cross section as it works for particles that are small in all with Fe/Mg κ ~ 0.05 at 0.5 µm for a pyroxene glass with
dimensions, i.e., represent quasi-equidimensional (not nee- Fe/Mg = 1 and k ~ 0.1 for an olivine glass with Fe/Mg = 1.0.
dles or disks) compact particles of x << 1. It is also a good Consequently, pure Mg silicates in a comet coma near 1 AU
approximation for submicrometer particles in a porous ag- would be much colder than a blackbody while Fe-rich sili-
gregate so that the interaction between particles is weak. cate grains would be warmer than a blackbody. Composi-
Using the thus estimated absorption cross section Cabs one can tional measurements indicate that the silicates in comets are
use equation (2) to find the temperature for grains of a vari- Mg-rich (Hanner and Bradley, 2004), so one might expect
ety of sizes and composition (Mukai, 1977; Hanner, 1983). them to be cold. However, even a small admixture of ab-
This revealed a set of general regularities in thermal emis- sorbing material can increase the temperature significantly.
sion from small grains shown in Fig. 7. The computed temperature for a submicrometer absorb-
Particles of absorptive materials, e.g., glassy carbon or ing grain varies approximately as R–0.35 instead of observed
magnetite, showed temperatures higher than for a black- R–0.5 (Fig. 7) that would be also expected for a blackbody
body; the smaller the particles, the higher the temperature. in equilibrium. Whether this indicates a change in size dis-
Particles made of transparent materials were found to be tribution with R, dominance by larger particles or the short-
cooler than a blackbody and their temperature did not de- coming of the computations for small spheres is not clear.
pend much on particle size. Small grains of an absorbing Chances are that this is a result of combination of optical
(e.g., carbonaceous) material absorb strongly at visual wave- characteristics of both small and large particles exhibited by
lengths, but cannot radiate efficiently in the infrared at aggregates of small grains (see section 3.3.3).
The observed 3–20-µm SED for comets cannot gener-
ally be fit by the F(λ) computed for a single grain of any
size or composition. However, models using a size distri-
bution of absorbing particles dominated by micrometer- to
submicrometer-sized grains provide a match to the observed
SED (Li and Greenberg, 1998b; Hanner et al., 1999). Com-
ets with the strongest dust emission (such as P/Halley and
Hale-Bopp) that also display a higher color temperature at
3–8 µm than at 8–20 µm indicate an enhanced abundance
of hot, submicrometer-sized grains.
By fitting the observed SED with a model of thermal
emission from a size distribution of grains, the total dust
mass within the coma can be estimated. When combined
with a size-dependent velocity distribution for the dust, the
rate of dust production from the nucleus can also be esti-
mated (Hanner and Hayward, 2003).
Extensive observations of Comet Hale-Bopp from the
European Space Agency’s ISO (the photometer PHOT
measured the thermal flux through filters at 7–160 µm,
Fig. 7. Temperature of a grain vs. heliocentric distance. Dotted
while the two spectrometers recorded the spectrum from 5
lines show results for absorptive particles (glassy carbon) of ra-
to 160 µm) enabled the SED to be obtained at long wave-
dius 0.1, 0.5, and 10 µm. Dashed lines are for olivine particles of
radius 0.1 and 10 µm. The thin solid line is the blackbody tem- lengths and fit by an emission model having a size distri-
perature. The thick solid line shows the results for Comet Halley bution of the form n(r) ~ r –a, with a ≤ 3.5 (Grün et al.,
(Tokunaga et al., 1988). The comet dust temperature is higher than 2001). For an outflow velocity v(r) ~ r –0.5, this result implies
a blackbody, indicating the presence of submicrometer absorptive that the dust production size distribution from the nucleus
particles. had a slope a ≤ 4 and the mass was concentrated in large
588 Comets II

particles. Yet Hale-Bopp displayed the highest 3–13-µm ity, which in many cases [spheres, spheroids, ellipsoids,
color temperature and strongest silicate feature ever seen disks, cylinders, see, e.g., Bohren and Huffman (1983)]
in a comet, clearly indicating that the thermal emission at admits analytical solution.
shorter wavelengths arose from a high abundance of sub- When x|m – 1| << 1 and |m – 1| << 1, the Rayleigh-Gans
micrometer grains compared to other comets. approximation applies. This approximation is often used not
While Mie theory can be used to compute the absorp- by itself but as a first approximation for the successive it-
tion (or emission) cross section Cabs for a compact particle erations to obtain more general approximations (see, e.g.,
that is small in comparison to the wavelength in all its di- Haracz et al., 1984). Muinonen (1996) applied this approxi-
mensions, in cases where Cabs varies slowly with wave- mation to stochastic irregular particles. Closely related to
length, it cannot be applied to calculations for an emission the Rayleigh-Gans approximation is the coherent Mie scat-
feature, where the optical constants are rapidly varying. tering approximation developed to treat porous aggregates
Analysis of the 10-µm silicate emission feature in comets of spheres (Zerull et al., 1993). Only phase interrelations
indicates the presence of both glassy and crystalline sili- between waves scattered by constituent particles in an ag-
cate components (Hanner et al., 1999; Wooden et al., 1999; gregate of spheres are taken into account. This approxima-
Hanner and Bradley, 2004). The optical constants of the tion works better with increasing porosity of the aggregate;
glassy silicates vary slowly across the 8–13-µm range and usually the porosity should be more than 90% (Xu and
Mie theory will not be too inaccurate for computing Cabs. Wang, 1998).
However, the crystalline components, especially crystalline When x >> 1, |m – 1| << 1, we may apply the anomalous
olivine, which has a strong resonance at 11.2 µm in natu- diffraction approximation (van de Hulst, 1957). This ap-
rally occurring samples, cannot be treated using Mie theory proximation is based on the assumption that the rays are
since a resonance is very sensitive to particle shape (Bohren negligibly deviated inside the particle, thus only absorption
and Huffman, 1983). Mie theory does not even predict the inside the particle and interference of light passed through
correct wavelength of the peak, let alone the correct peak the particle and around it can be taken into account. This
height (Yanamandra-Fisher and Hanner, 1998). Thus, most allows easy calculation of the absorption and extinction
researchers make use of measured reflectivity or mass ab- cross sections, which sometimes can be expressed through
sorption coefficients to obtain Cabs within the spectral feature analytical formulas. This method was widely applied to
(Wooden et al., 1999, 2000; Hayward et al., 2000; Harker estimate cross sections of particles very different from
et al., 2002). spheres, such as prismatic and hexagonal columns, cubes,
Mie theory influenced our understanding of cometary and finite cylinders. The accuracy of the method increases
dust, constraining it as an ensemble of dark, polydisperse, with decreasing absorption.
and nonspherical particles whose main contribution to the For the sake of completeness, we mention an approxima-
thermal emission comes from particles of size parameter tion called perturbation theory, which treats the radius r of an
close to one unit. It still remains an important tool when irregular particle as a function of coordinates ϑ and ϕ and
estimating the thermal radiation from cometary dust, since r = r0(1 + ξf(ϑ,ϕ)), where r0 is the radius of “unperturbed”
the particle shape does not affect the absorption cross sec- sphere and |ξf(ϑ,ϕ)| < 1. The solution is obtained as an ex-
tions as long as the particles can be considered as compact pansion of the boundary condition in series in ξ (Oguchi,
and roughly equidimensional or sufficiently porous ag- 1960). This method provides accurate results only for parti-
gregates of such particles so that particle interactions can cles of x ≤ 7 and only if the deviations from spherical shape
be neglected. However, angular and spectral dependencies are smaller than the wavelength. It is a convenient method
of intensity and polarization of cometary dust indicate that when effects of the surface roughness are of interest.
these properties cannot be calculated using the model of x >> 1 is the geometric optics case, now often referred
spherical homogeneous particles. to as the “ray-tracing approximation.” It considers the in-
cident field as a set of independent rays, each of which
3.2. Approximations to Treat Nonspherical reflects according to Snell’s law and Fresnel’s equations on
Inhomogeneous Particles the surface of the particle. The size restriction is in part
relaxed when geometric optics is combined with Fraunhofer
Along with techniques that consider light scattering in diffraction. For particles of complicated shape, the ray trac-
rigorous terms through the solution of Maxwell’s equations, ing is usually performed using the Monte Carlo approach.
there are some useful approximations that allow fast com- On this basis results have been obtained for stochastic parti-
putations subject to the size parameter and/or refractive cles (Muinonen, 2000) and particles with inclusions (Macke,
index of the particle. 2000). The Web site by A. Macke (http://www.ifm.uni-kiel.
When x << 1 and |mx| << 1 the Rayleigh (1897) approxi- de/) contains a collection of ray-tracing codes. The com-
mation applies. Such a particle can be considered as a di- parison of ray-tracing calculations with exact solutions, e.g.,
pole with an inherent polarizability that defines the dipole for spheres or cylinders, shows that the discrepancies be-
moment induced in the particle by the incident electromag- tween the approximation and the exact solution start for
netic field. In the case of a very small particle, the field near transparent particles of size parameter x < 100 (Wielaard
it can be treated as an electrostatic field. This allows the et al., 1997); for larger absorption the ray-tracing technique
derivation of a simple equation for the particle polarizabil- can be applied to smaller size parameters. Waldemarsson
 Kolokolova et al.: Physical Properties of Cometary Dust 589

and Gustafson (2003) developed a combination of ray-trac- of mixing rules have been developed for a variety of inclu-
ing technique with diffraction on the edge for light scatter- sion types (non-Rayleigh, nonspherical, layered, anisotro-
ing by thin plates (flakes) that provides a reasonable accu- pic, chiral) and topology of their distribution within the
racy down to particle sizes of x ~ 1. medium, including aligned inclusions and fractal structures
Cometary dust is not dominated by very small or very (see an extensive review by Sihvola, 1999). However, still
large particles, but the approximations described above can the most popular remain the simplest Maxwell Garnett
be applied to calculations for wide size distributions of (Garnett, 1904)
nonspherical particles at the edges of the size distribution.
For example, Bonev et al. (2002) calculated the color of
εeff − εm εi − εm
cometary grains assuming them to be polydisperse sphe- = fi (6)
roids and using the T-matrix method (see section 3.3.2) for εeff + 2εeff εeff + 2εeff
size parameters x < 25 and the ray-tracing technique for
larger particles. A similar approach can be used to calcu- and Bruggeman (Bruggeman, 1935)
late light scattering when a broad range of wavelengths need
to be covered, as was done by Min et al. (2003), who also
εeff − εi ε − εeff
found a criterion for selecting the ray-tracing or anomalous fi = fm m (7)
diffraction approximations to calculate cross sections. εi + 2εeff εm + 2εeff
Kolokolova et al. (1997) showed that in the color, pre-
sented as the difference of logarithms of intensity at two mixing rules. In equations (6) and (7) εi and εm are dielec-
wavelengths, the contribution of intermediate particles is tric constants of inclusions and matrix respectively, and fi
canceled and small and large particles dominate. If the size is the volume fraction of the inclusions in the mixture. The
distribution is smooth (e.g., of power-law type) and wide Maxwell Garnett rule represents the medium as inclusions
[i.e., includes small (Rayleigh) and large (ray-tracing) par- embedded into the matrix material with εm, the result of
ticles], then the color can be expressed analytically through which depends on the material chosen as the matrix. The
the radii of the smallest and largest particles, the power of Bruggeman rule was obtained for particles with εi and εm
the size distribution, and two parameters that describe the embedded into the material with ε = εeff, so the formula is
particle composition. These analytical expressions have five symmetric with respect to the interchange of materials. This
unknowns that can be found if five colors are measured as makes it easy to be generalized for the n-component me-
has been done for Comet C/1996 Q1 Tabur (Kolokolova et dium
al., 2001b).
n
The approximations listed above were developed to treat
nonspherical but homogeneous particles. To describe light ∑ f (ε
i =1
i i − εeff )/(ε i + 2εeff ) = 0 (8)
scattering by heterogeneous particles one can use approxi-
mations called mixing rules or effective medium theories. Since the derivation of the mixing rules was based on
The main idea behind these approximations is to substitute assuming the external field as electrostatic, the inclusions
a composite material with some “effective” material whose were assumed to be much smaller than the wavelength of
refractive index provides the correct light-scattering char- electromagnetic waves. More exactly, the criterion of their
acteristics of the heterogeneous medium. It is a reasonable validity is xRe(m) << 1 (Chylek et al., 2000), where x is the
approximation when inhomogeneities (inclusions) are much size parameter of inclusions and Re(m) is the real part of
smaller than the wavelength (Rayleigh-type) and the size the refractive index for the matrix material. Comparison of
of the macroscopic particle is much larger than the size of effective medium theories with DDA (see section 3.3.3) cal-
the inclusions. In large scale, such a medium acts as an culations (Lumme and Rahola, 1994; Wolff et al., 1998) and
isotropic homogeneous medium for which the displacement experiments (Kolokolova and Gustafson, 2001) show that
D is related to the electrostatic field E by a linear relation- even for xRe(m) ~ 1 effective medium theories provide rea-
ship D = εE where ε is the complex dielectric constant of sonable results. The best accuracy can be obtained for cross
the material related to the refractive index as m = ε . For a sections and the worst for polarization, especially at phase
macroscopically homogeneous isotropic mixture, D and E angles α < 50° and α > 120°.
can be averaged within the medium as There were a number of attempts to consider heteroge-
neous cometary grains using effective-medium theories, par-
∫ D(x,y,z)dxdydz = ∫ ε(x,y,z)E(x,y,z)dxdydz = ticularly to treat aggregates as a mixture of constituent par-
(5)
εeff ∫ E(x,y,z)dzdydz ticles (inclusions) and voids (matrix material) (e.g., Green-
berg and Hage, 1990; Mukai et al., 1992; Li and Greenberg,
1998b). In the visual region the cometary aggregates with
where E, D, and ε are determined for a point inside the ma- the size parameter of constituent particles x > 1 are, most
terial with coordinates (x,y,z). Using the Maxwell equation likely, out of the range of the validity of the effective me-
divD = 0 and assuming some size, shape, and distribution dium theories. For the thermal infrared region, cometary
of the inclusions, one can obtain expressions, in some case aggregates can be treated with effective medium theories
analytical, for the effective dielectric constant εeff. Dozens if they are sufficiently large (remember that the number of
590 Comets II

inclusions must allow the macroscopic particle to be con- pands the incident and scattered fields into vector spheri-
sidered as a medium). Using the mixing rules, one should cal functions with the scattered field expanded outside a
be careful to calculate the refractive index for core-mantle sphere circumscribing a nonspherical particle. The main ad-
particles. Even for particles of size parameter x ≥ 0.3, sig- vantage of the resulting formulation is that the T-matrix is
nificant differences in cross sections from exact core mantle defined only by physical characteristics of the particle it-
calculations appeared (Gustafson et al., 2001). self, i.e., it is computed only once and then can be used for
any incidence/scattering direction and polarization of the
3.3. Numerical Solutions for Inhomogeneous incident light. A significant development of the method was
Nonspherical Particles an analytical orientation-averaging procedure (Mishchenko,
1991) that made calculations for randomly oriented particles
Further characterization of cometary dust requires more as efficient as for a fixed orientation of the same particle.
advanced light scattering theories. We consider them in this T-matrix computations are especially efficient for axisym-
section, mainly outlining the strengths and drawbacks of the metric, including multilayered, particles; however, the meth-
methods that have been applied to study cometary dust. As od can be extended to any shape of the scatterer. Although
well as Mie theory, solutions of the Maxwell equations for computational complexity greatly increases for particles
nonspherical particles cannot be used directly to solve the without rotational symmetry, recently solutions were ob-
inverse problem for cometary dust, but instead provide some tained for ellipsoids, cubes, and aggregates of spherical
constraints through fitting procedures and investigation of particles. The latter case is of special interest in the field of
general trends in the dependence of light-scattering char- astrophysics. It presents the T-matrix development of the
acteristics on particle properties. separate-variable method for the aggregates of spheres con-
3.3.1. Separation of variables method. The main idea sidered above. Since the scattered field for the individual
behind Mie theory, expansion of the electromagnetic waves sphere does not depend on the incident light direction and
in the coordinate system that corresponds to the shape of polarization, the expansions for individual spheres can be
the body (e.g., cylindrical, spheroidal) and then separates transformed into a single expansion centered inside the ag-
the variables, has provided a number of solutions for non- gregate. Such an expansion is equivalent to the T-matrix of
spherical but regular particles: multilayered, optically an- the aggregate and thus can be used in analytical averaging of
isotropic, and radially inhomogeneous spheres, cylinders, scattering characteristics over aggregate orientations (Mish-
slabs, and spheroids (see the review by Ciric and Cooray, chenko et al., 1996).
2000). Among solutions obtained with this method, the most A variety of computational T-matrix codes are available
popular are solutions for cylinders (Bohren and Huffman, on line at Mishchenko’s Web site (http://www.giss.nasa.gov/
1983), core-mantle spheres (Toon and Ackerman, 1981), ~crmim), among them codes for polydisperse axial-sym-
spheroids (Asano and Yamamoto, 1975; Voshchinnikov and metric particles and aggregates of spheres. The computa-
Farafonov, 1993), and core-mantle spheroids (Farafonov et tional complexity of the T-matrix method increases as x3–x4,
al., 1996). Although this method can provide exact solu- i.e., the method is a fast and convenient way to test results
tions to Maxwell’s equations, the problem requires numeri- obtained with other codes (see, e.g., Lumme and Rahola,
cal treatment to solve the boundary condition even for 1998) or for survey-type studies. Kolokolova et al. (1997)
simple particle shapes. This limits the applicability of the used it to check the sensitivity of color and polarization to
method to rather small size parameters (x < 40 for sphe- the size and composition of nonspherical particles. The
roids) or to nonabsorbing materials. However, in the range results were found to be similar to the results for polydis-
of their applicability, these theories provide highly accurate perse spheres. However, details in polarization for non-
results, which makes them a good tool for testing other spherical particles differ significantly from those calculated
approaches. for equal-volume or equal-area spheres (Mishchenko and
The solution of the separation of variables for a single Travis, 1994). For example, randomly oriented spheroids
sphere can be extended to aggregates of spheres representing show no oscillations in angular dependencies of intensity
the total scattering field as a superposition of spherical wave and polarization at size distributions 10–20× narrower than
functions, which expand the field scattered by each sphere is necessary to wash out the oscillations for spheres. Polar-
and use the translation addition theorem for spherical func- ization for polydisperse silicate spheroids (Fig. 8) at inter-
tions (Bruning and Lo, 1971). The method was extended mediate phase angles changes from negative, typical for
for aggregates of spheroids, cylinders, multilayered spheres, spheres (Fig. 6), to positive, leaving a negative branch at
and spheres with inclusions (see Xu, 1997; Fuller and Mac- α < 30°. For elongated particles at α ~ 90°, polarimetric
kowski, 2000, and references therein). The computational color is positive and shows the angular trend similar to the
complexity of the method (the number of numerical opera- observed one (it gets larger with increasing phase angle)
tions in the algorithm) depends on the number of particles for a broad range of particle size (Fig. 8). The angular de-
and their size parameter, shape, and configuration. pendence of the intensity is also reminiscent of the cometary
3.3.2. T-matrix approach. A popular T-matrix ap- scattering function (Fig. 1) except at phase angles 10°–60°,
proach was initially introduced by Waterman (1965) under where it reaches a deep minimum instead of being flat. The
the name “extended boundary condition.” This method ex- spheroids demonstrate color that changes rather rapidly its
 Kolokolova et al.: Physical Properties of Cometary Dust 591

Fig. 8. Same as Fig. 6 but for prolate spheroids (ratio of axis is 1 : 3) of the refractive index m = 1.55 + i0.005; the effective size
parameter xeff corresponds to this for equal-volume sphere.
592 Comets II

value and even sign with phase angle. Randomly oriented The most popular among such methods is probably the
cylinders exhibit similar tendencies (Mishchenko et al., coupled dipole approximation, often called the discrete di-
2002). Using higher absorption one can get higher values pole approximation (DDA) since it represents a particle as
of color and polarimetric color, but the negative polariza- consisting of elementary cells, polarizable units called di-
tion and backscattering peak disappear, eliminating the re- poles (Purcell and Pennypacker, 1973). Each dipole is ex-
semblance of the calculated scattering function and polari- cited by the external field and the fields scattered by all
zation curve to the observed ones. other dipoles. This representation allows one for a N-dipole
Mishchenko et al. (1997) showed that appending the particle to derive N linear equations describing the N fields
model by a shape distribution (a range of aspect ratios of that excite each dipole. The numerical solution of the sys-
spheroids) can provide a good fit to the cometary scatter- tem of these N equations provides the partial field scattered
ing function for polydisperse silicate spheroids at 6 < xeff < by each dipole, and finally the total scattered field is cal-
24. For the size distribution with xeff > 8 and a constant culated. Draine and Flatau (1994) and Lumme and Rahola
refractive index m = 1.53 + i0.008, the color becomes neu- (1994) improved the computational efficiency of the DDA,
tral and then red with a very weak angular change. How- which allowed them to study larger particles, in particular
ever, polyshaped silicate spheroids fail to reproduce the cor- aggregates of larger size. Lumme et al. (1997) considered
rect polarization (Mishchenko, 1993). aggregates up to 200 particles of x = 1.2–1.9. The most
Petrova et al. (2000) used the T-matrix code by Mac- popular has been the DDSCAT code by Draine and Flatau
kowski and Mishchenko (1996) for a systematic compari- (see http://www.astro.princeton.edu/~draine/DDSCAT.html).
son of cometary observations with the calculations for ag- The code includes geometry implementations for ellipsoids,
gregated particles. They considered aggregates built from finite circular cylinders, rectangular parallelepipeds, hexag-
particles of size parameters 1 < x < 3.5 for a set of refrac- onal prisms, and tetrahedra, uniaxial and coated particles
tive indexes with the real part equal to 1.65 and the imagi- as well as for systems of particles. The great advantage of
nary part varying within the range 0.002–0.1. The maxi- the coupled dipole approximation is that it can be applied
mum number of particles in each aggregate was limited to to particles of arbitrary shape, structure, and composition.
43 by the code convergence. “Cometary” type polarization However, it has limited numerical accuracy, requires a sepa-
with low maximum at α ~ 90° and negative branch at small rate calculation for each orientation of particle, and slows
phase angles was obtained for a power-law size distribution down dramatically with increasing N, so that its computa-
of aggregates built of 8–43 constituent particles of x = 1.3, tional complexity increases as the ninth order of the parti-
1.5, and 1.65, although a smooth shape of the curve and cle size parameter.
the quantitative fit to the observational polarization curve Using DDA, West (1991) undertook the first systematic
was not achieved. The characteristics of the negative po- theoretical study of aggregates. He considered the constant
larization depend on the composition (it becomes less pro- refractive index m = 1.7 + i0.029. West demonstrated that
nounced with increasing absorption from 0.01 to 0.05) and for compact aggregates both intensity and polarization be-
porosity (more pronounced for more compact aggregates). have as is more typical for the spherical equivalent of the
A rather good qualitative fit to the cometary scattering func- aggregate. For loose aggregates the projected area of the
tion was achieved for the polydisperse aggregates with x = whole aggregate mostly defines the intensity in the forward-
1.3 and κ = 0.01. In a later paper, Petrova and Jockers scattering domain, whereas the polarization is defined by
(2002) studied the spectral dependence of polarization for the size of the constituent particles. Kozasa et al. (1993)
a variety of size distributions and a range of refractive in- confirmed that even aggregates of thousand constituent
dexes within n = 1.65, 0 < κ < 0.1, assuming the refrac- particles of x < 1 behave like Rayleigh particles in polariza-
tive index independent of wavelength. They showed that the tion regardless their composition.
aggregate model successfully reproduced the observed posi- Xing and Hanner (1997) accomplished a detailed study
tive polarimetric color. However, the color of such aggre- of aggregates with a variety of sizes, shapes, and composi-
gates was found to be blue, unlike the observed red color. tions of constituent particles and their packing within the
The extinction calculations by Petrova et al. (2000) are aggregate. They confirmed that polarization is more sen-
mainly sensitive to the overall size of the aggregate and are sitive to the properties of constituent particles whose size
close to the results for equal-volume spheres if the aggre- and refractive indexes determine most of the polarization,
gates have size parameters x < 3, but becomes larger for whereas shape, number, and packing generate scattering
larger aggregates. This is an indication that the equal-vol- effects of the second order. A reasonable fit to the observed
ume sphere calculations can be used to estimate cross sec- cometary polarization and intensity was achieved for the
tions of aggregates in the thermal infrared but not in the mixture of carbon and silicate aggregates of an intermedi-
visual. ate (touching-particle) porosity. The calculations of cross
3.3.3. Coupled dipole approximation and similar tech- sections showed that in the case of short wavelengths (size
niques. The methods described above are based on the parameter x > 1) the values of extinction cross section per
solution to the boundary conditions on the particle surfaces, unit volume is close to those typical for constituent particles,
while a set of more flexible methods rely on solutions of the but at long wavelengths (x << 1) constituent particles and
internal field from which the scattered field is calculated. aggregates show significant differences that are more pro-
 Kolokolova et al.: Physical Properties of Cometary Dust 593

nounced the more compact the aggregate. When the poros- of the scattering function. The number of particles in the
ity is less than 60%, the temperature of the particle is close aggregates, at least if it is within 64 ≤ N ≤ 256, as well as
to that of an equal-volume sphere. Loose aggregates have their porosity, was found not to be important. But a change
a temperature typical for the constituent particle, i.e., ther- in composition (carbon instead of silicate) could dramati-
mal emission from a large but aggregated particle looks the cally affect the value of maximum polarization, eliminate
same as its small constituent particle regardless of its shape the negative branch, and make the scattering function more
(see also Greenberg and Hage, 1990; Li and Greenberg, flat at the medium phase angles. Kimura’s (2001) results
1998b). Davidsson and Skorov (2002) obtained similar demonstrate the best fit to the observational data achieved
DDA results for single-scattering albedo. This means that so far, although the spectral characteristics of intensity and
thermal infrared data do not allow distinguishing loose ag- polarization have not been checked.
gregates from single particles of the size of their constitu- Similar to DDA, the method of moments (MOM) ap-
ent particles. proach also divides a particle into small elements, but con-
The DDA was used by Yanamandra-Fisher and Hanner siders them not as dipoles but as small cells with a constant
(1998) to study the light scattering and emission by non- refractive index. The price of this straightforwardness of
spherical but regular particle shapes of size parameter 1 < MOM in comparison with DDA is the necessity of calcu-
x < 5, as well as heterogeneous and porous particles. They lating a self-interaction term; different approaches in MOM
showed that compact particles of different shapes produce usually diverge in the way they treat this term. The MOM
very different angular dependence of polarization for a has strengths and drawbacks similar to those for DDA.
transparent material (silicate), but the dependence on par- Using MOM, Lumme and Rahola (1998) considered comet-
ticle shape is reduced for absorbing particles (carbon). They ary particles as stochastically shaped, i.e., particles whose
concluded that negative polarization at small phase angles shape can be described by a mean radius and the covari-
could be produced by nonspherical silicate particles of x ≥ ance function of the radius given as a series of Legendre
2. Introducing porosity for a transparent (silicate) particle polynomials (for details, see Muinonen, 2000). Lumme and
caused the polarization to resemble that of a smaller par- Rahola (1998) made computations for a variety of particle
ticle, while porosity had less of an effect on an absorbing shapes and size parameter (x = 1–6) using the refractive in-
particle provided that the particle remained opaque. Al- dex m = 1.5 + i0.005. Like many previous authors, Lumme
though the use of regular shapes caused oscillations that and Rahola found that the particles should be of x > 1 to
would be absent in the scattering by an irregularly shaped provide negative polarization at small phase angles and low
particle, the authors showed that a macroscopic mixture of maximum polarization. Also, they showed that monodis-
silicate and absorbing particles with a distribution of size perse particles, even of very complicated, irregular shape,
parameters 1 < x < 5 could produce curves for polarization demonstrate oscillating behavior of light-scattering charac-
and angular scattering qualitatively similar to the curves ob- teristics that can be eliminated by considering a polydis-
served for cometary dust. A similar conclusion was reached persion of particles. The same oscillating behavior is shown
by Xing and Hanner (1997) based on the scattering by small by color and polarimetric color that can be seen from the
aggregates. comparison of the intensity and polarization for x = 2, 4,
Yanamandra-Fisher and Hanner (1998) also applied the 6. Particles with the size distribution of the form n(r) ~ r –3
DDA code to examine particle shape effects in the mid- show angular functions of intensity and polarization that are
infrared emission features produced by crystalline olivine. rather similar to cometary ones. However, one also needs
Both the shape and the peak wavelength of the spectral to fit to the spectral characteristics to judge how close the
features depend on the particle shape; moreover, olivine is model is to real cometary dust.
an anisotropic crystal, and the differing optical constants 3.3.4. Other numerical methods. Above we considered
generate peaks at different wavelengths. To reproduce the numerical techniques that have been used in cometary phys-
observed silicate feature the authors had to rule out extreme ics. However, there are other light-scattering techniques that
shapes (disks, needles) as well as ideal spheres. Polariza- may be worth applying, among them the finite difference
tion within the 10-µm silicate feature was studied by Hen- time domain method (FDTD) and the finite element method
ning and Stognienko (1993), who demonstrated that shape (FEM). Both these methods are based on a straightforward
and porosity of particles affect the spectral dependence of solution to equation (4). The FDTD discretizes space and
polarization, both the strength and shape of the feature, even time, making a grid in the time-space domain and then
stronger than the spectral dependence of the intensity. solves equation (4) for each space-time cell, whereas the
Combining the T-matrix technique with the DDA, Ki- FEM discretizes the scattering particle itself into small vol-
mura (2001) considered aggregated particles of fractal struc- ume cells. Then boundary conditions (continuity of the elec-
ture, ballistic particle-cluster aggregates (BPCA) and ballis- trical vector across the surface) are applied on the boundary
tic cluster-cluster aggregates (BCCA) (see Mukai et al., of each cell. Both methods are applicable to particles of
1992), of hundreds and thousands of constituent particles. arbitrary shape, structure, and composition. The main dis-
He showed that aggregates of silicate particles of x = 1.57 advantage of these methods is time-consuming computa-
reproduce the cometary polarization with a very good fit. tions, aggravated by the fact that the computations should
They also provide rather good fit to the “cometary” shape be repeated for each orientation of the particle with respect
594 Comets II

to the incident wave. The computational complexity of the parameters. Giese et al. (1978) showed that, unlike com-
FDTD increases as the fourth power of the particle size pact and rather regular particles, irregular, porous particles
parameter and varies between x4 and x7 for FEM depend- in the size range of a few micrometers exhibit positive and
ing on the computational technique. negative polarization typical for cometary dust. Thus in the
More details of the methods discussed above and other 1970s the microwave method provided the results obtained
numerical methods and approximations can be found in only in theory in the late 1990s. Greenberg and Gustafson
recent reviews (Mishchenko et al., 2000, 2002; Kahnert, (1981) showed that models consisting of a tangle of rods,
2003). Some codes are available via online libraries such so-called “Bird’s Nests,” could provide the observed angu-
as http://atol.ucsd.edu/~pflatau/scatlib/ (P. Flatau), http:// lar dependencies of intensity and polarization. This experi-
www.t-matrix.de/ (T. Wriedt), http://www.emclab.umr.edu/ mental test of the aggregated nature of cometary dust then
codes.html, http://urania.astro.spbu.ru/DOP/, and http:// was extended to the study of a variety of aggregates of
www.astro.uni-jena.de/Users/database/. The latter Web site spherical, including core-mantle, particles by Zerull et al.
also contains a huge collection of refractive indexes for ma- (1993).
terials of astrophysical interest (Jäger et al., 2003). The systematic study of light scattering by complex
particles has been performed using a new generation of
3.4. Experimental Simulations microwave facilities designed and built at the University of
Florida (Gustafson, 1996, 2000). This facility works across
The complexity of cometary and other cosmic dust and a 2.7–4-mm waveband to simulate a region 0.4–0.65 µm
planetary aerosols and the ensuing difficulty treating them in the visual, and thus can study not only angular but also
using theoretical means generated several approaches for spectral dependencies of light scattering (colors). Gustafson
solving the scattering problem through experimental simu- and Kolokolova (1999) reported results from a systematic
lation. As before, we will not discuss all experiments con- study of light scattering by aggregates. Among these results
ducted so far to understand light scattering by particles, but is that the polarization is mainly determined by the size and
only those representative examples that provided significant composition of constituent particles and the size parameter
results for cometary dust. We will not discuss here the ex- of cometary constituents must be 1 < x < 10 to produce a
perimental setups detailed in the papers cited below. low maximum polarization and negative polarization at
One experimental technique to study light scattering by small phase angles that confirms the theoretical results
particles uses streams or suspensions of small particles, considered above (e.g., West, 1991; Xing and Hanner, 1997;
often powdered terrestrial rocks, that are illuminated by a Lumme et al., 1997; etc.). The color and polarimetric color
source of light, recently mainly by a laser. The light scat- of aggregates also primarily depend on the size and com-
tered by the particles is measured to obtain intensity, polari- position of the constituent particles. For aggregates made
zation, Stokes parameters, and even the complete scattering of particles whose size parameters covered the range 0.5–
matrix for a range of phase angles. The other technique, 20, an increase in the size of constituent particles results in
called the microwave analog method, introduced by Green- larger (more red) color and smaller polarimetric color (the
berg et al. (1961), simulates light scattering using micro- refractive index was m = 1.74 + i0.005, constant through-
wave radiation. It actually takes advantage of the same out the wavelength range). The same tendencies result from
scaling used in all theoretical approaches where the particle increasing the imaginary part of the refractive index that
dimensions are given through its size parameter, i.e., as a may provide a clue to the negative polarimetric color ob-
ratio to the wavelength. In such a simulation the light scat- served for Comet P/Giacobini-Zinner (Kiselev et al., 2000).
tering problem is scaled to longer wavelengths that precisely A combination of positive polarimetric color and blue color
preserve the characteristics of the scattering problem as long is typical of aggregates of nonabsorbing particles of 0.5 <
as the size parameter of the scatterer and its refractive in- x < 10, whereas red color and positive polarimetric color are
dex are preserved. This allows light scattering by a single indicative of dark, absorbing aggregates. From the above,
submicrometer or micrometer particle to be simulated us- the aggregates, which similarly scatter light to the cometary
ing a manageable millimeter or centimeter analog model. dust, consist of absorptive constituent particles of size pa-
3.4.1. Microwave analog experiments. The early micro- rameter x > 1.The shape of constituent particles could not
wave simulations were measurements of cross sections and be seen to influence the aggregates’ color and only slightly
scattering functions for spheroids, finite cylinders, rods, and changes the position and amount of maximum polarization.
a variety of compact irregular particles (Greenberg et al., Notice that the results were obtained for the refractive in-
1961; Zerull et al., 1977) directed to determine the appli- dex that does not change with wavelength. The intensity and
cability of Mie theory to nonspherical particles. The study polarization data for a variety of particles, including aggre-
was then extended to polarization and color of nonspherical gates, are given at http://www.astro.ufl.edu/~aplab.
particles (Zerull and Giese, 1983). A systematic study of Even though implementation of some theoretical meth-
particle shape effects was carried out by Schuerman et al. ods, e.g., DDA, on modern computers allows a study of
(1981). Significant discrepancy between the data for non- similar accuracy for aggregates of similar characteristics as
spherical particles and Mie theory was obtained for both the at microwave measurements, the microwave method is still
shape of measured curves and values of light-scattering much faster and can provide a large scope of the results in
 Kolokolova et al.: Physical Properties of Cometary Dust 595

a reasonable time. For example, single-wavelength DDA pound, e.g., kerogen or tholin (Wallis et al., 1987) or an
calculations for a silicate aggregate of 1024 constituent organic refractory (Greenberg and Li, 1998). This assump-
particles of size parameter x = 0.733 (Kimura, 2001) took tion is consistent with the observed increase in albedo with
more than a month on the Alpha station, whereas scatter- the distance from the nucleus and might also explain the
ing from an aggregate of any number of particles of x > 1 gradient in the near-infrared colors.
can be measured in one week providing data at 50 discrete 3.4.2. Light-scattering experiments in the visual. Among
wavelengths. This allows systematic studies to obtain quan- early experimental works that contributed to our under-
titative characteristics of the light scattering, e.g., multifactor standing of light scattering by cosmic grains, Weiss-Wrana
analysis (similar to that described in Kolokolova et al., (1983) showed a significant difference between light scatter-
1997) of sensitivity of light-scattering characteristics to ing by terrestrial/meteoritic particles and Mie calculations.
physical properties of particles. Some results of such a study The work also showed that transparent compact irregular
of aggregates are presented in Table 1, which summarizes particles ~30 µm in size had the polarization curve with the
a study of large (500–5000 constituent particles) aggregates. maximum located at α ≈ 45° and negative polarization at
The aggregates were built to satisfy the most plausible large phase angles; large (28–80 µm) absorbing (κ = 0.66)
model of cometary dust aggregates resulted from theoreti- compact particles had a bell-shaped polarization curve with
cal simulations: The size parameter of the constituent par- high (about 50%) polarization maximum; and fly ash,
ticles was in the range 1.5–5, the constant refractive index, slightly absorbing (κ = 0.01) loose aggregates with an aver-
m = 1.74 + i0.005, simulated a silicate-organic mixture, and age size of 41 µm had an angular dependence of polariza-
the porosity varied within 50–90%. The larger numbers in tion similar to the cometary one.
Table 1 indicate a stronger correlation between the dust Extensive measurements of all 16 elements of the scatter-
characteristic and the light-scattering parameter; negative ing matrix F were performed by the group from Amsterdam
values show that they anticorrelate. Table 1 shows quanti- (Hovenier, 2000; Hovenier et al., 2003; see also http://www.
tatively that the size of constituent particles is the main char- astro.uva.nl/scatter/). Muñoz et al. (2000) studied the scat-
acteristic that determines all light-scattering parameters. The tering matrix of polydisperse, heterogeneous, irregular par-
influence of the porosity is much smaller, and within the ticles presented by terrestrial (light-colored olivine) and
range investigated the number of particles in the aggregate meteoritic (dark carbonaceous chondrite) powders at wave-
has almost no influence on the light-scattering parameters. lengths of 0.442 and 0.633 µm. The effective radius of the
The data from Table 1 show that the correlations between particles was approximately a few micrometers so that the
color and polarization (their simultaneous decrease or in- size parameter of the particles peaked within the range x =
crease) in the near-nucleus coma observed by K. Jockers and 10–20. Both terrestrial and meteoritic samples showed po-
colleagues (Kolokolova et al., 2001a) could not be explained larization curves of shape similar to the cometary ones and
by the changing size of the aggregates (overall size influ- positive polarimetric color. However, the values and angle
ences neither color nor polarization) or the changing size of the minimum polarization almost twice exceeded the ob-
of the constituent particles (color and polarization should served ones, whereas the maximum polarization was almost
then anticorrelate). Change in the porosity could produce half the observed values. Also, the color was blue, i.e., the
a correlation, but then the color should anticorrelate with intensity at 0.442 µm exceeded the intensity at 0.633 µm.
the polarimetric color that has not been observed. More- The study shows that polydisperse heterogeneous irregular
over, the simultaneous increase in color and polarization ob- particles cannot be ruled out as candidates for cometary
served for Comet Hale-Bopp could be provided only by dust, although, at least for size distributions that peak at x =
unrealistic increasing compactness of the aggregate on its 10–20, they are not able to correctly reproduce all the ob-
way out from the nucleus. Microwave measurements for served characteristics.
materials of a variety of refractive indexes show that such Light-scattering experiments under reduced gravity (mi-
a correlation may be a consequence of evaporation/destruc- crogravity) have been proposed to avoid sedimentation of
tion of some dark material contained in the aggregates. Such the studied dust as well as particle sorting or orientation
a slowly evaporating dark material can be an organic com- that can occur for particles dropped or suspended in air-
flow. The microgravity PROGRA2 experiment was concen-
trated on light-scattering measurements of levitated particles
TABLE 1. The strength of correlation (normalized to during parabolic flights (Worms et al., 2000). The angular
the color/radius correlation) between light-scattering dependences of polarization were retrieved for various types
characteristics and properties of the aggregates. of compact particles (Worms et al., 1999) and aggregates
(Hadamcik et al., 2002). This experiment later provided
Radius of Number of polarization images in two wavelengths (Hadamcik et al.,
Constituent Constituent
2003).
Particles Particles Porosity
Hadamcik et al. (2002) performed a systematic micro-
Color 1.00 0.212 –0.923 gravity study of aggregated particles. The majority of the
Polarization –3.23 0.030 –0.262 samples were made of 12–14-nm particles of silica, alumina,
Polarimetric color –2.36 –0.316 1.34 titanium dioxide, or carbon. The particles formed complex
596 Comets II

structures of three-level hierarchy: submicrometer-sized disperse grains with the predominance of submicrometer
chains of particles were combined into several-micrometer- particles or are aggregates of submicrometer particles. The
sized aggregates, and the aggregates in turn formed milli- major constraints on the dust properties came from polari-
meter-sized particles, “agglomerates,” that were levitated metric and thermal infrared data. Angular dependence of
and measured. The most striking result of this study was polarization puts constraints on the size of particles and
that the particles, even though composed of nanometer con- limits the refractive index. The SED of the thermal emis-
stituents, did not show Rayleigh-type scattering properties sion implies a broad size distribution of the dust; the ex-
unlike other aggregates of small particles considered above cess color temperature above a blackbody at λ < 20 µm
(Zerull et al., 1993; Gustafson and Kolokolova, 1999; West, indicates grains of r < 1 µm, while the slow decrease in flux
1991; Kozasa et al., 1993). The microscopic photographs at longer wavelengths indicates larger particles with a size
show that although “agglomerates” are rather porous struc- parameter comparable to the wavelength. Aggregates of
tures, “aggregates” look as if they were made of solid ma- submicrometer grains with a range of porosities would be
terial, demonstrating rather high packing of “chains” in the compatible with thermal SED. Spectral midinfrared features
aggregates. Since the size of constituents in “aggregates” identify silicates as a component of the dust material. The
is of the order of some micrometers, their size can be the composition could be refined using the spectral changes in
factor that determines the light scattering. The polarimet- the scattered light (color and polarimetric color); it is likely
ric curves have a low maximum at α ~ 100° and demon- that they indicate spectral dependence of the average re-
strate positive polarimetric color at large phase angles. At fractive index of the material. A change in the characteris-
small phase angles the samples made of a single type of tics of the scattered and emitted radiation with distance from
constituent demonstrate positive polarization, which may the nucleus is a helpful tool to further determine the size
become negative for mixtures of small and large or dark and distribution and composition of cometary dust as it reflects
light particles that can be evidence of a heterogeneous struc- the dynamic sorting of particles and composition changes,
ture of cometary grains. e.g., sublimation of volatiles. Although observational data
The most recent microgravity study of the wavelength accumulated so far, as well as their interpretation, are not
dependence of polarization (Hadamcik et al., 2003) showed sufficient to provide reliable information about cometary
that a mixture of fluffy aggregates of submicrometer silica dust from the correlations between the light-scattering and
and carbon grains demonstrates a positive polarimetric thermal-emission characteristics (section 2.4), such corre-
color, whereas gray compact particles with size greater than lations can be valuable to further constrain the properties
the wavelength exhibit a negative polarimetric color. This of cometary dust and to compare the dust in different parts
can explain the difference between the polarimetric color of the coma and in different comets.
of comets and asteroids as well as changes in polarimetric
color within cometary comae. 4. CONCLUSIONS AND CONSISTENCY
The COsmic Dust Aggregation (CODAG) experiment WITH THE RESULTS OBTAINED
intends to study dust aggregation during rocket flights (Blum USING OTHER TECHNIQUES
et al., 2000; Levasseur-Regourd et al., 2001). These experi-
ments (1) study the formation and evolution of dust grains Below we discuss the physical properties of cometary
and aggregates under a variety of physical conditions rep- dust obtained using light-scattering techniques, comparing
resentative of the protoplanetary nebula, (2) monitor the them with the results of studying cometary dust using its
dust particles in three colors at α = 5°–175° to study the dynamical properties, in situ measurements, and study of
changes in their light scattering that accompany the aggre- interplanetary dust particles (IDPs).
gation process, and (3) provide validation of the light-scat-
tering codes. Low-temperature studies to reveal the dust 4.1. Shape
light-scattering properties during condensation or sublima-
tion of ices on the grains will hopefully be performed on- The shape of cometary particles is significantly non-
board the International Space Station (Levasseur-Regourd spherical. Evidence of this is the complete absence of reso-
et al., 2001). nant oscillations in intensity, polarization, and color. Such
oscillations are typical for non-Rayleigh spherical particles
3.5. Summary even with a rather wide size distribution. None of the at-
tempts to fit the scope of observations with a model based
Table 2 summarizes the observational data and results on spherical particles has been successful. Additional sup-
of the theoretical and laboratory simulations of light scat- port for this conclusion are observations of star occultations
tering by cometary dust. One can see that the theoretical that show nonzero polarization at α = 180° and the presence
and laboratory simulations of light scattering and thermal of circular polarization and polarization whose plane is in-
emission by cometary dust show that a plausible model of clined to the scattering plane. Such observations require that
cometary dust can be heterogeneous (silicates and some the symmetry inherent in spherical particles be broken. Sim-
absorbing material) particles that are either irregular, poly- ulated mid-infrared spectral features demonstrate noticeable
 Kolokolova et al.: Physical Properties of Cometary Dust 597

TABLE 2. Observational facts and their interpretations.

Cometary Dust Model that can Reproduce the Observational

Observational Fact and Section Where It is Discussed Fact and Section Where It is Discussed
Brightness characteristics:
1. Low geometric albedo of the particles (2.1.1) 1. Absorbing particles (κ > 0.02) (3.4.1). Decrease in the particle
size increases albedo for slightly absorbing particles.

2. Prominent forward-scattering and gentle backscattering 2. Aggregates of particles of x = 1–5 (3.3.2, 3.3.3, 3.4.1), silicate
peaks in the angular dependence of intensity, “flat” polydisperse (power law) elongated particles (e.g., spheroids)
behavior at medium phase angles (α) (2.1.2) with a distribution of the aspect ratios (3.3.2), silicate polydis-
perse (power law) irregular particles (3.3.3).

Polarization characteristics:
1. For a broad range of wavelengths angular dependence 1. Polydisperse (power law) irregular submicrometer particles
of linear polarization (2.2.1) demonstrates (3.3.2, 3.3.3; 3.4.2); aggregates of particles of x = 1–5 (3.3.2,
• negative branch of polarization for α < 20° with the 3.3.3, 3.4.2). The best fit is provided by aggregates of large
minimum P ≈ –2% number of constituent particles (3.3.3) or polydisperse aggregates
• bell-shaped positive branch with low maximum of (3.3.2). Absorption seems to reduce the negative polarization but
value P ≈ 10–30% at α ≈ 90°–100°. increases the maximum polarization (3.3.2, 3.3.3).

2. Small circular polarization V < 2% (2.2.4). 2. Nonspherical particles or particles containing optically anisotro-
pic materials.

Spectral optical characteristics:

1. Usually red or neutral color for a broad range of 1. Slightly absorbing particles of x > 6 (3.3.2); absorbing particles
wavelength λ (2.1.3). of x >1 (3.4.1); particles, containing material with a spectrally
dependent refractive index (3.3.3).

2. Polarization at a given α above ≈30° usually increases 2. Aggregates of particles of x = 1–5 (3.3.2, 3.3.3, 3.4.1, 3.4.2) or
with λ (positive polarimetric color) (2.2.2). polydisperse nonspherical particles of x > 1 (but not x >> 1)
(3.4.2) for a broad range of refractive indexes independent of
wavelength; particles made of materials with spectrally depen-
dent refractive index.

Spatial distribution of optical characteristics within the coma:

1. Increase in albedo with the distance from the nucleus 1. Change in the particle composition (evaporation of some dark
(2.1.1). material) (3.4.1) or decreasing size of silicate particles

2. Variations in the value of color and polarization 2. Variations in size distribution of cometary dust or in their
(2.1.1, 2.2.3) composition (if the changes in color and polarization correlate)
(3.1, 3.4.1)

3. Deviations in the polarization plane throughout the 3. Nonspherical particles or particles containing optically anisotro-
coma (2.2.4) pic materials

Thermal infrared characteristics (2.3):

1. 3- to 20-µm color temperature higher than the blackbody 1. Absorbing grains of r < 1 µm (3.1.1); porous aggregates of
temperature. submicrometer absorbing grains (3.3.2).

2. Midinfrared emission features typical of silicates in 2. Silicate grains of size r < 1 µm or porous aggregates of
some comets. submicrometer silicate grains (Hanner and Bradley, 2004).

3. Thermal emission does not decrease more steeply than 3. Evidence of a broad size distribution that includes larger than
a blackbody at λ > 20 µm micrometer-sized particles.
598 Comets II

the Giotto spacecraft during the flyby of Comet P/Halley

(McDonnell et al., 1991). If the measured Giotto mass dis-
tribution is typical of comets, then most of the particulate
mass shed from the nucleus is concentrated in large par-
ticles, whereas the cross section is broadly distributed or
concentrated in the small particles (Fig. 9), thus making
submicrometer- and micrometer-sized particles dominant in
the visual and thermal infrared. This most likely is true for
all comets, although the detailed size distribution may vary
from comet to comet as well as within a coma. For example,
size distribution is different for jets and regular coma with
predominance of smaller particles in the jets. The size dis-
tribution varies with the distance from the nucleus as a re-
sult of both dynamical sorting of particles by radiation pres-
sure and sublimation of volatiles.

4.3. Composition

Cometary dust consists of heterogeneous particles that

include a dark material, which determines the low albedo,
as well as silicates responsible for the spectral features in
the mid-infrared. A distributed source of CO near the comet
Fig. 9. Relative cross section (\\\), mass (/// ), and thermal nucleus, trends in color, polarization, and albedo support
emission (– – –) vs. particle radius for the size distribution meas- the notion of a slowly sublimating organic material (Green-
ured by Giotto, as adapted to fit the SED of Comet 81P/Wild 2 berg and Li, 1998; Kolokolova et al., 2001a). Thus, not only
(Hanner and Hayward, 2003). For power-law size distributions with the size distribution but also the composition of cometary
a ≥ 3, submicrometer particles dominate in the light scattering. grains changes as they move out from the nucleus. A sig-
nificant specific of the cometary dust is its red color, which
does not vary with the phase angle. This cannot be easily
dependence of the feature’s position and shape on the shape simulated even for polydisperse nonspherical particles. It
of dust particles, and thus mid-infrared spectral data can may be the result not of a specific size or structure of parti-
be used to further constrain the particle shape. cles but of a spectral change in the refractive index. Compo-
sitional analysis of dust particles during the Halley flybys as
4.2. Size Distribution well as analysis of IDPs and infrared spectra indicate that
the dust grains are composed largely of silicates and carbo-
As was shown in Table 2, observations in the visible naceous (CHON) material (Hanner and Bradley, 2004)
and their interpretation based on light-scattering methods mixed together on a very fine scale. The composition of
equally support two models of cometary dust: (1) rather the cometary organics may be inferred from its sublimation
large or polydisperse aggregates of submicrometer particles, constants gauged by studying the trends in colors, polariza-
and (2) irregular particles with a power-law size distribution tion, and thermal-emission characteristics with the cometo-
dominated by submicrometer particles. The study of the centric distance.
dust thermal emission allows us to constrain characteristics
of the size distribution. This can be done by fitting the ob- 4.4. Structure
served spectral energy distribution (SED) with a calculated
one using energy balance equation (2). The increase in color As mentioned above, polydisperse irregular particles can
temperature indicates the contribution of submicrometer reproduce most of the light-scattering properties of comet-
grains, while the slow decrease in flux at longer wave- ary dust. The same can be achieved with a model of ag-
lengths indicates larger particles. Grün et al. (2001) fit the gregated particles. Porous aggregates of submicrometer
broad thermal flux from 7 to 160 µm from Comet Hale- particles are better candidates to explain the data on ther-
Bopp with the size distribution of form n(r) ~ r –a with a ≤ mal emission. An aggregated structure of cometary particles
3.5. Observations in the submillimeter spectral range indi- is also supported by other studies. Thus, evolutionary ideas
cate the presence of millimeter-sized particles. Results for about growing cometesimals in protoplanetary disks sup-
other studies confirm that the dust emitted from comets port the idea of an aggregated nature of cometary refracto-
spans a broad size range, from submicrometer to millime- ries (see, e.g., Greenberg, 1982). The most developed model
ter or centimeter and larger. This is known from analysis by Greenberg and Li (1999) describes cometary grains as
of the trajectories of dust particles in comet tails (Sekanina, fluffy (porous) aggregates of particles that are 0.1-µm sili-
1996) and measurements of the mass of particles impacting cate cores coated by an organic refractory mantle and outer
 Kolokolova et al.: Physical Properties of Cometary Dust 599

mantle of predominantly water ice, which contains embed- ization and the polarization plane are necessary, not only
ded carbonaceous and polycyclic aromatic hydrocarbon to study any alignment of the dust particles within the coma,
(PAH)-type particles with sizes in the 1–10-nm range. When but also to obtain information about the shape of the par-
limited by relative cosmic abundances, the water is con- ticles and possible optical anisotropy and optical activity
strained to be close to 30% by mass and the refractory to of the cometary dust material.
volatile ratio is close to 1 : 1. Theoretical and laboratory surveys are necessary to chart
Captured IDPs of probable cometary origin can give us the differences in observable characteristics for aggregates
insight into the morphology of cometary dust. These IDPs and irregular polydisperse particles. The surveys should be
consist primarily of submicrometer-sized compact, nonspheri- directed to simulate not individual observational facts but
cal grains and angular micrometer-sized crystals clumped the whole scope of the observational data, i.e., angular and
into aggregates having a range in porosity. spectral characteristics of both scattered and emitted radia-
tion. Contribution from submicrometer- and micrometer-
4.5. Future Work sized particles is required by the realistic size distributions,
and thus light scattering by aggregates of hundreds and
Further progress in remotely determining physical prop- thousands of constituent particles or large (but with size still
erties of dust from their light-scattering and emission re- below geometric-optics validity) irregular particles should
quires new observations and new theoretical and laboratory be simulated. The influence of the structure of the aggre-
simulations. gates, the morphology and shape of the constituent parti-
The most useful observations are likely to be multiwave- cles, as well as the morphology and specific shapes of irreg-
length monitoring of comets within a broad range of he- ular large particles should be studied. Such studies most
liocentric distances and phase angles. The observations can likely require development of new theoretical techniques or
provide new insight into the classification of comets accord- systematic use of controlled laboratory measurements. More
ing to their maximum polarization; heliocentric tendencies comprehensive modeling of cometary dust composition is
in colors (including near-infrared); correlated or anti-cor- necessary: The refractive indexes used in calculations
related change in such characteristics as color, polarization, should satisfy the confirmed presence of both silicates and
and albedo; and thermal emission characteristics (tempera- absorbing constituents in the dust and must be consistent
ture, shape, and strength of a silicate feature) with heliocen- with the Kramers-Kronig relations (Bohren and Huffman,
tric distance and within the coma. The correlation between 1983, section 2.3.2) across all wavelengths. More realistic
light-scattering and emission properties, e.g., between the mixtures of silicates and carbonaceous materials or core-
value of maximum polarization and the strength of the sili- mantle particles should be a point of special interest. The
cate feature, might be indicative of the diversity of dust average, effective refractive index can be considered when
from one comet to another. In the framework of light-scat- the silicate and dark materials are mixed on a very small
tering and emission methods, more information about the scale compared to the wavelength, e.g., when an admixtures
comet dust size distribution might be obtained from detailed of FeNi or FeS typical for IDPs (Hanner and Bradley, 2004)
studies of forward-scattering characteristics of the scattered in submicrometer silicate grains are simulated. The need for
light (as with, e.g., the Sun-grazing comets detected by studies of spectral characteristics of the light scattered by
SOHO), heliocentric dependence of the dust temperature, particles whose material has a realistic wavelength-depen-
and measurements of the SED at far-infrared and submilli- dent refractive index is apparent. This also refers to labora-
meter wavelengths (or shorter wavelengths at larger helio- tory light-scattering simulations that should address spec-
centric distances). Spectrophotometric and spectropolari- tral dependencies, and we therefore need to concentrate on
metric data of improved spectral resolution will be impor- particles with realistic and controlled refractive indexes
tant to better eliminate the influence of gas contamination across the studied spectral range. Simulations should also
as well as to get more precise values of spectral gradients provide an explanation of stability or diversity of the ob-
of intensity and polarization and their change with wave- servational characteristics, as well as correlations between
length. Good-quality images of comets or high-spatial-reso- them, and should be consistent with the data obtained from
lution scans along the coma are necessary to see the divers- other studies of cometary dust, e.g., dynamical, evolutional,
ity of cometary dust within the coma (e.g., in jets, shells, and cosmic abundance studies, studies of IDPs, and in situ
etc.) and the dust changes with the distance from the nu- measurements.
cleus. The latter can result from both dynamic sorting of
particles by radiation pressure (i.e., can be used to refine
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 Ip: Global Solar Wind Interaction and Ionospheric Dynamics 605

Global Solar Wind Interaction and Ionospheric Dynamics

Wing-Huen Ip
National Central University, Taiwan

The spacecraft missions to Comets 21P/Giacobini-Zinner and 1P/Halley in the mid-1980s

revolutionized our knowledge of comets and their interaction with the solar wind. Besides the
large-scale plasma structures, the spacecraft in situ measurements produced many exciting and
surprising results about the ion distribution and magnetic field configuration in the inner regions
of cometary comae. These earlier scientific explorations laid the foundation for the Deep Space 1
mission to Comet 19P/Borrelly and groundbased observations of recent bright comets such as
Comets 1996 B2 (Hyakutake) and 1995 O1 (Hale-Bopp). In this chapter, we review the mor-
phological structures of cometary ion tails, analytical and numerical simulations of comet-solar
wind interactions, plasma boundaries and the ionospheric contact surface identified by spacecraft
measurements, and plasma instabilities and waves.

1. INTRODUCTION hypothesis that the interplanetary space is actually infiltrated

with a magnetic field of solar origin (Alfvén, 1957). When
Since the first in situ measurements of the solar wind in- a comet moves through the interplanetary medium, its iono-
teraction and plasma environment of Comet 21P/Giacobini- sphere will sweep up the interplanetary magnetic field lines
Zinner by NASA’s International Cometary Explorer (ICE) in the manner illustrated in Fig. 3. With the draping of the
spacecraft in 1985, comets have been recognized as a per- interplanetary magnetic field (IMF) into a magnetic tail, the
fect laboratory to study plasma physics from microscopic to cometary ions will be channelled along the radial direction,
macroscopic scales. The subsequent encounters with Comet hence facilitating efficient momentum transfer between the
1P/Halley by a flotilla of space probes in 1986 added a tre- solar wind plasma and the cometary ions.
mendous amount of information about the plasma structures Thus, well before the space age, which dawned at the
and processes involved in the production and transport of launch of the Sputnik satellite in 1958, the study of comet-
cometary ions. Data analyses and theoretical models of ary ion tails already told us about the existence of the solar
these in situ observations enriched our understanding of wind as a continuous stream of charged particles and the
natural plasma physics (as opposed to laboratory plasma omnipresence of magnetic fields in interplanetary space. As
physics, such as thermal fusion control) to an unprecedented described later, modern observations of ion tails have con-
level. This point may be appreciated by noting the dramatic tinued to reveal important things about the three-dimen-
surge in recent years of the number of publications in space sional structures of the solar wind and the heliosphere, which
physics dealing with cometary plasmas. Despite these recent are not easily accessible to space probes.
advances, we must not forget the major contributions made
to modern plasma physics by several key figures about a
half century ago. In a historical context, the study of the
comet-solar wind interaction began with Ludwig Biermann’s
(Fig. 1) statistical study of the pointing direction of com-
etary ion tails (Biermann, 1951). From the determination of
an average aberration angle of about 3°, Biermann made the
famous deduction that a solar corpuscular radiation (i.e., a
continuous flux of charged particles) must exist in the inter-
planetary space in order to sweep away the cometary ions.
The radial velocity of these solar charged particles, namely,
the solar wind, was derived to be on the order of a few hun-
dred km s–1. However, an impossibly large electron num-
ber density of the solar corona would have to be invoked,
if the momentum transfer is to be facilitated by collisional
Coulomb interaction between the solar corpuscular radia-
tion and the cometary ions alone. To overcome this major Fig. 1. Photo of Ludwig Biermann (with glasses) and Reimer
discrepancy, Hannes Alfvén (Fig. 2) suggested the ingenious Lüst. Courtesy of P. Biermann.

605
606 Comets II

(Susei, Vega 1 and 2, and Giotto), 26P/Grigg-Skjellerup

(Giotto), and, most recently, 19P/Borrelly (Deep Space 1).
Last but not least, we survey the different kinds of plasma
waves and plasma instabilities generated in the comet-so-
lar wind interaction process in section 5.
We note that there are already a number of reviews de-
voted to the subject of cometary plasmas, e.g., Huebner
(1990) and Johnstone (1991). In addition, the two volumes
entitled Comets in the Post-Halley Era (Newburn et al.,
1991), have a large number of review chapters on cometary
plasmas. Cravens and Gombosi (2003) provide a contem-
porary review of the subject. Materials covered in these
works are used extensively here.

2. MORPHOLOGICAL STRUCTURES

Fig. 2. Hannes Alfvén (right) and Asoka Mendis discussing 2.1. Composition/Spectra
comet-solar wind interactions at the University of California at
San Diego, ca. 1970. Courtesy of A. Mendis. Bright comets usually display strong ion emission in the
anti-Sun direction, which is dominated by CO+ in the 3800–
4800-Å region and H2O+ in the 5600–7000-Å region (see
The organization of this chapter is as follows. The global comprehensive review by Wyckoff, 1982). The CO+ emission
morphology of cometary ion tails, which is the most con- has also been observed in Comets Morehouse (1908 R1) and
spicuous manifestation of cometary plasma from ground- Humason (1961 R1) at large distances from the Sun (Lüst,
based observations, is described in section 2. This is fol- 1962; Wurm, 1968). The H2O+ ion itself was first identified
lowed in section 3 by a summary of the analytical models much later in C/Kohoutek (1973 E1) (Wehinger et al., 1974).
and numerical simulations of large-scale solar wind inter- An example of a recent cometary spectral image is shown in
actions with comets. Related physical processes, such as Fig. 4.
photoionization, electron impact ionization, and charge ex- The optical emissions from neutral gas molecules (e.g.,
change effects, are also described. In that section, the new CN and C2) are nearly symmetrical about the comet’s nu-
results of strong X-ray emission in cometary comae will be cleus, while the spatial distribution of the ions (e.g., CO+
highlighted (see also Lisse et al., 2004). In the second half and CO+2 ) are elongated in the antisolar direction. The ion
of this chapter, we focus on the knowledge gained from tail structure becomes more and more diffuse at larger and
spacecraft observations. In section 4, we describe the ma- larger distances from the nucleus until its presence cannot
jor findings of cometary plasma structures by the various be traced by optical emission. In one case, namely that of
space probes to 21P/Giacobini-Zinner (ICE), 1P/Halley the great comet of 1843 (C/1843 D1), the ion tail was traced
to a distance of 2 AU (Ip and Axford, 1982). This record has
recently been broken by magnetometer observations on the
Ulysses spacecraft, which found that the ion tail of Comet
Hyakutake (C/1996 B2) extended to a radial distance of
more than 3.8 AU (5.5 × 108 km) from the comet center and
the corresponding ion tail diameter is as large as 7 × 10 6 km
(Jones et al., 2000).

2.2. Envelope and Ion-Ray Folding

Owing to the weak emissions from the cometary neutrals

and dust, the plasma structures traced by the CO+ ions in
the comae and ion tails of C/Morehouse (1908 R1) and C/
Humason (1961 R1) could be easily identified. It was found
that ion structures in the form of “receding envelopes” could
be followed after their formation to a projected distance of
1–1.5 × 105 km on the sunward side of the optical center
(Lüst, 1962; Wurm, 1968). Upon reaching a distance of about
5 × 104 km, the ion envelopes intermix with the general
Fig. 3. Alfvén’s magnetic field draping model, describing dif- background and become indistinguishable in the photo-
ferent stages of the formation of the ion tail. graphic plates. A modern view of this intriguing phenom-
 Ip: Global Solar Wind Interaction and Ionospheric Dynamics 607

Fig. 4. The top panel is an optical spectrum of Comet 153P/Ikeya-Zhang centered on the nucleus. The bright horizontal streak is the
cometary continuum. The more diffuse emissions are from neutral and ionized gas molecules in the coma. The bottom panel was
taken during the same observations, but the spectrograph slit was offset tailward from the nucleus. The ionic emissions become stron-
ger relative to the neutral emissions in the tailward spectrum. The stronger neutral and ionic emissions in the spectra are labeled. The
feature labeled “N+2” is almost certainly terrestrial airglow, rather than cometary emission. Data courtesy of A. Cochran.

enon is illustrated in Fig. 5, in which a system of plasma are formed by the continuous inflow of new plasma in time
envelopes in CO+ emission in the coma of C/Hale-Bopp is sequence.
clearly shown. The elongation of the end points of the enve- The exact cause of the ion-ray formation is still a matter
lopes probably leads to the formation of symmetric pairs of debate. In fact, whether projection effect might play a
of narrow ion rays folding toward the central axis. A good role is still to be clarified (Jockers, 1991). That is, if the ion
example showing the ion ray system in the plasma tail of structures in cometary plasma tails are organized by the
C/Kobayashi-Berger-Milon (1975 N1) can be found in direction and configuration of the interplanetary magnetic
Fig. 6. In other cases, the ion tails were comprised of a field, it is to be expected that different morphologies might
bundle of narrow ion rays, suggesting that the main ion tails result, depending on whether the line-of-sight is nearly
perpendicular to the IMF direction, or instead is parallel to
it. This point also brings us back to the original idea pro-
posed by Ness and Donn (1966), in which the ion rays are
plasma sheets sandwiched between two regions of oppo-
site magnetic polarities. According to this view, the ion rays
would therefore most likely form when a comet crosses a
sector boundary of the IMF [see Niedner and Brandt (1978)
and discussion below]. A number of numerical simulations
have been performed to investigate whether a 90° or 180°
turn of IMF could result in dense plasma structures (Schmidt
and Wegmann, 1982; Schmidt-Voigt, 1989). The advantage
of a 90° turn in IMF is that such events are far more fre-
quent than the sector crossing, which requires a 180° turn.
An alternative explanation, somewhat different from the
traditional magnetohydrodynamical (MHD) view, is that the
ion rays are of thermodynamical origin intrinsic to the com-
Fig. 5. The system of receding envelopes in CO+ emission ob- etary ionospheres. The main idea is that the ion content in
served in the coma of Comet Hale-Bopp (C/1995 O1). Courtesy of the cometary ionospheres, and hence the ion tails, is par-
S. Larson. tially controlled by the solar wind electron heat flux. Note
608 Comets II

Fig. 7. A schematic view of the formation of cometary ion rays

by means of modulation of the size of the ionospheric photochemi-
cal regime with electron temperature Te > 300 K. (a) The radius
of the electron temperature transition region re is greater than the
apex ro of the magnetic flux tube; (b) re < ro, and the magnetic
flux tube is filled with outflowing ionospheric plasma leading to
the formation of narrow ion rays. From Ip (1994).

electron heat flux (Fe) in the solar wind. From model cal-
culations it can be shown that a change in the solar wind
Fig. 6. The time sequence of the pairs of symmetric narrow ion
electron heat flux could lead to the expansion or contrac-
rays folding on to the central axis of Comet Kobayashi-Berger-
tion of the photochemical equilibrium region of the comet-
Milon (C/1975 N1). Time tags from left to right: 03:37, 05:06,
and 06:12. Images taken at the Joint Observatory for Cometary ary ionosphere of low electron temperature (Te ~ 300 K) by
Research. Courtesy of K. Jockers. a factor of 3 or more in size. Figure 7 shows that, if the
thermal condition of the draped magnetic flux tube is such
that the inner coma of cold electron temperature has a large
that the original models of Ness and Donn (1966), and the size, many of the cometary ions would be lost to electron
subsequent extensions by later authors (see Schmidt and dissociative recombination without being injected into the
Wegmann, 1982), invoke the time variation of the orienta- ion tail. On the other hand, if the inner coma is filled with
tion of IMF as the source mechanism. In other words, the warm electrons with Te ~ 2 × 104 K, the majority of the
formation of the tail rays would necessarily be initiated at the cometary ions would be flushed into the tailward side.
outer coma where the IMF irregularities are being mapped From solar wind measurements (Feldman et al., 1975), it
onto the cometary ionosphere. Yet another possibility is that is known that the electron heat flux has an average value of
the ion rays are of internal origin. That is, the generation of about 10 –3 ergs cm–2 s–1 in the slow solar wind and an aver-
the ion rays is controlled by the time variations of the ion age value of 10–2 ergs cm–2 s–1 in the high-speed wind. Also,
production rate of the inner coma. The production of com- Fe could vary by 30% from minute to minute. This makes
etary ions and the subsequent channeling of the cometary the solar wind variability a possible production mechanism
ions into the ion tail are determined by a balance between for the ion rays and emphasizes that the transition region
photoionization and electron dissociative recombination between the cold inner ionosphere and the warm outer iono-
loss. As discussed in Cravens and Korosmezey (1986) and sphere might actually become a key source region. We will
Ip (1994), the electron temperature profile along a magnetic return to this issue in section 4 when discussing the iono-
flux tube threading through the inner coma is related to the spheric pileup region.
 Ip: Global Solar Wind Interaction and Ionospheric Dynamics 609

Fig. 8. An ion tail disconnection event (DE) observed in Comet Hale-Bopp (C/1995 O1) on March 25, 1996. Images taken at the
National Astronomical Observatory by H. Fukushima and D. Kinoshita. From Kinoshita et al. (1996).

2.3. Ion Tail Disturbances and Disconnection Events plasma clouds would be peeled off from the coma, leading
to the formation of folding ion rays.
While Alfvén’s magnetic field line draping model has
formed the basis of our understanding of cometary ion tail
dynamics, its physical ingredients have also been applied
to the interpretation of the occurrence of fine plasma struc-
tures such as ion rays (cf. Schmidt and Wegmann, 1982),
as well as some large-scale disturbances (Wegmann, 1995,
2002). The most dramatic change to cometary ion tail
morphology must belong to the so-called ion tail disconnec-
tion events (DEs). As shown in Fig. 8, a large ion cloud is
observed to detach itself from the comet head and move
gradually away. In some other cases, the whole ion tail could
be cut away from the comet head. How does this happen?
Niedner and Brandt (1978) were the first to provide a
physical model for such DEs. The basic idea is that when
a cometary ionosphere encounters a sector boundary of the
IMF, where two regions of opposite magnetic field polari- Fig. 9. The Neidner-Brandt model of (a) reconnection on the
ties are separated by a thin layer of the heliospheric current frontside cometary ionosphere as the comet intercepts a reversal of
sheet (HCS), reconnection of the opposite-pointing mag- magnetic field polarity associated with a heliospheric current sheet.
netic field lines might take place on the front side facing (b) Reconnection on the tailward side, which might also occur.
the Sun (Fig. 9a). As a consequence, symmetrical pairs of From Ip (1985).
610 Comets II

Correlations of the DEs with the crossings of comets and posed that the charge transfer process, as described in equa-
heliocentric current sheets have always been difficult. This tions (2) and (3), could provide “new” heavy ions in ex-
is because, except for the special situation when a space- cited states, and that subsequent radiative transitions to
craft was in the vicinity of a comet (such as during the space lower energy states lead to the emission of soft X-ray pho-
missions to Comet Halley), large uncertainties exist in the tons or extreme ultraviolet photons. The X-ray brightness
interplanetary conditions. For this reason, the reconnection distribution can consequently be considered as a map of the
model advocated by Niedner and Brandt (1978) has always penetration of the solar wind ions into the cometary coma.
been subjected to spirited debates (Saito et al., 1987; Yi et The symmetrical pattern of crescent shape with the central
al., 1993, 1994; Wegmann, 1995). Brandt et al. (1999) car- axis pointing along the radial direction is a consequence of
ried out a very detailed study of 19 major DEs of Halley’s the collisional absorption effect of the solar wind (Fig. 10).
comet in 1985–1996. What is special about this investiga- That the X-ray emissivity could vary on short timescales is
tion is that a potential model of the coronal magnetic field also consistent with the time variability of the solar wind
based on photospheric magnetic field observations (see flux (Kharchenko and Dalgarno, 2001). Finally, X-ray
Hoeksema, 1989) is used to reconstruct the large-scale struc- spectroscopic observations of C/1999 S4 (LINEAR) by the
ture of the heliospheric current sheet at different positions Chandra telescope have shown quite conclusively that the
of the heliosphere. It is then possible to map the magnetic emission lines at 320, 400, 490, 560, 600, and 670 eV origi-
field current sheet to different regions of the heliosphere. nated from the electron capture and radiative deexcitation
These authors reach the statistical conclusion that DEs occur by the solar wind minor ions C5+, C6+, C7+, N7+, O7+, and
at IMF sector boundaries (Niedner and Brandt, 1978; Yi et O8+ (Lisse et al., 2001). The reader is referred to Lisse et al.
al., 1994). (2004) and Cravens (2002), and the references therein, for
We note that Russell et al. (1986) and Ip and Axford further detail.
(1990) proposed a variant of this reconnection model by in- Another important effect of the solar wind charge trans-
voking a magnetic field merging process — but on the tail- fer and charge exchange process has to do with the produc-
ward side — triggered by plasma instabilities (see Fig. 9b). tion of new cometary ions such as O+, OH+, and H2O+ up-
Furthermore, the possibility of triggering an ion cloud dis- stream of the comet. Photoionization could also contribute
ruption by a sort of flute instability due to the interaction significantly to the production of new ions. The addition
of the cometary ionosphere with a high-speed solar wind of new mass in the solar wind flow is a central issue stud-
stream has also been proposed (Ip and Mendis, 1978). Fi- ied long before in the pioneering work by Biermann et al.
nally, Wegmann (1995, 2002) shows that a variety of solar (1967) and by Wallis (1971), who proposed that the comet
wind variations, including strong interplanetary shocks and bow shock could be weak with a Mach number of M ~ 2
coronal mass ejection events, can produce large density dis- or even nonexistent. The physical argument was that be-
turbances in the ion tails. cause of the solar wind interaction, the upstream solar wind

3. THEORETICAL MODELS:
MAGNETOHYDRODYNAMIC AND
KINETIC SIMULATIONS

3.1. Analytical Theory

The expanding atmosphere of a comet is subject to the

ionizing effect of solar radiation

H2O + hν → H2O+ + e (1)

and of the charge transfer process with the solar wind

H2O + H+ → H2O+ + H (2)

H2O + O6+ → H2O+ + O5+ (3)

Recent observations by space X-ray telescopes like ROSAT

and Chandra have revealed vivid images of the latter pro-
cess, beginning first with the serendipitous discovery of
strong X-ray emission in C/Hyakutake (1996 B2) (Lisse et Fig. 10. An X-ray image of Comet Hyakutake (C/1996 B2)
al., 1996). Subsequently, many more comets were found to taken with the ROSAT Wide Field Camera. The length of the im-
display X-ray emission (Dennerl et al., 1997). The gener- age is about 6.5 × 105 km. Courtesy Max-Planck-Institut für Extra-
ally accepted theory is due to Cravens (1997), who pro- terrestriche Physik.
 Ip: Global Solar Wind Interaction and Ionospheric Dynamics 611

plasma would be heated and slowed down by the continu- where

ous mass loading by the cometary ions. The early work on
solar wind-comet interaction therefore focused on the kind
of effect that mass accretion would have on the global flow
∫
ρiνi = ~
qdX (10)

dynamics of the cometary plasma. The behavior of the two- Thus in the fluid approximation, a shock must form in the
component fluid (solar wind protons and cometary ions of cometary accretion flow before the condition
the water-group molecules, CO, and CO2) along the comet-
Sun axis can be described by the one-dimensional equations ρiνi ≥ [γ 2/γ 2 − 1]ρi∞νi∞ (11)
(Wallis and Ong, 1975)
is met (Biermann et al., 1967; Wallis, 1971). Therefore, the
general consensus in the early analytical investigations
d(ρiνi) ~
≈q (4) pointed to the formation of a weak shock with a Mach num-
dX ber (M) ~ 2 (Wallis, 1973; Brosowski and Wegmann, 1972;
Schmidt and Wegmann, 1982). Subsequent studies em-
ploying full magnetohydrodynamic (MHD) computational
d B2
ρiν2i + p⊥ + =0 (5) techniques have fully verified this basic point (Schmidt and
dX 2µ0 Wegmann, 1982; Ogino et al., 1988). It is now common
knowledge that the spacecraft observations at 1P/Halley
found very clear signatures for the bow shock formation with
d m ν2
[ρiνif(νi,µ)] = ~
qδ µ − i i (6) M ~ 2 (Gringauz et al., 1986; Mukai et al., 1986; Johnstone
dX 2B et al., 1986). The ICE measurements at 21P/Giacobini-Zinner
are not as definite, however (Bame et al., 1986). This might
and be a consequence of the finite gyroradius effect of the heavy
cometary ions, as described below.
~ Qmi
q= (7) The analytical solutions for the combined fluid, i.e., solar
4πνnτiX2 wind plasma plus comet ions, with M = 2 and B = 0, are
illustrated in Fig. 11. Several important features can be rec-
Here νi is the mass-loaded solar wind plasma flow speed, ognized: Most notable is the rapid increase of the thermal
ρi the mass density of the ions of mass mi (the cometary pressure, p, at the bow shock; the thermal pressure has in-
ions are assumed to co-move with the solar wind plasma
and ρi∞ and νi∞ are values at infinity), p⊥ the thermal pres-
sure perpendicular to the magnetic field B, Q the comet gas
production rate, vn the expansion speed of the neutral coma
gas, τi the ionization timescale, µ the magnetic moment of
the cometary ions at creation, and f(νi, µ) the distribution
function of µ at flow speed νi. It is further assumed that
the magnetic moment is invariant and the magnetic field is
perpendicular to the flow direction. Finally, the strength of
the magnetic field may be estimated by using the relation-
ship between the magnetic field and the flow velocity that
holds for the conserved component of the subsonic flow for
the case of axially symmetric flow along the central axis
(Schmidt and Wegmann, 1982): B2νi/nsw = constant.
In the supersonic flow, the effect of the magnetic field
is small. Hence with B = 0 and γ the ratio of specific heats,
the above equations yield

γ+1 γ ρ ν3
ν2i ρiνi − ρi∞νi∞ν2i + i∞ i∞ = 0 (8)
2(γ − 1) γ−1 2

with solutions
Fig. 11. Radial variations of (a) the number density, (b) the axial
γ ρi∞νi∞ (γ 2 − 1)ρiνi flow velocity, and (c) the thermal pressure, from a one-dimensional
νi± = νi∞ 1± 1− (9) analytical model of the cometary mass-loading flow. Values are
γ+1 ρiνi γ 2ρi∞νi∞ scaled to Comets 21P/Giacobini-Zinner and 1P/Halley at a helio-
centric distance of 1 AU.
612 Comets II

Fig. 12. A sketch of the general characteristics of the comet-solar wind interaction. (a) The general plasma environment of a com-
etary coma in which high levels of magnetic field and plasma turbulences are generated by the ionization of the new cometary ions.
(b) The variation of the solar wind velocity as a function of axial distance from the nucleus. (c) A sketch of the gradual increase of the
magnetic field strength and the formation of a magnetic field-free cavity in the inner coma where the magnetic field drops to zero.
From Ip and Axford (1986).

creased about 30 times while the flow speed has decreased

by only about 25%. At the bow shock crossing, there is a
further stepwise increase of the thermal pressure and thus,
in the subsonic region, the plasma is essentially incompress-
ible. Also of note is the fact that the flow speed continues to
decrease rapidly up to a point where the plasma flow be-
comes stagnant.
Galeev et al. (1985) discussed how the additional effect
of the magnetic field pressure gradient could accelerate the
mass-loaded solar wind toward the comet center. The above
analytical work suggests that the global comet-solar wind
interaction, as sketched in Fig. 12, can be broadly divided
into two regimes: (1) the strong momentum coupling regime
in the outer coma, where cometary ions are assimilated into
the solar wind flow as a result of pickup and wave-particle
interaction; and (2) the J × B acceleration region, where the
Lorentz force is effective in accelerating cometary plasma
in the antisunward direction until being balanced by the ion-
neutral frictional force.

3.2. Magnetohydrodynamic Simulations

Useful as they are, the analytical treatments have now

been overtaken by numerical calculations, which can deal
with much more complex situations such as three-dimen-
sionality, nonstationary solar wind interaction, and magnetic
field effects. The rapid progress can be seen by comparing
the work by Schmidt et al. (1988), not long after the space-
craft encounters of Comet Halley, and the work by Gombosi
Fig. 13. Numerical simulations of the bow shock structure (the
et al. (1997), immediately after the perihelion passage of
color contour maps extend to 106 km on each side of the comet nu-
C/Hale-Bopp. Some of the most advanced computational cleus): (a) ion temperature (K); (b) velocity (km s–1) with stream-
techniques have now been applied to this field, thus per- lines; (c) magnitude of the magnetic field (nT) with field lines
mitting the study of the behaviors of cometary plasma flow separated by time intervals of 600 s; (d) electron temperature (K);
at different scale lengths. Let us first examine the global (e) electron number density (cm–3); and (f) mean molecular weight of
features by following the numerical results of Wegmann et the ions, including solar wind protons. Courtesy of R. Wegmann.
 Ip: Global Solar Wind Interaction and Ionospheric Dynamics 613

al. (1987). In Figs. 13a,b, the color-coded diagrams illus- 3.3. Kinetic Simulations
trate the sharp transitions in temperature and flow velocity
at an upstream distance of about 4 × 105 km. This indicates Within the framework of hydrodynamic approximation,
the location of the weak cometary shock. The bow shock the dimension of the bow shock is proportional to the com-
follows a parabolic shape and the solar wind flow moves etary gas production rate (Q). That is, if the upstream shock
in a straight line upstream of the bow shock. position (rshock) of a comet with Q ~ 6 × 1029 molecules/s
Inside the bow shock, the plasma flow can be seen to is 8 × 105 km, we have rshock ~ 8 × 105 × (Q/6 × 1029) km
be deflected around the comet. For uinf = 500 km/s, u for the same solar wind condition (Fig. 11). Such a linear
reaches below 50 km/s along the central axis on the tailward approximation has limitations, however. First, the cometary
side. As will be discussed later, the plasma flow could be- plasma flow is composed of solar wind protons, solar wind
come stagnant in the inner coma. Figure 13c shows how the minor ions, and heavy cometary ions, so it is actually a
interplanetary magnetic field interacts with the comet. The multispecies fluid. The new cometary ions, such as H2O+
field draping effect (Alfvén, 1957) is clearly present. The and O+, have very different velocity distributions from the
folding of the magnetic field in the central region, where solar wind flow (see section 5). The most important effect
the plasma is densest and the electron and ion temperatures for the case in point has to do with the finite gyroradii of
are coldest, lead to a hair-pin shape of the magnetic field the new cometary ions. For an interplanetary magnetic field
configuration. of 5 nT, the O+ ions with a gyrovelocity of 400 km/s will
Because of the pileup of the magnetic field, the mag- have a gyroradius of about 1.5 × 104 km. This means that
netic field pressure will become increasingly important. plasma discontinuities in the cometary flow, such as the
Also, because of the directionality of the magnetic field and shock transition, should be described in terms of boundary
the resultant Lorentz force on the plasma, the cometary structures of finite thickness.
plasma flow will deviate strongly from axial symmetry. The To take into account these kinetic effects, Galeev and
most dramatic effect can be seen in the inner coma region. Lipatov (1984) were the first to use numerical simulations
Figure 14 depicts a schematic view of how the magnetic capable of treating the motions of individual charged parti-
field will be stacked up in front of the contact surface shield- cles to study the comet-solar wind interaction. They showed
ing the solar wind plasma inflow from the cometary iono- that the cometary shock front thickness has a scale of a few
spheric outflow. In the plane containing the solar wind flow gyroradii of the heavy cometary ions, rather than the gyro-
(x) and the interplanetary magnetic field (y), the cometary radius of a solar wind proton. This is a principal differ-
plasma inflow will converge toward the central region. A ence between the cometary bow shock structure and the
more detailed description is given by Gombosi et al. (1997). bow shock structure of Earth’s magnetosphere, which has a
In their model calculations using a self-adapted computa- thickness of less than approximately a few proton gyroradii.
tional mesh method, the plasma flow in the XY plane is seen It is important to point out that an interesting conse-
to merge on the tailward side. On the other hand, the plasma quence of the particle kinetics is to introduce a dependence
flow in the XZ plane — perpendicular to the magnetic of the shock structures on the orientation of the interplan-
field — will simply move around the cometary ionosphere. etary magnetic field. Omidi and Winske (1987, 1991) pro-
duced simulations of the cometary shock transition for the
cases when the cone angle between the interplanetary mag-
netic field and the solar wind is Q = 90° (for perpendicular
shock) and when Θ = 5° (for parallel shock). As shown in
Fig. 15, the perpendicular shock case is characterized by
very well-defined and well-correlated sharp jumps in mag-
netic field strength and number density — with the shock
thickness ~ proton gyroradius — to be followed by a se-
quence of fluctuations downstream. In contrast, the paral-
lel shock case displays significant variations in magnetic
field and number density ahead of the shock jump of much
broader structure. The large-amplitude plasma fluctuations
downstream of the shock jump are uncorrelated. For an
intermediate theta value (Θ = 55°), the cometary shock
structure displays yet another type of behavior. That is, no
shock jump could be identified in the large amplitude varia-
tions when the thickness is much larger than the typical
gyroradius of solar wind protons.
Clearly, for a comet with the shock position Rshock <
105 km, the shock thickness will be a significant fraction
Fig. 14. The flow pattern of ionospheric plasma in the vicinity of the solar wind interaction region — except perhaps for
of the contact surface separating the solar wind flow from the the special case of Θ ~ 90°. This is the situation for comets
cometary plasma flow. with Q < 1029 molecules/s such as 21P/Giacobini-Zinner
614 Comets II

Fig. 16. The distributions of the cometary ions and solar wind
protons for weakly outgassing comets. The gas production rates,
from left to right, are (a) Q = 8.4 × 1026 mol s –1; (b) 2.5 ×
1027 mol s–1; and (c) 5 × 1027 mol s–1. From Lipatov et al. (2002).

for which shock distances are comparable or smaller than

the gyroradii of the cometary heavy ions? This question is
also of importance for in situ measurements to be carried
out by the Rosetta mission at large solar distances when the
particle kinetic effects are expected to dominate the solar
wind interaction process. A number of numerical simula-
tions have recently been performed to address this issue
(Hopcroft and Chapman, 2001; Lipatov et al., 2002). Fig-
ure 16 shows the two-dimensional cuts of the cometary ion
density distributions for three different gas production rates
from the three-dimensional hybrid simulations of Lipatov
et al. for the case when the interplanetary magnetic field is
parallel to the y direction. For Q = 8.4 × 1026 molecules/s,
the ion density profile in the XZ plane appears to follow
the gyromotion of the individual cometary ions. In other
words, the cometary ion tail may be regarded as a beam of
individual ions. The interplanetary magnetic field is only
slightly modified. For Q > 2.5 × 1027 molecules/s, the asym-
metric structure of the ion tail is still evident, while the
magnetic field disturbance becomes stronger. These authors
point out that for Q = 8.4 × 1026 molecules/s, a symmetric
Mach cone exists in the vicinity of the comet, while a sym-
metric detached bow shock will form for Q > 5 × 1027 mol-
ecules/s.

4. PLASMA BOUNDARIES

Fig. 15. Plots of the total magnetic field and density as a func- 4.1. Upstream Region and Shock Crossing
tion of distance at different cone angles (θ) between the IMF and
the solar wind flow direction: (a) θ = 90°; (b) θ = 5°; and (c) θ = In this section, we describe different regions of cometary
55°. From Omidi and Winske (1991). plasma boundary structures as observed by particles-and-
fields instruments onboard spacecraft. As a function of dis-
tance from the nucleus, these structures are divided into
during the ICE encounter. (We will return to the ICE mea- (1) shock, (2) cometosheath, (3) cometopause, (4) ion pileup
surements in the next section.) An important question that region, and (5) magnetic field-free cavity. A summary of
emerges from this consideration is therefore what happens the spacecraft encounter geometries before the most recent
to the solar wind interaction of weakly outgassing comets Deep Space 1 mission is given in Fig. 17.
 Ip: Global Solar Wind Interaction and Ionospheric Dynamics 615

detectors detected no signature of a sharp jump in plasma

parameters as appropriate for a classical shock formation
(Smith et al., 1986; Bame et al., 1986). For example, the
magnetic field strength shows a very gradual increase em-
bedded with a series of large-amplitude fluctuations at about
09:30–10:00 UT inbound, and a similar pattern but for re-
duced field strength at about 11:50–12:20 UT outbound
(Fig. 19). The solar wind velocity profile, as determined by
the electron detector, does not display clear-cut sharp jumps
in these intervals, which have been called “slow transition
regions” by Bame et al. (1986).
In view of the presence of large-amplitude waves in most
of the solar wind interaction region, Omidi and Winske
(1991) developed the interesting idea that the bow shock
at 21P/Giacobini-Zinner is actually composed of an en-
semble of shocklets instead of one single standing bow
shock. Figure 20 shows a schematic view of such a mul-
tiple-shock model. In this scenario, the solar wind will be
decelerated little by little upon transversing the shocklets.
It is in such a manner that the supersonic solar wind will
gradually reach subsonic speed over a length scale much
larger than a few gyroradii of the heavy cometary ions.
While the bow shock of 21P/Giacobini-Zinner at the time
of the ICE encounter is not well-defined, the situation at
Comet Halley during the encounters of Susei, Vega 1 and 2,
and Giotto is just the opposite. A drop in the solar wind
velocity, plus significant angular deflection, were clearly
observed by the plasma instrument on Susei (Mukai et al.,

Fig. 17. A description of the encounter geometries for the space-

craft measurements at Comets 21P/Giacobini-Zinner and 1P/
Halley. ICE = International Cometary Explorer; V1, V2 = Vega 1
and Vega 2; G = Giotto. The approximate positions of the bow
shock, or bow wave, are also given. From Reme (1991).

The first test of the theoretical models of comet-solar

wind interaction was provided by the tail-crossing of 21P/
Giacobini-Zinner by the ICE spacecraft in September 1985.
Figure 18 compares the spatial distribution of the plasma
wave activity with that of the energetic ion flux measured
by the plasma instruments onboard the spacecraft (Ipavich
et al., 1986; Scarf et al., 1986). It is noteworthy that a sig-
nificant level of solar wind interaction effects could be
found at distances as far as 1,000,000 km from the comet.
As will be examined in more detail in section 5, such en-
hanced wave activity and energetic ion population are re-
lated to each other as a consequence of the pickup process
of new cometary ions.
In spite of the mass-loading effect and finite gyroradius
effect of the pickup ions, a weak bow shock is nevertheless
expected. The ICE results are, however, somewhat mixed
because different experiments gave different answers. Amid
the large-amplitude upstream waves, the plasma waves and Fig. 18. A composite view of the plasma wave turbulence and
energetic particle observations (Scarf et al., 1986; Hynds the energetic particle flux in the vicinity of Comet 21P/Giacobini-
et al., 1986) indicated the presence of a bow shock struc- Zinner as observed by the ICE spacecraft. From Scarf et al. (1986)
ture. On the other hand, the magnetometer and electron and Ipavich et al. (1986).
616 Comets II

1986), providing unequivocal evidence of a cometary bow

shock. Similar behaviors were registered by the experiments
on Vega 1 and 2 and Giotto at the far flanks of the comet
(Gringauz et al., 1986). The locations of these shock cross-
ings, together with the theoretical position of the bow shock
along the comet-Sun axis, define a parabolic shape of the
standing bow shock as shown in Fig. 17.

4.2. Cometosheath

Because of the continuous addition of heavy cometary

ions, the postshock solar wind flow in the extended coma
will slow down further. The first observational indications
of such process can be seen in the time-sequence of energy-
per-charge spectra obtained by the solar direction ion ana-
lyzer onboard the Vega 1 spacecraft (Gringauz et al., 1986).
The JPA plasma instrument on the Giotto probe observed
Fig. 19. A comparison of the variations in the square of the mag- similar behavior. As shown in Fig. 21, the trace of solar wind
netic field magnitude and the electron plasma density (rectangu- protons denoted by (P) moves to lower-energy bins at closer
lar curve) as observed at Comet 21P/Giacobini-Zinner. For the and closer distances to the nucleus. At the same time, the
interval illustrated, the two parameters are strongly correlated, trace of heavy cometary ions on the upper track (because
indicating that the fluctuations are fast mode MHD waves. From of higher mass and therefore higher kinetic energy) starts
Tsurutani et al. (1987).
by following a separate route but later tends to merge with
the protons.
A more recent view of this mass-loading effect in ion
mass spectra is provided by the Deep Space 1 measure-
ments at Comet 19P/Borrelly. In this observation, the space-
craft reached a closest approach distance of 2171 km. The
preliminary report showed that the peak of the solar wind
proton count rates falls from a value near the ambient so-
lar wind speed to just a few tens of kilometers per second
near the closest approach. The flow velocity of cometary
heavy ions follows a similar pattern (Nordholt et al., 2003).

4.3. Cometopause

At cometocentric distances r < 2 × 105 km, the plasma

instruments on Giotto designed to detect medium- and low-
energy ions began to measure heavy cometary ions in in-
creasing fluxes. Figure 22 shows the radial profiles of
several major species of cometary ions obtained by the IMS
experiment (Balsiger et al., 1986). Some of the main fea-
tures may be summarized as follows: As the Giotto probe
approached the comet nucleus to radial distances r < 2 ×
105 km, the number density of the water-group ions, H2O+,
H3O+, and O+, was seen to increase rapidly, with the H3O+
ions displaying the steepest gradient. The atomic ions, C+
and S+, were observed to be very abundant (Balsiger et al.,
1986; Balsiger, 1990), and their radial gradients appear to
be more gradual than those of the water-group ions.
At a distance of about 105 km, suprathermal cometary
ions created in the solar wind flow at large distances up-
stream begin to disappear and be replaced by cold ions pro-
duced locally. Figure 23 summarizes the behavior of both
Fig. 20. A schematic view of how the dynamic interaction be- the hot and cold ions as detected by the IMS experiment.
tween the solar wind and comets can result in the formation of There are a number of points of note. First, at the radial
multiple shocks, which eventually lead to a heated and subsonic position (sometimes called the cometopause) where the
wind. From Omidi and Winske (1991). magnetic field strength jumped by 20 nT (Neubauer et al.,
 Ip: Global Solar Wind Interaction and Ionospheric Dynamics 617

Fig. 21. The variations of the ion flow speeds [(P) for solar wind protons and (1) and (2) for heavy cometary ions] in the coma of
Comet 1P/Halley as measured by the JPA instrument onboard the Giotto spacecraft. From Johnstone et al. (1986).

Fig. 22. Ion density profiles for mass/charge 16, 17, 18, 19 amue–1
as a function of distance from the comet nucleus. Data are from
the HIS and HERS sensors of the IMS experiment on Giotto. The
solid lines are theoretical data from the MHD model by Schmidt
et al. (1988). From Altwegg et al. (1993).

1986), the number density of solar wind protons was ob-

served to drop by a factor of 2 (Balsiger, 1990) and a simi-
lar reduction was detected in the He++ flux (Fuselier et al., Fig. 23. A summary of the number density profiles of several
1988). This feature could be related to a tangential disconti- water-group ions as observed by the two sensors (HIS and HERS)
nuity or propagating rotational discontinuity in the solar of the IMS experiment on Giotto. From Ip (1989).
wind (Neubauer, 1987). On the other hand, the reduction
in the number density of solar wind particles need not be
caused by charge exchange loss (Gringauz et al., 1986; 4.4. Ion Pileup Region
Gombosi, 1987; Ip, 1989). It should be noted that the solar
wind protons and the hot oxygen ions disappeared com- As the Giotto spacecraft moved closer to the nucleus of
pletely at r ~ 6–8 × 104 km, essentially as a result of charge Comet Halley, the total ion density was observed to follow
exchange losses. This effect can be seen clearly by compar- a radial dependence of 1/r. Such spatial variation is basi-
ing the number density of the cold O+ ions measured by the cally the result of production of cometary ions plus the
high-intensity (HIS) instrument and that of the hot O+ ions slowdown of the mass-loaded plasma flow. This trend was
from the high-energy (HER) instrument in Fig. 23. interrupted at r ~ 12,000 km, at which point a sharp drop
618 Comets II

Fig. 24. Comparison between model calculations and measure-

ments by the Giotto IMS for mass 19. From Häberli et al. (1995).
Fig. 25. Electron temperature profile, as used in the model cal-
culations for the ion pileup region. From Häberli et al. (1995).
in ion number density was detected (see Fig. 24). Upon its
initial discovery, this plasma feature was called the “ion
pileup region” (Balsiger et al., 1986). Subsequent consid- pileup region. Observations of Comets Hale-Bopp and Hya-
erations pointed to two possible physical mechanisms. The kutake have also shown similar structures (Bouchez et al.,
first one, proposed by Galeev (1987), suggested that the ion 1999). This means that the ion pileup effect must be a com-
density enhancement was caused by an anomalous ioniza- mon property of the comet-solar interaction. The stability
tion effect. The other one, which has now been accepted of such plasma structures against changes in solar wind con-
as the more likely explanation, was due to Ip et al. (1987), dition (i.e., solar wind pressure or interplanetary magnetic
who proposed that such a density jump was produced by a field orientation) remains unclear, however. This is because
sudden decrease in electron temperature (from a few 10 4 K the ion density peak of C/Hale-Bopp was observed to move
to a few hundred K) at r < 12,000 km. The main reason is from the sunward side to the tailward side at certain time
simply that the rate coefficients of electron dissociative intervals (see Fig. 26). How did that happen? This also sug-
recombination depend strongly on the electron temperature gests that time-series CCD photometry and/or spectrogra-
(Te). For an electron dependence of Te–0.5, a change in electron phy will be a very powerful tool in deciphering the inner
temperature by a factor of 100 will lead to a corresponding dynamics of cometary ionospheres and their response to
change in electron and ion number density by a factor of solar wind conditions.
about 3–10.
A quantitative analysis of this somewhat unexpected 4.5. Ionosphere
phenomenon is complicated because detailed accounts must
be given to the different ionization effects. This is because While the bow shock as discussed in section 4.2 may
the cometary ion production depends on a number of pro- be considered as the outer boundary delineating the free-
cesses, including photoionization, electron impact ionization flowing solar wind and the plasma flow significantly mass-
by photoelectrons, and solar wind suprathermal electrons; loaded by cometary ions, there exists another important
these estimates necessarily involve model calculations of the boundary in the inner coma separating the mass-loaded
electron energetics, transport process, and thermal conduc- solar wind flow from the plasma outflow of purely cometary
tion along the magnetic field lines (Gan and Cravens, 1990; origin. To a certain extent, the radial expansion of cometary
Haider et al., 1993; Ip, 1994; Häberli et al., 1995). Häberli ionospheric plasma has some similarities to the interaction
et al. (1995) used an electron temperature profile, as shown of the solar wind with the interstellar medium in which the
in Fig. 25, to carry out chemical network calculations and solar wind flow is terminated by the formation of a helio-
found that the ion density variations of the water group ions pause. In this context, Wallis and Dryer (1976) were the
plus NH+4 ions could be satisfactorily explained. first to consider a similar structure with the formation of a
Groundbased spectrographic observations of Comet contact surface separating the cometary ionospheric flow and
Halley showed a shell-like structure of the H2O+ ion bright- the mass-loaded solar wind plasma. The key is, of course,
ness distribution at the 6198-Å emission line. Ip et al. (1988) that the cometary ions in the inner coma are collisionally
interpreted this feature in terms of the formation of the ion coupled to the supersonic expanding neutral gas. A contact
 Ip: Global Solar Wind Interaction and Ionospheric Dynamics 619

Fig. 26. Models of the radial distribution of H2O+ at Comet Hale-Bopp (C/1995 O1) assuming hemispherical symmetry of the coma.
Best-fit radial density models (thin line) are shown along with the consequent column density distributions (bold line) and the ob-
served column density profiles in March and April 1997 (points). From Bouchez et al. (1999).

Fig. 27. (a) Schematic flow regions and parameters for the solar source in interstellar gas. Regions A, C1, and C2 are subsonic; B
and D are supersonic. The interstellar gas returns to its ambient velocity by passing through a compression fan, which becomes a tail
shock. (b) Schematic flow regions for the comet source in the solar wind. The circular radius ∆ denotes the position where the radially
expanding neutral gas flow becomes collision-free. The shock and slip-plane structure in the wake could be complex because the wake
is supersonic. From Wallis and Dryer (1976).

discontinuity would be necessarily formed between a pair of and the cometary inner shock. Subsequently, Houpis and
shocks (the inner and the outer shock) such that the super- Mendis (1980) proposed an analytical model for a hyper-
sonic cometary plasma could be diverted into the lateral sonic ionospheric outflow, and Damas and Mendis (1992)
direction near the boundary. Figure 27 compares the theo- used an axially symmetric hydrodynamic model to investi-
retical models of the termination shock of the heliosphere gate the three-dimensional structure of the inner shock layer.
620 Comets II

Ip and Axford (1982), on the other hand, suggested that the For a solar wind number density of nsw ~ 5 cm–3 and ve-
position of the ionospheric contact surface should be de- locity of νsw ~ 400 km/s, we have Bmax ~ 60 nT. At the point
termined by a balance between the frictional gas drag of where the magnetic field reaches its maximum, i.e., dB/dr =
the neutral gas on the cometary ions and the J × B Lorentz 0, the force balance depends on the equilibrium between
force exerted by the draped magnetic field at the nose of the curvature force of the draped magnetic field and the
the cometary ionosphere. The implication is that the inner frictional force of the outward expanding neutral gas. For
ionosphere of purely cometary origin should be free of mag- a radius of curvature (Rs) of the magnetic field in the inner
netic field, while the ionospheric plasma outside of the con- coma, we have
tact surface should be magnetized. However, Ershkovich and
Mendis (1983) carried out an analysis of the stability of the
B2s
interface and found that the ion-neutral force should ren- ≈ kinniminnνn (13)
der the boundary extremely unstable; they predicted a fully µ0Rs
magnetized ionosphere. The stage was thus set before the
Giotto encounter with Comet Halley, as it would have pene- where kin is the ion-neutral collision rage, nn the neutral
trated through the predicted location of the cometary iono- number density, ni the ion number density, and νn the neu-
pause. tral speed. In the case of Comet Halley during the Giotto
What the magnetometer experiment onboard Giotto encounter, it could be found that rc ~ 2400–7300 km at the
found was a total surprise. When the space probe reached subsolar point depending on the ion number density, ni.
a cometocentric distance of 4700 km, it went through a Cravens (1986) and Ip and Axford (1987) give a one-dimen-
sharp layer with a width of only 20 km dividing a diamag- sional global treatment of the force balance by taking into
netic cavity (Neubauer et al., 1986). As shown in Fig. 28, account the magnetic pressure gradient term. The magnetic
this structure repeated itself on the outbound passage. To field strength in the inner coma is then determined by the
understand the spatial variation of the magnetic field, we following equation
follow the arguments below. First, as the solar wind slows
down in the cometary coma because of the mass-loading
1 dB 1 B2
effect, the magnetic field strength will be amplified accord- B + = kinniminnνn (14)
ingly. The upper limit of the magnetic field strength in the µ0 dR µ0 R
stagnant cold plasma region is estimated by equating the
magnetic pressure to the solar wind ram pressure. That is which has a simple solution

B2s [1 + 2 ln(R/Rmax)]1/2
= nswmswν2sw (12) B(R/Rmax) = Bmax (15)
2µ0 R/Rmax

where Rmax is proportional to Q3/4. A good match of the

theoretical profile to the observed magnetic field variation
can be obtained by adjusting the physical parameters. The
general features of the plasma flow and magnetic field
variation along the Sun-comet axis have been depicted in
a numerical calculation by Baumgaertel and Sauer (1987),
in which they compare the effect of artificially changing
the electron dissociative recombination rate on the possible
formation of the ion pileup region. The plasma velocity
variation in Fig. 29 is illuminating in the sense that the
outward expansion with a flow speed ~1 km/s within the
first 5000 km is suddenly switched to a stagnant flow with
small inward speed (~0–0.5 km/s), indicating the location
of the contact surface. It is interesting to note the existence
Fig. 28. Magnetic field measurements made by the magnetom- of a small peak in the ion number density right at this
eter experiment on Giotto showing the inner pileup region inbound boundary. This feature is caused by the accumulation of
and outbound and the magnetic cavity region. Curve (1) is ob-
ions from both sides of the converging flows. At higher
tained by taking into account the magnetic pressure gradient ef-
spatial resolution, this density peak should be even sharper
fect in the force balance; curves (2) and (3) are obtained by
including the curvature force term but with different ion number as indicated by a one-dimensional theoretical model of Cra-
density profiles. The observational result obtained by the magne- vens (1989). Goldstein et al. (1989) examined the fine time
tometer experiment on Giotto is denoted by curve (4). The experi- resolution of the ion mass spectrometer measurements at
mental curves are from Neubauer (1986) and the theoretical curves the crossing of the contact surface and found the signatures
from Wu (1987). for a recombination layer and a spike of hot ions, which
 Ip: Global Solar Wind Interaction and Ionospheric Dynamics 621

Fig. 30. The magnetic field free cavity surrounding the cometary
nucleus is defined by a sharp boundary separating the external
region with a magnetic field of several tens of nanoteslas from
the internal region of the zero magnetic field. The surface defined
by B = 3 nT is used as an approximation to such an envelope pro-
jected onto a plane with the look angle tilted by (a) 20° and
(b) 70° from the direction of the IMF. Courtesy of R. Wegmann.

Zinner, which might be interpreted as the extension of the

tadpole-like ionospheric tail modeled by Schmidt and Weg-
mann (1991).
Fig. 29. Plasma velocity, magnetic field, and plasma density from
a one-dimensional steady-state calculation assuming a constant 5. PLASMA INSTABILITIES AND WAVES
electron dissociative recombination coefficient (a) = 3 × 10–13 m3/s
for R < 104 km (solid curves) and (b) = 3 × 10 –13 m3/s everywhere 5.1. Microinstabilities
(dashed curves). From Baumgaertel and Sauer (1987).
In the fluid or magnetohydrodynamic description of the
comet-solar wind interaction, it is common practice to as-
could be interpreted as particles accelerated at the contact sume that all charged particles, whether they are solar wind
surface. protons, electrons, or cometary ions, are mixed together into
Using an MHD treatment, Schmidt and Wegmann (1991) one single fluid flow moving with the same velocity. Also,
produced a three-dimensional picture of the ionospheric it is customary (and necessary) to further assume that the
contact surface (Fig. 30). Because of the orientation of the cometary ions share the same thermal temperature with the
interplanetary magnetic field, the contact surface bounding bulk plasma. At the same time, the velocity distribution of
the diamagnetic cavity is highly asymmetric. It may be said the cometary ions is taken to be isotropic and Maxwellian. As
to mimic the shape of a tadpole with a flat tail, which is shown by the spacecraft observations at Comets Giacobini-
basically the neutral sheet separating the two parts of op- Zinner and Halley, this is far from being true. In many cir-
posite magnetic polarities. The only spacecraft that has cumstances, the dynamics of the cometary ions are com-
passed through a cometary ion tail is ICE. The plasma in- pletely different from that of the solar wind. Particle kinetic
struments onboard ICE detected the presence of a cold dense effects turn out to play a dominant role in the whole pro-
plasma region at the center of the ion tail of 21P/Giacobini- cess of comet-solar wind interaction (Fig. 31). Indeed, it is
622 Comets II

because of this unique property that the study of cometary

plasma processes has become a very intriguing topic in plas-
ma physics, attracting many of the best minds in this field.
The whole enterprise began with the fundamental paper of
Wu and Davidson (1972), who investigated the plasma ef-
fect of the photoions created in the exosphere of Mercury.
Translated to the context of the comet-solar wind interac-
tion, we could start with the following description.
Suppose a cometary neutral gas atom or molecule is
ionized by solar ultraviolet radiation or charge exchange
with the solar wind protons (see section 3). The particle will
immediately be accelerated by the convective electric field
E = –V × B in the stationary frame. In the above equation,
the initial velocity of the new ion relative to the solar wind
is V = –Vsw + Vc, where Vsw is the solar wind velocity, Vc
is the spacecraft velocity, and B is the interplanetary mag-
netic field. In the following consideration, we have ignored
the coma expansion speed, which is only on the order of
1 km s–1. To simplify the conceptual discussion further, we
could omit Vc since it is on the order of 20–30 km/s. The
motion of the new cometary ion is given by the equation
of motion under the Lorentz force: du/dt = qE = –qV ×
B. The velocity V can be resolved into two components,
one parallel to B (V|| = V cosϕ) and the other perpendicu-
lar to B (V⊥ = V sinϕ); see Fig. 32. The solution to the equa-
tion of motion in the solar wind frame can then be described
by the superposition of two motions: The first one has to
do with a gyration of the new ion around the magnetic field
with velocity V⊥, and the second one is a steady motion
along the magnetic field with velocity V|| = –Vsw cosϕ. For
Vsw ⊥ B (i.e., ϕ = π/2), the ion trajectory in the solar wind
frame is purely a gyration with V⊥ = Vsw since V|| = 0. In
the observer’s frame, namely the spacecraft frame, the ion
motion will be a combination of the solar wind flow plus

Fig. 31. Phase space-density distributions of cometary hydrogen

ions upstream of the bow shock of Comet 1P/Halley as observed
by the IMS experiment on Giotto, during the time period 0803–
0908 UT, March 13, 1986, when the Giotto spacecraft was at a
distance of about 8 × 106 km from the nucleus. They show the
evolutionary effect of pitch angle scattering from the point of Fig. 32. The two initial velocity components, V⊥ and V||, of the
injection into a partially filled shell. From Neugebauer et al. new cometary ions. Pitch-angle scattering transfers the ring distri-
(1987). bution into a spherical shell.
 Ip: Global Solar Wind Interaction and Ionospheric Dynamics 623

the gyration motion. The resultant trajectory is a cycloidal 5.2. Source of the Free Energy
motion with u = 0 at the cusp and u = 2Vsw at the top. It
can be seen that a charged particle detector onboard a space- Because of the photoionization and charge exchange
craft would see modulation of the cometary ion flux as a ionization of the cometary neutral gas in the large coma
function of the look angle with respect to the solar wind region, new ions are continuously created at distances as
direction. That is, the ion flux (and particle energy) should far away as 1,000,000 km from the cometary nucleus (cf.
be at maximum when the detector is looking antiparallel Fig. 18). The pickup process leads to the generation of a
to the solar wind flow and at minimum when looking in very significant level of wave activity with δB/B ~ 0.5. The
the opposite direction. This is, in fact, what was observed large-amplitude waves are accompanied by the presence of
(Richardson et al., 1987). The initial motion of the new an intense flux of energetic heavy ions. Because the parti-
cometary ions can be described in terms of a ring distribu- cle energy exceeds the initial pickup energy (~20 keV) of
tion in the velocity phase space. the water-group ions, a certain kind of particle acceleration
The other extreme case is for B || Vsw with ϕ = 0. Here, and hence energy transfer from the waves to the energetic
no gyration will be executed since V⊥ = 0. Instead, the ini- ion population must be taking place in the cometary coma
tial velocity of the new ion will be V|| = –Vsw in the solar (Richardson et al., 1986). The central issue in cometary
wind frame. As a consequence, the new ions remain mo- plasma physics is therefore to understand how the three-
mentarily at rest in the stationary (i.e., the spacecraft) frame, way transfers of free energy can be facilitated. For this, we
while forming an ion beam in the solar wind frame. need to estimate the energy budget available to drive these
The value of the ϕ angle varies between 0 and π/2. The different kinds of plasma effects.
initial velocity distribution of the new cometary ions is thus For pedagogical reasons, we will essentially follow the
often a combination of the ring distribution and the beam heuristic approach described in Coates et al. (1990) and
distribution described above. For convenience, it is gener- Johnstone et al. (1991). Figure 33 illustrates how the reso-
ally called the ring-beam distribution. The important thing nant wave particle interaction proceeds. In the solar wind
is that such initial anisotropic velocity distributions repre- frame, the parallel propagating Alfvén waves moving up-
sent a source of free energy in the plasma flow. The contri- stream (k > 0) and moving downstream (k < 0) are related
bution by Wu and Davison (1972) and Wu and Hartle (1974) to the pickup ions gyrating at the ion cyclotron frequency
(see also Lee and Ip, 1987; Lee, 1989) is to first show that Ωi by the resonance conditions
plasma instabilities could be generated with a rapid growth
of the corresponding ion cyclotron waves serving to isotrop- ω – kV|| = –Ωi (L mode);
ize the pitch angle distribution and hence pick up the new anomalous Doppler /larger pitch angle
cometary ions. Under the assumption that the initial distri-
bution function of the new ions can be presented as δ(v||– and
v||0) δ(v–v0), the dispersion equation of the plasma waves
has its two most unstable roots at ω + kV|| = Ωi (R mode);
normal Doppler/smaller pitch angle
ϖ ≈ κν||0 – Ω ≈ ±κVA (16)
The first condition with the negative sign on the lefthand
representing the left- and righthand polarized Alfvén (L and side is for a righthand polarized wave in which the electric
R) waves for ω << Ωi. The wave growth wave can be derived vector rotates in the direction of the electronic cyclotron
as motion. Ions with V|| satisfying the above conditions will
give up energy to the related Alfvén waves. In a resonant
1~ 1/3 wave-particle interaction we have the following relation
~γ ~ Ω VA 2 nimiν⊥2
i (17) (Kennel and Petschek, 1966)
ν||0 B20 /(2µ0)
V⊥2 + (V|| – Vph)2 = constant
In the case of the ring-beam velocity anisotropy, three dif- For parallel propagating Alfvén waves, Vph = ±VA. This
ferent low frequency instabilities can be generated, namely means the distribution of the particle velocity in the V|| –V⊥
an ion cyclotron instability, a parallel propagating nonoscil- coordinate should follow the segments determined by the
latory mode, and a fluid mirror instability (Tsurutani, 1991). two spheres as defined in Fig. 34. It can be seen that, be-
The ion cyclotron instability produces resonant lefthand cause of the interaction with the Alfvén waves with Vph =
waves propagating antiparallel to the ions. In the case of ±VA, the total velocity [V = (V2|| + V⊥2)1/2] is effectively re-
the beam velocity distribution, two types of instabilities can duced (Galeev and Sagdeev, 1988; Coates et al., 1990). This
be generated: a righthand resonant helical beam instabil- is also the source of the free energy for wave growth. Note
ity and a nonresonant firehose instability. The condition for that the particles could also absorb energy from the waves
the cyclotron resonance is ω = k ⋅ V + nΩi where ω is the by tracing the contour of the maximum radius in different
wave frequency, k and V the wave k vector and particle quadrants of such a bispherical shell structure. In this op-
velocity (k || V), n an integer, and Ωi the ion gyrofrequency. posite case, we would have particle acceleration by wave
The firehose instability grows when P|| > P⊥ + B2/4π. damping (see section 4.6.3).
624 Comets II

Fig. 33. A summary diagram of resonant wave-particle interactions in the velocity space of the particles in the solar wind moving
frame. The upper part is for waves traveling upstream and the lower part for waves traveling downstream. The unstable regimes are
marked by the gray shading; N is for the normal Doppler resonance, and A is for anomalous Doppler resonance. From Johnstone et
al. (1991).

In the original ring-beam velocity distribution, the ki-

netic energy from the beam motion and the thermal energy
from the gyromotion are, respectively,

kinetic energy = 1/2ρiv2s cos2Φ

thermal energy = 1/2ρiv2s sin2Φ

The immediate result of wave-particle interaction is to iso-

tropize the pitch angle distribution covering the bisphere
by wave scattering. The center of the bisphere will move
with the Alfvén speed; this will also define the kinetic en-
ergy of the whole system. Now, if the waves are dominated
by upstream propagating components at the beginning, the
velocity distribution will be dictated by the spherical shell
projected into the upper part of Fig. 33. For such shell struc-
Fig. 34. Velocity-space representation of the pitch angle scttered ture, we have
bispherical shell geometry in the solar wind frame, where vinj is
the position of the pickup ion injection into the initial ring distri- kinetic energy = 1/2ρivA2
bution. From Huddleston et al. (1992). thermal energy = 1/2ρi[v2s sin2Φ + (vs cosΦ – vA)2]
 Ip: Global Solar Wind Interaction and Ionospheric Dynamics 625

The difference between the ring-beam energy and the shell

energy gives us the free energy available for the generation
of Alfvén waves in the solar wind flow

∆E = Ering – E shell = ρi(vAvs cosΦ – vA2)

5.3. Plasma Waves and Magnetic Turbulences

Note that in the spacecraft frame with Vsw|| > VA, both
R- and L-mode waves are lefthand polarized since the wave
polarization in this frame is dominated by the Doppler shift.
The propagation direction of these waves should be
sunward along the average, spiral magnetic field direction
as observed in the 100-s waves. For Alfvén waves, ω/k =
VA; the resonant frequency of the waves in the solar wind
frame will therefore be

ΩiVA
ϖsw = (18)
V||Vph

with Vph = ±VA depending on the direction of the wave

prop-agation. For spacecraft observations, the frequency of
the resonant wave will be Doppler-shifted to be

(Vsc − Vph)
ϖsc = Ωi (19)
(V|| − Vph)
Fig. 35. The frequency spectrum of MHD waves as measured
where vsc is the spacecraft velocity in the solar wind moving by the ICE spacecraft at Comet 21P/Giacobini-Zinner. A power-
frame; in the case of the ring distribution or Vsc ≈ Vsw, we law curve representative of an active solar wind is also shown for
thus have ωsc ≈ Ωi (Tsurutani and Smith, 1986). It is for this comparison. The wave intensities are well above solar wind fluc-
tuation levels. The waves are considerably more intense than those
reason that the gyrofrequency of the dominant water-group
at Comet 1P/Halley. From Tsurutani and Smith (1986).
ions was discovered to be the “pump” wave with a period
of about 100 s as seen in the power spectra of cometary
plasma turbulence in the coma of Comet Giacobini-Zinner
(see Fig. 35). cometary ions, different levels and wave types could be gen-
In the case of the ICE observations of Comet Giacobini- erated. Figure 36 compares the power spectra of the mag-
Zinner, similar ultra-low-frequency (ULF) fluctuations were netic field variations at Comets 26P/Grigg-Skellerup, 21P/
also observed in the solar wind electron number density and Giacobini-Zinner, and 1P/Halley. There are important simi-
the solar wind flow velocity (Gosling et al., 1986; Tsurutani larities. That is, they all show a prominent “pump” wave
et al., 1987). Figure 19 shows the correlation between these feature at the 100-s periodicity and, at higher frequency,
magnetic field variations and the solar wind plasma param- tend to follow a power law P(f) ~ f α with the power index
eters, which suggest that the waves are fast-mode magneto- α ≈ –2. At the same time, we also find important differences
sonic waves. Note that the magnitude of the fluctuations in the wave forms. In fact, each is different from the other.
increases as the bow shock was crossed (at about 09:30 UT) The case of 26P/Grigg-Skjellerup is characterized by sinu-
at a radial distance of about 2 × 105 km. Furthermore, at soidal, noncompressive lefthand-polarized waves (Mazelle
large distances from the comet, R > 3 × 105 km, the 100-s et al., 1995); the case of 21P/Giacobini-Zinner has phase-
waves were lefthand polarized; the polarization then changed steepened and compressive magnetosonic (RH) waves led
from lefthand elliptical and linear in regions near and inside by large amplitude whistler packets; and Comet Halley’s
the bow shock at R < 2 × 105 km. Superposed on the long- upstream waves, which are composed of linearly polarized
period linearly polarized waves, lefthand-polarized whistler turbulence, have no obvious structure (Tsurutani et al.,
waves of shorter periods of 1–3 s were detected. Tsurutani 1995).
(1991) developed the theory that the upstream whistler wave
packets could be generated by steepening of the magneto- 6. SUMMARY AND DISCUSSION
sonic waves.
Depending on the solar wind conditions (i.e., the orien- The advances made in the study of cometary plasma
tation of the interplanetary magnetic field with respect to physics over the last two decades have been spectacular.
the solar wind flow direction) and the production rate of the This achievement is, in part, due to the spacecraft missions
626 Comets II

Fig. 36. Power spectra of the transverse components of the magnetic field at three comets. From Tsurutani et al. (1995).

to Comets 1P/Halley, 21P/Giacobini-Zinner, 26P/Grigg- A., Neugebauer M., Rosenbauer H., and Shelley E. (1993) The
Skjellerup, and, most recently, 19P/Borrelly. The in situ ion population between 1300 km and 230000 km in the coma
measurements enabled by particles-and-fields instruments of Comet P/Halley. Astron. Astrophys., 279, 260–266.
have provided tremendous amounts of new information on Balsiger H. (1990) Measurements of ion species within the coma
of Comet Halley from Giotto. In Comet Halley 1986: World-
the comet-solar wind interactions and insights into the
Wide Investigations, Results, and Interpretations (J. Mason et
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al., eds.), pp. 129–146. Horwood Ltd., Aylesbury.
astronomical facilities is also crucial to the success of this Balsiger H. and 18 colleagues (1986) Ion composition and dy-
field. For example, the observational data on Comet Hale- namics at Comet Halley. Nature, 321, 330–334.
Bopp (1995 O1) are still to be digested. It is expected that Bame S. J., Anderson R. C., Asbridge J. R., Baker D. N., Feldman
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Last, but not least, sophisticated computational simulations P/Halley’s ionosphere. Astron. Astrophys., 187, 307–310.
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strahlung. Z. Astrophys., 29, 274–286.
centerpiece of planetary and cometary plasma physics. This
Biermann L., Brosowski B., and Schmidt H. U. (1967) The in-
new tool is still to be explored fully.
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eines Kometenmodells. MPI/PAE-Astro-46.
knowledge will be supplied within a decade by a new gen-
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exploration. We promise them that this field will be much locity distributions of water group ions at comet Halley: Giotto
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Cravens T. E. (1986) The physics of the cometary contact sur-
Acknowledgments. I thank the editors for encouragement in face. In 20th ESLAB Symposium on the Exploration of Halley’s
producing this chapter and T. Cravens for a careful review. I also Comet (B. Battrick et al., eds.), pp. 241–246. ESA SP-250,
thank B. Yu-M. Lin for most helpful assistance in preparing this Noordwijk, The Netherlands.
manuscript. This work was partially supported by the National Cravens T. E. (1989) A magnetohydrodynamical model of the
Council of Taiwan under NSC 90-2112-M-008-032 and NSC 91- inner coma of comet Halley. J. Geophys. Res., 94, 15025.
2111-M-008-028, and by the Ministry of Education of Taiwan Cravens T. E. (1997) Comet Hyakutake X ray source: Charge
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ity of Comets (E. J. Rolfe and B. Battrick, eds.), pp. 69–73. connection events of 1986 April 13–18 and the cessation of
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Wurm K. (1968) Structure and kinematics of cometary type 1 tails. J., 414, 883.
Icarus, 8, 287–300. Yi Y., Caputo F. M., and Brandt J. C. (1994) Disconnection events
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630 Comets II
 Lisse et al.: X-Ray and Extreme UV Emission from Comets 631

X-Ray and Extreme Ultraviolet Emission from Comets

C. M. Lisse
University of Maryland

T. E. Cravens
University of Kansas

K. Dennerl
Max-Planck-Institut für Extraterrestrische Physik

The discovery of high energy X-ray emission in 1996 from C/1996 B2 (Hyakutake) has
created a surprising new class of X-ray emitting objects. The original discovery (Lisse et al.,
1996) and subsequent detection of X-rays from 17 other comets (Table 1) have shown that the
very soft (E < 1 keV) emission is due to an interaction between the solar wind and the comet’s
atmosphere, and that X-ray emission is a fundamental property of comets. Theoretical and ob-
servational work has demonstrated that charge exchange collisions of highly charged solar wind
ions with cometary neutral species is the best explanation for the emission. Now a rapidly chang-
ing and expanding field, the study of cometary X-ray emission appears to be able to lead us to
a better understanding of a number of physical phenomena: the nature of the cometary coma,
other sources of X-ray emission in the solar system, the structure of the solar wind in the helio-
sphere, and the source of the local soft X-ray background.

1. INTRODUCTION total X-ray power, or luminosity, of C/Hyakutake was mea-

sured to be approximately 109 W. The emission was also
Astrophysical X-ray emission is generally found to origi- extremely “soft”, or of low characteristic photon energy —
nate from hot collisional plasmas, such as the million-degree only X-rays of energies less than ~1 keV (or wavelengths
gas found in the solar corona (e.g., Foukal, 1990), the 100- longer than ~1.2 nm) were detected from C/Hyakutake. The
million-degree gas observed in supernova remnants (e.g., total amount of energy emitted in X-rays from a comet is
Cioffi, 1990), or the accretion disks around neutron stars and approximately 10–4 the energy delivered to a comet from
black holes. As electromagnetic radiation with wavelength λ the Sun due to photon insolation and solar wind impact
between about 0.01 nm and 100 nm (1 nm = 10 –9 m), ex- (Lisse et al., 2001).
treme ultraviolet (EUV) and X-ray radiation are important
for solar system and astrophysical applications because the 2. OBSERVED CHARACTERISTICS OF
photons are sufficiently energetic and penetrating to ionize COMETARY X-RAY EMISSION
neutral atoms and molecules, and can thus drive chemical
reactions. In fact, current estimates of the X-ray burden per Shortly after the initial C/Hyakutake detection, soft X-ray
atom in the young solar system are some 103–10 4 photons emission from four other comets was found in the ROSAT
per atom, even as far out as the proto-Kuiper belt, as the archival database, confirming the discovery (Dennerl et al.,
young Sun was much more X-ray active than now (Feigel- 1997). X-ray emission has now been detected from 18 com-
son, 1982; Dorren et al., 1995). ets to date (Table 1) using a variety of X-ray sensitive space-
The Sun is not the only source of X-rays in the solar sys- craft — BeppoSAX, ROSAT, the Extreme Ultraviolet Ex-
tem (Cravens, 2000a, 2002a). Prior to 1996, X-rays were plorer (EUVE), and more recently, Chandra and XMM-
found in scattering of solar X-rays from the terrestrial atmos- Newton. All comets within 2 AU of the Sun and brighter
phere and in the terrestrial aurora, as scattered solar X-rays than V = 12 have been detected when observed. We now
off the illuminated surface of the Moon, and from the jovian recognize that X-ray emission is a characteristic of all ac-
aurora. Nonetheless, the 1996 discovery, using the Röntgen tive comets.
Satellite (ROSAT), by Lisse and co-workers (Lisse et al., The observed characteristics of the emission can orga-
1996) (Fig. 1) of strong X-ray emission from Comet C/ nized into the following four categories: (1) spatial mor-
1996 B2 (Hyakutake) was very surprising because cometary phology, (2) total X-ray luminosity, (3) temporal variation,
atmospheres are known to be cold and tenuous, with charac- and (4) energy spectrum. Any physical mechanism that pur-
teristic temperatures between 10 and 1000 K. Compared to ports to explain cometary X-ray emission must account for
other X-ray sources, comets are moderately weak — the all these characteristics.

631
632 Comets II

TABLE 1. Observation times, instruments, and energies* for comets detected†

through December 2002 in the X-ray or extreme ultraviolet.

Comet Time Instrument Energy (keV) Detection Reference

45P/Honda-Mrkos-Pajdušáková Jul 1990 ROSAT PSPC/WFC 0.09–2.0 Yes [1]

C/1990 K1 (Levy) Sep 1990 ROSAT PSPC /WFC 0.09–2.0 Yes [1]
Jan 1991 0.09–2.0 Yes [1]

C/1991 A2 Arai Nov 1990 ROSAT PSPC/WFC 0.09–2.0 Yes [1]

C/1990 N1 (Tsuchiya-Kiuchi ) Nov 1990 ROSAT PSPC/WFC 0.09–2.0 Yes [1]

Jan 1991 0.09–2.0 Yes [1]

2P/Encke Nov 1993 EUVE DS 0.02–0.10 No [8]

Jul 1997 EUVE Scanners 0.02–0.18 Yes [9]
Jul 1997 ROSAT HRI/WFC 0.09–2.0 Yes [9]

19P/Borrelly Nov 1994 EUVE DS 0.02–0.10 Yes [8]

6P/d’Arrest Sep 1995 EUVE DS 0.02–0.10 Yes [8]

C/1996 B2 (Hyakutake) Mar 1996 ROSAT HRI /WFC 0.09–2.0 Yes [2]
Mar 1996 EUVE DS 0.02–0.10 Yes [3]
Mar 1996 ALEXIS 0.06–0.10 No
Apr 1996 XTE PCA 2.0–10.0 No
Jun 1996 ASCA 0.20–6.0 No
Jun 1996 ROSAT HRI /WFC 0.09–2.0 Yes [4]
Jul 1996 ROSAT HRI /WFC 0.09–2.0 Yes
Aug 1996 ROSAT HRI /WFC 0.09–2.0 Yes
Sep 1996 ROSAT HRI /WFC 0.09–2.0 Yes

C/1995 O1 (Hale-Bopp) Apr 1996 ROSAT HRI/WFC 0.09–2.0 No

Sep 1996 EUVE Scanners 0.02–0.10 Yes [5]
Sep 1996 BeppoSAX 0.1–200 Yes [6]
Sep 1996 ROSAT HRI/WFC 0.09–2.0 Yes? [7]
Sep 1996 ASCA 0.20–6.0 No [5]
Mar 1997 XTE PCA 2.0–10.0 No
Oct 1997 ROSAT HRI /WFC 0.09–2.0 No
Nov 1997 ROSAT HRI /WFC 0.09–2.0 No
Nov 1997 EUVE DS 0.02–0.10 Yes [8]
Feb 1998 ROSAT PSPC/WFC 0.09–2.0 No

C/1996 Q1 (Tabur) Sep 1996 ASCA 0.20–6.0 No

Sep 1996 ROSAT HRI /WFC 0.09–2.0 Yes [1]
Oct 1996 ROSAT HRI /WFC 0.09–2.0 Yes [1]

55P/Temple-Tuttle Jan 1998 EUVE Scanners 0.02–0.18 Yes

Jan 1998 ASCA SIS 0.20–6.0 No
Jan 1998 ROSAT HRI /WFC 0.09–2.0 Yes
Feb 1998 ROSAT HRI /WFC 0.09–2.0 Yes

103P/Hartley 2 Feb 1998 ROSAT PSPC/WFC 0.09–2.0 Yes

C/1998 U5 (LINEAR) Dec 1998 ROSAT PSPC/WFC 0.09–2.0 Yes

C/2000 S4 (LINEAR) Jul 2000 Chandra ACIS-S 0.2–10.0 Yes [10]

Aug 2000 Chandra ACIS-S 0.2–10.0 Yes [10]

C/1999 T1 McNaught-Hartley Jan 2001 Chandra ACIS-S 0.2–10.0 Yes [11]

Jan 2001 XMM-Newton 0.2–12.0 Yes
Feb 2001 FUSE 0.113–0.117 No [12]
 Lisse et al.: X-Ray and Extreme UV Emission from Comets 633

TABLE 1. (continued).

Comet Time Instrument Energy (keV) Detection Reference

C/2001 A2 (LINEAR) Jun 2001 Chandra HRC/LETG 0.2–2.0 No
Jun 2001 XMM-Newton 0.2–12.0 Yes?
Jul 2001 FUSE 0.113–0.117 No [12]

C/2000 WM1 (LINEAR) Dec 2001 Chandra ACIS/LETG 0.2–2.0 Yes

Dec 2001 FUSE 0.113–0.117 Yes [12]
Jan 2002 XMM-Newton 0.2–12.0 Yes [13]

C/2002 C1 (Ikeya-Zhang) Apr 2002 Chandra ACIS-S 0.2–10.0 Yes [13]

May 2002 XMM-Newton 0.2–12.0 Yes? [13]
*The full energy range of the observing instrument is given.
† This table summarizes published and unpublished (1) dedicated observations, whether successful or not; and (2) successful serendipitous

observations. The table is sorted according to time of first observation of the comet.

References: [1] Dennerl et al. (1997); [2] Lisse et al. (1996); [3] Mumma et al. (1997); [4] Lisse et al. (1997a); [5] Krasnopolsky et
al. (1997); [6] Owens et al. (1998); [7] Lisse et al. (1997b); [8] Krasnopolsky et al. (2000); [9] Lisse et al. (1999); [10] Lisse et al.
(2001); [11] Krasnopolsky et al. (2002); [12] Weaver et al. (2002); [13] K. Dennerl et al. (personal communication, 2003).

2.1. Spatial Morphology al., 2002) at distances that exceed 104 km for weakly ac-
tive comets, and can exceed 106 km for the most luminous
X-ray and EUV images of C/1996 B2 (Hyakutake) made (Dennerl et al., 1997) (Fig. 2). The spatial extent for the
by the ROSAT and EUVE satellites look very similar (Lisse most extended comets is independent of the rate of gas emis-
et al., 1996; Mumma et al., 1997) (Fig. 1). Except for im- sion from the comet. The region of peak emission is cres-
ages of C/1990 N1 (Dennerl et al., 1997) and C/Hale-Bopp cent-shaped with a brightness peak displaced toward the
1995 O1 (Krasnopolsky et al., 1997), all EUV and X-ray Sun from the nucleus (Lisse et al., 1996, 1999). The dis-
images of comets have exhibited similar spatial morpholo- tance of this peak from the nucleus appears to increase with
gies. The emission is largely confined to the cometary coma increasing values of Q, and for Hyakutake was located at
between the nucleus and the Sun; no emission is found in rpeak ≈ 2 × 10 4 km.
the extended dust or plasma tails. The peak X-ray bright-
ness gradually decreases with increasing cometocentric dis- 2.2. Luminosity
tance r with a dependence of about r –1 (Krasnopolsky, 1997).
The brightness merges with the soft X-ray background The observed X-ray luminosity, Lx, of C/1996 B2 (Hya-
emission (McCammon and Sanders, 1990; McCammon et kutake) was 4 × 1015 ergs s–1 (Lisse et al., 1996) for an aper-

Fig. 1. Images of C/Hyakutake 1996 B2 on 26–28 March 1996 UT: (a) ROSAT HRI 0.1–2.0 keV X-ray; (b) ROSAT WFC 0.09–
0.2 keV extreme ultraviolet; and (c) visible light, showing a coma and tail, with the X-ray emission contours superimposed. The Sun is
toward the right, “+” marks the position of the nucleus, and the orbital motion of the comet is toward the lower right in each image.
From Lisse et al. (1996).
634 Comets II

Fig. 2. Spatial extent of the X-ray emission vs. the comet’s out- Fig. 3. X-ray vs. optical luminosity plot for the eight detected
gassing rate. Plot of the gas production rate Qgas vs. radial dis- ROSAT comets and the Chandra comets C/1999 S4 (LINEAR)
tance from the comet nucleus required to encircle 95% of the total and C/1999 T1 (McNaught-Hartley) observed at 1–3 AU. Groups
observed cometary X-ray flux (triangles). Upper curve: Broken of equal emitted dust mass to emitted gas mass ratio (D/G), as
power law with radial extent ~Q1.00 29 –1
gas up to Qgas ~ 10 mol s and measured in the optical by the ratio Afρ/QH2O, are also shown.
~106 km for higher values fits the imaging data well. Lower curve: For Encke and other “gassy”, optically faint comets, the resulting
Estimated radius of the bow shock for each observation, allowing slope Lx/Lopt is roughly constant. Above Lopt ~ few × 1019 erg s–1,
for variable cometary outgassing activity and heliocentric distance however, Lx appears to reach an asymptote of ~5 × 1016 erg s–1.
(boxes). X-ray emission has been found outside the bow shock for A possible explanation is that the coma is collisionally thick to
all comets except C/1996 B2 (Hyakutake) in March 1996. the solar wind within the neutral coma radius of ~106 km at 1 AU
(Lisse et al., 2001). It is also possible that the relatively large
amounts of dust in these comets, as noted from their increasing
D/G ratio, may be somehow inhibiting the CXE process. Follow-
ing Dennerl et al. (1997); copyright journal Science (1997).
ture radius at the comet of 1.2 × 105 km. [Note that the pho-
tometric luminosity depends on the energy bandpass and
on the observational aperture at the comet. The quoted value
assumes a ROSAT photon emission rate of PX ≈ 1025 s–1
(0.1–0.6 keV), in comparison to Krasnopolsky et al.’s (2000) impulsive spikes of a few hours’ duration, and maximum
EUVE estimate of PEUV ≈ 7.5 × 1025 s–1 (0.07–0.18 keV and amplitude 3 to 4 times that of the baseline emission level
120,000 km aperture.] A positive correlation between opti- (Lisse et al., 1996, 1999, 2001). Figure 4 demonstrates the
cal and X-ray luminosities was demonstrated using obser- strong correlation found between the time histories of the
vations of several comets having similar gas (QH2O) to dust solar wind proton flux (a proxy for the solar wind minor
[Afρ, following A’Hearn et al. (1984)] emission rate ratios ion flux), the solar wind magnetic field intensity, and a com-
(Fig. 3) (Lisse et al., 1997b, 1999, 2001; Dennerl et al., et’s X-ray emission for the case of Comet 2P/Encke 1997
1997; Mumma et al., 1997; Krasnopolsky et al., 2000). Lx (Lisse et al., 1999). Neugebauer et al. (2000) compared the
correlates more strongly with the gas production rate Qgas ROSAT and EUVE luminosity of C/1996 B2 (Hyakutake)
than it does with Lopt ~ Qdust ~ Afρ (Figs. 2 and 3). Particu- with time histories of the solar wind proton flux, oxygen
larly dusty comets, like Hale-Bopp, appear to have less X-ray ion flux, and solar X-ray flux, as measured by spacecraft
emission than would be expected from their overall optical residing in the solar wind. They found the strongest corre-
luminosity Lopt. The peak X-ray surface brightness decreases lation between the cometary emission and the solar wind
with increasing heliocentric distance r, independent of Q oxygen ion flux, a good correlation between the comet’s
(Dennerl et al., 1997), although the total luminosity appears emission and the solar wind proton flux, but no correlation
roughly independent of r. The maximum soft X-ray lumi- between the cometary emission and the solar X-ray flux.
nosity observed for a comet to date is ~2 × 1016 erg s–1 for For the four comets for which extended X-ray light-
C/Levy at 0.2–0.5 keV (Dennerl et al., 1997) (Fig. 3). curves were obtained during quiet Sun conditions, the time
delay between the solar wind proton flux and the comet’s
2.3. Temporal Variation X-ray impulse (Table 2) was well predicted by assuming a
simple latitude-independent solar wind flow, a quadrupole
Photometric lightcurves of the X-ray and EUV emission solar magnetic field, and propagation of the sector bound-
typically show a long-term baseline level with superimposed aries radially at the speed of the solar wind and azimuth-
 Lisse et al.: X-Ray and Extreme UV Emission from Comets 635

Fig. 4. Temporal trends for Comet 2P/Encke 1997 on 4–9 July Fig. 5. Chandra ACIS-S medium resolution CCD X-ray spec-
1997 UT. = ROSAT HRI lightcurve, 4–8 July 1997. = EUVE trum for Comet C/1999 S4 (LINEAR). Soft X-ray spectrum of
scanner Lexan B lightcurve 6–8 July 1997 UT, taken contempo- C/1999 S4 (LINEAR) obtained by the Chandra X-ray Observa-
raneously with the HRI observations, and scaled by a factor of 1.2. tory (crosses) and a six-line best-fit “model” spectrum (solid line).
All error bars are ±1σ. Also plotted are the WIND total magnetic The positions of several possible atomic lines are noted. Adapted
field Btotal ( ), the SOHO CELIAS/SEM 1.0–500-Å solar X-ray from Lisse et al. (2001).
flux ( ), and the SOHO CELIAS solar wind proton flux ( ).
There is a strong correlation between the solar wind magnetic
field/density and the comet’s emission. There is no direct corre-
lation between outbursts of solar X-rays and the comet’s outbursts.
for Comet C/1995 O1 (Hale-Bopp) (Owens et al., 1998).
After Lisse et al. (1997a).
These observations were capable of showing that the spec-
trum was very soft (characteristic thermal bremsstrahlung
temperature kT ~ 0.23 ± 0.04 keV) with intensity increasing
toward lower energy in the 0.01–0.60 keV energy range,
ally with period one-half the solar rotation period of 28 d and established upper limits to the contribution of the flux
(Lisse et al., 1997b, 1999; Neugebauer et al., 2000) from K-shell resonance fluorescence of carbon at 0.28 keV
and oxygen at 0.53 keV. However, even in these “best” spec-
∆t total = ∆t Carrington rotation + ∆tradial =
tra, continuum emission could not be distinguished from a
longitudecomet – longitudeEarth (rcomet – rEarth) multiline spectrum. Nondetections of Comets C/Hyakutake,
+
14.7˚/d 400 km/s ⋅ 86400 s/d C/Tabur, C/Hale-Bopp, and 55P/Temple-Tuttle using the
XTE PCA (2–30 keV) and ASCA SIS (0.6–4 keV) imaging
spectrometers were consistent with an extremely soft spec-
2.4. Spectrum trum (Lisse et al., 1996, 1997b).
Higher-resolution spectra of cometary X-ray emission
Until 2001, all published cometary X-ray spectra had have just appeared in the literature. The Chandra X-ray Ob-
very low spectral energy resolution (∆E/E ~ 1 at 300–600 eV), servatory (CXO) detected soft X-ray spectra from Comet
and the best spectra were those obtained by ROSAT for C/ C/1999 S4 (LINEAR) (Lisse et al., 2001) over an energy
1990 K1 (Levy) (Dennerl et al., 1997) and by BeppoSAX range of 0.2–0.8 keV, using an energy resolution with a full-

TABLE 2. Predicted and observed lightcurve phase shifts using the latitude-independent model.

Time of Impulse ∆tlong ∆tradial ∆ttotal ∆tobserved

Comet (00:00H UT) (d) (d) (d) (d)
Hyakutake 27 Mar 1996 –0.23 0.032 –0.20 –0.24
Hale-Bopp 11 Sep 1996 –4.60 5.9 1.30 +1.4
Encke 7 Jul 1997 –0.26 0.093 –0.17 –0.1
Temple-Tuttle 29 Jan 1998 –2.31 0.37 –1.94 –2.5
Time shifts assume solar wind velocity as measured near-Earth; positive time shifts = impulse happens at Earth first,
comet next; negative time shifts = boundary hits comet first, Earth next.
636 Comets II

Fig. 6. EUVE observations of line emission from C/1996 B2 (Hyakutake), following Krasnopolsky and Mumma (2001). (a) MW
(middle wavelength) 0.034–0.073 keV spectrum on March 23, 1996. (b) LW (long-wavelength) 0.018–0.04 keV. The extreme ultra-
violet spectra are clearly dominated by line emission. The best agreement with CXE model predictions are for the O4+, C4+, and Ne7+
lines. (c) FUSE observations of three comets, with a marginal detection of the CXE OVI line in C/2001 WM1 (LINEAR) at 1032 Å
(following Weaver et al., 2002). The nondetections in Comets C/2001 A2 (LINEAR) and C/1999 T1 (McNaught-Hartley) and the mar-
ginal detection in C/2001 WM1 (LINEAR) are consistent with CXE predictions for the luminosity of these lines.

width half-maximum (FWHM) of ∆E = 0.11 keV (Fig. 5). Hartley) and, more recently, in CXO spectra of C/2001 WM1
The spectrum is dominated by line emission, not by con- (LINEAR) and C/2002 Ikeya-Zhang (K. Dennerl et al. and
tinuum. Using the CXO, a new spectrum of Comet C/1999 C. M. Lisse et al., personal communication, 2003). An
T1 (McNaught-Hartley) (Krasnopolsky et al., 2002) shows XMM-Newton spectrum of C/2001 WM1 (LINEAR) shows
similar line-emission features. Line emission is also found characteristic CXE X-ray signatures in unprecedented detail
in XMM-Newton spectra of Comet C/1999 T1 (McNaught (K. Dennerl et al., personal communication, 2003). A re-
 Lisse et al.: X-Ray and Extreme UV Emission from Comets 637

analysis of archival EUVE Deep Survey spectrometer spec- Mechanisms based on dust grains also have a number
tra (Krasnopolsky and Mumma, 2001) suggests EUV line- of problems. It has been known since 1996 that Rayleigh
emission features from Comet C/1996 B2 (Hyakutake) scattering of solar X-ray radiation from ordinary cometary
(Figs. 6a,b). Recent FUSE observations (Weaver et al., dust grains (i.e., about 1 µm in size) cannot produce the
2002) also indicate the presence of possible O VI 1032-Å observed luminosities — the cross section for this process
emission lines in far-UV spectra of C/2001 WM1 (LIN- is too small (Lisse et al., 1996). A potential solution to this
EAR) (Fig. 6c). problem is to invoke a population of very small, attogram
(10 –19 g) grains with radii on the order of the wavelengths
3. PROPOSED X-RAY MECHANISMS of the observed X-ray radiation, 10–100 Å, which can reso-
nantly scatter the incident X-ray radiation. The abundance
A large number of explanations for cometary X-rays of such attogram dust grains is not well understood in com-
were suggested following the discovery paper in 1996. ets, as they are undetectable by remote optical observations;
These included thermal bremsstrahlung (German for “brak- however, there were reports from the VEGA Halley flyby
ing radiation”) emission due to solar wind electron colli- of a detection of an attogram dust component using the
sions with neutral gas and dust in the coma (Bingham et al., PUMA dust monitor (Vaisberg et al., 1987; Sagdeev et al.,
1997; Dawson et al., 1997; Northrop, 1997; Northrop et al., 1990). However, the statistical studies of the properties of
1997; Uchida et al., 1998; Shapiro et al., 1999), microdust several comets (Figs. 2 and 3) demonstrate that X-ray emis-
collisions (Ibadov, 1990; Ip and Chow, 1997), K-shell ion- sion varies with a comet’s gas production rate and not the
ization of neutrals by electron impact (Krasnopolsky, 1997), dust production rate (Dennerl et al., 1997; Lisse et al., 1999,
scattering or fluorescence of solar X-rays by cometary gas or 2001). Furthermore, the cometary X-ray lightcurves (Lisse
by small dust grains (Lisse et al., 1996; Wickramasinghe and et al., 1996, 1999, 2001; Neugebauer et al., 2000) corre-
Hoyle, 1996; Owens et al., 1998), and by charge exchange late with the solar wind ion flux and not with solar X-ray
between highly ionized solar wind ions and neutral species intensity. Finally, dust-scattering mechanisms cannot ac-
in the cometary coma (CXE) (Cravens, 1997a; Häberli et count for the pronounced lines seen in the new high-reso-
al., 1997; Wegmann et al., 1998; Kharchenko and Dalgarno, lution spectra — emission resulting from dust scattering of
2000; Kharchenko et al., 2003; Schwadron and Cravens, solar X-rays should mimic the Sun’s X-ray spectral con-
2000). In the thermal bremsstrahlung mechanism, fast elec- tinuum, similar to what is observed in the terrestrial atmos-
trons are deflected in collisions with charged targets, such phere for Rayleigh scattering of sunlight (Krasnopolsky,
as the nuclei of atoms, and emit continuum radiation. Elec- 1997).
tron energies in excess of 100 eV (T > 106 K) are needed for The CXE mechanism requires that the observed X-ray
the production of X-ray photons. In the K-shell mechanism, emission is driven by the solar wind flux and that the bulk
a fast electron collision removes an orbital electron from of the observed X-ray emission be in lines. Localization of
an inner shell of the target atom. Early evaluation of these the emission to the sunward half of the coma, a solar wind
various mechanisms (Dennerl et al., 1997; Krasnopolsky, flux-like time dependence, and a line-emission-dominated
1997; Lisse et al., 1999) favored only three of them: the spectral signature of the observed emission all strongly
CXE mechanism, thermal bremsstrahlung, and scattering of point to the solar wind charge exchange mechanism as
solar radiation from very small (i.e., attogram; 1 attogram = being responsible for cometary X-rays.
10 –19 g) dust grains.
A significant problem with mechanisms involving solar 4. SOLAR WIND CHARGE EXCHANGE
wind electrons (i.e., bremsstrahlung or K-shell ionization) X-RAY MECHANISM
is that the predicted emission luminosities are too small by
factors of 100–1000 compared to observations. The flux of The solar wind is a highly ionized but tenuous gas (i.e.,
high-energy solar wind electrons near comets is too low a plasma) (Cravens, 1997b). At its source in the solar co-
(Krasnopolsky, 1997; Cravens, 2000b, 2002a). Furthermore, rona, the million-degree gas is relatively dense and in colli-
X-ray emission has been observed out to great distances sional equilibrium, but its density drops within a few solar
from the nucleus, beyond the bow shock (Fig. 2), and the radii into a freeflow regime wherein collisions are infre-
thermal energy of unshocked solar wind electrons at these quent. Both the solar wind and corona have “solar” com-
distances is about 10 eV. No emission has ever been found position — 92% hydrogen by volume, 8% helium, and 0.1%
to be associated with the plasma tail of a comet, which has heavier elements. The heavier, “minor ion” species are
similar plasma densities and temperatures. Finally, the new, highly charged (e.g., oxygen in the form of hydrogen-like
high-resolution spectra demonstrating multiple atomic lines O7+ or helium-like O6+ ions, N6+/N5+, C5+/C4+, Ne8+, Si9+,
are inconsistent with a continuum-type mechanism or a Fe12+, etc.) due to the high coronal temperatures (Bame,
mechanism producing only a couple of K-shell lines as the 1972; Bocshler, 1987; Neugebauer et al., 2000).
primary source of cometary X-rays. Lisse et al. (2001) tried The solar wind flow starts out slowly in the corona but
several thermal bremsstrahlung continuum model fits to the becomes supersonic at a distance of few solar radii (Parker,
C/1999 S4 spectrum, and Krasnopolsky and Mumma (2001) 1963; Cravens, 1997b). The gas cools as it expands, fall-
tried the same for the C/1996 B2 (Hyakutake) spectrum, but ing from T ≈ 106 K down to about 105 K at 1 AU. The aver-
neither was successful. age properties of the solar wind at 1 AU are proton number
638 Comets II

density ≈7 cm–3, speed ≈450 km s–1, temperature ≈105 K, netic field lines pile up into a “magnetic barrier” in this stag-
magnetic field strength ≈5 nT, and Mach number ≈8 (Hund- nation region and drape around the head of the comet forming
hausen et al., 1968). However, the composition and charge the plasma tail in the downwind direction (Brandt, 1982).
state distribution far from the Sun are “frozen in” at coro- From experimental and theoretical work in atomic and
nal values due to the low collision frequency outside the molecular physics it is found that solar wind minor ions
corona. The solar wind contains structure, such as slow readily undergo charge transfer (or exchange) reactions
(400 km s–1) and fast (700 km s–1) streams, which can be (Phaneuf et al., 1982; Dijkkamp et al., 1985; Gilbody, 1986;
mapped back to the Sun. The solar wind “terminates” in a Janev et al., 1988; Wu et al., 1988) when they are within
shock called the heliopause, where the ram pressure of the ~1 nm of a neutral atomic species
streaming solar wind has fallen to that of the instellar ma-
terial (ISM) gas (Suess, 1990). The region of space that con-
Aq+ + B → A(q – 1)+* + B+ (1)
tains plasma of solar origin, from the corona to the helio-
pause at ~100 AU, is called the heliosphere. A very small
part of the solar wind interacts with the planets and comets; where A denotes the solar wind projectile ion (e.g., O, C,
the bulk of the wind interacts with neutral ISM gas in the Si . . . ), q is the projectile charge (e.g., q = 5, 6, 7) and B
heliosphere and neutral and ionized ISM material at the denotes the neutral target species (e.g., H2O, OH, CO, O,
heliopause. H . . . for cometary comae) (Fig. 8). The cross section for
As the solar wind streams into a comet’s atmosphere, this process is large, on the order of 10 –15 cm2, about 1 or-
cometary ion species produced from solar UV photoioniza- der of magnitude larger than the hardsphere collisional cross
tion of neutral coma gas species are added to the flow as section.
“pick-up ions.” The resulting mass addition slows down the The product ion deexcites by emitting one or more pho-
solar wind due to momentum conservation and a bow shock tons (A(q – 1)+* → A(q – 1)+* + hν, where hν represents a pho-
forms upwind of the comet (Galeev, 1991; Szegö et al., ton). It is the characteristic radiation of the product ion that
2000) (Fig. 7). The flow changes from supersonic to sub- is measured with astronomical X-ray instrumentation, and
sonic across the shock, and the magnetic field strength in- so one labels the radiation detected by the charge state of
creases by a factor of ~5. Closer to the nucleus, where the the final ion. The deexcitation usually takes place via a cas-
cometary gas density is higher and collisions more frequent, cade through intermediate states rather than in one step to
the flow almost completely stagnates (Flammer, 1991). The the ground state. For large enough values of q, the deexci-
outer boundary of this stagnation region is often called the tation transitions lead to the emission of X-ray photons. For
cometopause (cf. review by Cravens, 1991). The observed species and charge states relevant to comets, the principal
X-ray brightness peak resides within this boundary. Mag- quantum number of the ion A(q – 1)+ is about n = 4 or 5

Fig. 8. Energy level diagram for a CXE process. Electron po-

tential energy (atomic units, a.u.) vs. distance from the target atom
nucleus (assumed here to be an H atom) for a charge transfer
Fig. 7. Spatial schematic of the solar wind-comet interaction. reaction involving a projectile ion Be4+. The internuclear distance
The relative locations of the bow shock, the magnetic barrier, and chosen is 10 Bohr radii or 5.29 × 10 –10 m, the curve-crossing
the tail are shown (not to scale). The Sun is toward the left. Also distance for the n = 3 ion final state. The target energy level (and
represented is a charge transfer collision between a heavy solar binding energy Eb) and product ion (Be3+) energy levels are shown
wind ion and a cometary neutral water molecule, followed by the in units of hartrees (1 hartree = 27.2 eV). A possible cascading
emission of an X-ray photon. After Cravens (2002b); copyright pathway for the deexcitation by photon emission is shown. After
journal Science (2002). Cravens (2002b); copyright journal Science (2002).
 Lisse et al.: X-Ray and Extreme UV Emission from Comets 639

(Ryufuku et al., 1980; Mann et al., 1981). The cross section 4.2. Charge Exchange Luminosity
for charge exchange between a high charge state solar wind and Temporal Variation
ion and an ionized coma gas species is negligible in com-
parison, due to the effects of Coulomb repulsion between To first order, the CXE local X-ray power density Px can
the two reactants. Once a coma neutral atom is ionized, be estimated assuming only one CXE collision per solar
either by CXE processes or solar UV flux, the CXE mecha- wind ion per coma passage. This approximation yields the
nism is no longer an important energy transfer process. expression

4.1. Charge Exchange Morphology Px = αnswuswnn (2)

Numerical simulations of the solar wind interaction with where nsw usw, and nn are the solar wind proton density, solar
Hyakutake including CXE have been used to generate X-ray wind speed, and neutral target density respectively (Cra-
images. A global magnetohydrodynamic (MHD) model vens, 1997a, 2002a). All the “atomic and molecular details”
(Häberli et al., 1997) and a hydrodynamic model (Wegmann as well as the solar wind heavy ion fraction fh are combined
et al., 1998) were used to predict solar wind speeds and into the parameter α, given by α ≈ fh〈sct〉Eave, where 〈sct〉 is an
densities and the X-ray emission around a comet. The simu- average CXE cross section for all species and charge states,
lated X-ray images are similar to the observed images, and Eave an average photon energy. A simple spherically
which is relatively unsurprising, as any dissipative solar symmetric approximation to the neutral density in the coma
wind–coma process with total optical depth near unity is given by nn = Q/[4πunr2], for r less than the ionization
would create the observed morphology (Fig. 1). The emis- scale length R = unt, where t ≈ 106 s is the ionization life-
sion is found to lie in the sunward hemisphere of the neu- time [for 1 AU (Schleicher and A’Hearn, 1988)] and un ≈
tral coma, varying from collisionally thin to collisionally 1 km s–1 the neutral gas outflow speed. Integration of Px
thick as the solar wind approaches the nucleus. Emission over the volume of the neutral coma yields an X-ray lumi-
is predicted to be in the soft X-ray, UV, and optical wave- nosity typically within a factor of 2–3 of the observed lu-
lengths, with the softest photons emitted closest to the nu- minosity (Cravens, 1997a, 2000a; Lisse et al., 2001). The
cleus. However, the spatial models to date have included observed luminosity is a function of both the solar wind
only highly simplified models of the CXE deexcitation cas- flux density and the com-etary neutral gas production rate
cade, as compared to the detailed spectral models of the glo- up to the limit of 100% charge exchange efficiency of all
bal behavior discussed below. solar wind minor ions within an ionization scale length of
As an example of the potential of studying the behavior 106 km. The maximum expected X-ray luminosity at 1 AU
of the solar wind inside the coma using CXE reactions, we and 0.2–0.5 keV is ~1016 erg s–1 (Fig. 3). Temporal varia-
consider the dissimilar morphologies of the extended Ly- tions of the solar wind flux directly translate into time varia-
man α comae and the X-ray emitting regions of comets (cf. tions of the X-ray emission (Fig. 4).
Keller, 1973; Festou et al., 1979; Combi et al., 2000). The
CXE mechanism should not only transfer electrons from 4.3. Charge Exchange Spectra
cometary neutrals to solar wind minor ions, but to the so-
lar wind majority ions H+ and He2+ as well. These ions are Model CXE spectra are in good agreement with the low-
roughly 1000 times more abundant than the X-ray active resolution X-ray spectra of cometary X-ray emission, and
highly ionized minor ions. The prompt photon-emission the line centers of the high-resolution spectra have been
energy produced from CXE by He2+ ions produces at least successfully predicted using CXE theory (Figs. 5 and 6)
three times the energy released by all the minor ions com- (Lisse et al., 1999, 2001; Krasnopolsky and Mumma, 2001;
bined (D. Shemansky, personal communication, 2003). Weaver et al., 2002). The application of the CXE model to
Further, the neutral atoms produced are capable of scatter- comets has entailed a number of approaches to date. Some
ing emission from the Sun. At luminosities of ~1016 erg s–1, work has included only a few solar wind species but used a
and production rates of ~1027 s–1, the HI created by CXE careful cascading scheme (Häberli et al., 1997). Other ap-
should be detectable in Lyman α comet images. The fact proaches have used a simple cascading scheme and simple
that it is not is puzzling. A possible solution is that the neu- collision cross sections, but included a large number of
tral hydrogen atoms produced by CXE retain relatively large solar wind ions and charge states (Wegmann et al., 1998;
velocities with respect to the Sun, i.e., the solar wind is not Schwadron and Cravens, 2000). Kharchenko and colleagues
appreciably slowed at the cometary bow shock. This large (Kharchenko and Dalgarno, 2000; Kharchenko et al., 2003)
remnant velocity redshifts the CXE-produced neutral hydro- have treated the atomic cascading process more carefully
gen with respect to the peak of the solar Lyman α emission, than other modelers, although the spatial structure of the
so that fluorescence from these atoms is greatly reduced in solar wind–cometary neutral interaction in their model was
efficiency vs. H atoms produced from dissolution of comet- highly simplified. They predicted the existence of a large
ary water group species. Recently Raymond et al. (2002) number of atomic lines, including O5+ (1s25d → 1s22p) at
have reported the effects of highly redshifted neutral hydro- 106.5 eV, C4+ (1s2s → 1s2) at 298.9 eV, C5+ (2p → 1s) at
gen created by CXE emission in SOHO UVCS measure- 367.3 eV, C5+ (4p → 1s) at 459.2 eV, and O6+ (1s2p → 1s2)
ments of 2P/Encke during its 1997 apparition. at 568.4 eV. At least some of these lines appear in the best
640 Comets II

cometary X-ray spectra to date, the CXO ACIS-S spectra of Further theoretical progress will require the integration
C/1999 S4 (LINEAR) and C/1999 T1 (McNaught-Hartley). of several ingredients into a single model: (1) accurate solar
The peak measured near 0.56 keV is certainly the combi- wind composition for a range of solar wind types; (2) a
nation of three closely spaced helium-like O6+ (1s2p and suitable MHD model of the solar wind interaction with the
1s2s → 1s2) transitions (which comes from CXE of solar coma, in order to accurately predict the densities of ions
wind O7+) and the line located at 0.32 keV is due to helium- and neutrals in equation (2); and (3) a more detailed under-
like C4+ (1s2p and 1s2s → 1s2). Similar identifications have standing of the atomic processes, in order to improve our
been made for the EUVE spectrum of C/1996 B2 (Hyaku- understanding of the parameter α in equation (2). Success
take) (Krasnopolsky and Mumma, 2001). The spectral prob- for the first point requires new and improved measurements
lem is still far from totally solved, however. Careful com- of the solar wind throughout the heliosphere, and/or large
parisons and calculations needed to interpret the subtleties number statistical studies of cometary X-ray emission
of the high-resolution spectral observations, including the throughout the heliosphere; the second point requires im-
role of collisions after charge transfer, solar wind ion–dust proved MHD codes on modern supercomputers; and to
interactions, and the exact species present at each point in achieve the third point, additional laboratory measurements
the coma, are only now starting to be done (Krasnopolsky et of state-specific CXE cross sections will be required. The
al., 2002; Kellett et al., 2003). first and second points are being actively pursued by as-
tronomers and modelers in the field. New laboratory work
5. THE FUTURE OF COMETARY is now being undertaken (Beiersdorfer et al., 2000, 2001;
X-RAY EMISSION STUDIES Greenwood et al., 2000; Hasan et al., 2001) to measure
CXE cross sections for cometary target species such as H2O
The discovery that comets are X-ray sources can now at collision energies relevant to the solar wind (a few keV/
be explained by charge exchange reactions of highly charged amu). Recent measurements have indicated, for example,
solar wind ions with neutral atoms and molecules residing that multiple as well as single-electron CXE makes a con-
in the cometary coma. The energy required to power this tribution to the X-ray emission (Hasan et al., 2001; Green-
emission originates in the hot solar corona and is stored as wood et al., 2001; Gao and Kwong, 2002). Given detailed
potential energy in highly stripped solar wind ions (Cra- MHD models of the solar wind passing through the coma
vens, 2000a, 2002b; Dennerl, 1999). Charge exchange reac- and accurate cross sections for the CXE process, we will
tions with neutral species, like cometary coma neutral atoms be able to map out the density of solar wind minor ions in
and molecules, release this potential energy in the form of the coma.
X-ray and UV radiation. This simple model can explain the
gross features of the observed crescent-shaped emission 5.2. Remote Sensing of the Solar Wind
with its sunward displaced peak, the maximum spatial ex-
tent of the emission of ~106 km (Figs. 1 and 2), the maxi- Driven by the solar wind, cometary X-rays provide an
mum observed luminosity of ~1016 erg s–1 (Fig. 3), and spec- observable link between the solar corona, where the solar
tra dominated by line emission (Fig. 4). wind originates, and the solar wind where the comet resides.
Once we have understood the CXE mechanism’s behavior
5.1. Plasma-Neutral Interactions in the in cometary comae in sufficient detail, we will be able to
Cometary Coma use comets as probes to measure the solar wind through-
out the heliosphere. This will be especially useful in moni-
However, a more careful treatment of the CXE mecha- toring the solar wind in places hard to reach with space-
nism is needed to fully understand the phenomenon of com- craft — over the solar poles, at large distances above and
etary X-ray emission. One complication is that the multiple below the ecliptic plane, and at heliocentric distances greater
CXE collisions take place in regions close to the nucleus than a few AU (Lisse et al., 1996, 2001; Krasnopolsky et
where the target density is high (the so-called “collisionally al., 2000). For example, approximately one-third of the ob-
thick” case). The charge state for the initially hydrogen-like served soft X-ray emission is found in the 530–700-eV
or helium-like solar wind minor ion is reduced by one dur- oxygen O7+ and O6+ lines; observing photons of this energy
ing each CXE collision, ultimately leading to its conversion allows studies of the oxygen ion charge ratio of the solar
to a neutral atom. When the ion’s charge state becomes too wind, which is predicted to vary significantly between the
low, X-ray photons are no longer emitted. When the number slow and fast solar winds (Neugebauer et al., 2000; Schwad-
of neutrals in a volume of space becomes too low, due to ron and Cravens, 2000; Kharchenko and Dalgarno, 2001).
coma expansion and ionization of coma gas molecules by
solar UV radiation, X-ray photons are no longer detectable. 5.3. Emission from Other Planetary Systems
Another complication is that spectral differences are ex-
pected for slow and fast solar wind streams, with the slow The CXE mechanism operates wherever the solar wind
solar wind, with its higher coronal freeze-in temperature, (or any highly ionized plasma) interacts with a substantial
producing a harder spectrum than does the fast solar wind quantity of neutral gas. Motivated in part by the discovery
(Schwadron and Cravens, 2000). of the new class of cometary X-ray emitters, further meas-
 Lisse et al.: X-Ray and Extreme UV Emission from Comets 641

urements of potential solar system sources (Holmström et al., relations that have been found between measured solar wind
2001; Cravens and Maurellis, 2001) of X-ray emission have fluxes and measured X-ray background intensities (Cravens
been undertaken recently. X-rays have now been observed et al., 2001; Robertson et al., 2001). Recent large angular
from Venus as solar X-rays fluorescently scattered by the scale measurements of the diffuse soft X-ray background in
thick (compared to comets) venusian atmosphere (Dennerl a 100-s rocket flight by McCammon et al. (2002) and in the
et al., 2002), and from Mars as ~90% fluorescently scat- Chandra background toward MBM12 (R. Edgar et al., per-
tered solar X-rays from the thick martian atmosphere and sonal communication, 2001) show a clear peak at 560 eV, as
~10% CXE-derived X-rays (Dennerl, 2002). The solar wind expected for CXE-driven emission (Fig. 4). A significant frac-
is known to approach very closely to these planets due to tion of the line emission observed in the soft X-ray back-
their weak intrinsic magnetic fields, which cannot act as ef- ground, e.g., the 560-eV emission, is probably due to CXE
fective obstacles to the external flow, allowing for CXE pro- emission in our solar system and around other stars.
cesses to occur. The small spatial extent and high density
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644 Comets II
PART VII:
INTERRELATIONS
 Barucci et al.: Surface Characteristics of TNOs and Centaurs 647

Surface Characteristics of Transneptunian Objects

and Centaurs from Photometry and Spectroscopy
M. A. Barucci and A. Doressoundiram
Observatoire de Paris

D. P. Cruikshank
NASA Ames Research Center

The external region of the solar system contains a vast population of small icy bodies, be-
lieved to be remnants from the accretion of the planets. The transneptunian objects (TNOs)
and Centaurs (located between Jupiter and Neptune) are probably made of the most primitive
and thermally unprocessed materials of the known solar system. Although the study of these
objects has rapidly evolved in the past few years, especially from dynamical and theoretical
points of view, studies of the physical and chemical properties of the TNO population are still
limited by the faintness of these objects. The basic properties of these objects, including infor-
mation on their dimensions and rotation periods, are presented, with emphasis on their diver-
sity and the possible characteristics of their surfaces.

1. INTRODUCTION cally with even the largest telescopes. The physical char-
acteristics of Centaurs and TNOs are still in a rather early
Transneptunian objects (TNOs), also known as Kuiper stage of investigation. Advances in instrumentation on tele-
belt objects (KBOs) and Edgeworth-Kuiper belt objects scopes of 6- to 10-m aperture have enabled spectroscopic
(EKBOs), are presumed to be remnants of the solar nebula studies of an increasing number of these objects, and signifi-
that have survived over the age of the solar system. The cant progress is slowly being made.
connection of the short-period comets (P < 200 yr) of low We describe here photometric and spectroscopic studies
orbital inclination and the transneptunian population of pri- of TNOs and the emerging results.
mordial bodies (TNOs) has been established and clarified
on the basis of dynamics (Fernández, 1999), and it is gen- 2. OBSERVATIONAL STRATEGY AND
erally accepted that the Kuiper belt is the source region of DATA REDUCTION TECHNIQUES
these comets. Centaur objects appear to have been extracted
from the TNO population through perturbations by Neptune. 2.1. Photometry
While their present (temporary) orbits cross the orbits of
the outer planets, Centaurs do not come sufficiently close Visible- and near-infrared (NIR)-wavelength CCDs with
to the Sun to exhibit normal cometary behavior, although broad-band filters operating in the range of 0.3 to 2.5 µm
2060 Chiron has a weak and temporally variable coma. provide the basic set of observations on most objects dis-
We do not know if the traditional and typical short-period covered so far, yielding color indices, rotational properties
comets, which have dimensions of a few kilometers to less and estimates of the sizes of TNOs. The color indices (e.g.,
than 1 km, are fragments of TNOs or if they are themselves U-V, B-V, V-R, V-I, V-J, V-H, V-K) are the differences be-
primordial objects. The surface material of TNOs may not tween the magnitudes measured in two filters, and repre-
survive entry into the inner solar system (Jewitt, 2002) sent an important tool to study the surface composition of
where it can be observed and (eventually) sampled, so it is these objects and to define a possible taxonomy. [The broad-
particularly important to investigate the composition of band filters commonly used (and their central wavelength
TNOs, which may be the most primitive matter in the solar position in micrometers) are U (0.37), B (0.43), V (0.55),
system. The surfaces of the Centaurs may represent inter- R (0.66), I (0.77), J (1.25), H (1.65), and K (2.16).]
mediate stages in the compositional evolution of TNOs to Because of their faintness, slow proper motion, and ro-
short-period comets. tation, TNOs require specific observational procedures and
As a consequence of their great distances and relatively data reduction techniques. The typical apparent visual mag-
small dimensions, TNOs and Centaur objects are very faint; nitude is about 23 or fainter, although a few objects brighter
the first one, discovered by Jewitt and Luu (Jewitt et al., than 22 have been found. A signal-to-noise ratio (SNR) of
1992) at magnitude ~22.8 was some 7400 times fainter than about 30 (precision of 0.03–0.04 mag) is the photometric
Pluto. Even the brightest TNOs presently known are mag- accuracy required for color analysis. Two problems limit
nitude ~19, making them difficult to observe spectroscopi- the signal precision achievable: (1) the sky contribution to

647
648 Comets II

the measured signal and (2) the contamination of the sig- Spectroscopic observations face the same problems as
nal by unseen background sources, such as field stars and photometric observations due to the specific nature of TNOs
galaxies. For instance, the error introduced by a magnitude discussed in the previous section. With 8-m-class telescopes,
26 background source superimposed on an object of mag- the limiting magnitude at the present time is V = 22.5 mag
nitude 23 is as large as 0.07 mag. One solution for allevi- for visible spectroscopy, and the object must be brighter
ating these problems is the use of a very small synthetic than ~21 mag (in V) for NIR spectroscopy. On the same
aperture around the object when measuring its flux on a large-aperture telescope, the exposure time required is be-
CCD image, and the application of the aperture correction tween one and several hours for the faintest objects. Dur-
technique (Howell, 1989). ing long exposures the rotation rate is not negligible and
Even though TNOs orbit at large heliocentric distances, the resulting spectra probably arise from signals from both
their motion on the sky restricts observations to relatively sides of the object. Careful removal of the dominant sky
short exposure times. At opposition, the nonsidereal mo- background (atmospheric emission bands) in the infrared
tions of TNOs at 30, 40, and 50 AU are about 4.2, 3.2, and and the choice of good solar analogs are essential steps to
2.6"/h respectively, thus producing a trail of ~1.0" in 15-min ensure high-quality data.
exposure time (in the worst case). Trailed images have dev-
astating effects on the SNR since the flux is diluted over a 3. DIAMETER, ROTATIONAL
larger and noisier area of background sky. Thus, increasing PROPERTIES, AND SHAPE
exposure time will not improve the SNR. Practically, expo-
sure times should be chosen so that the trail length does not Many useful physical and compositional parameters of
exceed the seeing disk. One alternative would be to follow TNOs can be derived from broadband photometry. Size,
the object at its proper motion. But in this case the point rotational properties, and shape are the most basic param-
spread function (PSF) of the object is different from field eters defining a solid body. The rotation spin can be the re-
stars, thus thwarting the aperture correction technique, which sult of the initial angular momentum determined by forma-
must be calibrated from the PSFs of nearby field stars. The tion processes, constraining the origin and evolution of this
proper motions of TNOs and the long exposure times needed population of objects. Some of the large TNOs might con-
to detect them at an adequate SNR limit the number of ob- serve their original angular momentum, while many others
jects that can be observed, even with a big telescope. For suffered collisional processes and do not retain the memory
each individual B, V, R, etc., magnitude obtained, 1σ un- of the primordial angular momentum.
certainties are based on the combination of several uncer-
tainties: σ = (σpho2 + σap2 + σcal2)1/2, where the photometric 3.1. Diameter
uncertainty (σpho) is based on photon statistics and sky noise,
the uncertainty on the aperture correction (σap) is determined The sizes of TNOs cannot be measured directly, as the
from the dispersion among measurements of the different objects are not in general spatially resolved. At the time of
field stars, and σcal is the uncertainty derived from absolute writing the largest known TNO, 50000 Quaoar, is resolved
calibration through standard stars. in an HST image at 40.4 ± 1.8 milliarcsec, yielding a diam-
eter of 1260 ± 190 km (Brown and Trujillo, 2003). Only a
2.2. Spectroscopy few objects have been observed at thermal and millimetric
wavelengths and thus have directly determined diameters
Reflectance spectroscopy (0.3 to 2.5 µm) provides the and albedos (Table 1), while for the majority an indication
most sensitive and broadly applied remote sensing tech- of the diameter can be obtained from the absolute magni-
nique for characterizing the major mineral phases and ices tude, assuming an albedo value. With an assumed value for
present on TNOs. At visible and NIR wavelengths, recog- the surface albedo pv of an object, the absolute magnitude
nizable spectral absorptions arise from the presence of the (H) can be converted into the diameter D (km) using the
silicate minerals pyroxene, olivine, and sometimes feldspar, formula from Harris and Harris (1997). Owing to the lack
as well as primitive carbonaceous assemblages and organic of available albedo measurements, it has become the con-
tholins. The NIR wavelength region carries signatures from vention to assume an albedo of 0.04–0.05, which is com-
water ice (1.5, 1.65, 2.0 µm), other ices (CH4 around 1.7 mon for dark objects and cometary nuclei (e.g., Lamy et
and 2.3 µm, CH3OH at 2.27 µm, and NH3 at 2 and 2.25 µm), al., 2004). This assumption introduces a large uncertainty
and solid C-N bearing material at 2.2 µm. Water-bearing in the size estimates; for instance, if we instead used an
minerals such as phyllosilicates also exhibit absorption fea- albedo of 0.14 (i.e., the albedo of the Centaur 2060 Chiron),
tures at visible wavelengths. all the size estimates would have to be divided by about two.
Although the most reliable mineralogical interpretations
require measurements extending into the NIR, measure- 3.2. Rotational Period
ments restricted to the visible wavelengths (0.3–1.0 µm) can
be used to infer information on the composition, particularly The observed variations of brightness with time allow
for the especially “red” objects, whose reflectance increases the determination of the rotational period of a body. In
rapidly with wavelength in this region (see below). Table 1 a fairly complete list of the most reliably determined
 Barucci et al.: Surface Characteristics of TNOs and Centaurs 649

TABLE 1. Dynamical type (Centaurs and classical, Plutinos and scattered for the TNOs),
rotational period, lightcurve amplitude, diameters, albedo, and spectral signature
characteristics for each object (numbers shown in brackets are references).

Amplitude Diameter
Name Type Rotation Periods (h) (mag) (km) Albedo pv Spectral Signatures*
2060 Chiron Centaur 5.917813 ± 0.000007 [1] 0.04 [1] 148 ± 8 [2] 0.17 ± 0.02 [2] H2O ice varying with
activity
5145 Pholus Centaur 9.9825 ± 0.0040 [3] 0.15 [3] 190 ± 22 [4] 0.04 ± 0.03 [4] Water ice + hydrocarbons
8405 Asbolus Centaur 8.9351 ± 0.0003 [5] 0.55 [5] 66 ± 4 [2] 0.12 ± 0.03 [2] Controversial
10199 Chariklo Centaur Long ? [6] 0.31 [6] 302 ± 30 [7] 0.045 ± 0.010 [7] H2O ice
273 ± 19 [8] 0.055 ± 0.008 [8]
15789 (1993 SC) Plutino 15.43 [9]? 0.5 [9] 328 ± 66 [10] 0.022 ± 0.013 [10] Controversial
19308 (1996 TO66) Classical 7.9 [11] 0.25 [11] ≈748 — H2O ice
6.25 ± 0.01 [12] 0.12–0.33 [12] Variation
20000 Varuna Classical 6.3442 ± 0.0002 [13] 0.42 [13] 1060 ± 220 [14] 0.038 ± 0.022 [14] H2O ice
6.3576 ± 0.0002 [14] 0.42 [14] 900 ± 145 [15] pR = 0.07 ± 0.03 [15]
26308 (1998 SM165) Classical 7.966 [16] 0.56 [16] ≈411 —
7.1 [11] 0.45 [11]
26375 (1999 DE9) Scattered No variation over 24 h [17] ≈682 — Hydrous silicates
28976 Ixion Plutino 1065 ± 165 [23] — No features
31824 Elatus Centaur 13.25? [18] 0.24 [18] ≈57 — H2O ice?
13.41 ± 0.04 [19] (single peak) 0.102 [19] Variation?
32532 Thereus Centaur 8.3 [22] 0.16 [22] ≈95 — Surface variation
8.3378 ± 0.0012 [20] 0.18 [20]
32929 (1995 QY9) Plutino 7.3 [11] 0.60 [11] ≈188 —
33128 (1998 BU48 ) Centaur 9.8–12.6 [17] 0.68 [17] ≈216 —
35671 (1998 SN165) Classical 10.1 ± 0.8 [21] 0.15 [21] ≈411 —
38628 Huya Plutino No variation over 24 h [5] <0.06 [17] ≈682 — Hydrous silic.?
40314 (1999 KR16 ) Classical 11.680 ± 0.002 [17] 0.18 [17] ≈411 —
47171 (1999 TC36 ) Plutino ≈622 — H2O ice
47932 (2000 GN171) Plutino 8.329 ± 0.005 [17] 0.61 [17] ≈375 — Nonident.
52872 Oxyrhoe Centaur ≈33 — H2O ice?
54598 (2000 QC243) Centaur 4.57 ± 0.04 [22](single peak) 0.7 [22] ≈180 — H2O ice?
*Descriptions of the spectra and related references are given in section 5.
When the albedo is not available (—) an approximate diameter has been computed assuming an albedo of 0.05.
References: [1] Marcialis and Buratti (1993); [2] Fernández et al. (2002); [3] Buie and Bus (1992); [4] Davies et al. (1993); [5] Davies et al. (1998); [6] Peixinho et al.
(2001); [7] Jewitt and Kalas (1998); [8] Altenhoff et al. (2001); [9] Williams et al. (1995); [10] Thomas et al. (2000); [11] S. Sheppard (personal communication, 2003);
[12] Hainaut et al. (2000); [13] Jewitt and Sheppard (2002); [14] Lellouch et al. (2002); [15] Jewitt et al. (2001); [16] Romanishin et al. (2001); [17] Sheppard and Jewitt
(2002); [18] Gutiérrez et al. (2001); [19] Bauer et al. (2002); [20] Farnham and Davies (2003); [21] Peixinho et al. (2002); [22] Ortiz et al. (2002); [23] D. Jewitt (personal
communication, 2003).

results is presented. The faintness of these objects makes some indication on the elongation of the body. Assuming a
the analysis of the lightcurves difficult. In a photometric triaxial ellipsoid shape with semimajor axes a > b > c and
study by Sheppard and Jewitt (2002), 9 of 13 objects meas- no albedo variation, we can estimate the lower limit of the
ured showed no detectable variation, implying a small ampli- semimajor axis ratio: a/b ≥ 10 0.4∆m.
tude, or a period ≥24 h, or both. Some objects show hints of A few large TNOs seem to have elongated shapes (Shep-
variability that might yield a lightcurve with higher-quality pard and Jewitt, 2002). For example, using ∆m = 0.61 mag
data. The rotational periods seem to range between 6 and (see Table 1) for 47932 (2000 GN171), an estimate of a/b ≥
15 h, but a bias effect can exist because of the difficulty in 1.75 can be obtained. Sheppard and Jewitt, analyzing all
determining long periods and the faintness of these objects. the available lightcurves, found that over 22 objects, 32%
have ∆m ≥ 0.15 mag, while 23% have ∆m ≥ 0.4 mag.
3.3. Shape
4. TRENDS AND COLOR PROPERTIES
Stellar occultations and photometric observations can
give important but limited information on the shape of these From broadband photometric observations, colors and
bodies, although no occultation results are available at the spectral gradients are used for statistical analysis and to
present time due to the lack and the difficulty of precise search for relationships among physical properties and or-
predictions. About 5% of the total number of TNOs seem bital characteristics.
to have companion objects and are therefore binary (Noll
et al., 2002). The first object discovered to have a compan- 4.1. Color Diversity
ion was 1998 WW31 (Veillet et al., 2002).
The lightcurve is the only technique currently available One of the most puzzling features of the objects in the
to give contraints on the shape. The amplitude can give Kuiper belt, and one that has been confirmed by numerous
650 Comets II

On the other hand, and paradoxically, there is a com-

plete consensus for continuous color diversity when the
color analysis is extended to longer wavelengths. For in-
stance, color-color plots similar to Fig. 1 that include the I
filter (~0.77 µm) or J filter (~1.2 µm) do not show any evi-
dence of color bimodality (see Boehnhardt et al., 2001;
Jewitt and Luu, 2001).
The information contained in the color indices can be
converted into a very-low-resolution reflectance spectrum,
as illustrated in Fig. 2. Reflectance spectra have been com-
puted using BVRIJ color data of the object (with the color
of the Sun removed). [The reflectance spectrum R(λ) is
given by R(λ) = 10–0.4 [(M(λ) – M(V)) – (M(λ) – MSun(V))], where
M and MSun are the magnitude of the object and of the Sun
at the considered wavelength. The reflectance is normalized
to 1 at a given wavelength (conventionally, the V central
wavelength, 0.55 µm).] The spectra range from neutral or
slightly red to very red, thus confirming the wide and con-
Fig. 1. B-V vs. V-R plot of the transneptunian objects. The dif- tinuous diversity of surface colors suggested by the individ-
ferent classes of TNOs are represented: Plutinos, classical, and ual color-color diagrams. Almost all the objects are charac-
scattered. The star represents the colors of the Sun. From Dores- terized by a linear reflectance spectrum, with no abrupt and
soundiram et al. (2002). significant changes in the spectral slope (within the error
bars) over the whole wavelength range. This result was con-
firmed by McBride et al. (2003) on a large dataset of 29
mostly simultaneous V-J colors. They found their V-J col-
surveys, is optical color diversity. This diversity is peculiar ors broadly correlated with published optical colors, thus
to the outer solar system bodies and exceeds that of the suggesting that a single coloring agent is responsible for
asteroids, cometary nuclei, and small planetary satellites. the reddening from the B (0.4 µm) to the J (1.2 µm) regime.
Originally pointed out in Luu and Jewitt (1996a), this color
diversity is an observational fact that is widely accepted by
the community (e.g., Barucci et al., 2000b; Doressoundiram
et al., 2001; Jewitt and Luu, 2001; Delsanti et al., 2001;
Tegler and Romanishin, 2000; Boehnhardt et al., 2002, and
references therein). Colors range continuously from neutral
(flat spectrum) to very red (see Fig. 1). The different dynam-
ical classes (e.g., Centaurs, Plutinos, classical, and scattered)
seem to share the same color diversity. However, Tegler and
Romanishin (1998) concluded earlier, on the basis of the
visible (B-V vs. V-R) colors derived from 11 TNOs and 5
Centaurs, that there are two distinct populations: one with
objects having neutral or slightly red colors similar to the
C asteroids, and the other one including the reddest objects
known in the solar system. They confirmed this result later
on a larger dataset of 32 objects (Tegler and Romanishin,
2000) but with a lesser separation between the two popu-
lations in a color-color plot. Other groups working on this
subject could not confirm this bimodality of color distribu-
tion. In particular, Doressoundiram et al. (2002), on the
basis of a larger and homogeneous BVR dataset of 52 ob-
jects, did not see any clear and significant bimodality of
color distribution. Hainaut and Delsanti (2002) have per-
formed some statistical tests on a combined color dataset
of 91 Centaurs and TNOs. They cautiously concluded that
almost all the color-color distributions are compatible with Fig. 2. Example of reflectivity spectra of TNOs and Centaurs,
both a continuous and a bimodal distribution. High-quality normalized at the V filter (centered around 550 nm). Color gradient
data with very small error bars will be necessary to estab- range from low (neutral spectra) to very high (very red spectra).
lish the final word on this issue. From color data of Barucci et al. (2001).
 Barucci et al.: Surface Characteristics of TNOs and Centaurs 651

This remarkable property may help identify the agent

among the low-albedo minerals with similar colors (Jewitt
and Luu, 2001).
The extreme color diversity seen among the outer solar
system objects is usually attributed to the concomitant ac-
tion of two competing mechanisms acting on the TNOs over
the age of the solar system. First, space weathering due to
solar radiation processing and solar or galactic cosmic-ray
irradiation both tend to the reddening of surfaces of all air-
less objects. Second, the resurfacing effect of mutual colli-
sions among TNOs would regularly restore neutral-colored
ices to the surface. This is the so-called collision-resurfacing
hypothesis CRH (Luu and Jewitt, 1996a). Collisions and
irradiation have reworked the surfaces of TNOs, especially
in the inner part of the belt, and extensive cratering can be
expected to characterize their surfaces (Durda and Stern,
2000). Another resurfacing process resulting from possible
sporadic cometary activity has been suggested (Hainaut et
al., 2000). Resurfacing by ice recondensation from a tem- Fig. 3. Inclination vs. B-R color plot of classical objects. The
porary atmosphere produced by intrinsic gas and dust activ- linear least-squares fit has been plotted to illustrate the correla-
ity might be an efficient process affecting the TNOs closest tion. From Doressoundiram et al. (2002).
to the Sun (the Plutinos).

4.2. Correlations

To date, B-V, V-R, and V-I colors are available for more needed in order to investigate the real compositional taxon-
than 150 objects, while only a few tens of them have V-J omy of the transneptunian and Centaur objects.
colors determined (Davies et al., 1998, 2000; Jewitt and Luu, Jewitt and Luu (1998) presented a linear relationship
1998; McBride et al., 2003). A few of them have measured between V-J and body size, implying that the smaller ob-
J-H and H-K colors. With this significant dataset, especially jects are systematically redder, a result subsequently invali-
in the visible spectral region, we can now extend physical dated by Davies et al. (2000) on a much larger dataset. Such
studies of TNOs from merely description to extended char- a relationship, if found, would have been important because
acterization by performing statistical analysis and deriving it is a prediction of the collisional resurfacing hypothesis.
some potentially significant trends. Some of the outstand- Objects with perihelion distances around and beyond
ing questions include: (1) Are the surface colors of the Cen- 40 AU are mostly very red. This characteristic was origi-
taur and TNOs homogeneous? (2) Is it possible to define a nally pointed out by Tegler and Romanishin (2000), who
taxonomy, as for the asteroids? (3) Are there any trends with also noticed, as did Doressoundiram et al. (2001), that clas-
physical and orbital parameters? For instance, are there any sical objects with high eccentricity and inclination are pref-
trends in color with size? erentially neutral/slightly red, while classical objects at low
On the first point, we note that there is a general agree- eccentricity and inclination are mostly red (Plate 18). This
ment between colors measured by different observers at feature was first quantified by Trujillo and Brown (2002),
random rotational phases, suggesting that color variation is who found a significant 3.1σ correlation between color and
rare. However, Doressoundiram et al. (2002) have high- orbital inclination (i) for classical and scattered objects. A
lighted a few objects among the 52 objects of their survey, similar but stronger correlation (3.8σ) was later found by
for which color variation has been found and thus that may Doressoundiram et al. (2002) on a homogeneous dataset
be diagnostic of true surface compositional and/or texture of 22 classical objects that did not include the scattered
variation. The issue of the color heterogeneity remains objects (Fig. 3). It is noteworthy that such a correlation was
ambiguous. not seen among the Plutinos or the Centaurs. Instead, Plu-
The TNOs exhibit a wide range of V-J colors. Based on tinos appear to lack any clear color trends. Hainaut and Del-
a sample of 22 BVRIJ data, Barucci et al. (2001) made the santi (2002), as well as Doressoundiram et al. (2002), found
first statistical analysis of colors of TNOs population, find- also significant correlations with orbital excentricity (e) and
ing four “classes” showing a quasicontinuous spreading of perihelion distance (q) for the classical TNOs, although less
the objects between two end members (those with neutral strong than with (i). Levison and Stern (2001) also found
spectra and those with the reddest known spectra). The most that low-i classical TNOs are smaller (greater H). Strikingly,
important contribution in discriminating the “classes” comes Jewitt and Luu (2001) did not find any correlation with
from the V-J reflectance. This fact shows the necessity of color in their sample of 28 B-I color indices. This apparent
the V-J color in any taxonomic work. A larger dataset is discrepancy is certainly due to the high proportion of reso-
652 Comets II

nant objects included in their sample that completely masks puted reflectance slopes range from 0 or slightly negative
the correlation. (in the case of Chiron) up to 58%/100 nm for Pholus or
Hainaut and Delsanti (2002) analyzed a combined data- Nessus, which are the reddest known objects in the solar
set of 91 Centaurs and TNOs. Although large, this dataset system. The computed slopes vary a little as a function of
is not homogeneous, as the colors were collected and com- the wavelength range analyzed, but do not seem to be re-
bined from different sources. They found a trend for classi- lated to the perihelion distance of the objects.
cals with faint H to be redder than the others, but the trend is Broad absorptions have been found only for two Pluti-
opposite for the Plutinos (faint H tends to be bluer). Dores- nos: 38628 Huya and 47932 (2000 GN171). In the spectrum
soundiram et al. (2002) did not find any correlation with of 47932 (2000 GN171), an absorption centered at around
size in their homogeneous but smaller dataset. These con- 0.7 µm has been detected with a depth of ~8%, while in
flicting results require confirmation by the analysis of a the spectrum of 38628 Huya two weak features centered at
larger dataset, but in any case the physical interpretation 0.6 µm and at 0.745 µm have been detected with depths of
remains difficult. ~7% and 8.6% respectively (Lazzarin et al., 2003). These
Although hypothetical, the collisional resurfacing sce- features are very similar to those due to aqueously alterated
nario offers the advantage of making relatively simple pre- minerals, found in some main-belt asteroids (Vilas and
dictions concerning the color correlation within the Kuiper Gaffey, 1989, and subsequent papers). Since hydrous ma-
belt. Basically, the most dynamically excited objects should terials seem to be present in comets, and hydrous silicates
be most affected by energetic impacts, and thus should have are detected in interplanetary dust particles (IDPs) and in
the most neutral colors. Several authors (Hainaut and Del- micrometeorites (and probably originated in the solar neb-
santi, 2002; Doressoundiram et al., 2002; Stern, 2002) have ula), finding aqueous altered materials in TNOs would not
found a good correlation between the color index and be too surprising (see de Bergh et al., 2003).
Vk(e2 + i2)½, apparently because both i and e contribute to In the infrared region some spectra are featureless, while
the average encounter velocity of a TNO. some others show signatures of water ice and methanol or
Considering that optical and infrared colors are corre- other light hydrocarbon ices. Very few of these objects have
lated, one could presume that the correlations found be- been well studied in both visible and NIR and rigorously
tween orbital parameters and optical colors can be general- modeled. In fact, these objects are faint, and even observa-
ized to infrared colors. Indeed, the V-J observations have a tions with the largest telescopes [Keck and the Very Large
much wider spectral range and are therefore likely to be Telescope (VLT)] do not generally yield good-quality spec-
more robust in showing color correlations. However, such tra. The interpretation is also very difficult because the
statistical analysis is still tentative because of the relatively behavior of models of the spectra depends on the choice
few V-J colors available. The first such attempt made by of many parameters. Some of the visible and NIR spectra
McBride et al (2003) seems to support the color and peri- obtained at VLT [European Southern Observatory (ESO),
helion distance, as well as the color and inclination rela- Chile] are shown in Fig. 4, with the best model fitting of
tionships. the data. The general spectral characteristics are listed in
Table 1.
5. VISIBLE AND INFRARED A general review of Centaurs is presented in Barucci
SPECTROSCOPY et al. (2002a), while details of a few objects, recently ob-
served, are discussed below.
Broadband photometric observations can provide rough 8405 Asbolus has yielded controversial results: Brown
information on the surface of the TNOs and other objects, (2000) and Barucci et al. (2000a) observed it, finding no
but the most detailed information on their compositions can spectral signatures in the NIR. Later, Kern et al. (2000),
be acquired only from spectroscopic observations, espe- using the HST, obtained several (1.1–1.9 µm) spectra, which
cially in the NIR spectral region. Unfortunately, most of the revealed a significantly inhomogeneous surface character-
known TNOs are too faint for spectroscopic observations, ized on one side by water ice mixed with unknown low-
even with the world’s largest telescopes, and so far only the albedo constituents. They speculated that the differences
brightest have been observed by visible and infrared spec- across the surface of Asbolus might be caused by an im-
troscopy. pact that penetrated the object’s crust, exposing the under-
The first visible spectrum of a TNO, 15789 (1993 SC), lying ice in the surface region. Romon-Martin et al. (2002)
was observed by Luu and Jewitt (1996b), who obtained a re-observed Asbolus at VLT (ESO, Chile), obtaining five
reddish spectrum that is intermediate in slope between those high-quality infrared spectra covering the full rotational
of the Centaurs 5145 Pholus and 2060 Chiron. Others have period, and found no absorption features at any rotational
been observed subsequently, but only a few data are avail- phase. Using different radiative transfer and scattering
able; 5 Centaurs have been observed by Barucci et al. models (Douté and Schmitt, 1988; Shkuratov et al., 1999),
(1999), 5 TNOs by Boehnhardt et al. (2001), and 12 TNOs Romon-Martin et al. (2002) modeled the complete spectrum
and Centaurs by Lazzarin et al. (2003). The spectra show from 0.4 to 2.5 µm with several mixtures of Triton tholins,
a generally featureless behavior with a difference in the Titan tholins, ice tholins, amorphous carbon, and olivine.
spectral gradient ranging from neutral to very red. The com- None of the models successfully matched the visible part
 Barucci et al.: Surface Characteristics of TNOs and Centaurs 653

important constraint on the modeling, but on the assump-

tion of a low-albedo surface two models have been com-
puted to interpret the different behavior of the two spectra.
One spectrum seems to be well fitted with a model con-
taining 15% Titan tholin, 70% amorphous carbon, 3% oli-
vine, and 12% ice tholin, and having an albedo of 0.09
(shown in Fig. 4). For the other spectrum an acceptable
model with an albedo of 0.06 and 90% amorphous carbon,
5% Titan tholin, and 5% water ice was obtained.
Dotto et al. (2003b) observed two Centaurs: 52872
(1998 SG35), now named Oxyrhoe, and 54598 (2000 QC243)
in the H and K regions, giving tentative models of these two
bodies with similar percentages of kerogen (96–97%), oli-
vine (1%), and water ice (2–3%) (Fig. 4).
63252 (2001 BL41) has been observed by Doressoun-
diram et al. (2003). A model with 17% Triton tholin, 10%
ice tholin, and 73% amorphous carbon fits the spectrum.
31824 Elatus was found by Bauer et al. (2002) to have
markedly different spectral reflectance when observed on
two successive nights. While one spectrum shows a rather
neutral reflectance, 1.2–2.3 µm, the other shows a strong red
reflectance extending to 2.3 µm, with absorption bands ap-
proximately matched by a model using amorphous H2O ice.
The TNOs are even fainter than Centaurs, and only a few
Fig. 4. V + NIR spectra of two TNOs and five Centaurs obtained spectra are available, generally with very low SNR. Al-
at VLT, ESO, with FORS and ISAAC. The spectra, normalized though only a small number have been observed to date,
to 1 on V, have been shifted in relative reflectance by 1 for clar- their surface characteristics seem to show wide diversity.
ity. The dots represent the V, J, H, and K colors, used to adjust 15874 (1996 TL66) and 28978 Ixion have flat featureless
the spectral ranges. A best-fit model is shown for each spectrum spectra similar to that of water ice contaminated with low-
(see section 5 for details).
albedo, spectrally neutral material (Luu and Jewitt, 1998;
Licandro et al., 2002). 15789 (1993 SC), observed by Brown
et al. (1997), shows features that may be due to hydrocar-
bon ices with a general red behavior suggesting the pres-
of the spectrum, while the best fit to the infrared part was ence of more complex organic solids. Jewitt and Luu (2001)
obtained with 18% Triton tholin, 7% Titan tholin, 55% amor- also observed 1993 SC with the same telescope and found a
phous carbon, and 20% ice tholin (Fig. 4). The steep red featureless spectrum. The difference in these results requires
spectral slope is the principal characteristic of the data that resolution, best accomplished with additional (and higher-
forces the use of organic compounds (kerogen, tholins, etc.) quality) data. McBride et al. (2003) show that 1993 SC is
in the models. Kerogen is necessary to reproduce the red one of the reddest TNOs studied so far.
slope of spectra in the visible region, while tholins (Khare 38628 Huya has been observed by many authors (Brown
et al., 1984) are the only materials (for which optical con- et al., 2000; Licandro et al., 2001; Jewitt and Luu, 2001;
stants are available) able to reproduce the unusual red slope deBergh et al., 2003) and appears generally featureless in
(0.4–1.2 µm). Both Titan and ice tholins are synthetic mac- the NIR [except Licandro et al. (2001) and de Bergh et al.
romolecular compounds, produced from a gaseous mixture (2003) show that a possible feature appears beyond 1.8 µm].
of N2:CH4 (Titan tholins) or an ice mixture of H2O:C2H6 The interpretation of these spectra is challenging.
(ice tholins). 19308 (1996 TO66) shows an inhomogeneous surface
10199 Chariklo, after the first detection of water ice by with clear indications of water ice absorptions at 1.5 and
Brown and Koresko (1998) and by Brown et al. (1998), was 2 µm. A model of water ice mixed with some other minor
observed again by Dotto et al. (2003a), who still confirmed components matches the region 1.4–2.4 µm (Brown et al.,
water ice detection and showed small spectral behavior var- 1999). Evidence that the intensity of water ice bands varies
iation (Fig. 4). with the rotational phase suggests a patchy surface. 20000
32532 (2001 PT13), now named Thereus, was observed Varuna also shows a deep water-ice absorption band (Lican-
(Barucci et al., 2002b) from 1.1 to 2.4 µm at two different dro et al., 2001), while 26181 (1996 GQ21), observed by
epochs and the spectra seem quite different, indicating spa- Doressoundiram et al. (2003), shows a featureless spectrum
tial differences in the surface composition. One of the ob- interpreted with a geographical mixture model composed
servations shows clear evidence for a small percentage of of 15% Titan tholin, 35% ice tholin, and 50% amorphous
water ice. The lack of albedo information eliminates one carbon (Fig. 4).
654 Comets II

In contrast, 26375 (1999 DE9) shows solid-state absorp- semitransparent components, inhomogeneous transparent
tion features near 1.4, 1.6, 2.00, and probably at 2.25 µm grains, etc.) have begun to emerge (e.g., Douté and Schmitt,
(Jewitt and Luu, 2001). The location of these bands has 1998; Shkuratov et al., 1999).
been tentatively interpreted by Jewitt and Luu as evidence Real planetary surfaces are composed of many different
for the hydroxyl group with possible interaction with an Al materials mixed in various configurations. There can be spa-
or Mg compound. An absorption near 1 µm may be con- tially isolated regions of a pure material (e.g., H2O ice or a
sistent with olivine. If the presence of the hydroxyl group pyroxene-dominant rock) or a mixture of materials (e.g.,
is confirmed, this might imply the presence of liquid water olivine, pyroxene, and opaque phases). The nature of the
and a temperature near the melting point for at least a short mixture can range widely. For example, there can be an inti-
period of time. The H region has been re-observed by Dores- mate granular mixture in which each component is an indi-
soundiram et al. (2003), but because of the low SNR, they vidual scattering grain of a particular composition, lying in
were not able to confirm the 1.6-µm feature. contact with grains of its own kind or a different material.
47171 (1999 TC36), observed by Dotto et al. (2003b) in Or, materials might be mixed at the molecular level, such
the J, H, and K region, shows a weak absorption around that a sunlight photon entering an individual grain will en-
2 µm, and the surface composition has been interpreted with counter molecules of different composition within that grain
a mixture of 57% Titan tholin, 25% ice tholin, 10% amor- before exiting. Many other configurations, including com-
phous carbon, and 8% water ice (Fig. 4). plex layering, are also possible.
In some cases repeated observations of the same object The net result of all the processes that occur on airless
give different results, sometimes because of inferior qual- solar system bodies is that they exhibit a large range of geo-
ity data (see Table 1), but in other cases the surfaces may metric albedos, differing slopes in their reflectance spec-
be variable on a large spatial scale. A few objects in addi- tra, and the presence or absence of absorption bands arising
tion to 31824 Elatus clearly show surface variations, such from minerals, ices, and organic solids.
as 19308 (1996 TO66) and 32532 Thereus. While the mod- The case of Centaur 5145 Pholus (Fig. 5) offers a view
els noted here represent the best current fit to the data, they of some of the challenges in modeling Centaur and TNO
are not unique and depend on many free parameters, such surfaces (details are found in Cruikshank et al., 1998). This
as grain size, albedos, porosity, etc. object has a steeply sloped spectrum from 0.45 to 0.95 µm
and moderately strong absorption bands at 2.0 and 2.27 µm,
6. MODELING SURFACE COMPOSITION while the geometric albedo at 0.55 µm is 0.04. The steep
red slope cannot be matched by minerals or ices, but is
We have already noted the modeling results of a few characteristic of some organic solids, notably the tholins.
Centaurs and TNOs by various investigators, and have seen The absorption bands are identified as H2O ice (2.0 µm) and
that organic solids (tholins) are used to achieve a fit to the (probably) methanol ice (CH3OH) at 2.27 µm. A Hapke
strong red color that most of these objects exhibit. In this
section we consider some details of modeling the spectral
reflectance of the solid surface of an outer solar system body.
The goal of modeling the spectral reflectance of a plan-
etary surface is to derive information on that object’s com-
position and surface microstructure. Thermal emission can
also be modeled, but in the case of TNOs and Centaurs,
there are insufficient astronomical data of this kind to yield
compositional information through a modeling approach.
Compositional information can be derived from straightfor-
ward spectrum matching (e.g., Hiroi et al., 2001) and from
linear mixing of multiple components (e.g., Hiroi et al.,
1993). More rigorous and more informative quantitative
modeling using scattering theory goes beyond spectrum
matching and linear mixing by introducing the optical prop-
erties (complex refractive indices) of candidate materials
into a model of particulate scattering. Quantitative model-
ing of planetary surfaces using scattering theory has pro-
gressed in recent years as more and more realistic models
are developed and tested against observational data. Mul-
Fig. 5. Spectrum of 5145 Pholus (lower trace) with the Hapke
tiple scattering models provide approximate but very good model of Cruikshank et al. (1998) (solid line). The four principal
solutions to radiative transfer in a particulate medium. The components for which complex refractive indices (n, k) were in-
semiempirical Hapke model (Hapke, 1981, 1993) has been cluded in the model are shown schematically in the four upper
most widely used, while other models incorporating addi- traces. The model of Poulet et al. (2002) using the Shkuratov code
tional physical configurations (e.g., layers of transparent or is also shown.
 Barucci et al.: Surface Characteristics of TNOs and Centaurs 655

scattering model using the real and imaginary refractive served in the belt: e, i, Vrms, and particularly q, but there
indices of tholin, H2O, CH3OH, and the mineral olivine, are also clear departures from the observed color distribu-
plus amorphous carbon (which affects only the albedo level tion. For example, the Plutinos became uniformly bluer in
of the model), was found to match the spectrum from 0.45 the simulations.
to 2.4 µm. The Hapke model formulation of Roush et al. Computational models to check the validity of the CR
(1990) was used. The model consisted of two components scenario, such as those of Thébault and Doressoundiram
spatially separated on Pholus; the main component is an (2003), show that the origin of the color diversity is still
intimate mixture of 55% olivine, 15% Titan tholin, 15% unclear. The solution might lie in a better understanding of
H2O ice, and 15% CH3OH ice, with various grain sizes. In the physical processes involved, in particular the fact that
the model, the main component covers ~40% of the surface, the long-term effect of space weathering might significantly
while carbon covers the remaining 60%. depart from continuous reddening (see below). Another alter-
The principal problem with this model is that the Titan native would be that the classical objects may consist of the
tholin particles had to be only 1 µm in size, thereby violat- superposition of two distinct populations, as suggested by
ing a tenant of the Hapke theory that the particle sizes have Levison and Stern (2001), Brown (2001), and Doressoun-
to be significantly greater than the wavelength of the scat- diram et al. (2002). One population would consist of pri-
tered light. This conflict can be resolved by using the Shkur- mordial objects with red surfaces, low inclination, and small
atov modeling theory, in which very small amounts of Titan sizes, and the second population would consist of more
tholin can be introduced as contaminants in the water ice evolved objects with larger sizes, higher inclination, and
crystals without violating any optical constraints of the more diverse surface colors.
theory. Poulet et al. (2002) have shown that Pholus can be Centaurs and TNOs appear very similar in spectral and
modeled with the Shkuratov theory using the same organic, color characteristics, and this represents the strongest ob-
ice, and mineral components used in the Hapke model, al- servational argument for a common origin, supporting the
though in slightly different proportions, without any con- hypothesis that Centaurs are ejected from the Kuiper belt
flict with particle size constraints. The Poulet et al. model by planetary scattering. The rotational properties of the few
is also shown in Fig. 5. available Centaurs and TNOs also seem to be similar, even
though it is still difficult to interpret the distribution due to
7. CONCLUSIONS the lack of data. Judging from the observed lightcurve am-
plitudes, large TNOs can exist with elongated shapes. As
One of the most puzzling features of the Kuiper belt, opposed to the Centaurs, the color distribution of cometary
confirmed by numerous surveys, is the optical color diver- nuclei does not seem to match that of TNOs (Jewitt, 2004);
sity that seems to prevail among the observed TNOs (Fig 1). the very red color seems absent among comets. 2060 Chiron
With the relatively few visible-NIR color datasets available, can be considered an example of a temporarily dormant
the color diversity seems also to extend to the NIR. Statis- comet; the other Centaurs and TNOs might be dormant
tical analyses point to correlations between optical colors comets containing frozen volatiles that would sublimate in
and some orbital parameters (i, e, q) for the classical Kuiper particular heating conditions.
belt. On the other hand, no clear trend is obvious for Pluti- The wide diversity of color is confirmed by the differ-
nos, scattered objects, or Centaurs, and no firm conclusions ent spectral behavior, even though only a few high-quality
can be drawn regarding correlation of colors with size or spectra exist. The spectra show a large range of slope; some
heliocentric distance. The correlations of color with i, e, and are featureless with almost constant gradients over the vis-
q are important because they may be diagnostic of some ible-NIR range, and some show absorption features of H2O
physical effects of processing the surfaces of TNOs. The or light hydrocarbon ices. A few objects show features at-
collisional resurfacing (CR) scenario is generally invoked tributable to the presence of hydrous silicates, but this still
to explain the color diversity, which could be the result of needs to be confirmed. Several models of the spectral re-
two competing mechanisms: the reddening and darkening flectance of TNOs and Centaurs have been proposed, but
of icy surfaces by solar and galactic irradiation, and the each is subject to the limitations imposed by the quality of
excavation of fresh, primordial (and thus more neutral) ices the astronomical spectra, the generally unknown albedo, and
as the results of collisions. While the reddening process is to the limited library of materials for which optical constants
believed to act relatively homogeneously throughout the have been determined. The models of red objects all use
belt, the collision-induced blueing should vary significantly organic materials, such as tholins and kerogen, because
with the rate and efficiency of collisions within the belt. As common minerals (and ices) cannot provide a sufficiently
a consequence, the CR scenario should leave a character- red color.
istic signature with the bluer objects located in the most The H2O absorption bands detected so far on a few ob-
collisionally active regions of the belt. Thébault and Dor- jects are generally weak. H2O ice is presumed to be the
essoundiram (2003) first performed deterministic numeri- principal component of the bulk composition of outer so-
cal simulations of the collisional and dynamical environ- lar system objects (formed mostly at the same low tempera-
ment of the Kuiper belt to look for such a signature. Their ture of 30–40 K) and should constitute at least about 35%
results do match several main statistical correlations ob- of the bulk composition of this population. Thus H2O ice
656 Comets II

has to be present even if it is not detectable on the spectra, Barucci M. A., Romon J., Doressoundiram A., and Tholen D. J.
but its absorption bands can be reduced to invisibility by (2000b) Composition surface diversity in the Trans-Neptunian
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Romon J., and Boehnhardt H. (2001) Analysis of Trans-Nep-
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tunian and Centaur colours: Continuous trend or grouping?
uppermost surface layer. The observed surface diversity can
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different degrees of surface alteration due to space weather- (2002a) Physical properties of Trojans and Centaur Asteroids.
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ment by high-energy radiation of mixtures of CH3OH, CH4, spectroscopy of the Centaur 32532 (PT13). ESO Large Program
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that are dark, hydrogen-poor, and carbon-rich, and show red Astrophys., 392, 335–339.
spectra. These red spectra may become flat again, e.g., as Bauer J. M., Meech K. J., Fernández Y. R., Farnham T. L., and
Roush T. L. (2002) Observations of the Centaur 1999 UG5:
demonstrated by Moroz et al. (2003), who simulated an
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al., 2002) are in progress to simulate weathering effects on tunian objects. Results from ESO and Calar Alto telescopes.
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 Jewitt: The Rise and Demise of Comets 659

From Cradle To Grave:

The Rise and Demise of the Comets
David C. Jewitt
Institute for Astronomy, University of Hawai‘i

The active comets are a dynamic ensemble of decaying bodies, recently arrived from cold
storage locations in the Kuiper belt and Oort cloud. In this chapter, we discuss the processes
that drive the physical transformation and decay of cometary nuclei as they move from the
frigid outer regions into the hot environment of the inner solar system.

1. INTRODUCTION vides a measure of the relative velocity of approach to Ju-

piter: Jupiter itself has TJ = 3, most comets have TJ < 3,
In this chapter, we discuss the processes that drive the while main-belt asteroids generally have TJ > 3. Unfortu-
physical transformation and decay of cometary nuclei as nately, the dynamical definition of comet-hood does not
they move from the frigid outer regions into the hot environ- always match the observational or compositional defini-
ment of the inner solar system. Fundamentally, comets and tions. A number of comets (including the famous 2P/Encke)
asteroids are distinguished by their volatile content, which is have asteroid-like TJ > 3, while many bodies with comet-
itself a measure of the temperature of the environment in like TJ < 3 are asteroids scattered from the main belt. There
which they accreted. Comets possess a substantial fraction are other difficult cases: The jovian Trojan asteroids have
of bulk water ice that is not expected in the asteroids of the TJ ~ 3 and probably possess ice-rich interiors (and so are
main-belt [Whipple (1950) thought comets might contain comets by the physical definition), but are too cold to sub-
a water ice fraction near 50% by mass but recent data sug- limate, show no comae, and are labeled “asteroids.”
gest smaller fractions. Reach et al. (2000), for example, Evidently, this is not a clean subject. Even the defini-
estimate a ratio 3% to 10% in 2P/Encke, while Grün et al. tion of the term “comet” is arguable, and the reader will
(2001) find that only 10–15% of the mass lost from C/Hale see that much of the following discussion will be drawn
Bopp was from sublimated ice.] Unfortunately, we possess no inexorably toward objects whose cometary nature is debat-
direct way to measure the bulk fraction of water ice within able. To try to maintain focus we adopt a tutorial style that is
any nucleus or asteroid. The fundamental distinction be- intended to highlight connections between seemingly dis-
tween comets and asteroids is not reflected in any clean- parate subjects and that deliberately dissects and simplifies
cut, practical means by which to distinguish them. complicated problems to make them understandable. Suf-
Instead, the widely applied practical definition is that a ficient references are given that the interested reader may
comet is defined by showing a resolved coma at some point take an easy step into the research literature, but we have
in its orbit. Deciding whether an object is an asteroid or a made no attempt to be complete since the number of rele-
comet thus depends critically on the instrumental resolution vant publications is already very large. Aspects of this sub-
and sensitivity to low surface brightness coma. A weakly ject have been reviewed elsewhere (Degewij and Tedesco,
active comet might not be detected as such if observed with 1982; Jewitt, 1996a; Weissman et al., 2002).
insufficient resolution or sensitivity. Thus, there arises a gray
zone in which the cometary vs. asteroidal nature of a given 2. COMETARY RESERVOIRS
body cannot easily be ascertained by observations.
A third distinction between asteroids and comets may Comets are observationally defined as solar system bodies
be drawn based on the respective dynamical properties. The that maintain at least transient gaseous, or dusty, comae. The
Tisserand invariant with respect to Jupiter is a popular dis- comae are gravitationally unbound (escaping) atmospheres
criminant. It is defined by produced by classical sublimation of near-surface ices in
response to heating by the Sun. Their small sizes (typically
aJ a
1/2 a few kilometers) and resulting short sublimation lifetimes
TJ = + 2 (1 − e2 ) cos(i) (1) (typically ~10 4 yr) guarantee that the observed comets are
a aJ recent arrivals in the inner solar system. If a steady-state
population is to be maintained, the comets must be continu-
where a, e, and i are the semimajor axis, eccentricity, and ally resupplied from one or more long-lived reservoirs.
inclination of the orbit while aJ = 5.2 AU is the semimajor Two primary reservoirs of the comets, the Oort cloud and
axis of the orbit of Jupiter. This parameter, which is con- the Kuiper belt, are now recognized (Fig. 1). In the absence
served in the circular, restricted three-body problem, pro- of contrary evidence, it is assumed that both are primordial,

659
660 Comets II

(see Wiegert and Tremaine, 1999). Still, the uncertain nature

of the fading parameter on which its success depends re-
mains disconcerting.
The collision time in the Oort cloud is τc ~ τoc/γ, where
γ is the optical depth, equal to the ratio of the sum of the
cross-sections of the constituent nuclei to the effective geo-
metric cross-section of the cloud. We write

2
rn
γ ~ Noc (2)
Roc

where rn is the effective nucleus radius. We assume that the

cross-section is dominated by the smallest objects and take
rn = 1 km. Substitution gives γ ~ 10 –14 and, with τorb ~ 107 yr,
we find that τc >> τSS and so is effectively infinite. Any colli-
Fig. 1. Current interrelations among the planetary small body sional processing of the Oort cloud comets must have oc-
populations. JFC = Jupiter-family comet, HFC = Halley-family curred at early times, prior to their emplacement in distant
comet, LPC = long-period comet (also known as isotropic source heliocentric orbits (Stern and Weissman, 2001).
comets). Question marks indicate the uncertain path from the Oort
cloud to the HFCs and the unknown contribution to the JFCs from 2.2. Halley-Family Comets
the Trojans of the giant planets. The defunct comets include both
dead (totally devolatilized) and dormant (volatiles shielded from
The Halley-family comets (HFCs, also known as Halley-
solar insolation) bodies. Adapted from Jewitt and Fernández
(2001). type comets) are a separate group distinguished by having
short orbital periods but a wide spread of inclinations, in-
cluding retrograde orbits that are absent in the Jupiter fam-
ily. These bodies have Tisserand parameters (equation (1))
of age τSS = 4.5 × 109 yr. (Timescales mentioned in the text TJ < 2. The prototype 1P/Halley (a = 17.8 AU, e = 0.97, i =
are summarized graphically in Fig. 2.) 162°, TJ = –0.61) is typical. They are thought to derive from
the inner Oort cloud by gravitational capture, principally
2.1. Oort Cloud by interaction with the massive gas giant planets (Bailey and

The Oort cloud was identified first from the peculiar

distribution of the semimajor axes of long-period comets
(LPCs) (Oort, 1950). It supplies a nearly isotropic flux of
LPCs to the planetary region and is of vast extent, with char-
acteristic length scale Roc ~ 100,000 AU and orbital periods
near τoc ~ 106–107 yr.
The total number of Oort cloud comets larger than about
1 km in radius is on the order of Noc ~ 1012 (see Rickman,
2004; Dones et al., 2004). Comets now in the Oort cloud
are thought to have originated in the protoplanetary disk
between Jupiter and Neptune, while most were scattered out
by Uranus and Neptune (Hahn and Malhotra, 1999).
The dynamical part of Oort’s model predicts a ratio of
returning comets relative to first-appearing comets that is
larger than is observed. Oort’s solution was to introduce a
“fading parameter” to diminish the number of returning
comets. Ideas about the nature of the fading mechanism
range from the sublimation of supervolatile frosting ac-
creted from the interstellar medium to physical disintegra-
Fig. 2. Timescales relevant to the cometary nucleus. The repre-
tion of the nuclei soon after entry into the planetary region.
sentative size ranges of the well-measured Sun-grazers, JFC nu-
The need for a spherical source to supply the isotropic or- clei, and Centaurs are shown as separate for clarity: In fact, their
bital inclination distribution seems secure, as does the large size ranges overlap. Labeled curves and lettered points are de-
effective size of the source (indicated by the large semima- scribed in the text. Lines for τdv and τex refer to outgassing from
jor axes of the LPCs). No plausible alternatives to Oort’s comets at a = 3.5 AU, typical of the JFCs. Adapted from Jewitt
model have been found in the 50 years since its introduction (1996a).
 Jewitt: The Rise and Demise of Comets 661

TABLE 1. The known cometary Centaurs.

Perihelion Semimajor Inclination Tisserand

Object (AU) Axis (AU) Eccentricity (deg) Parameter
C/2001 M10 5.30 26.66 0.80 28.0 2.59
29P/SW1 5.72 5.99 0.04 9.4 2.98
39P/Oterma 6.83 7.25 0.24 1.9 3.01
2060 Chiron 8.45 13.62 0.38 6.9 3.36
C/2001 T4 8.56 13.92 0.38 15.4 3.29

Emel’yanenko, 1996; Levison et al., 2001; Rickman et al., Most appear asteroidal but five have been observed to show
2002). However, the details of this capture and their impli- comae and thus are also properly recognized as comets
cations for the structure of the inner Oort cloud are contro- (Table 1). A further 140 known objects dip into the plan-
versial. The HFCs follow a complex dynamical evolution etary region from the Kuiper belt and beyond (i.e., q ≤ aN
under the control of mean-motion and secular resonances, and a > aN).
ending with ejection from the planetary system or impact Once trapped as Centaurs the dynamical lifetimes are
with the Sun after a mean time on the order of 106 yr (Bailey limited by strong gravitational scattering by the giant planets
and Emel’yanenko, 1996). These objects are rare compared to τCen ≈ 107 yr (Dones et al., 1999). Most Centaurs are
to Jupiter-family comets in the observational sample only ejected from the solar system. The survivors that become
because there is a strong observational bias against them. trapped inside Jupiter’s orbit tend to sublimate and are ob-
In absolute numbers, the HFCs may outnumber the Jupiter servationally relabelled as JFCs. Their median dynamical
family by a large factor. lifetime (Levison and Duncan, 1994) is τJFC = 3.3 × 105 yr.
Note that the dynamical evolution is chaotic and the reverse
2.3. Kuiper Belt, Centaurs, and transition from JFC to Centaur is common (as happened re-
Jupiter-family Comets cently with Comet/Centaur 39P/Oterma).
The comets follow chaotic trajectories among the plan-
The Jupiter-family comets (JFCs) occupy small orbits ets [with dynamical memories ~1000 yr (Tancredi, 1995)],
with modest inclinations and eccentricities. Their Tisserand and elaborate numerical models must be used to track their
parameters are 2 ≤ TJ < 3 (Levison, 1996). Most JFCs prob- orbital evolution (Levison and Duncan, 1994, 1997). Very
ably originate from a transneptunian source known as the roughly, the probability that a comet or Centaur will be
Kuiper belt (Fernández, 1980; Duncan et al., 1988), whose scattered inward following its encounter with a planet is p ~
inclination distribution is similar to that of the JFCs them- 1/2. This means that the fraction of the escaped KBOs that
selves. In this scenario, the kilometer-sized JFCs could be are scattered inward by Neptune is just p, while the frac-
collisionally produced fragments of larger Kuiper belt ob- tion that scatter between the four giant planets down past
jects, or KBOs (Stern, 1995; Farinella and Davis, 1996; Jupiter is p4 ~ 0.05. If we assume that the KBOs have an
Duncan et al., 2004). The representative orbital period in effective lifetime comparable to τSS, then the steady-state
the Kuiper belt is τKB ~ 102–103 yr. population of the Centaurs, NCen, relative to that of the
The number of Kuiper belt comets larger than 1 km ra- KBOs, NKBO, may be crudely estimated from
dius, N1, is crucial if the Kuiper belt is to supply the JFCs.
However, this number is highly uncertain. Early estimates
NCen τ
based on extrapolation from 100-km-scale KBOs gave N1 ~ ~ p Cen ~ 10 –3 (3)
1010 (Jewitt et al., 1998). The first direct measurements of NKBO τSS
~10-km-scale KBOs in the classical region of the belt, when
extrapolated to 1 km, give N1 ~ 108 (Bernstein et al., 2003), With NKBO ~ 70,000 [diameter D > 100 km (Jewitt et al.,
which may be too small for the classical belt to supply the 1998; Trujillo et al., 2001)], this gives NCen ~ 70, in good
JFCs. However, the number of scattered KBOs remains ob- agreement with observational estimates of NCen ~ 100 meas-
servationally unconstrained at small sizes, and this popula- ured to the same size (Sheppard et al., 2000).
tion could supply the JFCs for the age of the solar system. In the same spirit of approximation, the steady-state pop-
The Centaurs are dynamically intermediate between the ulation of the JFCs is given by
Kuiper belt and the JFCs. We here define Centaurs as ob-
jects with perihelia q > aJ and semimajor axes a < aN, where
N JFC τ
aJ = 5.2 AU and aN = 30 AU are the semimajor axes of ~ p4 JFC ~ 5 × 10 –6 (4)
Jupiter and Neptune respectively (Jewitt and Kalas, 1998). N KBO τSS
By this definition, there are currently (as of October 2002)
42 known Centaurs, including the prototype 2060 Chiron, This leads us to expect that in steady state ~0.4 JFCs
also known as 95P/Chiron (a = 13.6 AU, e = 0.38, i = 15°). have diameter D ≥ 100 km, consistent with the observation
662 Comets II

that there are currently none. The number of KBOs with highly volatile carbon monoxide, CO, which is thought to
D ≥ 100 km is NKBO ~ 7 × 10 4 based on a simple extrapola- produce the comae observed around some Centaurs in the
tion from survey data (Jewitt et al., 1998). The number of middle solar system (R ~ 10 AU; Table 1, Fig. 3). However,
KBOs with D ≥ 1 km is very uncertain because an extrapo- most Centaurs show no comae (e.g., Fig. 4), either because
lation of the size distribution must be made. A current best- they have already lost their near-surface volatiles through
guess population is NKBO ~ (1–10) × 109 (but see Bernstein outgassing or because their surfaces consist of nonvolatile,
et al., 2003). With equation (4), this gives 5000 ≤ NJFC ≤ complex organic and silicate mantles produced by energetic
50,000. Although very uncertain, the lower end of this range particle bombardment (see Barucci et al., 2004). Although
is comparable to the (equally uncertain) “several thousand CO is the most volatile abundant ice in comets, the main
to about 104” JFCs observationally estimated by Fernández driver of activity, as recognized long ago by Whipple (1950),
et al. (1999; see also Delsemme, 1973). A more detailed is the sublimation of water ice, beginning near the orbital
estimate should include, in addition to a proper treatment radius of Jupiter.
of the dynamics, a correction for the loss of JFC nuclei Solar heat propagates into the interior of the nucleus. The
through such processes as devolatization and disruption. A timescale for the conduction of heat to the center of a spher-
numerical treatment by Levison and Duncan (1997) finds ical nucleus of radius rn is given by solution of the conduc-
that the source region of the JFCs must contain 7 × 109 tion equation
objects, in agreement with early estimates but larger than
dT(r,t)
the number of appropriately sized KBOs in the classical k∇2T(r,t) = ρcp − ρH(r,t) (5)
belt. A significant problem in comparing source models dt
with population measurements is that the sizes of the ob- where T(r,t) is the temperature as a function of radius and
jects being compared (cometary nuclei vs. KBOs) are not time, k is thermal conductivity, ρ is bulk density, cp is the
well determined because the albedos are not well known. specific heat capacity and H(r,t) is the specific power pro-
duction due to internal heat sources (e.g., radioactivity, phase
2.4. Other Sources of Comets

The distributions of color (Jewitt and Luu, 1990) and

albedo (Fernández et al., 2003a) of the jovian Trojan “aster-
oids” are formally indistinguishable from those of the com-
etary nuclei. This suggests (but does not prove) an intriguing
compositional similarity between the two classes of body,
at least at the surface level where irradiation and solar heat-
ing may play a role. No ices have been spectroscopically
detected on the Trojans (Jones et al., 1990; Luu et al., 1994;
Dumas et al., 1998) but this is not surprising given the high
surface temperatures (~150 K) and the expected rapid loss of Fig. 3. Cometary Centaur C/2001 T4 in a 300-s, R-band image
exposed ice by sublimation. Beneath their refractory man- taken by the author using the University of Hawai‘i 2.2-m tele-
tles, however, the Trojans may be ice rich. They may contrib- scope on UT 2002 September 4. The heliocentric and geocentric
ute to the comet population through dynamical instabilities distances were R = 8.57 AU and ∆ = 7.97 AU respectively, and the
and collisional ejection (Marzari et al., 1995). Once re- phase angle was 5.6°. Image is 96 arcsec wide. North is to the top,
east to the left.
moved from the vicinity of the Lagrangian L4 and L5 points,
they quickly lose dynamical traces of their origin. There are
too few jovian Trojans to supply more than ~10% of the flux
of JFCs (Marzari et al., 1995; Jewitt et al., 2000), but Tro-
jans of the other giant planets, if they exist, could be signi-
ficant additional sources, and the total flux of escaped Tro-
jans from all giant planets should be considered unknown.
A narrow ring of orbits between Uranus and Neptune may
be another source (Holman, 1997) although these orbits may
not remain populated if the outer planets experienced sub-
stantial radial migration (Brunini and Melita, 1998).
Fig. 4. Centaur 1998 SG35 in a 900-s, R-band image taken by
3. ONSET OF ACTIVITY
the author using the University of Hawai‘i 2.2-m telescope on
UT 2002 September 8. The heliocentric and geocentric distances
Equilibrium surface temperatures in the cometary res- were R = 8.72 AU and ∆ = 8.12 AU respectively, and the phase
ervoirs are low (~10 K in the Oort cloud and ~40 K in the angle was 5.5°. Image has the same orientation and scale as Fig. 3.
Kuiper belt). As orbital evolution carries the comets closer In sharp contrast to C/2001 T4 (Fig. 3), this Centaur shows no
to the Sun, rising temperatures induce the sublimation of coma or tail when observed at a nearly identical heliocentric dis-
surface volatiles. The first abundant ice to sublimate is the tance and for a longer time.
 Jewitt: The Rise and Demise of Comets 663

transitions). Dimensional treatment of this equation gives depth [LD ~ (κProt)1/2 where Prot is the nucleus rotation pe-
the characteristic e-folding timescale for heat transport by riod], in order to inhibit sublimation. For representative
conduction as values Prot = 6 h, κ = 10–7 m2 s–1, we obtain LD ~ 5 cm. The
timescale for so-called rubble mantle growth (neglecting
r 2n cohesion) is (Jewitt, 2002)
τc ~ (6)
κ
ρ nL D
τM ~ (8)
where κ = k/(ρcp) is the thermal diffusivity. For a nominal mfM
thermal diffusivity κ = 10–7 m2 s–1, we have
in which ρn is the density of the nucleus, fM(rn,R) is the
τc ~ 3 × 105r 2n yr (7) fraction of the solid matter in the nucleus too large to be
ejected by gas drag, and m(R) is the specific mass sublima-
with rn expressed in kilometers. Setting τc = τSS gives rn ~ tion rate. This timescale is only ~103 yr at 5 AU, falling to
100 km as the maximum size for effective conductive heat 1 yr at 3 AU for a water ice composition (Fig. 5). The es-
transport (Point A in Fig. 2). All known cometary nuclei, sential points are that rubble mantles can be very thin and
but not the Centaurs or KBOs, are smaller than this. Note should readily form as byproducts of cometary activity on
that τc > τJFC for rn > 1 km, meaning that the deep interiors timescales that are short compared to τJFC. A feature of the
of the nuclei of most JFCs are effectively thermally de- rubble mantle model is that such structures should be un-
coupled from their surfaces. stable to ejection on comets whose perihelia diffuse inward,
since rising temperatures and gas pressures can easily over-
4. EFFECTS OF ACTIVITY come the local gravitational force. Cohesion between man-
tle grains is needed to convey long-term mantle stability to
Mass loss due to sublimation can exert a profound influ- such objects (Kührt and Keller, 1994).
ence on the physical nature of the cometary nucleus, per- A second kind of mantle is postulated for the cometary
haps changing the shape, size, rotation, and even survival nuclei. The so-called irradiation mantle consists of material
time in the inner solar system. Furthermore, these effects are that has been chemically transformed and devolatilized by
likely interrelated. Anisotropic mass-loss produces torques prolonged exposure to energetic photons and particles. Cos-
on the nucleus that change the spin and the nucleus shape, mic rays with MeV and higher energies penetrate to col-
leading to a change in the distribution of active areas and umn densities ~103 kg m–2, corresponding to depths ~1 m
in the torque. Centripetal effects may lead to loss of mate- in material of density 103 kg m–3. The timescales for com-
rial from the rotational equator, affecting the size, shape, plete processing of this surface layer are of order 108 ± 1 yr
spin, and mantling. For clarity of presentation, these effects (Shul’man 1972). This is short compared to the storage
are discussed separately here, but they are in reality closely times for bodies in the Oort cloud and Kuiper belt and the
intertwined. upper layers of residents of these populations are likely to

4.1. Mantle Formation

The existence of refractory surface mantles is suggested

by groundbased observations of many comets (A’Hearn et
al., 1995) and by direct imaging of the nuclei of Comets
1P/Halley and 19P/Borrelly at subkilometer resolution. The
observations show that sublimation of cometary volatiles is
restricted to active areas occupying a fraction of the surface
area 10 –3 ≤ f ≤ 10–1 [larger active fractions ~1 are some-
times reported, but these may reflect gas production from
secondary sources in an icy grain halo about the nucleus
(Lisse et al., 1999)]. The corresponding f for the nuclei of
LPCs is observationally not well established. The inactive
regions correspond to volatile-depleted surface thought to
consist of refractory crust or mantle material. Many com-
ets with f << 10 –3 cannot be easily distinguished from aster-
oids owing to the practical difficulty of detecting very weak
dust (Luu and Jewitt, 1992a) or gas comae (Chamberlin et
Fig. 5. Timescale for the growth of a rubble mantle in model
al., 1996). nuclei of radii 5 km and 50 km, in response to sublimation of H2O
In the so-called rubble mantle model, the mantles are and CO ices and computed from equation (8). The orbits are as-
thought to consist of refractory blocks that are too large to sumed to be circular. Adoption of more realistic eccentric orbits
be ejected by gas drag against the gravity of the nucleus. would increase the mantling time relative to the plotted curves,
Such mantles need only be thicker than the thermal skin but mantling is always rapid at small R. From Jewitt (2002).
664 Comets II

be significantly processed down to meter depths. Optical

photons, on the other hand, probe a surface layer only a
few micrometers thick. The timescale for processing this
visible layer is probably short, but the timescales for build-
ing a rubble mantle are even shorter. Thus, we expect that
bodies with perihelia beyond the water sublimation zone
(KBOs, Centaurs) might retain irradiation mantles but that
these will have been ejected or buried on the nuclei of near-
Earth comets. One observation consistent with this is the
lack of ultrared matter, of the type seen on the surfaces of
half the KBOs and Centaurs, on the nuclei of JFCs (Jewitt,
2002) (see section 4.7).
Irradiation breaks the chemical bonds of common mol-
ecules. In the process H, because of its small size, is able
to escape from the irradiated layers of the nucleus into
space. The irradiation mantle is thus composed of material
in which the C/H and O/H ratios are high. The high C frac-
tion may be responsible for the low albedos of cometary
nuclei (Campins and Fernández, 2002; Moroz et al., 2003).
The low H fraction may explain why near-infrared spectra
of outer solar system bodies, including KBOs, Centaurs,
jovian Trojans, and cometary nuclei, are mostly devoid of the
absorption bands of common bonds (e.g., C-H, O-H, N-H).

4.2. Thermal Devolatilization

The timescale for the loss of volatiles from a mantled

ice nucleus is
ρ nr n Fig. 6. Orbitally averaged specific mass loss rate for sublimating
τdv ~ (9) water ice as a function of the semimajor axis and eccentricity. The
fm
instantaneous mass loss rate was computed from the energy balance
where m (kg m–2 s–1) is the specific mass loss rate averaged equation and integrated around the orbit using Kepler’s equation.
around the cometary orbit, ρn is the density, and f is the A low (0.04) albedo surface was assumed and thermal conduction
so-called “mantle fraction,” the fraction of the surface from was neglected. Curves are labeled by the orbital eccentricity.
which sublimation proceeds. The specific mass loss rate can
be estimated from equilibrium sublimation of H2O ice to
be about m ~ 10–4 kg m–2 s–1 at R = 1 AU, varying roughly
as R–2 for R ≤ 2 AU and faster than R–2 at greater distances and LPCs, the latter of which sublimate only for a limited
(Fig. 6). For nonzero orbital eccentricities, the sublimation period near perihelion.
rate at a given semimajor axis is higher than for the circu- The lifetimes of kilometer-scale nuclei against sublima-
lar orbit case because of enhanced sublimation near peri- tion, given by equation (10), are comparable to the dynami-
helion. This effect is large only for orbital semimajor axes cal lifetime. Note that τdv < τJFC for rn < 1 km (Point B in
greater than about 3 AU, which is the critical distance be- Fig. 2). This means that the subkilometer comets should lose
yond which sublimation consumes a negligible fraction of their volatiles on timescales short compared to their dynami-
the absorbed solar energy. This is shown in Fig. 6, in which cal lifetimes, leaving behind a population of “dead comets.”
we plot the orbitally averaged water ice sublimation rate Note also that τdv < τc for rn > 1 km (Point C in Fig. 2),
as a function of semimajor axis and eccentricity. For the meaning that for almost all observed comets the volatiles are
canonical JFC orbit with a = 3.5 AU and e = 0.5, we esti- lost from the surface before the thermal conduction wave
mate m = 10–5 kg m–2 s–1 (Fig. 6). With ρn = 500 kg m–3 has reached the core. This inequality suggests another end
and f = 0.01 (A’Hearn et al., 1995), we find state as “dormant comets” (Hartmann et al., 1987; Kresák,
1987), having devolatilized, inactive surface regions shroud-
τdv ~ 2 × 105rn yr (10) ing an ice packed core.

with rn again expressed in kilometers and τdv is measured 4.3. Size Evolution
in years. The effect of nonzero eccentricity is small for com-
ets whose semimajor axis is less than the critical distance Mass loss should modify the size distribution of the
for strong sublimation of water ice (R ≤ 3 AU; Fig. 6). Thus, comets by selectively depleting the smallest objects (equa-
JFC lifetime estimates are much less affected than HFCs tion (10)). The size distribution of the parent KBOs has been
 Jewitt: The Rise and Demise of Comets 665

measured, albeit only for large objects, from the slope of while most studied comets have rn ≤ 5 km. Size-dependent,
the cumulative luminosity function (i.e., the cumulative rather than evolutionary, effects might be present. It will be
number of objects per square degree of sky brighter than a important to extend the KBO size distribution to typical
given magnitude). Different researchers have converged on cometary nucleus scales.
a power-law-type distribution in which the number of ob- In summary, the size distributions of the KBOs and Cen-
jects with radius between r and r + dr is taurs appear identical, within the uncertainties, and consis-
tent with the link between KBOs and Centaurs. Measure-
n(r)dr = Γr –qdr (11) ments of the size distributions of the cometary nuclei have
been attempted, but the reported values are discordant and
with Γ and q constants of the distribution. The best-fit value are, in any case, afflicted by discovery and coma contamina-
for KBOs is q = 4.0+0.6 –0.5 (Trujillo et al., 2001). In such a dis- tion biases that are poorly understood.
tribution, the mass is spread uniformly in equal logarith-
mic intervals of radius while the cross-section is dominated 4.4. Shape Evolution
by the smallest objects in the distribution. The Centaurs are,
by and large, less well observed than the KBOs. The avail- The shapes of cometary nuclei can be estimated from
able data are compatible with q = 4.0 ± 0.5 (Sheppard et their rotational lightcurves (strictly, the lightcurves give only
al., 2000). This is identical to the value in the Kuiper belt, the projection of the shape in the plane of the sky). If the
as expected if the latter is the source of the Centaurs. nuclei are collisionally produced fragments, then it seems
The size distribution of the cometary nuclei is poorly reasonable that their shapes should be distributed like those
determined by comparison. Fernández et al. (1999) used of impact fragments produced in the laboratory by impact
spatially resolved photometry of comets to find q = 3.6+0.3 –0.2 , experiments. The comparison is made in Fig. 7 where we
while the same technique used independently by Weissman show the photometric ranges of well-measured nuclei with
and Lowry (2003) gave q = 2.6 ± 0.03 and Lamy et al. the range distribution of impact fragments measured in the
(2004) found q = 2.6 ± 0.2 to q = 2.9 ± 0.3. The results are laboratory by Catullo et al. (1984).
inconsistent at the 5σ level of significance. To understand The distributions are clearly different, with the comets
this, it is important to remember that the cometary nuclei showing a larger fraction of highly elongated shapes than
are in general observed in the presence of coma. Coma con- the impact fragments. The well-measured cometary nuclei
tamination of the nucleus photometric signal may confuse are also elongated, on average, compared to main-belt aster-
the results obtained by one or more of these groups. Fur- oids of comparable size (Jewitt et al., 2003). This can be
thermore, the short-period comets that form their samples naturally explained as a simple consequence of anisotropic
have been discovered by a variety of techniques, each of mass loss from the comets, which should act to modify the
which must impress onto the sample its own distinctive dis-
covery bias. Naively, this bias is expected to favor cometary
nuclei with large active areas because these objects will be
bright and therefore more easily detected. Overrepresenta-
tion of the bright comets will lead to a measured size distri-
bution that is flatter than the intrinsic distribution.
What should we expect? Sublimation lifetimes of other-
wise equal bodies vary in proportion to the radius (equa-
tion (10)). Thus, in steady state, we expect that a source
population described by r –q should be flattened by sublima-
tion to r –(q – 1), as a result of the more rapid loss of the smaller
objects. From q = 4 in the Kuiper belt, we expect to find q = 3
among the JFCs, which is in between the measured values.
Comets with rn ≤ 700 m have τc ≤ τdv (equations (7) and
(10) and Point C in Fig. 2). In such objects, the thermal con-
duction wave reaches ices still frozen in the core. The re-
sulting gas pressure produced by sublimation in the core is
likely to explosively disrupt the nucleus. This provides one
possible explanation for the often-reported depletion of very
small comets relative to extrapolations of the power-law size
distribution as determined at kilometer and larger nucleus
scales. The very short timescale for rotational spinup of sub-
kilometer nuclei (Fig. 2 of Jewitt, 1999) provides an even
more compelling mechanism for their destruction by rota-
tional bursting. Fig. 7. Apparent axis ratios of cometary nuclei (from Jewitt et al.,
It should be noted that the sizes of the measured KBOs 2003) with published rotational lightcurves compared with impact-
and comets are quite different. Most KBOs have rn ≥ 50 km, produced rock fragments (from Catullo et al., 1984).
666 Comets II

overall shape on a timescale comparable to τdv. Anisotro- for example, could occupy a rotationally excited state
pic mass loss may also provide a mechanism for splitting (Giblin and Farinella, 1997) for only ~107 yr before damp-
on this timescale (Hartmann and Tholen, 1990). Note that ing away. This is comparable to the median transport time
most of the axis ratios reported in Table 1 of Lamy et al. from the Kuiper belt to the inner solar system. Comets much
(2004) are smaller than those in Fig. 7. The difference might smaller than ~2 km, and those with spin periods much
occur because the Lamy et al. data are lower limits obtained longer than 6 h, might retain excited rotational states pro-
from sparsely sampled photometric series, whereas the pro- duced collisionally in the Kuiper belt, although we do not
jected axis ratios in Fig. 7 were all determined from well- expect this to be the general case because the injection of
measured lightcurves. a nucleus in a Neptune-crossing orbit may occur long after
its collisional production.
4.5. Spin Evolution Nucleus excitation is much more likely to be actively
produced once comets begin to outgas inside the orbit of
Noncentral mass loss from the comets generates torques Jupiter. The timescales for excitation (equation (12)) and
that can both change the spin period and drive the nucleus damping (equation (13)) of the spin are equal at the criti-
into an excited rotational state (i.e., a state other than prin- cal size
cipal axis rotation around the short axis). The relevant ex- 1/4
4πµQVth kTfm
citation timescale is rn = (15)
ρ2K23ω4
ωρr 4n
τex ~ (12)
VthkTM which, with m = 10–5 kg m–2 s–1, Vth = 103 m s–1, ρ = 500 kg
m–3, f = 0.01, P = 6 h, and other parameters as given earlier,
where M (kg s–1) is the net mass loss rate from all active yields rn ~ 20 km (Point D in Fig. 2). Since most known
areas (for a spherical nucleus M = 4πr2nfm), kT is the dimen- cometary nuclei are smaller than this critical size, we con-
sionless moment arm for the torque (kT = 0 for radial ejec- clude that most are potentially in rotationally excited states.
tion and kT = 1 for tangential mass loss), and Vth is the Numerical simulations show that equation (12), while pro-
mass-weighted outflow speed (cf. Samarasinha et al., 1986; viding a good estimate of the timescale for spinup, may give
Jewitt, 1991). The dimensionless moment arm has been esti- only a lower limit to the timescale for driving a nucleus into
mated analytically from a block model of the nucleus as excited rotational states (Gutiérrez et al., 2003). Thus it is
kT ~ 0.05 (Jewitt, 1999) and from numerical simulations as possible that equation (15) overestimates the critical radius.
0.01 ≤ kT ≤ 0.04 (Gutiérrez et al., 2003). For plausible esti- Observational evidence for precession of the nuclei is
mates of the parameters we find τex < τJFC (Fig. 2), meaning limited, both because measurements are complicated by
that outgassing torques can drive comets toward rotational the effects of near-nucleus coma and because few attempts
instability, perhaps providing one mechanism for destruc- have been made to secure adequate temporal coverage. The
tion of the nucleus (Fig. 2) (Jewitt, 1999). best case is for the nucleus of 1P/Halley (Samarasinha and
Excited rotational motions create periodic internal A’Hearn, 1991) while, more recently, 2P/Encke has shown
stresses that lead to minute (but, over long periods, signifi- indications of a time-varying lightcurve that might indicate
cant) frictional dissipation of energy. Relaxation into the nucleus precession (Fernández et al., 2000). Spinup might
minimum rotational energy (maximum moment of inertia) be expected to lead to rapid rotation among the comet nuclei,
state occurs on the timescale (Burns and Safranov, 1973) especially at small sizes. A few nuclei [(P/Schwassmann-
Wachmann 2 (Luu and Jewitt, 1992b)] are indeed rotating
µQ close to the centripetal limit for densities ρ ~ 500 kg m–3.
τdamp ~ (13)
ρK23r2nω3 Less-direct evidence for rotational destruction of small nu-
clei might be evident in the depletion of these objects rela-
Here, µ (N m–2) is the rigidity, Q is the quality factor (frac- tive to power-law extrapolations from larger sizes.
tional loss of energy per cycle), K3 is a shape-dependent
numerical factor, and rn (m) is the mean radius. The damp- 4.6. Active Area Evolution
ing parameters appropriate to cometary nuclei are not well
known. We follow Harris (1994) and take µQ = 5 × 1011 The active areas and the mantle should evolve in paral-
(N m–2) and K23 ~ 0.03 (based on data for Phobos). Substi- lel. The lifetime of an active area can be estimated as fol-
tuting ρ = 500 kg m–3 we obtain lows. In the limiting case in which all the incident solar
energy is used to sublimate ice, the subsolar specific mass
loss rate is given by
P3
τdamp ~ 1.0 × 105 (14)
r2n S
m= (16)
LR2
for the damping time in years, with P in hours and rn in
kilometers (Fig. 2). A 2-km-radius nucleus created colli- in which S = 1360 W m–2 is the solar constant, R (AU) is
sionally in the Kuiper belt with an initial spin period of 6 h, the heliocentric distance, and L is the latent heat of sublima-
 Jewitt: The Rise and Demise of Comets 667

tion at the (sublimation depressed) temperature of the sur- C/2001 T4 likewise displays a prominent, variable coma at
face ice. (We consider the limiting case only because it gives R ~ 8.5 AU [see Fig. 3 and Bauer et al. (2003b)]. In the
a convenient analytic expression for m.) The corresponding comets (and to a lesser extent the Centaurs) reactivation and
rate of recession of the sublimating surface is just the formation of new active areas may be driven by the
progressively rising temperatures leading to increasing gas
pressures that can destabilize the mantle (Brin and Mendis,
m
r~ (17) 1979; Rickman et al., 1990). In the rather stable orbits of the
ρ Kuiper belt, reactivation can be caused by impacts that dis-
rupt the mantle.
An exposed plug of ice of area πa2 = 4πr 2nf would subli-
mate into the nucleus, creating a cavity or vent that deepens 4.7. Colors and Albedos
at rate r. When the vent becomes too deep, self-shadowing
by the walls will inhibit further sublimation. Accumulation Figure 8 shows distributions of the optical colors of dif-
of a blocky rubble mantle at the bottom of the vent will ferent types of small bodies (Table 2 summarizes the data).
also suppress sublimation. We assume that this happens first The KBOs show a wide range of colors from nearly neu-
when the vent reaches a critical depth d ~ a. The timescale tral (S' > 0%/1000 Å) to very red (S' ~ 50%/1000 Å) with a
for the vent to reach this depth is just τv ~ a/r. From equa- median value S' = 25%/1000 Å. Here, the slope, S', is meas-
tion (17) we obtain ured in the best-observed V-R region of the spectrum (i.e.,
5500 Å to 6500 Å wavelength). The similarity between the
wide spread of colors on the KBOs and on the Centaurs
2f1/2ρR2Lrn
τv ~ (18) (here taken from Bauer et al., 2003b) shows that mantling
S on the Centaurs is relatively minor, even though these bod-
ies may sometimes be active (Fig. 8). Instead, a dramatic
where ρ is the density of the solid ice. For H2O ice (L = change in the color distribution appears only once the bod-
2 × 106 J kg –1) with ρ = 500 kg m–3, f = 0.01 and R = 1 AU, ies have perihelia inside Jupiter’s orbit and can begin to sub-
we obtain limate water ice. The comets show a smaller range of S' and,
specifically, are deficient in the ultrared material with S' >
τv ~ 5rn yr (19) 25%/1000 Å (Jewitt, 2002; see also Hainaut and Delsante,
2002). This may be a result of mantling of the cometary nu-
with rn expressed in kilometers. In equation (19), the life- clei driven by sublimation in response to rising tempera-
time is in units of years of exposure to sunlight in a circu- tures as they approach the Sun. Objects that are likely, on
lar orbit at R = 1 AU. A 5-km-radius nucleus would have dynamical grounds, to be dead comets show a color distribu-
τv ~ 25 yr. The vent lifetime on the nucleus of an equivalent
comet moving in an eccentric orbit will be larger because
the mean insolation and the mean mass loss rate are smaller.
For example, a JFC with a = 3.5 AU, q = 1.0 AU would
have a vent timescale longer than given by equation (19)
by a factor of ~10 to account for the greater mean distance
from the Sun. Still, the vent lifetimes are expected to be
very short compared to the dynamical lifetime, τJFC, for
comets on all but the most eccentric orbits. Observational
constraints on JFC active area lifetimes are few: Sekanina
(1990) concludes that changes in active areas should be evi-
dent on timescales comparable with the observing records
of many comets, consistent with equation (19).
For a CO-powered vent (L = 2 × 105 J kg –1) on a KBO
at R = 40 AU, the timescale is still a short τv ~ 8 × 102 yr.
Active areas on the same object moved to R = 10 AU would
become self-shadowing in only ~50 yr, a tiny fraction of
the dynamical lifetime. We conclude that the KBOs and
Centaurs may occasionally display spectacular CO-powered
comae from exposed vents (e.g., craters produced by im-
pact), but that these are short-lived and should therefore be
Fig. 8. Histograms of normalized optical reflectivity gradients
rare unless the vents are reactivated or replaced. Centaur (%/1000 Å) for objects in the major categories of this review. Plot-
2060 Chiron exhibits brightness outbursts in the 8 ≤ R ≤ ted are KBOs, nuclei, and dead comets (Jewitt, 2002); Centaurs
19 AU range with a timescale of ~10–20 yr (Bus et al., (Bauer et al., 2003b); and jovian Trojans (Jewitt and Luu, 1990).
2001). It is not unreasonable to suppose that this activity is The ultrared matter, with reflectivity gradient ≥25%/1000 Å, is
modulated by the evolution of CO-powered vents. Centaur present only in the Kuiper belt and on the Centaurs.
668 Comets II

TABLE 2. Mean reflectivity gradients and color indices.

Object S' V-R N Reference

KBOs 23 ± 2 0.61 ± 0.01 28 Jewitt and Luu (2001)
Centaurs 22 ± 4 0.58 ± 0.01 24 Bauer et al. (2003b)
Nuclei 8±3 0.45 ± 0.02 12 Jewitt (2002)
Dead comets 7±2 0.44 ± 0.02 12 Jewitt (2002)
D-types 8.8 ± 0.5 0.45 ± 0.01 19 Fitzsimmons et al. (1994)
Trojans 10 ± 1 0.46 ± 0.01 32 Jewitt and Luu (1990)

tion that is formally indistinguishable from that of the nuclei KBOs. The implication is that surface materials that are
of active comets, suggesting that the mantles on these bodies common in the middle and outer solar system, including
are stable over long periods [and may indeed be responsible frosts and the ultrared material, have been ejected or buried
for the deaths of the comets (Rickman et al., 1990)]. (Jewitt, 2002) or are thermodynamically unstable (Moroz
A similar conclusion can be drawn from Fig. 9, in which et al., 2003) on the JFCs. The significance of this result is
we show available measurements of the colors and albedos that spacecraft launched to investigate the nuclei of JFCs
of the small-body populations. It is evident that the com- may fail to sample the primitive materials present on the
etary nuclei occupy a restricted region of the color-albedo surfaces of their more distant progenitors.
plane near pR ~ 0.04, S' ~ 10%/1000 Å while the Centaurs
are much more widely dispersed. The few measured nuclei 5. COMETARY END STATES
fall near the region occupied by the D-type asteroids and
the similarity to the Trojans is impressive (Jewitt and Luu, 5.1. Dead and Dormant Comets
1990). The corresponding data for KBOs, although few in
number, already show wide separation in the color-albedo Dormant comets lack near-surface volatiles but may
plane and are very different from any cometary nucleus yet possess ice-rich interiors while dead comets are completely
measured. Observationally, we can already state with con- devolatilized. Identifying such objects from their physical
fidence that the albedos and colors of the cometary nuclei properties is not easy, since the nuclei possess a wide range
occupy a smaller range than is found in the Centaurs or of optical properties that overlaps those of some classes of
asteroids. The orbital properties provide a separate clue:
Dead and dormant comets are likely to possess comet-like
Tisserand invariants, TJ ≤ 3. Objects selected on this basis
indeed possess low, comet-like geometric albedos, pR ~ 0.04
(see Fig. 10), quite distinct from the TJ > 3 asteroids. This
finding has been used to infer that about 10% of the near-
Earth objects (NEOs) might be dead comets (Fernández et
al., 2001). Dynamical models of the near-Earth population
allow a similar (~6%) fraction of dead comets (Bottke et
al., 2002). However, the latter models are incomplete in that
they neglect nongravitational forces and/or perturbations
from the terrestrial planets. Orbits decoupled from Jupiter,
like that of Comet P/Encke (TJ = 3.03), cannot be repro-
duced without including these effects. Calculations in which
these forces are included suggest that the dead JFC fraction
of the near-Earth population is ≤20% (Fernández et al.,
2002) to 50% (Harris and Bailey, 1998). The results remain
uncertain, in part, because the form and time-dependence
Fig. 9. Plot of normalized reflectivity gradient vs. geometric al- of the nongravitational acceleration remain poorly known.
bedo for jovian Trojan asteroids, cometary nuclei, Centaurs, and Furthermore, the magnitude of the nongravitational accel-
two KBOs (see legend for a key to the symbols). Boxes mark the eration, all else being equal, varies inversely with the nu-
approximate regions of the P and D asteroid spectral classes ac-
cleus radius so that size-dependent effects in the dynamics
cording to Dahlgren and Lagerkvist (1995). The Trojan data are
should be expected. Realistic modeling of the orbital evo-
compiled from Jewitt and Luu (1990) and Tedesco et al. (2002);
Centaur data are from Jewitt and Luu (2001), Hainaut and Del- lution of outgassing comets is potentially very complicated
santi (2002), and Campins and Fernández (2002), and KBO data and deserves more attention than it has yet received.
are for Pluto (Tholen and Buie, 1997), 20000 Varuna (Jewitt et al., Rubble mantles, unless held together by granular cohe-
2001; Hainaut and Delsanti, 2002), and 28978 Ixion and 50000 sion, are susceptible to ejection in response to decrease of
Quaoar (Marchi et al., 2003; Bertoldi et al., 2002). the perihelion (Rickman et al., 1990). The transition to the
 Jewitt: The Rise and Demise of Comets 669

Fig. 11. Trailed (unguided) image of asteroid-comet transition

object 107P/1949 W1 (Wilson-Harrington) taken UT 1949 Novem-
ber 19. The trailed image of the central nucleus is about 1 arcmin
in length in this 720-s integration. North is at the top, east to the
left, and the tail extends toward the east (antisolar) direction. The
comet was 0.2 AU from Earth and 1.1 AU from the Sun. Palomar
sky image from Fernández et al. (1997).

object 3200 Phaethon appears dynamically associated with

the Geminid meteor stream, yet has shown no evidence for
recent outgassing and occupies a thoroughly un-comet-like
orbit. Lastly, asteroid 7968 was found to show a dust trail
in images taken in 1996, leading to this object being cross-
identified with Comet 133P/Elst-Pizzaro. The confinement
Fig. 10. Plot of red (0.65 µm) geometric albedo, p, vs. Tisserand of the dust to the vicinity of the orbit plane shows that the
parameter, TJ, for small solar system bodies including dynami- observed particles experience a small ratio of forces due to
cally asteroidal near-Earth objects (TJ > 3), unresolved objects radiation pressure relative to solar gravitational attraction.
likely to be inactive comets on dynamical grounds (TJ ≤ 3), and This, in turn, suggests that the particles are large, probably
the nuclei of active comets. From Fernández et al. (2003b). at least 10–20 µm in size. The existence of a dust trail from
this object is particularly puzzling, since it is dynamically
a main-belt asteroid with orbital elements consistent with
those of the Themis family (Table 3). It has been suggested
asteroidal state may include a protracted period of intermit- that the appearance of outgassing activity might have been
tent cometary activity as the mantle cracks and reseals. Sev- created by a recent collision with a smaller asteroid (Toth,
eral examples of comets in which the activity is extremely 2000), but this explanation seems unlikely given the reap-
weak (e.g., 49P/Arend-Rigaux, 28P/Neujmin 1) or may even pearance of the trail in Mauna Kea data in 2002, six years
flicker on and off are known (Kresák, 1987). after the initial detection (Hsieh et al., 2003) (see Fig. 12).
Several comets and likely comets are known to follow Either 133P/Elst-Pizzaro is an asteroid somehow triggered
asteroid-like orbits [see Table 3 and Weissman et al. (2002) to lose mass or it is a comet somehow driven into an aster-
for more detailed descriptions]. The most famous example oid-like orbit. The aphelion of 133P/Elst-Pizzaro at 3.80 AU
is Comet 2P/Encke, which is a bona-fide comet that has is far from Jupiter’s orbit. Nongravitational accelerations
decoupled from Jupiter’s control (TJ = 3.03). Comet 107P/ from outgassing might produce this type of decoupling from
Wilson-Harrington (also known as asteroid 1949 W1) dis- Jupiter but with very low efficiency (Fernández et al., 2002).
played a diffuse trail at discovery in 1949 (Fig. 11) but has A number of objects in comet-like (TJ ≤ 3) or bits pos-
appeared asteroidal ever since (Fernández et al., 1997). The sess no resolvable coma or tail and must be physically clas-

TABLE 3. Comets and likely comets in asteroid-like orbits.

Perihelion Semimajor Inclination

Object (AU) Axis (AU) Eccentricity (deg) Tisserand
2P/Encke 0.34 2.22 0.85 11.8 3.03
3200 Phaethon 0.14 1.40 0.89 22.1 4.51
107P/Wilson-Harrington 1.00 2.64 0.62 2.8 3.08
7968 133P/Elst-Pizarro 2.63 3.25 0.17 1.4 3.18
670 Comets II

that the JFCs are active for between 3000 and 30,000 yr
(with a best estimated value of about 12,000 yr) after their
perihelion first reaches q ≤ 2.5 AU. The corresponding ratio
of dead to active JFCs is 2 ≤ Nd/Na ≤ 6.7, with a best esti-
mate of Nd/Na = 3.5 (Levison and Duncan, 1997). Whether
or not the difference between the measured and model val-
ues of Nd/Na is significant is unclear.

5.2. Tidal Breakup

A small number of comets have been observed to break

Fig. 12. 133P/(7968) Elst-Pizarro in a 3900-s, R-band compos- up in response to gravitational stresses induced by close
ite image taken on UT 2002 September 07 at the University of proximity to the Sun (e.g., the Kreutz Sun-grazer group) or a
Hawai‘i 2.2-m telescope. Short trails are background stars and planet (commonly Jupiter, as with P/Brooks 2 and D/Shoe-
galaxies. The nucleus of 133P has been placed at the lower right. maker-Levy 9). The properties of the “string of pearls” com-
Image is 180 arcsec wide, with north at the bottom and east to the et chain produced from D/Shoemaker-Levy 9 are well ex-
right. The heliocentric and geocentric distances were 2.88 AU and
plained by a disrupted, gravitationally sheared aggregate
1.96 AU respectively, and the phase angle was 9.9°. A dust trail is
body of negligible tensile strength and density ρn ~ 500 kg
visible across the full width of the image in the raw data. Image
by Henry Hsieh and the author. m–3 (Asphaug and Benz, 1996).
Some 4% of the Centaurs pass within the Roche radius
of a gas giant planet during their lifetimes (Levison and
Duncan, 1997). If, like D/Shoemaker-Levy 9 (which had
sified as asteroidal (see Table 4). A fraction of these could 26 fragments), each object splits into a few dozen pieces,
be dead (or dormant) comets. Based on their lifetimes, the then the number of secondary fragments could rival or even
ratio of the numbers of dead, Nd, to active, Na, comets exceed the number of primary comets from the Kuiper belt.
should be This would have significant implications for the flux, size,
mass, and rotation distributions of the comets. For example,
Nd τ 2 tidal breakup could reduce the number of small KBOs
~ JFC ~ (20) needed to supply the JFC flux (cf. Bernstein et al., 2003).
Na τdv rn
Most split comet fragments would quickly mix with the pri-
mary unsplit population: Dynamical memory of the split-
The number of NEOs larger than ~1 km in size is ~1000 ting is quickly lost (Pittich and Rickman, 1994).
(Rabinowitz et al., 2000; Bottke et al., 2002). If ~10% of
these are dead or dormant comets (Fernández et al., 2001; 5.3. Nontidal Breakup
Bottke et al., 2002), then the number of such objects must be
~100. For comparison, about 200 JFCs are known, while the Most splitting events occur without obvious provocation
true (bias-corrected) population may number in the thou- and their cause is unknown (Sekanina, 1997). Statistically,
sands (Fernández et al., 1999). Empirically, then, Nd/Na < the nuclei of JFCs split at a rate τsplit
–1 ~ 10 –2 yr –1 per nucleus

0.5, whereas equation (20) gives Nd/Na ~ 2 for rn = 1 km. (Chen and Jewitt, 1994; cf. Weissman, 1980). With dynami-
Models of the orbital evolution of JFCs permit an inde- cal lifetimes of a few × 105 yr, each nucleus should split
pendent estimate of Nd/Na. The models show that the mean thousands of times. The rate for the observed long period
inclination increases with residence time in the inner solar comets is less well constrained but probably of the same
system (Levison and Duncan, 1994, 1997). To bring the order. The effect of repeated splittings on the mass of the
model and observed inclination distributions of the JFCs primary nucleus depends on δ, the mass-weighted fragment
into agreement, these authors found it necessary to assume to primary nucleus mass ratio. If splitting is a continuous

TABLE 4. Sample asteroids in comet-like orbits.

Perihelion Semimajor Inclination

Object (AU) Axis (AU) Eccentricity (deg) Tisserand
5335 Damocles 1.57 11.82 0.87 62.0 1.15
15504 1998 RG33 2.15 9.43 0.77 34.9 1.95
20461 1999 LD31 2.39 24.43 0.90 160.2 –1.54
3552 Don Quixote 1.21 4.23 0.71 30.8 2.32
1997 SE5 1.24 3.73 0.67 2.6 2.66
1982 YA 1.12 3.66 0.70 35.3 2.40
 Jewitt: The Rise and Demise of Comets 671

random process, the fraction of the mass remaining in the ary disintegration are known (see Boehnhardt, 2004). This
primary after time, t, is just does not mean that complete disintegration is rare, because
the probability that a brief, one-time event might be ob-
m (t ) served by chance is presumably very small. The causes of
~ (1 − δ)t/τsplit (21)
m ( 0) disintegration are not known.
Samarasinha (2001) suggested a model for the nucleus of
Setting t = τdv as an upper limit, we find m(τdv)/m(0) << 1 C/1999 S4 (LINEAR), namely that fragmentation was due to
for δ >> 10–3. Observationally, the situation is unclear. Most the buildup of gas pressure inside a loosely agglomerated
fragments of the Kreutz sungrazing comets have character- nucleus having substantial internal void space. High pres-
istic sizes of ~10 m, corresponding to δ ~ 10–6 for a kilo- sures have been observed in association with the heating of
meter-sized parent (Sekanina, 2002). If this is representative amorphous ice samples in which clathrate formation may
of splitting events as a whole, then it is unlikely that disin- also play a role (Blake et al., 1991). This “bomb model”
tegration plays a major role in shaping the nuclei. However, model predicts that small nuclei (e.g., SOHO comets) should
if breakup is a continuous process that extends to much detonate more readily than large ones, since the gravita-
larger, but rarer fragment sizes, then the effect on the pri- tional binding energy grows as r5n while the gas pressure is
mary mass may still be significant. independent of nucleus size. The real unknown in this model
The short timescales for spin excitation, τex (see Fig. 2), is the permeability to gas: If the gas can leak out, the pres-
suggest that rotational bursting may play a role. The cen- sure may never grow large enough to burst the nucleus.
tripetal and gravitational accelerations on the equator of a Rotational spinup (Fig. 2 and equation (12)) might also
spherical body of density ρ (kg m–3) are equal at the critical be implicated in cometary disintegration. An elongated nu-
rotational period cleus in simple rotation driven to the centripetal limit might
be expected to lose mass only from its tips. The same nu-
1/2 cleus in an excited rotational state might be pushed to dis-
3π
τr = (22) integrate by rotational instabilities, particularly if the nearly
Gρ strengthless internal constitution witnessed in D/Shoemaker-
Levy 9 is typical. Rotational ejection could also expose pre-
where G = 6.6 × 10–11 (N kg –2 m2) is the gravitational con- viously shadowed volatiles, initiating a sudden burst of out-
stant. Strengthless objects rotating with periods Prot < τr are gassing and perhaps precipitating global instability of the
susceptable to rotational bursting. For the more general case nucleus.
of an elongated body in minimum energy rotation (about the Why some nuclei disintegrate while others split and oth-
shortest axis), the critical period is ers remain coherent is a mystery. Neither do we know if
splitting and disintegration occur with uniform probability
1/2 across all comets, or whether some comets are “born tough”
1000
τr ~ 3.3 fr h (23) and resist splitting and disintegration until their eventual
ρ demise. In the latter case, the surviving comets might not be
at all representative of the comets prior to their entry into
where fr is a numerical factor that depends on the axis ra- the inner solar system. This possibility has been suggested
tio of the body (e.g., fr = 1 for spheres, fr ~ 4/3 for prolate as an explanation of the presumed fading of LPCs (Levison
bodies with axis ratio a/b = 2). Observationally, all but the et al., 2002).
smallest (strongest) asteroids, and all measured comets,
have Prot ≥ 2 h and consistent with ρ ≥ 500 (kg m–3) (Pravec 5.5. Debris Streams
et al., 2002). The most elongated comets may be rotating
close to their corresponding centripetal limits (Jewitt and Meteor streams represent the final products of cometary
Meech, 1988; Weissman et al., 2004). disintegration. The known streams are observationally pre-
For example, the nucleus of C/1999 S4 (LINEAR) may selected to intersect the orbit of Earth and are biased to-
have been as small as 100 m in radius prior to break up into ward LPC and HFC cometary sources (the luminosity of a
fragments at 0.85 AU (Weaver et al., 2001). Equation (12) meteor of given mass varies with a high power of the rela-
gives τex ~ 10 d for such a small object when close to the tive velocity so that LPC and HFC sources produce brighter
Sun. The nucleus could have been driven to rotational burst- meteors than JFC or asteroidal orbits, all other things be-
ing during the time taken to free fall toward the Sun. Split ing equal). Counterparts of the meteor streams for comets
fragments themselves would be subject to rapid spinup, whose orbits do not intersect that of Earth are found in com-
leading to a cascade of rotationally bursting fragments. etary dust trails detected thermally (Sykes and Walker, 1992)
and optically (Ishiguro et al., 2003). Some parameters of the
5.4. Disintegration major streams and their likely parents are listed in Table 5.
The wide range of Tisserand invariants in Table 5 shows
Except for the sungrazing comets observed by SOHO, the dynamical diversity of the sources of the major meteor
only a few well-documented examples of complete comet- streams. Some are clearly linked to still-active comets; others
672 Comets II

TABLE 5. Major meteor streams.

Quantity Quadrantid Perseid Orionid Geminid Leonid

Parent Object 5496 109P 1P 3200 55P
Parent Type Asteroid HFC HFC Asteroid HFC
Perihelion q (AU) 0.88 0.9595 0.5860 0.14 0.9764
Eccentricity e 0.64 0.9632 0.9671 0.89 0.9055
Inclination i (deg) 68.0 113.5 162.3 22.1 162.5
Semimajor axis a (AU) 2.44 26.1 17.8 1.27 10.33
Tisserand TJ 2.53 –0.28 –0.61 4.51 –0.64
Stream Mass, Ms (kg) 1.3 × 1012 3.1 × 1014 3.3 × 1013 1.6 × 1013 5.0 × 1012
Meteor Density (kg m–3) 1900 ± 200 1300 ± 200 — 2900 ± 600 400 ± 100
Parent radius (km) 1.8 10.5 5.0 2.6 1.8
Parent Mass, Mp (kg) 1.2 × 1013 2.4 × 1015 2.6 × 1014 3.7 × 1013 1.2 × 1013
Ms/(Ms + Mp) 0.10 0.13 0.13 0.38 0.29

are associated with objects that appear asteroidal (Hughes vided the stream debris lifetimes are long compared to the
and McBride, 1989; Williams and Collander-Brown, 1998). source lifetimes.
Source diversity is also indicated by the wide range of me- The lifetimes of the streams are poorly determined. Es-
teor densities listed in Table 5. The absolute values of den- timates based on dynamical scattering of Perseids suggest
sity are limited in accuracy by the fragmentation models lifetimes of 4 × 104 yr to 8 × 104 yr (Brown and Jones,
applied in the interpretation of meteor data, but the rela- 1998). Independently, the mass loss rate from the Perseid
tive densities should be meaningful (Babadzhanov, 2002; parent 109P/Swift-Tuttle has been estimated at 5 × 1011 kg/
Rubio et al., 2002). For example, debris from the Leonid orbit from submillimeter observations (Jewitt, 1996b). To
parent 55P/Tempel-Tuttle is much less dense (more po- supply the 3.1 × 1014 kg in the stream would require about
rous?) than debris from Geminid parent 3200 Phaethon. The 600 orbits, corresponding to 8 × 104 yr, in good agreement
stream masses are estimated from the flux of meteors as a with the dynamical lifetime estimates above.
function of time and are thought to be accurate to within a
factor of ±4 or so (Hughes and McBride, 1989; Jenniskens 6. SUMMARY
and Betlem, 2000). Table 5 shows that the ratio of the stream
mass to the stream plus parent nucleus mass is 0.1 ≤ Ms/ Substantial progress has been made in recent years to-
(Ms + Mp) ≤ 0.4. What is behind this ratio? ward exploring and understanding two major storage re-
Consider a model of a spherical nucleus shrinking at a gions of the comets, the Oort cloud and the Kuiper belt.
constant rate and, for simplicity, neglect mantle formation. The latter, in particular, has been transformed from conjec-
Assuming that mass is not lost from the stream on the subli- ture into a dynamically rich and observationally accessible
mation timescale, the ratio of the mass of the stream, Ms, to region of the solar system, about which we seemingly learn
the total mass of the parent and stream, Ms + Mp, is given by more every month. On the other hand, the processes of
decay of the comets, and the relationships that exist between
these objects and other small bodies in the solar system,
Ms r 3 – r 3(t)
= fs 0 (24) remain subjects of considerable uncertainty. The latter have
Ms + Mp r 30 been the troublesome subjects of this chapter.
Observationally, there are at least two challenging prob-
where r0 is the initial nucleus radius and r(t) = r0 – βt (β is lems. First, the physical properties of the all-important com-
a constant equal to the sublimation distance per unit time) etary nucleus are difficult to measure, because of coma
is the radius at time t (t ≤ r0/β). The quantity fs is the frac- contamination when near the Sun and because of nucleus
tion of the mass of the parent that is contained in refrac- faintness when far from it. In order to study how the com-
tory matter. ets evolve and decay, reliable measurements of the nuclei
Averaged over the time interval 0 ≤ t ≤ r0/β, the value of are indispensable. We possess very few. Second, telescopic
equation (24) is given by data in any case sample only the outermost, optically ac-
tive surface layers. We can learn relatively little about fun-
damental aspects of the internal structure or composition
Ms 3
= fs (25) by sampling only reflected sunlight.
Ms + Mp 4 In terms of dynamics, the comets occupy difficult terri-
tory in which forces due to mass loss may play an impor-
With fs = 1/2, we have Ms/(Ms + Mp) = 3/8 ~ 0.4 which tant long-term role. The nuclei are pushed by asymmetrical
is very close to the measured values (Table 5). The obser- (sunward-directed) ejection of matter. Their angular mo-
vations are therefore consistent with the simple model, pro- menta are changed by outgassing torques and their very
 Jewitt: The Rise and Demise of Comets 673

lifetimes as comets may be limited by the loss of mass due 6. What fraction of the Centaurs are fragments of pre-
to sublimation, and by rupture due to centripetal effects. cursor objects that were disrupted by passage through the
Purely dynamical models appear to have been pushed to Roche spheres of gas giant planets?
their limits. The next step is to couple dynamical models 7. Is there any firm evidence for outgassing in the KBOs?
with thermophysical models in order to more realistically 8. What is the physical basis of the “fading parameter”
account for the effects of outgassing forces on the comets. in Oort’s model of the LPCs? Is our understanding of the
In terms of their formation, the comets and the asteroids dynamics of the LPCs complete?
represent two ends of a continuum. The asteroids, at least
those of the main belt, mostly formed at temperatures too Acknowledgments. The author thanks D. Cruikshank, Y.
high for the inclusion of water as ice while we think the Fernández, M. Festou, J. Luu, N. Samarasinha, and S. Sheppard
comets accreted water ice in abundance. In between lies a for their comments on this manuscript. Support from NASA and
large gray zone, in which the identity of the objects is in- NSF is gratefully acknowledged.
distinct, both observationally and compositionally. We have
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 Sykes et al.: Interplanetary Dust Complex and Comets 677

The Interplanetary Dust Complex and Comets

Mark V. Sykes
Steward Observatory

Eberhard Grün
Max Planck Institut für Kernphysik

William T. Reach
California Institute of Technology

Peter Jenniskens
SETI Institute

With the advent of spacebased in situ and remote sensing technologies, our knowledge of
the structure and composition of the interplanetary dust cloud has changed significantly. Both
asteroidal and cometary sources of the cloud interior to Jupiter have been directly detected. A
distant contributing source, the Kuiper belt, has been also been detected beyond Saturn. Analysis
of the morphology and composition of collected interplanetary dust particles (IDPs) is increas-
ingly sophisticated. Meteor storms are more accurately predicted. Yet the fundamental ques-
tion of whether asteroids or comets are the principal sources of interplanetary dust is still open
and more complex. By understanding the origin and evolution of our own interplanetary dust
cloud, and tracing its constituent particles to their roots, we are able to use these particles to
provide insights into the origin and evolution of their precursor bodies and look at dust pro-
duction in the disks about other stars and compare what is going on in those solar systems to
the present and past of our own.

1. INTRODUCTION

Earth moves through a cloud of interplanetary dust and

debris, extending in size from submicrometer to kilometers
and in distance from a few solar radii through the Kuiper
belt and beyond. That portion of the micrometer-sized par-
ticle cloud in the vicinity of the Earth’s orbit gives rise to
the zodiacal light, seen most prominently after sunset in the
spring and before dawn in autumn at northern latitudes
(Fig. 1). In 1693, Giovanni Cassini ascribed this to sunlight
scattering off dust particles orbiting the Sun. It was in the
late eighteenth and early nineteenth centuries that it was
realized that material from space might be showering down
on Earth. In 1794, Ernst Chladni, the father of acoustical
science, argued for the extraterrestrial origin of meteors,
fireballs, and meteorites (Yeomans, 1991). The spectacular
Leonid meteor shower in 1833, appearing to emanate from
a single location in the sky, convinced many scientists of
the day that these were indeed of extraterrestrial origin.
Almost immediately, a connection was made with comets
by W. B. Clarke and Denison Olmsted. Then Hubert Newton
correctly determined the orbit of the Leonids and predicted
their return in 1866. Work by Giovanni Schiaparelli and
others in the mid-1800s continued to press the connection
between meteor streams and comets. This was reinforced Fig. 1. The zodiacal light from Mauna Kea, Hawai‘i. Courtesy
when Comet Biela was seen to have broken up and Earth of M. Ishiguro, ISAS.

677
678 Comets II

experienced a meteor shower in 1872 when Earth subse-

quently passed near its orbit (Yeomans, 1991).
Comets are a logical source for the interplanetary dust
cloud. They are the only solar system objects visually ob-
served to emit dust, and meteor streams were also linked
to specific comets. In 1955, Fred Whipple applied his new
“icy conglomerate” model of comet nuclei to determine a
“quantitative relationship between comets and the zodiacal
light.” Since dust evolves toward the Sun under Poynting-
Robertson drag (e.g., Burns et al., 1979), it needs to be re-
plenished if it is to be maintained. Whipple (1955) estimated
that approximately 1 ton per second of meteoritic material
was required to maintain the zodiacal cloud against such
loss. He concluded that comets could easily supply that
amount of material. In the same paper, however, he also
noted that calculations by Piotrowski indicated that the
crushing of asteroids may also be an adequate source of zo-
diacal material. “Whether the comets or the asteroids pre-
dominate in zodiacal contribution must be decided on the
basis of other criteria . . . from meteoric and micrometeor- Fig. 2. Different methods of studying the interplanetary dust
itical information as well as from the shape of the zodiacal complex are sensitive to different size/mass ranges. Considered
cloud” (Whipple, 1955). together, a more complete picture of the production and evolution
In the 1930s, “cosmic spherules” found in deep sea sedi- of interplanetary dust can be constructed.
ments were found to be compositionally similar to meteor-
ites. Analysis of these findings led Ernst Öpik to estimate
that the Earth was accumulating 8 × 109 kg of meteoritic
material per year (Öpik, 1951). With the advent of the space
age, the question of the dust environment beyond Earth’s rizing the state of knowledge at that time, the most recent
atmosphere and its potential hazard to spacecraft and future of which is Grün et al. (2001). The reader is referred to
astronauts grew quickly in importance, later subsiding as this book and its antecedents for the detailed background
better spacebased detectors replaced those that had been that provides some of the context for this chapter.
providing anomalously high densities due to sensitivity to
more than just dust (cf. Fechtig et al., 2001). Returned orbit- 2. MORPHOLOGY OF THE CLOUD AND
ing surfaces from Skylab, orbiting facilities such as the Long ITS RELATION TO COMETS
Duration Exposure Facility (LDEF), and a series of space- AND ASTEROIDS
craft possessing dust detection systems, including Helios,
Hiten, Pioneer 9, Galileo, Ulysses, and Cassini, among At thermal infrared wavelengths, sky brightness viewed
others, soon gave new information and constraints on the from Earth orbit is dominated by the thermal emission of
interplanetary dust environment as did microcrater studies interplanetary dust particles (IDPs) heated by sunlight.
on returned lunar samples. These indicated that the inter- These particles are about 20–200 µm in size (Reach, 1988).
planetary dust cloud was complex, having a number of dif- The IRAS observed the sky in four bands between 12 and
ferent components of possibly different origins (e.g., Grün 100 µm over a range of solar elongations between 60° and
et al., 1985). 120° at a resolution of arcminutes, mapping the entire sky
In 1983, the first large-scale survey of the zodiacal cloud almost three times over the course of the mission. DIRBE
at thermal infrared wavelengths by the Infrared Astronomi- simultaneously observed in 10 wavebands from 1.25 to
cal Satellite (IRAS) (Hauser et al., 1984), revealed the over- 240 µm, covering the portion of sky between 64° and 124°
all cloud shape and, more importantly, the first spatial struc- solar elongation with fully sampled images at 1° resolution.
tures within the dust cloud (Low et al., 1984; Sykes et al., Using the DIRBE sky maps, the zodiacal light was charac-
1986; Sykes, 1988) directly relating to its asteroidal and terized using three components (Kelsall et al., 1998). The
cometary origins. This was followed by a thermal survey by smooth cloud is the dominant component, and its spatial
the Diffuse Infrared Background Experiment (DIRBE) on distribution was mathematically fitted with a parameterized
NASA’s Cosmic Background Explorer (COBE) satellite in function as follows in terms of spherical coordinates (r,θ,z)
1990 (Silverberg et al., 1993; Hauser et al., 1998). in AU where r is the cloud center distance, θ is the azimuthal
Since the late 1960s, the increasing amount and diver- angle, and z is the vertical distance from the cloud mid-
sity of dust observations sampling different components of plane:
the dust complex (Fig. 2) have spurred a series of regular
international conferences with associated volumes summa- n = nor –1.34exp[–4.14g(ζ)0.942]
 Sykes et al.: Interplanetary Dust Complex and Comets 679

where (a)

ζ = z/r

and (b)

g(ζ) = ζ2/0.378 for ζ < 0.189

and Fig. 3. (a) The last scan of the ecliptic plane made by IRAS
(76% complete). Ecliptic longitude increases from 0° (left) to 360°
g(ζ) = ζ – 0.0945 for ζ ≥ 0.189 (right) with ecliptic latitudes between –30° and 30°. The diagonal
structure crossing the ecliptic plane near 90° and 270° longitude
The smooth cloud is azimuthally symmetric, with its mid- is the galactic plane. The zodiacal cloud appears bright and wide
plane tilted by 2.03° from the ecliptic and its center offset at lower solar elongations, picking up the brighter thermal emis-
from the Sun by 0.013 AU. Both the tilt and offset are ex- sions of the warmer dust that lies closer to the Sun. At higher solar
plained by gravitational perturbations by the planets (Der- elongations, one looks through less dust near the Earth and sees
a greater fraction of colder fainter dust. (b) High-pass filtering in
mott et al., 1986); while the radial variation and the depend-
ecliptic latitude reveals structures in the zodiacal cloud associated
ence on z/r are to first order explained by Poynting-Robertson
with asteroid collisions and comets (Sykes, 1988).
drag, which yields an r –1 distribution and leaves orbital incli-
nation unchanged (Wyatt and Whipple, 1950).
The morphology of the main zodiacal cloud allows us,
in principal, to assess the fraction of dust that derives from (Reach et al., 1997), but that other prominent bands such
comets and asteroids. The Kelsall model above yields a half- as that initially associated with the Eos family (Dermott et
width at half-maximum number density of about 14° for al., 1984) were difficult to reconcile (Sykes, 1990; Reach,
dust particle inclinations, while some models based on in 1992; Grogan et al., 2001).
situ particle detections suggest that the inclination distribu- Another means of understanding the relationship of the
tion may have a half-width as wide as 20° to 30° (Dikarev zodiacal cloud to asteroids and comets is by simulation of
et al., 2002). For comparison, the half-width of the distri- its creation and the direct comparison with observations. In
bution of asteroid orbital inclinations (which is reasonably a review, Dermott et al. (2001) concluded on the basis of
structured) is between 12° and 16° (Minor Planet Center, such models that dust in the asteroid bands observed by
2003), consistent with the Kelsall model, whereas short- IRAS and COBE contributes about 30% of the total zodia-
period comets have inclinations generally less than 30° cal thermal emission. If only the Hirayama families (The-
(Marsden, 1974) and half have inclinations less than about mis, Koronis, and Eos) contribute that much, then the rest
10° — not very different from asteroids. Evidently cloud of the asteroid belt, according to the equilibrium model of
scale-height does not clearly distinguish between asteroids dust production, should contribute at least double that value,
and comets as principal suppliers of dust. leaving at most only 10% to a cometary contribution. This
The smooth cloud is supplemented by structures discov- would be difficult to reconcile with a zodiacal cloud span-
ered by IRAS: asteroidal dust bands (Low et al., 1984) and ning heliocentric ecliptic latitudes larger than the distribu-
cometary dust trails (Sykes et al., 1986) (Fig. 3). Trails rep- tion of asteroids (or comets for that matter) available to
resent the principal means by which comets contribute dust supply it.
to the zodiacal complex and are discussed in a later section. However, such a discrepancy (if it exists) may have been
The dust bands stretch across the ecliptic plane in north- mitigated by the identification of smaller asteroid families
south pairs that straddle a midplane tilted by about 1° from that are dynamically younger and associated with two of
the ecliptic. Soon after their discovery in the IRAS data, the three major pairs of dust bands (Nesvorný et al., 2002,
the bands were associated with the major Hirayama aster- 2003). This has given support to the nonequilibrium theory
oid families (Dermott et al., 1984) and explained as a natu- of dust production in the asteroid belt. A consequence of
ral consequence of the general collisional comminution of this result is that the contribution of the asteroid belt as a
the asteroid belt as a whole (since the families are regions whole to the zodiacal dust cloud is not expected to simply
of asteroid concentration). An alternative to this “equilib- scale with local asteroid density, increasing the complexity
rium” theory was proposed by Sykes and Greenberg (1986) (and uncertainty) of the detailed relationship between aster-
and Sykes (1990) in which the large-scale production of dust oids and the observed zodiacal cloud.
in the asteroid belt is stochastic (the “nonequilibrium” the- Whether asteroidal dust is produced continuously or sto-
ory). In this case, observable dust bands would most likely chastically, asteroids present a solid alternative to a purely
be associated with recent disruptions of small (~20 km) as- cometary origin of the zodiacal cloud. Asteroid particles are
teroids. Detailed studies indicated that some bands seemed dynamically distinct from cometary particles in that they
to be associated with the Themis and Koronis families have smaller initial orbital eccentricities. After being gen-
(Sykes, 1990; Reach et al., 1997) and the Maria family erated in the asteroid belt, this dust evolves toward the Sun
680 Comets II

under Poynting-Robertson drag. As it passes the orbit of The large end of this size range connects directly to the
Earth, some of it forms a circumsolar ring due to dust or- size range accessible by near-Earth-object searches such as
bits resonant with that of Earth (Dermott et al., 1994). The Spacewatch (Bottke et al., 2002a) and others. Ceplecha
ring is just outside Earth’s orbit, at 1.03 AU, as the exte- (1992) analyzes interplanetary bodies from millimeter-sized
rior resonances are more stable. The peak density in the ring meteoroids to kilometer-sized boulders. The size distribution
occurs in an enhancement that trails Earth, and amounts to of smaller meteoroids is best documented in the lunar micro-
about 30% in excess of the density of the smooth cloud crater record (Grün et al., 1985). Over this entire range the
(Kelsall et al., 1998). The ring density is actually highly slope of the number density of these interplanetary bodies
uncertain, being derived from a line-of-sight integral, but vs. mass in a log-log plot is close to 0.83. This slope indi-
the estimate may be significantly improved using back- cates that the population of these interplanetary bodies is
ground measurements by the Space Infrared Telescope Fa- in overall collisional equilibrium (Dohnanyi, 1970), i.e., the
cility (SIRTF) as it travels through the trailing enhancement number of particles created in a mass interval by fragmen-
during its planned mission lifetime (Werner et al., 2001). tation of larger objects equals the number of particles in that
An intriguing aspect of the zodiacal cloud observed by mass interval that are destroyed by collisions. However, in
IRAS and COBE/DIRBE is its azimuthal smoothness, about the local mass distribution there are significant deviations
5% with the principal variation arising from dynamics-in- from this slope: One hump is at 10–9 kg and another is at
duced asymmetries in the dust ring near Earth’s orbit (Der- 104 kg. A hump in the mass distribution at mh signals that
mott et al., 1994). This smoothness requires a source that there is an excess of particles more massive than mh, prob-
is similarly distributed over ecliptic longitude (i.e., with ably from an additional input in this mass range. One input
randomized orbital nodes or a very efficient process for is in the 100-µm to centimeter size range, i.e., the range of
randomizing the orbital nodes of the particles before they radar to visual meteors, and the other is in the 1–10-m size
spiral past Earth). The existence of the dust bands demon- range, i.e., the range of very bright meteors, the fireballs.
strates that observed asteroid dust arises from a node-ran- Collisions govern the lifetimes of particles having these
domized population of parent bodies. Comets are much “excess” size ranges as well as larger particles up to the size
fewer in number than asteroids, and material tracing their of asteroids (whereas sublimation and breakup determine
current orbits would produce a relatively “lumpy” cloud. the lifetime of comets in the inner solar system, <5 AU).
Whether a cometary component could be “smooth” depends Transport of these larger meteoroids through the solar sys-
on the outcome of the race between differential precession tem is facilitated by stochastic gravitational interactions with
of the ejected cometary particle orbits [104–107 yr depend- planets, by the systematically inward (toward the Sun) drift
ing on ejection velocity (Sykes and Greenberg, 1986)], colli- caused by the Pointing-Robertson effect, and by the Yar-
sional lifetimes, and orbital decay timescales. If the comet- kovsky effect (a thermal radiation force) acting in directions
ary contribution to the zodiacal complex were due to single that depend on the orientation of the spin axis, spin rate,
or multiple generational collision fragments from large and thermal properties of the object (e.g., Bottke et al.,
millimeter–centimeter cometary particles [suggested as a 2002b). However, since the collisional lifetime is shorter
possibility by Liou and Zook (1996)], the dispersion time- than the transport time, meteoroids only slowly diffuse away
scales would tend toward tens of millions of years. Disrup- from their place of origin while at the same time they are
tion of such particles would be most likely by the smallest ground down by collisions. Only meteoroids smaller than
particles capable of fragmenting them, resulting in low ejec- 0.1 mm rapidly drift by the Pointing-Robertson effect to-
tion velocities on timescales (e.g., Dohnanyi, 1970) com- ward the Sun where they sublimate. For fragments smaller
parable to or smaller than the dispersion timescales. The than about 1 µm in size in general, solar radiation pressure
rapid orbital decay of small fragments (wherein lie the sur- reduces solar gravity sufficiently to drive them out of the
face area) would result in the partial formation of a torus, solar system — they become beta-meteoroids — although
extended toward the Sun (Sykes, 1990). Azimuthal smooth- particles much smaller than 1 µm are less affected in this
ness of a purely cometary zodiacal cloud could be difficult manner (Burns et al., 1979).
to achieve. Better understanding of the detailed evolution of Many clear orbital associations have been found between
the nodes of cometary dust in addition to the other orbital meteor streams and comets from which they are presumed
elements is a necessary step toward solving this problem. to originate. [Even some asteroids may be extinct comets.
The morphology of the zodiacal cloud changes with the Several authors suggested that Apollo and Amor asteroids
size of particles being considered. As particle sizes increase are defunct comets. An argument for this thesis is that at
from tens of micrometers in size (to which IRAS and COBE/ least the peculiar asteroid Phaethon is associated with the
DIRBE were sensitive), their sensitivity to radiation forces Geminid meteor stream (Halliday, 1988). By dynamical
decrease and their spatial distribution begins to converge studies Gustafson (1989) showed that Phaeton’s cometary
upon the distribution of yet-larger bodies from which they active phase lasted for several hundred orbits about 1000
ultimately derive. years ago.] On the other hand, it has been observed that
Information on objects in the millimeter to several-meter visual meteor streams (millimeter and bigger sizes) are most
size range is obtained by meteor observations at Earth (since prominent in brightness and apparent point of origin on the
no such observations have yet been made at other planets). sky compared with the sporadic meteor background. The
 Sykes et al.: Interplanetary Dust Complex and Comets 681

contrast in these aspects between stream meteors and spo- projectiles in the laboratory found that microcraters gener-
radic meteors is reduced for smaller meteors and is only ated by low-density projectiles had a significantly shallower
weakly recognizable in radar meteor observations [100-µm depth than those generated in the same material by high-
size range (Galligan and Baggaley, 2001)]. No meteor density projectiles [ρ > 3 g/cm3 (Vedder and Mandeville,
streams have yet been identified in the dust range (microme- 1974; Nagel and Fechtig; 1980)]. Since cometary material
ter size range). This observation indicates that the input is generally associated with lower-density material than
from comets into the interplanetary dust cloud near Earth’s asteroidal material, these authors conclude that at least 30%
orbit is most significant in the millimeter and larger size of interplanetary meteoroids originate from comets. The
range, whereas smaller meteoroids are mostly collisional effects of the irregular shape of IDPs (e.g., Brownlee, 1985),
fragments of the bigger asteroidal ones, ground down and however, are not known. Analysis of impacts on NASA’s
transported to Earth’s distance by radiation forces. LDEF and ESA’s Eureca satellite indicate a mean density
of IDP impactors between 2.0 and 2.4 g/cm3 (McDonnell
3. INFERENCES FROM THE PHYSICAL and Gardner, 1998), somewhere in between canonical com-
PROPERTIES OF INTERPLANETARY DUST etary and asteroidal values.

3.1. Density: Meteors and Microcrater Studies 3.2. Interplanetary Dust Particles

The notion that fragments of comets have low density Interplanetary dust particles collected in Earth’s upper
comes from Whipple’s dirty snowball model where a comet atmosphere provide clues to their asteroidal or cometary
nucleus consists of an intimate mixture of ice and dust. origin. Some of these particles have the kind of open struc-
When the ice sublimates it leaves a filigree structure of dust tures that are associated with dust expected from comets
with much pore space from which the ice has been lost. (Fig. 4). Compositions of IDPs range from chondritic (most)
Laboratory sublimation experiments of ice dust mixtures to iron-sulfide-nickel and mafic silicates. Some particles are
confirm this picture (Grün et al., 1993a). A second line of melted as a consequence of atmospheric entry. Measure-
evidence comes from meteor observations that show that ments of the density of about 100 of these stratospheric
the terminal height (at which a meteoroid is sufficiently IDPs (having diameters of 5–15 µm) found that unmelted
decelerated so that it does not generate anymore light dur- chondritic particles have densities between 0.5 and 6.0 g/
ing its passage through the atmosphere), after scaling to the cm3, about half of which are below 2 g/cm3, but with no
same initial mass, inclination to horizon, and velocity dif- observed bimodality as one might hope with two distinct
fer so much that the whole range of heights covers an air source populations (Love et al., 1993).
density ratio of 1 : 1000 (Ceplecha, 1994). This observation Atmospheric entry heating was proposed as a means of
is interpreted as a consequence of a wide range of meteor- distinguishing between IDPs arising from comets and aster-
oid densities: Low-density meteoroids are decelerated at oids, given the greater average orbital eccentricity (hence
higher altitudes in the much more tenuous atmosphere than average impact velocity) of the former (Flynn, 1989). Entry
high-density meteoroids. It was found that especially me- velocities of IDPs were measured by Joswiak et al. (2000)
teor stream particles that have a clear genetic relation to
comets have very low material density, e.g., the Perseids
that originate from Comet P/Swift-Tuttle. Ceplecha (1977)
arrives at a classification of meteoroid orbits and densities
from radar meteors (m ~ 10 –8–10–6 kg) over photographic
meteors (10 –6–1 kg) to fireballs (1–10 6 kg). “Asteroidal”
meteoroids have high densities (~3 g/cm3) and orbits with
medium eccentricities (0.6) and low inclinations (10°).
“Short-period comet”-like meteoroids have orbits with
higher eccentricities and their densities are lower (1–2 g/
cm3). “Long-period comet”-like meteoroids have almost
parabolic orbits, random inclinations, and very low densi-
ties (0.2–0.6 g/cm3). From the study of fireballs from me-
teoroids larger than 1 m, Ceplecha (1994) concludes that
the majority of these bodies are of cometary origin and of
the weakest known structure.
At the lower end of the size distribution, lunar micro-
crater studies (Brownlee et al., 1973) suggested that about
30% of all craters observed on lunar rocks were generated Fig. 4. A 10-µm-diameter particle collected in Earth’s strato-
by low-density meteoroids. This result was derived from sphere. It is carbonaceous and very porous, suggesting that it may
measurements of the depth-to-diameter ratio of lunar micro- be of cometary origin, although an asteroidal origin is not excluded
craters. Crater simulation experiments with hypervelocity as a possibility. Courtesy of NASA.
682 Comets II

applying a model of atmospheric heating and helium release ticles detected. On the other hand, impacts outside the band
(Love and Brownlee, 1994). High- and low-velocity groups were mostly observed by the south sensor and must have
were distinguished, with the high-velocity (cometary) group higher eccentricities. Modeling shows that these “eccentric”
having an average density of 1.1 g/cm3 and exhibiting “fluffy, particles have eccentricities, eave ~ 0.7, and semimajor axes,
porous, aggregate textures” and the low-velocity (asteroidal) aave ~ 0.9. Grün et al. (1980) conclude that at least half the
group having average density of 2.5 g/cm3 and tending “to- eccentric particles should have densities below 1 g/cm3, sug-
ward smoother, compact forms” (Joswiak et al., 2000). gesting a cometary origin.
However, while the means were distinct, there was signifi- Four planned comet flybys (and an unintended one) from
cant overlap between the two groups in their ranges of prop- which in situ dust data became available were performed to
erties, making it difficult to assign a particle to one group or date. Four spacecraft took dust measurements within 104 km
another on the basis of density and morphology unless it of the nuclei of different comets. In 1985 the International
resided at the extremities associated with those groups. This Cometary Explorer (ICE) mission flew through the coma of
difficulty is in part due to the potential pumping up of a par- Comet Giacobini-Zinner, and the plasma wave instrument
ticle’s orbital eccentricity (or that of its collisional precursor) recorded dust impacts in the tailward region of the coma
by planetary perturbations. The properties of dust from a (Gurnett et al., 1986). One year later, a five-spacecraft ar-
specific known comet will be obtained by the Stardust mis- mada flew by Comet Halley, of which three spacecraft car-
sion when it collects dust from the environment of P/Wild 2 ried a range of dust instruments from simple impact count-
and returns it to Earth (Brownlee et al., 2000). This will be ers to sophisticated dust-mass analyzers. The two Russian
a great aid to further distinguishing cometary from asteroi- Vega spacecraft crossed the sunward side of the coma and
dal particles among collected IDPs. recorded dust impacts from the outer boundary at a distance
of 2 × 105 km down to about 8000 km from the nucleus
3.3. Helios and Other Missions (Mazets et al., 1987; Simpson et al., 1987; Vaisberg et al.,
1987). ESA’s Giotto spacecraft flew closest (600 km) to the
Other evidence for distinguishing cometary and asteroi- nucleus, but most measurements ended on approach at a dis-
dal particles on the basis of their orbits and physical prop- tance of about 3000 km when a millimeter-sized pebble hit
erties came from the Helios dust experiment. The dust in- the spacecraft with a speed of almost 70 km/s, causing some
strument on the Helios spacecraft consisted of two sensors damage onboard and interrupting telecommunication. Some
that were mounted differently in the spacecraft. The ecliptic time later ground control over the spacecraft was regained
sensor was sensitive to impacts arriving from both north and and several instruments continued their measurements. Six
south sides of the ecliptic plane. Since this sensor viewed years later, in 1992, the Giotto spacecraft was redirected to
the Sun once per spin revolution (the spacecraft spin axis fly through the coma of Comet Grigg-Skjellerup at a dis-
was perpendicular to the ecliptic plane) it was covered by tance of only 200 km from the nucleus (McDonnell et al.,
an aluminum-coated 0.3-µm-thick plastic film in order to 1993), although it ended up passing at a distance of ~100 km
prevent heat and solar UV radiation entering into the sen- (McBride et al., 1997). This was possible because the dust
sor. This film caused a penetration cut-off for meteoroids production of this comet was very low and only three parti-
that depended on the mass, density, and velocity of impact- cles between approximately 1 and 100 µm and a fourth par-
ing dust particles (Pailer and Grün, 1980). The south sensor ticle ~10 mg were recorded to hit the approximately 2-m2
had an open aperture that was shielded from solar radiation big bumper shield (a fairly flat distribution over several or-
by the spacecraft rim and hence recorded only dust impacts ders of magnitude, consistent with the mass distribution
arriving from south of the ecliptic plane. This sensor was seen at Halley). The latest flyby of Comet Borrelly by the
sensitive to somewhat smaller and/or lower-density meteor- Deep Space 1 spacecraft occurred in 2001. The plasma wave
oids. Both sensors had overlapping fields of view. instrument onboard recorded several dust impacts within
Helios measurements covered the range from 0.3 to 5 minutes of closest approach at 2000 km distance from the
1 AU heliocentric distance. The measured dust flux displays nucleus (Tsurutani et al., 2003). Almost 30 years earlier,
a steady increase toward the Sun by about a factor of 10. in 1974, the dust instrument onboard the HEOS-2 satellite
There are significant differences between the measurements recorded an enhanced impact rate of micrometer-sized parti-
by both sensors. The ecliptic sensor detected most impacts cles by a factor of 3 over what the instrument had observed
in a band centered about the apex direction (i.e., 90° off the in previous years (Hoffmann et al., 1976; Grün et al., 1976).
Sun in the direction of spacecraft motion), while the south During this period the instrument was pointed in the direc-
sensor observed particles from all around during a spin tion where Comet Kohoutek (1993 XII) was about one year
revolution with a predominance of small particles from the earlier and had displayed strong dust emission that led to its
solar direction (Grün et al., 1980). Modeling of the Helios detection at about 4 AU from the Sun. At the time of the re-
results show that these “apex” particles have low eccentrici- corded dust impacts the comet was already 3 AU from the
ties (eave ≤ 0.6) and small semimajor axes (averaging about Sun past its perihelion. Therefore, the dust recordings con-
0.6 AU). Since apex particles did penetrate the front film stitute measurements in the very distant tail of this comet.
of the ecliptic sensor, their density cannot be below 1 g/cm3 Besides the spatial extent of dust in cometary comae and
(Pailer and Grün, 1980), at least not for the smallest par- tails, the dust production rate and size distribution of comet-
 Sykes et al.: Interplanetary Dust Complex and Comets 683

ary dust was derived from the in situ measurements. Most tribution of the comet’s motion. For emission at perihelion,
data, of course, came from the comprehensive measure- the value of β for escape is a function of orbital eccentricity
ments at Comet Halley. It was found that the dust size distri- of the parent body
bution extends over a much wider range than was expected
from astronomical observations, mostly in the optical wave- βp ≥ (1 – e)/2
length range. The size distribution extends to both much
smaller particles in the submicrometer and even nanometer Thus, for a parabolic comet, all emitted particles would be
size range, and to much bigger particles in the millimeter lost. The solar system loses particles tens of micrometers
size range (McDonnell et al., 1987). It was also found that and smaller from long-period comets, while retaining par-
some particles fragment shortly after their release from the ticles on the order of several micrometers from short-pe-
nucleus (Simpson et al., 1987; Vaisberg et al., 1987), which riod Jupiter-family comets (Fig. 5). Almost all dust particles
indicates that their initial structure is very fluffy and contains tens of micrometers and smaller are released from these
materials that sublimates at distances as small as 1 AU from latter comets into Jupiter-crossing orbits — even comets
the Sun. As a consequence of this extended mass distribution whose orbits are completely interior to that of Jupiter’s
the dust production is significantly bigger than that which (Fig. 6). Subsequent perturbations on the orbits of these
has been derived from astronomical observations alone. In particles by Jupiter results in their loss while the distribu-
addition, the dust-to-gas mass ratio of Comet Halley ex- tion of many bear little resemblance to the elements of their
ceeds a value of 1 (McDonnell et al., 1991) compared to a parent comets (e.g., Gustafson et al., 1987). Making the
value of 0.1 from earlier estimates. assumption that such scattered particles have randomized
The dust mass spectrometer onboard the Giotto and Vega nodes (required to match the azimuthal symmetry of the
spaceprobes provided elemental and isotopic data for small cloud), Liou et al. (1995) was able to model a contribution
newly ejected cometary particles (Kissel et al., 1986). A to the cloud by single-sized particles from Encke, taking
major discovery was that of “CHON” particles, which con- into account radiation pressure, Poynting-Robertson and
sisted of material high in content of the elements H, C, N, corpuscular drag, and perturbations by Jupiter, which when
and O, showing that the dust was rich in organics (Kissel combined with a model contribution from asteroid dust
and Krüger, 1987). Magnesium isotope ratios showed only made good matches to selected scans of the zodiacal cloud
a slight variation around the nominal solar value, whereas by IRAS.
the isotopic ratio of 12C/13C showed large variations from Cometary particles may undergo considerable orbital
grain to grain, but on average it was also solar like (Jess- evolution with time, increasing the difficulty of distinguish-
berger and Kissel, 1991). The average elemental composi- ing them from asteroidal particles. Liou and Zook (1996)
tion was found to be solar like, but significantly enriched in
volatile elements H, C, N, and O compared to C1 chondrites
(Jessberger et al., 1987).

4. HOW COMETS SUPPLY THE CLOUD

4.1. General

When a comet is discovered, it is identified by virtue of

its fuzzy appearance, with perhaps a tail, arising from the
loss of gas and dust. This dust represents the smallest-sized
particle emissions from a comet [generally tens of microme-
ters and smaller, although significant coma surface area is
argued to reside in very large particles (see Fulle, 2004)].
These are entrained in the gas outflow and accelerated to
speeds up to ~1 km/s for the smallest particles. After de-
coupling from the gas, they are generally lost to the solar
radiation field. The sensitivity of a particle to solar radiation
pressure is described by the parameter, β, the ratio of radia-
tion force to gravitational force felt by the particle (Burns
et al., 1979). Most of the particles observed in a comet’s
tail at visible wavelengths are micrometer-sized and have
Fig. 5. Maximum β (minimum radius, assuming a density of 1 g/
β > 1. These particles are not gravitationally bound to the cm3) of particles from known comets on escape trajectories from
Sun and escape the solar system, not contributing to the the solar system, assuming perihelion emission and zero ejection
interplanetary dust complex. Particles having lower β can velocity. Aphelion distances of source comets are dashed lines.
also escape from the solar system when they are released For circular orbits, βp = 0.5. Particles are assumed to have zero
from an orbiting object like a comet, because of the con- albedo.
684 Comets II

“anomalous tail” to be the result of low-velocity emissions

of large particles, some of which may have occurred at least
1500 days prior to the observations (Eaton et al., 1984).
An examination of IRAS image products, in which in-
dividual IRAS scans were merged into images, revealed the
continuous emission of the reported Tempel 2 tail extending
over 48° of sky (Fig. 7). Similar features were found asso-
ciated with other comets (Sykes et al., 1986). Clearly, a new
cometary phenomenon had been discovered by IRAS and
was referred to as “trails.” An examination of all the IRAS
data yielded trails associated with eight short-period comets
(Table 1) and about an equal number of “orphans” not as-
sociated with any known comet (Sykes and Walker, 1992).
As with Eaton et al. (1984), all trails were found to be con-
sistent with low-velocity emissions and emissions from
years to more than a century before the time of observation.
Thus, trails offered a continuous record of the emission of
comets over that period of time. At the comet orbits, trails
have widths of several 10 4–105 km.
After IRAS, trails were no longer observed in the infra-
red until the launch of the Infrared Space Observatory (ISO)
more than a decade later. The ISO observed segments of
the Kopff (Davies et al., 1997) and Encke trails (Reach et
al., 2000). Unlike IRAS, ISO was a pointed and not a sur-
Fig. 6. Perihelion and aphelion distances of parent comets (open vey instrument, so its ability to study trails was limited.
circles) and the aphelia of emitted particles of different β (filled However, the Kopff trail showed changes due to emissions
circles). Jupiter’s perihelion and aphelion distances are indicated since IRAS. The Encke trail was observed from a particu-
by solid lines. larly favorable angle of 35° above its orbital plane and in-
cluded the comet allowing the emergence of the trail from
the comet coma to be studied. Dynamical modeling of the
determined that some cometary particles (from Tempel 2– Encke trail showed that the mass lost in trail particles (me-
like comets) could be injected into mean-motion resonances teoroids with radii of at least several millimeters) is much
with Jupiter and trapped for thousands of years, after which larger than the mass lost in gaseous or small-particle form,
their orbital eccentricities would be quite small. They would and the comet can only survive these large-particle losses
approach Earth with the low velocities expected for aster- for ~10,000 years (Reach et al., 2000).
oid particles. This would help explain the overlap in mor- At the time of its observation by IRAS, the Tempel 2 trail
phologies and compositions among collected “cometary” position was sent to ground observers who were unable to
and “asteroidal” IDPs, identified by their model atmospheric detect it at visual wavelengths (Davies et al., 1984; Stewart
entry speeds. et al., 1984). Several years later, a trail associated with P/
Faye was accidentally detected in the visible by the Space-
4.2. Dust Trails

4.2.1. Discovery and observations. In 1983, the first

survey of the entire sky at thermal infrared wavelengths was
conducted by IRAS (Neugebauer et al., 1984). Part of the
ongoing analysis during this mission was the IRAS Fast
Mover Program (Davies et al., 1984; Stewart et al., 1984;
Green et al., 1985) in which fast-moving solar system ob-
jects were sought. Six comets and a couple of Apollo as-
teroids (including Phaethon) were discovered. However, a
curiously extended tail associated with P/Tempel 2 was de-
tected over the course of a number of IRAS scans. This was
manifested by about 50 faint, relatively collinear sources at Fig. 7. The Tempel 2 dust trail is seen to extend over 30° in this
25 µm. It was found to extend 10° on the sky with a width of composite image constructed from IRAS scans. The comet coma is
4', and no similar feature was found by the program associ- seen at the left end of the trail. In the upper right corner is part of
ated with any other comet observed by IRAS (Davies et al., the central asteroid dust band. Background cloud-like structures
1984; Steward et al., 1984). Dynamical analysis showed this are interstellar cirrus.
 Sykes et al.: Interplanetary Dust Complex and Comets 685

TABLE 1. Cometary dust trail information from Sykes and Walker (1992).

Name θ W ∆vp Age LM D/G

Churyomov-Gerasimenko* 1 50 2 3–11 13.1 4.6
Encke 93 680 40 19–21 14.9 3.5
Gunn 6 111 3 27–74 13.8 3.6
Kopff 17 47 3 47–158 13.5 1.2
Pons-Winnecke 3 40 3 6–21 13.2 2.4
Schwassmann-Wachmann 1 10 769 5 114–148 14.5 1.6
Tempel 1† 7 68 4 14–38 13.4 3.5
Tempel 2 65 31 2 140–665 13.7 2.9
*Rosetta target.
† Deep Impact target.

Includes the observed angular extent, θ (deg.); the width, W (103 km); normal velocity assuming peri-
helion emission, ∆vp (m/s); an estimate of the age (in years) of the oldest emissions observed; an
estimate of the corresponding comet mass loss rates, LM (log g/century); and an estimate of the dust
to gas mass ratio of the comet, D/G.

watch Survey in the course of searching for near-Earth to sustain a latitudinal temperature gradient (Fig. 8). Low
objects. One evening, a band 1'–2' in width lay across one thermal conductivity can be achieved with porosity, which
of their half-degree scans. The next night, they traced the translates to low mass density.
band back to its cometary source. The trail extended 10° 4.2.3. What trails tell us about comets and their contri-
(Rabinowitz and Scotti, 1991). More recently, a program bution to the interplanetary dust cloud. Dust trails reveal
to observe trails from the ground at visual wavelengths has the principal mechanism by which short-period comets lose
been successful (Ishiguro et al., 2002), and other observers mass: via the low-velocity emission of large particles. Esti-
are beginning to report similar detections of dust trails (e.g., mates of refractory (dust) mass loss rates (Table 1), combined
Lowry et al., 2003). These observations are the harbinger with gas mass loss from visible groundbased observations,
of a new era of dust trail studies that will allow more ex- reveal an average cometary dust to gas mass ratio of about
tensive mapping and characterization of large particle mass 3 (Sykes and Walker, 1992), which is significantly higher
loss from comets than has been previously been available. than the canonical 0.1–1. This translates to roughly equal
4.2.2. Particle properties. Syndyne analysis of the volumes of “rock” and “ice” in a comet nucleus (assuming
Tempel 2 trail (comparing it with the predicted locations of a rock density of 3 g/cm3 and an ice density of 1 g/cm3), and
continuously emitted particles with zero emission velocity) is consistent with the dust to gas limit for Comet Halley’s,
suggested particle diameters of about 1 mm (β ~ 0.001),
assuming density of 1 g/cm3 (Eaton et al., 1984; Sykes et al.,
1990). Trail particles are dark. This is evidenced by the early
failure to detect the Tempel 2 dust trail from the ground
(Davies et al., 1984; Stewart et al., 1984) and supported by
initial estimates of the albedo of those particles using IRAS
measurements (Sykes, 1987). An extremely low albedo (on
the order of a percent) for Kopff trail particles has been
estimated on the basis of its groundbased detection (Ishiguro
et al., 2002).
Trail particles have color temperatures that tend to be in
excess of blackbody values (Sykes, 1987; Walker et al., 1989;
Sykes et al., 1990; Sykes and Walker, 1992), suggesting
either low-emissivity materials, a small particle component, Fig. 8. Color temperatures for individual 12, 25, and 60-µm
or sustaining temperature gradients. The low emissivities scans of the Tempel 2 dust trail were calculated and scaled to
1 AU. The top dashed line corresponds to the color temperature
required do not match that of any known nonmetallic ma-
of a sphere on which each point is in instantaneous radiative equi-
terials (Sykes and Walker, 1992). Particles small enough to
librium with solar insolation. The bottom dashed line corresponds
have the observed low β values would need to be smaller to the color temperature of a blackbody. The central solid line
than tens of nanometers (Burns et al., 1979), which would corresponds to the color temperature of randomly oriented, rapidly
not radiate efficiently at infrared wavelengths. Trail particles rotating spheres where each local latitude is in radiative equilib-
appear to be uniformly large, dark, rapidly rotating particles rium with the average diurnal solar insolation. Geometric albedo
that have thermal conductivity low enough to allow them is assumed to be zero.
686 Comets II

based on observations by Giotto (McDonnell et al., 1991).

Assuming all short-period comets have trails similar to
those identified in the IRAS observations, with a corre-
sponding average mass loss rate of 8.4 × 108 kg/yr (Sykes
and Walker, 1992), the amount of material contributed to
the zodiacal dust complex (assuming 150 comets) would be
1.3 × 1011 kg/yr, a significant fraction of the ~2.9 × 1011 kg/
yr lost within 1 AU that needs to be replenished if the cloud
is in steady state (Grün et al., 1985). A recent optical/ther-
mal imaging survey of comets also concludes that comet
dust is a major supplier of the IDP cloud (Lisse, 2002).

4.3. Meteor Streams

Fig. 9. Activity curve of the 2001 Leonid meteor storms. Closed
symbols are from the Leonid Multi-Instrument Aircraft Campaign;
The largest-sized particles supplied to the interplanetary
open circles are data gathered by the International Meteor Orga-
dust cloud by comets are observed as meteor showers. They nization (Jenniskens, 2002).
begin as dust trails, with individual returns by the parent
comet to perihelion causing separate trails in a pattern re-
flecting planetary perturbations of the comet orbit itself.
Perturbations on individual grains in the trail cause a cyclic showed the dust density in Earth’s path and along the orbit
motion of the node of the trail near Earth’s orbit. Meteor to exhibit a sharp core, but with “wings” well described by
outbursts (including meteor storms) are seen when Earth a Lorentzian, while the perpendicular dispersion in a sun-
passes through a dust trail (e.g., Kresák, 1993). Differences ward direction is wider and exponential (Jenniskens et al.,
in perturbations acting on different trail fragments result in 2000). Possible explanations include emission at large he-
these fragments superposing and smearing to the point that liocentric distances combined with a higher degree of frag-
they populate a filament. Dispersal of comet trail/meteor mentation of dust particles within the coma near perihelion
stream material into the background zodiacal cloud can be (Jenniskens, 2001). A mass loss rate of ~2.6 × 1010 kg/re-
inhibited by orbital resonances, which can maintain trail turn was measured.
cohesion for long periods of time [Asher et al. (1999), who
determined that the Leonid outburst of 1998 was dust 4.4. Kuiper Belt Dust
ejected in 1366]. Close encounters cause the grains to be
dispersed into a broader meteor stream responsible for an Another direct source of interplanetary dust in both the
annual shower, which can be identified with that comet’s inner solar system and beyond Jupiter is the source region
orbit for thousands of years before dissipating and becom- of the short-period comets themselves — the Kuiper belt.
ing indistinguishable from the background population of Flynn (1994) suggested that this might constitute a signifi-
particles in that size range. cant contribution to the interplanetary dust collected in
Success at predicting storms has been recently achieved Earth’s stratosphere. Liou et al. (1996) found that 20% of
with the work of Jenniskens (1994, 1997), who forecast the the grains generated in the Kuiper belt would evolve all the
return of the 1994 α-Monocerids based on the dust-trail way to the Sun (the remainder being scattered out of the
hypothesis, and Kondrat’eva and Reznikov (1985), who pre- solar system by the giant planets), and that particles between
dicted the return of the 1998 Draconid storm (Fujiwara et al., 9 and 50 µm diameter would be depleted due to mutual
2001) and the 2001/2002 Leonid storms. The latter consid- collisions and collisions with interstellar dust. They further
ered the ejection of a single particle at perihelion in the direc- found that particles surviving into the inner solar system
tion of motion of the parent comet and calculated the subse- would have low-eccentricity, low-inclination orbits, mak-
quent gravitational perturbations on an orbit with enough lag ing them dynamically indistinguishable from evolving as-
to allow for a timely collision with Earth. McNaught and teroidal particles (offering a possible explanation for the
Asher (1999) and Lyytinen (1999) applied a refined model IDPs having “cometary” physical properties, but heating
to the Leonids, identifying the spatial distributions of dust characteristics of asteroidal sources, above). More recently,
trails from its parent, P/Tempel Tuttle, which allowed mete- Moro-Martín and Malhotra (2003) modeled the dynami-
ors to be identified with emissions from specific epochs of cal evolution of dust particles from the Kuiper belt, taking
perihelion passage (e.g., Fig. 9). This allows for future stud- into consideration the combined effects of radiation pres-
ies of the effects of age on larger cometary dust particles. sure, Poynting-Robertson drag, solar wind drag, and the
A principal means of analyzing particle number densities gravitational forces of the planets (excluding Mercury and
within a meteor stream is via its zenith hourly rate (ZHR), Pluto) and concluded that near Earth, these grains would
the rate of visible meteors seen by a standard observer under have high eccentricities and inclinations, similar to cometary
ideal conditions (radiant in the zenith and the star limiting grains and not asteroidal grains, contradicting Liou et al.
magnitude = 6.5) (Jenniskens, 1995). Precise measurements (1996). They further concluded that between 11% and 21%
of the ZHR from aircraft during the 1999 Leonid event of particles with 0.01 ≤ β ≤ 0.4 would drift from the Kuiper
 Sykes et al.: Interplanetary Dust Complex and Comets 687

belt to interior to Jupiter [in rough agreement with Liou et ties of these particles exceeded the local solar system es-
al. (1996)], and that [assuming the dust production rates of cape velocity (Grün et al., 1994).
Landgraf et al. (2002)] the contribution to the IDPs cap- The motion of ISD through the solar system was found
tured in Earth’s atmosphere may be as low as 1–2%. to be parallel to the flow of neutral interstellar hydrogen
Because of their large heliocentric distance (beyond and helium gas with a speed of 26 km/s both for gas and
30 AU), Kuiper belt objects (KBOs) are not active. Dust dust. This proves that local interstellar dust and gas are
production in the Kuiper belt depends upon collisional ac- nearly at rest with respect to each other. The interstellar dust
tivity, constrained by their size distribution and detailed flow was continuously monitored by Ulysses and persisted
orbital-element distribution. This production has been esti- at a constant level at all latitudes above the ecliptic plane
mated by Stern (1996) to be between 9.5 × 108 to 3.2 × even over the poles of the Sun, whereas interplanetary dust
1011 g/s (far more than needed to replenish the loss of dust was strongly depleted away from the ecliptic plane. Start-
estimated to be lost each year within 1 AU!). In addition, ing in mid-1996 the flux of ISD began slowly to decrease
they determine that recent impacts would produce between and, in the year 2000, was about a factor of 3 lower [this is
zero and several hundred short trail-like structures, having related to the reversal of the magnetic field in the course
annual parallaxes of up to 2.6°. However, a parallactic sur- of the solar cycle (Landgraf, 2000].
vey making use of two-week to six-month baselines pro- Measurements in the ecliptic plane by Galileo confirmed
vided by separate maps of the sky by IRAS (Sykes et al., that outside about 3 AU the interstellar dust flux exceeds the
1994) produced no evidence of parallax in any extended flux of micrometer-sized interplanetary grains. Interstellar
structures at 60 and 100 µm. Yamamoto and Mukai (1998) grains observed by Ulysses and Galileo range from 10 –18 kg
estimated a production rate of dust grains between 3.7 × 105 to more than 10–13 kg. If compared with the ISD mass dis-
and 3.1 × 107 g/s with radii <10 µm as a consequence of tribution derived by astronomers, the mass distribution ob-
impacts of interstellar dust on KBOs. served by spacecraft overlaps only with the biggest masses
That dust from the Kuiper belt is being generated and observed by remote sensing. More recently, even bigger
transported to smaller heliocentric distances, however, is (10 –10 kg) interstellar meteoroids have been reliably identi-
supported by Landgraf et al. (2002) in their analysis of data fied by their hyperbolic speed (>100 km/s) at 1 AU (Bag-
from the dust experiments onboard Pioneer 10 and 11. galy, 2000). The flow direction of these big particles varies
Humes (1980) had reported an essentially constant spatial over a much wider angular range than that of small grains
density between 1 and 18 AU. Landgraf et al. (2002) con- observed by Ulysses and Galileo.
sidered three potential sources for the impacts recorded The deficiency of measured small grain masses is not
beyond Jupiter: P/Halley-type comets, P/Schwassmann- solely caused by the detection threshold of the in situ in-
Wachmann 1-type comets, and dust from the Kuiper belt. strumentation, but it indicates a depletion of small interstel-
They found that the amount of dust detected beyond Saturn lar grains in the heliosphere. Model calculations by Frisch
could only be explained by dust originating in the Kuiper et al. (1999) of the filtering of electrically charged grains
belt and evolving toward the Sun. Under their model, about in the heliospheric bow shock region and in the heliosphere
5 × 107 g/s would need to be generated in the Kuiper belt itself show that 0.1-µm-sized and smaller particles are
(between 0.01 and 6 mm in size), more than an order of mag- strongly impeded from entering the planetary system by the
nitude below the minimum estimate of Stern (1996). The interaction with the solar wind magnetic field.
required contributions from P/Halley-type comets were 3 ×
105 g/s and that from P/Schwassmann-Wachmann 1 comets 6. PRODUCTION OF DUST IN OTHER
were 8 × 10 4 g/s. It is interesting to note that dust produc- PLANETARY SYSTEMS
tion from P/Schwassmann-Wachmann 1 itself was estimated
to be ~105 g/s (Sykes and Walker, 1992, Table 1) in particles The interplanetary dust cloud offers a “blueprint” or
~1 mm in size. “laboratory” for understanding dust in other planetary sys-
tems. The scattered starlight and thermal emission from dust
5. EFFECT OF INTERSTELLAR around other stars — exozodiacal light — is, for most stars,
DUST PARTICLES the only indicator we can observe from Earth of the colli-
sional processes and small bodies around those stars. Further-
Interstellar dust particles are thought to play a role in more, these small bodies also provide evidence for planets
the production of interplanetary dust (e.g., Yamamoto and around other stars. An inner hole and significant warp were
Mukai, 1998) and its comminution (e.g., Liou et al., 1996). discovered in the β Pictoris disk (Lagage and Pantin, 1994;
As the solar system moves through the galaxy, dust grains Heap et al., 2000), and blobs were discovered around Vega
that pass through the planetary system have been detected (Wilner et al., 2002) and ε Eridani (Greaves et al., 1998;
by the dust detector onboard the Ulysses spacecraft (Grün Quillen and Thorndike, 2002) and Fomalhaut (Holland et
et al., 1993b). It came as a big surprise that after Ulysses al., 1998; Wyatt and Dent, 2002). These structures have all
flew by Jupiter, the dust detector recorded impacts of in- been explained by perturbations by planets around the stars,
terstellar dust (ISD) that arrived from a direction that was with the direct analogy to Earth’s circumsolar ring (dis-
opposite to the expected flow direction of interplanetary cussed above) providing key supporting evidence (Kuchner
dust grains. It was found that on average the impact veloci- and Holman, 2003). If viewed from afar, our own solar sys-
688 Comets II

tem might be recognizable as having at least two planets as The very different vantage points for viewing the zodia-
a consequence of structure in dust evolving from the Kuiper cal and exozodiacal light allow for very different insights
belt (Liou and Zook, 1999). Dust bands and trails in the into the collisional processes and evolution of small solid
interplanetary cloud have been tied to asteroid families and bodies. From inside the solar system, it is possible to use the
individual short-period comets; comparable structures have brightness as a function of look direction to obtain the scat-
not yet been observed around other stars, so the direct con- tering phase function (Hong, 1985; Kelsall et al., 1998); the
nection between parent bodies and the dust cloud can only phase function is needed to invert brightness distributions.
be studied in detail in the solar system. From the zodiacal light, it is possible to measure the density
Exozodiacal light studies also provide valuable clues to of interplanetary dust to within tens of solar radii, which is
understanding aspects of interplanetary dust that cannot be not possible around other stars because of glare from the
readily discerned from our vantage point inside the system photosphere. From the exozodiacal light, it is possible to
and in its midplane. Among nearby main-sequence stars, measure the distribution of material to hundreds of AU,
some 15% have far-infrared emission, in excess of the pho- which is not possible from Earth-based observatories be-
tosphere, that is believed to be due to circumstellar mate- cause of the bright foreground from dust in the inner solar
rial (Backman et al., 1997; Habing et al., 2001). Most of the system.
stars have “cold” infrared excess, detected at wavelengths
of 60 µm and greater. This is partly due to the rapid decline 7. THE FUTURE
in photospheric emission at longer wavelengths, making far-
infrared excess more prominent than mid-infrared excess. 7.1. Dust Detectors on Spacecraft
The cold excesses, with color temperatures ~80 K, are lo-
cated relatively far from the central star and roughly corre- The first dust detectors flown in space were simple mi-
spond to the Kuiper belt in the solar system. In at least four crophones that responded to dust impacts, but also to a wide
cases, dubbed the “fabulous four” by observers, the disks range of interferences that in interplanetary space occurred
are resolved: β Pictoris, Vega, ε Eridani, and Fomalhaut all more frequently than dust impacts. Once this was appreci-
have disks extended at least 100 AU from their central stars. ated more sophisticated multicoincidence detectors were
In all cases, the Poynting-Robertson loss time is shorter than developed that permitted the detection of dust impacts at a
the stellar lifetime, indicating that the disks must be replen- rate as low as one impact per month. Impact ionization
ished by collisions among a reservoir of larger bodies. This provided the means of at least two independent coincident
suggests it is likely that our own Kuiper belt may be colli- measurements of a dust impact: the plasma cloud gener-
sionally active and could be a source of dust, although that ated by an hypervelocity impact onto a solid target is sepa-
dust between 9 and 50 µm in diameter may only reside in rated by an electric field so that positive ions and negative
the outer solar system because its transport to the inner solar ions together with electrons are recorded separately. Time-
system is hindered by collisions with interstellar dust along of-flight analysis of the ions even provides mass analysis
the way (Liou et al., 1996). of the generated ions. Early detectors of this type had a
Exozodiacal light due to “warm” dust in the “terrestrial sensitive area of ≤0.01 m2, which had the consequence that
planet” zone around other stars is more rare than the colder only very few dust impacts were recorded in interplanetary
dust. This warmer dust is difficult to discern photometri- space. Therefore, the more recent dust detectors on the
cally, because the disk emission is generally fainter than the Galileo, Ulysses, and Cassini missions had sensitive areas
photosphere at wavelengths less than 30 µm (as opposed to that were 10 times larger. Several recent missions carry dust
the cold excesses, which are often larger than the photo- mass analyzers in which the impact-generated ions are ana-
sphere). A recent photometric survey found warm disks lyzed in a mass spectrometer (e.g., Kissel, 1986). The Cas-
around 5 out of 81 stars, and none of them had color tem- sini cosmic dust analyzer (Srama et al., 1996, 2004) is the
peratures higher than 120 K (Laureijs et al., 2002). Further- most sophisticated dust instrument to date. It combines a
more, none of the stars older than 400 m.y. had warm exo- 0.1-m2 impact ionization detector with a time-of-flight mass
zodiacal light. In contrast, the zodiacal light as viewed from spectrometer and charge sensing entrance stage for coarse
Earth has a color temperature around 262 K (Reach et al., velocity and direction determination.
1996) and the dust density has been shown to increase as a It is hoped that all future missions, particularly to the
power-law all the way in to less than 0.15 AU form the Sun outer solar system, will include dust experiments. Dust
(Leinert et al., 1981). One problem with searching for the beyond Saturn will be studied for the first time since Pio-
warmer dust, which would be the analog of dust produced neer 10 and 11 with the student dust counter planned for
by asteroid collisions and short-period comets, is angular the New Horizons mission to Pluto.
resolution. Mid-infrared spectra of the β Pictoris disk re-
veal a bright silicate emission feature from the warm dust, 7.2. DUNE Observatory
with a shape that is different from that of the silicate feature
found in the zodiacal light (Reach et al., 2003). A Keck ob- From knowledge of the dust particles’ birthplace and the
servation with high angular resolution showed that the sili- particles’ bulk properties, we can learn about the remote
cate feature arises only very close to the star (Weinberger environment out of which the particles were formed. This
et al., 2003). approach could be carried out by means of a dust telescope
 Sykes et al.: Interplanetary Dust Complex and Comets 689

on a dust observatory in space. A dust telescope is a combi- planetary dust cloud from observations made within it, near
nation of a dust trajectory sensor together with an analyzer its plane of symmetry. This makes distinguishing radial com-
for the chemical composition of dust particles. ponents difficult, because they are all coincident along our
Potential targets of a dust telescope are interstellar dust, line of sight and the stochastic nature of dust production
interplanetary dust (e.g., meteor stream dust, cometary, or within the cloud complicates the interpretation of structures,
asteroidal dust or dust from the Moon), and even space volume distributions, and excesses (or deficits) compared
debris (e.g., fine grains from solid rocket burns). to models. It would be extremely useful to have thermal ob-
The first goal of a dust telescope is to distinguish by their servations of the cloud from a vantage well away from the
trajectories dust particles from different sources: interstellar ecliptic plane, to look over the “top” of the zodiacal cloud
grains from the different types of interplanetary dust grains. interior to Jupiter and study outer solar system dust and dust
Interstellar dust flows narrowly collimated through the so- in the Kuiper belt directly. Peaking over the half-width of
lar system. This flow can be easily distinguished from the the Kelsall model of the zodiacal cloud at 1 AU, and assum-
flow of interplanetary particles. Young cometary particles ing the extent of this inner cloud runs with the main asteroid
have highly eccentric orbits, whereas asteroidal particles belt, an orbital inclination of about 45° would be required
have low eccentricity orbits. These different orbits are sepa- to observe dust in the Kuiper belt. This would parallactically
rated by measurement of the flight direction and speed. Dust shift the position of the inner cloud by more than 10°, allow-
in meteor streams occurs only during specific periods and ing for the contribution of distant cold dust to be more easily
is directly related to the parent comet. distinguished. In addition to detecting or placing meaningful
A state-of-the-art dust telescope would consist of an limits on dust being generated in the Kuiper belt, studies of
array of parallel mounted dust analyzers (Grün et al., 2000) the inner zodiacal cloud by such a system would greatly im-
and consists of several instruments sharing a common im- prove our understanding of the morphology of the cloud and
pact plane of about 1 m2 in size. Potential components are a the relative contributions of asteroid collisions and comet
high-resolution impact mass spectrometer, a dust analyzer emissions.
for the determination of physical and chemical dust proper-
ties, and large-area impact detectors with trajectory analysis. 7.4. Earth as a Detector
Dust particles’ trajectories are determined by the measure-
ment of the electric signals that are induced when a charged The valuable information provided by meteor stream
grain flies through an appropriately configured electrode observations on detailed structures of cometary emissions
system. After the successful identification of dust charges and the physical properties of those particles argue for the
of >10–15 Coulombs in space by the Cassini cosmic dust increasing application of modern technology to their study.
analyzer, trajectory analyzers that are in development have First, continued efforts to predict these events must be made
tenfold increased sensitivity of charge detection giving us to allow their observation. Long-term video and radar moni-
trajectories for submicrometer-sized dust grains. toring for the identification of new meteor streams should
Modern dust chemical analyzers have sufficient mass be conducted. Campaigns should focus on predicted me-
resolution to resolve ions with atomic mass numbers above teor outbursts with high-speed imagers and photometers,
100. However, since their impact area is only 0.01 m2, they and head-echo of meteors using high-power radar, particu-
can analyze statistically meaningful numbers of grains only larly focusing on small meteoroid masses, should be con-
in the dust-rich environments of comets or ringed planets. ducted to assess their fragmentation properties. Information
Therefore, a dust telescope should include several of the on meteoroid composition could be greatly improved by the
existing mass analyzers or a large area chemical dust ana- use of cooled CCD cameras for slitless optical spectroscopy,
lyzer of mass resolution >100 with at least 10 times greater and the development of instruments that would focus on
sensitive area, in order to provide statistically significant individual emission lines/bands and the indirect detection
measurements of interplanetary and interstellar dust grains of organics. Together these should not only provide infor-
in space. mation on properties, but also allow us to assess differences
among comets that might relate to different formation con-
7.3. Thermal Infrared Observations ditions and locations as well as ages.

Since IRAS and COBE there have been no surveys of 8. FINAL NOTE
the sky at thermal wavelengths. ISO allowed some studies
of cometary trails (Davies et al., 1997; Reach et al., 2000), The ability to associate IDPs collected at Earth’s orbit
and detailed SIRTF observations of a large number of short- with specific sources is of great value in that it provides
period comets may allow us to greatly improve upon the “sample return” information on these sources that might
estimates of cometary dust production contributing to the otherwise be impractical to obtain as well as provide great
zodiacal cloud (as well as an understanding of their emis- insight into the origin and evolution of those sources and
sion history, retained in the trails). Only by surveys, how- the solar system in general. The increase in our very diverse
ever, are we able to observe the cloud as a whole and model means of studying interplanetary dust, including atmos-
its evolution and supply by entire populations of objects. pheric collection, in situ studies by spacecraft, remote ob-
But we have been limited by trying to understand the inter- servations at visual and thermal wavelengths, and collisional
690 Comets II

and dynamical modeling have substantially increased the Dermott S. F., Nicholson P. D., and Wolven B. (1986) Preliminary
complexity (and interest) of the problem. The interplanetary analysis of the IRAS solar system dust data. In Asteroids,
dust complex is not in a steady-state condition. Evidence Comets, Meteors II (C.-I. Lagerkvist et al., eds.), pp. 583–594.
today bolsters the significant episodic infusion of dust by Uppsala, Sweden.
Dermott S. F., Jayaraman S., Xu Y. L., Gustafson B. Å. S., and
asteroid collisions, a greater potential cometary source due
Liou J.-C. (1994) A circumsolar ring of asteroidal dust in reso-
to the discovery of their large particle emissions, and the
nant lock with the Earth. Nature, 369, 719.
contribution at some level of dust from the Kuiper belt. Dermott S. F., Grogan K., Durda D. D., Jayaraman S., Kehoe
Studies of these sources and interplanetary dust are increas- T. J. J., Kortenkamp S. J., and Wyatt M. C. (2001) Orbital
ingly interrelated. We need to study both sources and dust evolution of interplanetary dust. In Interplanetary Dust (E.
in order to have a more complete understanding of all. Grün et al., eds.), pp. 569–640. Springer-Verlag, Berlin.
Dikarev V., Grün E., Landgraf M., Baggaley E. J., and Galligan D.
Acknowledgments. This chapter benefited from the detailed (2002) Interplanetary dust model: From micron-sized dust to
reviews of D. Brownlee and N. McBride, to whom the authors meteors. In Proc. Meteoroids 2001 Conf., pp. 609–615. ESA
express their appreciation. SP-495, Noordwijk, The Netherlands.
Dohnanyi J. S. (1970) On the origin and distribution of meteor-
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694 Comets II
 Colangeli et al.: Laboratory Experiments on Cometary Materials 695

Laboratory Experiments on Cometary Materials

L. Colangeli and J. R. Brucato
Istituto Nazionale di Astrofisica–Osservatorio Astronomico di Capodimonte

A. Bar-Nun
Tel Aviv University

R. L. Hudson
Eckerd College and NASA Goddard Space Flight Center

M. H. Moore
NASA Goddard Space Flight Center

Laboratory experiments to simulate cometary materials and their processing contribute to

the investigation of the properties and evolution of comets. Experimental methods can produce
both refractory materials and frozen volatiles with chemical, structural, and morphological char-
acteristics that reproduce those of materials observed and/or expected in comets. Systematic
analyses of such samples, before and after energetic processing by various agents effective in
the solar system, provide a wealth of useful quantitative information. Such data permit a more
complete interpretation of observations, performed remotely or in situ, and suggest ideas about
the chemical and physical evolution of cometary dust and ice. Finally, laboratory results help
to predict the environmental conditions that future space missions, such as the European Space
Agency’s Rosetta mission, will experience, and thus aid in properly planning mission and in-
strument development.

1. INTRODUCTION acceptable in the first case (Weissman, 1986), but a different

preferred size scale should exist in the latter [see Weissman
Comets are considered to be reservoirs of partially un- et al. (2004) for more details about comet nuclear structure].
contaminated primordial material from which the solar The exploration of Comet 1P/Halley provided a break-
system formed about 4.5 × 109 yr ago. The composition as through in the understanding of cometary structure and
well as the physical and structural properties of cometary composition, thanks to close observations of Halley’s nu-
dust and ice depend both on comet formation mechanisms cleus (see Keller et al., 2004). More recently, remote ob-
and postaccretion evolutionary processes. The so-called servations, such as with the Infrared Space Observatory
“interstellar grain” model (e.g., Greenberg and Hage, 1990; (ISO), have provided valuable insights into cometary chem-
Mumma, 1997; Notesco et al., 2003) supports the concept istry. Major progress has concerned the identification of a
that comets formed far (>20 AU) from the proto-Sun, at low large variety of volatile molecules (Bockelée-Morvan et al.,
temperatures (<100 K or so), so that their composition 2004) and a deeper characterization of the refractory com-
should reflect that of original interstellar cloud grains. In ponents of cometary and interstellar dust, especially silicates
contrast, the “nebular chemistry” model includes the pos- (Hanner and Bradley, 2004). This new information has al-
sibility that interstellar material may have been reprocessed lowed us to forge strong links between comet composition
prior to cometary formation (e.g., Lunine, 1989). The re- and interstellar dust evolution (Ehrenfreund et al., 2004).
sulting cometary chemistry is different in these two sce- Even with such new observations, uncertainties remain
narios, mainly due to the ice condensation temperature. concerning the properties and evolution of materials that
However, it is possible that cometary chemistry reflects both form comets. Laboratory experiments now play a funda-
the presence of original interstellar grains and reprocessed mental role in research programs designed to reveal the
materials (Engel et al., 1990). Details about comet forma- main components of comets and the effects of energetic
tion and evolution are described by Dones et al. (2004). processing experienced by cometary ice and dust. The ex-
The internal structure of comets also depends on the dy- perimental program applied to ice and dust investigations
namic evolution of the protosolar nebula. As settling toward is based on three main steps: (1) production of materials
the midplane of the nebula occurred, did infalling material by techniques that allow control of product characteristics;
collapse into kilometer-sized planetesimals (Goldreich and (2) analyses of dust and ice analogs by complementary
Ward, 1973), or did it accumulate into 50–100-m aggregates methods aimed at quantitative studies of morphology, struc-
(Weidenschilling, 1997)? The “rubble pile” model would be ture, chemistry, and optical behavior; and (3) processing to

695
696 Comets II

reproduce effects expected in space before, during, and after 2.1. Production and Characterization Through
comet formation. Spectroscopy of Materials
The results of such experiments are extremely useful for
quantitative interpretation of astronomical observations. By A wide variety of C- and silicon-based materials are ob-
studying dust and ice properties as a function of formation tained by vapor condensation to form “smokes” (see, e.g.,
conditions and levels of energetic processing, light can be Colangeli et al., 2003, and references therein). In practice,
shed on the formation and evolution of materials in the solar vaporization is achieved by applying sufficient energy to a
system in general and comets in particular. This approach solid by, e.g., laser bombardment of a homogeneous target
not only complements observations, but it has predictive or a mixture of different targets (Fig. 1), by arc discharge
power for observers and provides important constraints for between C or graphite electrodes (Fig. 1), or by laser py-
theoretical models. rolysis in a gas flow. If a metal vapor is present, at its satu-
This chapter provides an overview of past and ongoing ration pressure, in a cooling gas-phase mixture, then as the
experimental work. Section 2 is devoted to refractory ma- temperature falls molecular clusters can form, which then
terials (silicates and carbons) observed in comets. Produc- grow to solid particles. Alternatively, chemical processes,
tion and analytical techniques are briefly reviewed, with such as sol-gel reactions (Brinker and Scherer, 1990; Jäger
attention given to the determination of optical properties and et al., 2003) or grinding of natural rocks and minerals, can
the effects of processing. The information derived from be used to produce a wide variety of CDAs.
experiments aid in identifying major components of com- A careful selection of experimental conditions during
ets. Section 3 covers small- and large-scale experiments on CDA formation allows the “tuning” of the composition and
the physical properties of ices, while the chemical evolu- structure of the samples produced. Examples of CDAs pro-
tion of ices is described in section 4. The most widely used duced in the laboratory are summarized in Table 1. It is
in situ techniques are described, and some of the most rel- interesting to note that a wide variety of silicates, in addi-
evant recent results are summarized. Some conclusions are tion to those in Table 1, can be obtained by changing the
given in section 5. relative abundance of cations (e.g., Mg2+, Fe2+, Al3+, Ca2+)
in the original reaction mixture.
2. EXPERIMENTS ON The materials produced in laboratory must be carefully
REFRACTORY MATERIALS analyzed to check that they are reasonable CDAs and to link
their properties to production conditions. A large variety of
Refractory materials with morphological, chemical, and investigation techniques are based on the interaction of
structural properties suitable to reproduce compounds ob- matter with radiation and particles, while other methods are
served or expected in comets have been produced in the lab- based on the study of mechanical, electrical, magnetic, and
oratory through various methods of synthesis (e.g., Colan- thermal properties of matter. All the methods involving
geli et al., 1995; Rotundi et al., 2002; Nuth et al., 2002) and interaction of matter with radiation can be classified accord-
are usually termed cometary dust analogs (hereafter CDAs). ing to the kind of interaction in microscopy, diffractometry,

(a) (b)

Fig. 1. Methods for condensation of solid grains used at the Cosmic Physics Laboratory of Naples. (a) Nd-YAG pulsed laser device
for ablation of solid samples in an oxidizing, reducing, or inert atmosphere. (b) Device for production of C dust by arc discharge
between C or graphite rods in H-rich or inert atmosphere.
 Colangeli et al.: Laboratory Experiments on Cometary Materials 697

TABLE 1. Examples of laboratory cometary dust analogs.

Family Species Method of Production

Olivine (MgxFe1–x)2SiO4 Forsterite (x = 1) Laser bombardment in 10 mbar O2
Fayalite (x = 0) Laser bombardment in 10 mbar O2
Pyroxene (MgxFe1–x)SiO3 Enstatite (x = 1) Laser bombardment in 10 mbar O2
Ferrosilite (x = 0) Laser bombardment in 10 mbar O2
Amorphous C α-C Arc discharge in 10 mbar Ar
Hydrogenated amorphous C HAC Arc discharge in 10 mbar H2
Laser bombardment in 10 mbar H2
UV irradiation or ion bombardment
of ice mixtures

and spectroscopy. Methods falling in these categories give results of the analysis depends on both sample quality and
a vast amount and different kinds of information, unravel- technique. In particular, X-ray absorption spectroscopy
ing the relations among the properties of solid materials [see (XAS), extended X-ray absorption fine structure (EXAFS),
Marfunin (1995) for a wide and accurate description on and X-ray absorption near-edge structure (XANES) tech-
methods of investigation on refractory materials]. Many of niques are used to determine short- and medium-range order
these techniques are widely used in laboratories to charac- in partially amorphous materials (e.g., Thompson et al.,
terize CDAs. 1996). Elemental composition can be determined by analysis
Scanning, transmission, and analytical electron micros- of dispersed X-rays (Fig. 2), while specific aspects of ele-
copy are used to investigate the morphology and both the mental arrangement, such as the ratio of ferrous to ferric iron,
short- and long-range structural order of CDAs at nanom- can be investigated by wet chemical analyses (Köster, 1979).
eter and subnanometer scales (e.g., Rietmeijer et al., 2002; Raman spectroscopy is another method used to analyze
Fabian et al., 2000). These techniques use an electron beam the structure of materials, especially C-based ones. It is
accelerated by high voltage and focused by lenses on the based on the process of inelastic scattering of monochro-
sample surface. The beam is then moved or scanned across matic radiation hitting the target sample. The Raman scat-
the sample area to obtain images providing information on tering consists in the frequency shift of the Raman lines with
surface structures and morphology (Fig. 2). respect to the exciting radiation and results from the energy
Electron and X-ray diffraction are the most frequently exchange between the exciting radiation and the vibrational
used methods to determine the arrangement of atoms in the levels of the materials. Raman scattering is used to iden-
crystal structure of samples at small and large scales. The tify minerals embedded in matrix in a nondestructive way
analysis is based on the theories of symmetry and on the and is suitable to investigate the structure of minerals by
interaction of radiation with solids. The accuracy of the the analysis of the symmetry of vibrational modes. Vibra-

(a) (b)

Fig. 2. (a) Scanning electron micrograph of amorphous olivine as produced by laser ablation of a pure olivine target. (b) Energy
dispersive X-ray analysis of amorphous olivine.
698 Comets II

tional spectra are highly sensitive to the degree of order of

materials. Order/disorder degrees of carbonaceous materi-
als synthesized in the laboratory or present in meteorites
and interplanetary dust particles can be investigated with
respect to the processing experienced by materials during
their life as, e.g., ion irradiation (Wopenka, 1988; Strazzulla
and Palumbo, 2001; Baratta et al., 2004).
Although the techniques described above are fundamen-
tal tools for material characterization, spectroscopy remains
the most used and powerful way to investigate CDAs. In
fact, different aspects of materials can be revealed by dif-
ferent wavelengths of light. Measurements in the vacuum
ultraviolet probe electronic transitions of solids, while spec-
troscopy in the visible region allows the identification of
the electronic gap and thus the conduction properties of
materials. Midinfrared (IR) light is in the range where mo-
lecular vibrational resonances can be excited by incoming
radiation, while material structure and morphology drive the
spectral behavior in the far-IR region. Therefore, for the
study of material characteristics at all scales, a careful in-
vestigation over a wide spectral range provides an important
complement to information from other analytical tech-
niques. Moreover, results obtained in laboratory by spec- Fig. 3. Mass absorption coefficient (in arbitrary units) of (a) amor-
troscopic analysis of materials can be used in direct com- phous C, (b) amorphous olivine, and (c) crystalline olivine (Bru-
parison with astronomical observations or by modeling the cato et al., 1999b).
spectroscopic behavior of dust grains. Details on use of lab-
oratory spectra are described in the following sections.
2.1.1. Extinction and absorption. Considering the ex- absorption efficiency in the IR for silicates and C-based ma-
tinction and absorption of IR light by dust grains, the de- terials are shown in Fig. 3.
pendence of the mass extinction coefficient, K(λ), on wave- The motivation for determining these mass absorption
length, λ, can be derived from measurements on CDAs coefficients is that they can be used to extract information
synthesized in laboratory. The equation from absorption and emission observations of comets. If
scattering is negligible, then the mass column density, β,
S 1 and the temperature, T, of grains can be obtained under the
K (λ) = ln assumption of equilibrium conditions, for which Kirchhoff’s
M Tp(λ)
law applies (emittance = absorbance). The cometary emis-
sion flux, F(λ), is then interpreted as the sum of contribu-
links K(λ) to the measured transmittance Tp(λ) of a CDA tions from N components as
sample of mass M and cross section S, exposed to a radia-
N
tion beam of wavelength λ. Here Tp(λ) = I(λ)/I0(λ) is the
ratio of the intensities of a light beam after and before
F ( λ) = ∑ β · K · B(λ,T )
i=1
i i i

meeting a dust sample.

The above relation for K(λ) is valid under the assump- where B(λ,T) is the Planck function. By fitting F(λ) to com-
tion that grains interact as separate entities with light, so etary spectra (see section 2.3), one obtains quantitative in-
that multiple scattering is negligible (in other words, the formation on cometary coma grain properties. This proce-
distance between particles is greater than the wavelength dure is applicable only if laboratory measurements on K(λ)
of the incident radiation). When the size parameter x satis- for CDAs are available.
fies the relation 2.1.2. Scattering. Important information on solid ma-
terials is provided by an analysis of the light scattering
2πa process. Size, shape, and refractive index of particles are
x= << 1
λ intimately correlated to the scattering parameters. Exact
theories of light scattering are based on solving Maxwell’s
with a = grain radius (under the approximation of spheri- equations either analytically or numerically. In the case of
cal shape), the scattering contribution to extinction is negli- spherical homogeneous particles, calculations can be done
gible (see Bohren and Huffman, 1983), and K(λ) becomes accurately by using the Mie theory (Bohren and Huffman,
the mass absorption coefficient. Thus the absorption coeffi- 1983). Although this simple approximation is used in many
cient can be derived directly from transmission IR measure- applications, real (cometary) dust particles are inhomoge-
ments on submicrometer grains. Three examples of mass neous and irregular in shape.
 Colangeli et al.: Laboratory Experiments on Cometary Materials 699

To give an accurate description of the phenomenon for a maximum around 90°–100° (Levasseur-Regourd et al.,
irregular particles, the scattering properties have to be ei- 1996). Changes in the polarization intensity are observed
ther computed theoretically or measured experimentally. as a function of the distance from the nucleus, which are
Theoretical models, which have become increasingly so- attributed to differences in the size distribution and/or color
phisticated (see, e.g., Mishchenko et al., 2000), use the of cometary grains (Muñoz et al., 2000) or to different de-
optical constants of materials and take into account the de- grees of grain fluffiness (Hadamcik et al., 2002). The sub-
pendence of the scattering function on morphological prop- ject is presently matter of further laboratory investigation by
erties, such as size and shape. In recent years an effort has using different classes of CDAs (H. Volten, personal com-
been devoted to describe the effects of nonsphericity on munication, 2003).
scattering properties. In this frame, particles have been clas-
sified as solids, aggregates, and clustered particles. Lumme 2.2. Processing of Cometary Dust Analogs
et al. (1997) identified particle classes in a mathematical
sense as polyhedral solids, stochastically rough (smooth) Laboratory CDAs can be energetically processed by dif-
particles, and stochastic aggregates. Statistical approaches ferent methods to study their evolution and the efficiency
have been used for particles very small compared to the of extraterrestrial processes to modify the material’s opti-
wavelength of radiation (Rayleigh limit), but complications cal, structural, and chemical properties. We consider two
have been encountered in calculations outside the Rayleigh examples.
limit. The most important calculation methods can be sum- Silicates produced by condensation techniques are sub-
marized in two categories: exact theories (separation of jected to thermal annealing under vacuum, for specific tem-
variables method for spheroid, finite-element method, finite- peratures and times, in order to study variations induced by
difference time domain method, integral-equation methods, this process on physical, chemical, and structural proper-
discrete dipole approximation, T-matrix approach, superpo- ties of the samples. The most striking effects are structural
sition method for compounded spheres and spheroids) and modifications that tend to crystallize amorphous materials
approximate theories (Rayleigh, Rayleigh-Gans, anomalous (Hallenbeck et al., 1998, 2000; Brucato et al., 1999a, 2002;
diffraction approximations, geometric optics approximation, Fabian et al., 2000). Infrared spectroscopy is an efficient
perturbation theory). Details on mathematical description of method for monitoring changes caused by thermal anneal-
models and their limits and goals are given by Mishchenko ing. Wide IR absorption bands, typical of amorphous ma-
et al. (2000). terials, tend to sharpen, as expected for crystalline solids.
Complementary information that can lead to much im- Such amorphous-to-crystalline transitions can be quantita-
proved knowledge of electromagnetic scattering by non- tively characterized through the activation energy, Ea, de-
spherical particles is given by laboratory measurements. Ran- fined by
domly oriented ensembles of CDAs with irregular shapes are
used in laboratory experiments. The Stokes vectors of the in- Ea
t = ν –1 exp
cident and scattered beams are related by a scattering ma- kT
trix, whose elements are measured vs. the scattering angles
(van de Hulst, 1957). Usually, measurements in the visible, In this equation, t is the time for the material to reach
IR, and microwave spectral ranges are performed. The ac- long-range order inside the lattice, ν is a characteristic vibra-
curate characterization of CDAs size, shape, and composi- tional frequency of the material, and T is the temperature.
tion, i.e., performed by the analytical techniques described Activation energies have been measured in the laboratory
above, allows us to know fundamental parameters that are for a wide variety of materials that are relevant as CDAs.
linked to the scattering parameters (see, e.g., Hovenier and The results obtained for different silicate species are sum-
van der Mee, 2000; Muñoz et al., 2000; Volten et al., 2001; marized in Table 2. The implications of these results on the
Hadamcik et al., 2002). A different experimental approach evolution of silicates forming comets will be discussed in
in studying the light-scattering properties of submicrometer the next section.
grains is to measure microwave scattering by large analog Both pure-C and H-rich C grains can be produced by the
grain samples (Gustafson, 1996). In fact, no absolute dimen- evaporation techniques mentioned in section 2.1. Laboratory
sions are encountered in classical electrodynamics and con- experiments on such grains have shown that thermal anneal-
venient grain size and electromagnetic wavelength can be ing (Mennella et al., 1995), UV irradiation (Mennella et al.,
chosen. The light-scattering problem can therefore be scaled 1996), ion bombardment (Mennella et al., 1997), and inter-
up or down to any convenient dimension. action with gas (Mennella et al., 1999) are competitive pro-
The experimental approach can be used to check the cesses that determine chemical and structural transforma-
quality of results obtained by scattering models. Moreover, tions.
measurements are suitable for the direct interpretation of Among other diagnostic features, infrared C-H stretch-
astronomical observations. On this point, we recall that ob- ing modes in the 3.3–3.4-µm range, are suitable both for
servations of light scattered by particles present in the com- identifying the amount of H linked to the C structure and for
etary coma show a linear polarization. The measured phase disentangling the most important C structural arrangements.
curves display a negative branch for phase angles lower than In fact, the IR band intensity is related to the H abundance,
20°, while a positive branch is observed at larger angles with with dominant features around 3.3 or 3.4 µm, indicative of
700 Comets II

TABLE 2. Activation energies Ea/k (K) for crystallization.

Composition Hallenbeck et al. (1998) Brucato et al. (1999a) Fabian et al. (2000) Brucato et al. (2002)
SiO2 — — 49,000 —
MgSiO3 — 47,500 42,040 —
Mg2SiO4 45,500 — 39,100 40,400
Fe2SiO4 — — — 26,300
MgO-SiO2 — — — 45,800
MgO-SiO2-Fe2O3 — — — <49,700

aromatic (graphitic) vs. aliphatic networks, respectively, 2.3. Interpretation of Cometary Observations by
forming the grains. Laboratory Data and Future Steps
Results of experiments can be summarized as follows:
(1) Bombardment of pure amorphous C grains with about The presence of crystalline silicates in comets was first
1020 H atoms cm–2 produces the appearance of a neat ali- shown by observing the IR spectrum of Comet P/Halley
phatic 3.4-µm band (Mennella et al., 1999). (2) Processing 1986 III. A strong 11.3-µm emission peak was attributed
of hydrogenated amorphous C grains by UV irradiation to crystalline olivine grains (Campins and Ryan, 1989). A
(Lyman emission) or ion bombardment produces a progres- double peak at 9.8 and 11.3 µm indicated that amorphous
sive release of H and a transition from an aliphatic-domi- and crystalline silicates were coexisting components. How-
nated to a more aromatic material (Mennella et al., 1996, ever, groundbased observations of other comets showed
1997). (3) Irradiation of hydrogenated amorphous C grains different shapes for the emission features (Hanner et al.,
at fluences of about 1019 UV photons cm–2 produces a sig- 1994). Based on laboratory measurements (e.g., Colangeli
nificant decline of the 3.4-µm band, even when the dust is et al., 1996), these differences were attributed to the pres-
coated by Ar, H2O, or H2O-CO-NH3 ices (Mennella et al., ence of different silicates, whose origins could be traced to
2001). different formation conditions and to transformations by
It must be also noticed that UV irradiation and ion bom- various processing mechanisms (Table 3).
bardment of organic materials produce similar effects, loss The 1997 passage of Comet Hale-Bopp C/1995 O1 pro-
of function groups and polymerization (Jenniskens et al., vided the first opportunity to observe a new long-period
1993) (see also section 4). Oort cloud comet, both from the ground and from space.
These results provide guidance for following the evolu- The ISO satellite allowed an examination of cometary grain
tion of C-based materials in different space environments, emission over the full IR range (Crovisier et al., 1997), and
including comets, as discussed in the next section. led to the discovery of a rich variety of strong distinct emis-

TABLE 3. Mass percentage of submicrometer grains derived from fitting

cometary spectra with laboratory absorption data of different materials.

Crystalline Amorphous Amorphous Crystalline Amorphous

Comet AU Olivine Olivine Pyroxene Pyroxene Carbon
C/1989 Q1 Okazaki-Levy-Rudenko 0.65* 28 — — — 72
C/1989 X1 Austin 0.78* 12 — — — 88
1P/1982 U1 Halley 0.79* 33 — — 52 15
C/1987 P1 Bradfield 0.99* 42 — — 48 10
C/1983 H1 IRAS-Araki-Alcock 1.0* — 85 — — 15
1P/1982 U1 Halley 1.25* 22 — — 20 58
C/1987 P1 Bradfield 1.45* 24 — — 23 53
C/1990 K1 Levy 1.51* 20 36 — — 44
C/1990 K1 Levy 1.56* 19 47 — — 34
C/1994 E1 Mueller 2.06* 23 — — 30 48
C/1995 O1 Hale-Bopp 0.97‡ 30 17 25 8 20
1.21‡ 23 18 37 4 18
1.7‡ 25 14 33 8 21
2.8‡ 25 25 24 5 21
2.9† 69 20 — — 11
*Colangeli et al. (1996), spectral range 8–13 µm.
† Brucato et al. (1999a), spectral range 7–45 µm.
‡ Harker et al. (2002), spectral range 1.2–45 µm.
 Colangeli et al.: Laboratory Experiments on Cometary Materials 701

heating at 1100 K is sufficient to crystallize micrometer-

sized particles in few minutes, as has been proposed to
happen for precursors of meteoritic chondrules (prechon-
drules) (Rietmeijer, 1998). It has also been suggested that
the observed amount of crystalline silicates in cometary
grains is an indicator of the age of comets; older comets
should be rich in amorphous grains, while younger comets
should contain an abundance of crystalline silicates. In fact,
it is expected that thermal annealing of amorphous silicate
grains present in the hot inner part of the protosolar nebula
favors the increase of the fraction of crystalline material
over time. Thus, comets formed later in the nebular history
will contain a larger amount of annealed (crystalline) dust
with respect to those formed earlier. Instead, comets formed
very early in the solar nebula should consist almost exclu-
sively of amorphous silicates and unaltered interstellar ices
since little processed material was available when they
formed (Nuth et al., 2000).
Laboratory studies on olivine grains suggest that the
activation energy Ea decreases as the Mg/Fe abundance ratio
increases, in contrast with observations that provide no
Fig. 4. Fit of ISO observation of Comet Hale-Bopp [circles, evidence of crystalline Fe-rich silicates. In fact, if both iron
Crovisier et al. (1997)] with the optical properties of a combina- and magnesium, with about the same cosmic abundance,
tion of amorphous and crystalline materials measured in the labo- were incorporated into silicates forming precometary grains,
ratory (Brucato et al., 1999b). thermal annealing would favor crystalline Fe-rich over Mg-
rich silicates, and their presence should be detectable by IR
features. The absence of crystalline Fe-rich silicates could
sion features. Hale-Bopp’s IR spectrum was interpreted as be justified by the presence of iron as pure metal.
due to amorphous and crystalline silicates and amorphous As far as C in space is concerned, aromatic and aliphatic
C grains in the coma. A detailed match of all major peaks C-H IR features are observed in different space environ-
with laboratory data for silicate grains suggested the iden- ments. Features at 3.38, 3.41, and 3.48 µm have been de-
tification of crystalline Mg-rich olivine (forsterite) as one tected both in the diffuse interstellar (IS) medium (Pendle-
of the main components (Fig. 4). Groundbased Hale-Bopp ton et al., 1994) and in the protoplanetary nebula CRL 618
observations at different heliocentric distances (e.g., Hay- (Chiar et al., 1998). Similar bands are lacking in the dense
ward and Hanner, 1997; Wooden et al., 1999) indicated that IS medium, where only a weak 3.47-µm feature is observed,
a further component of crystalline Mg-rich pyroxene (ensta- attributed to tertiary C-H bonds (Allamandola et al., 1993).
tite) was also present (Table 3). These differences suggest that C suffers modifications in
Different silicate band profiles and peak positions in the transition from diffuse to dense clouds. Based on labora-
different comets may be correlated to comet formation and tory results (see previous section), the 3.4-µm aliphatic band
evolution. According to present evolution models, silicates observed in the interstellar medium and in protoplanetary
coming from the presolar cloud and infalling onto the proto- nebulae is attributed to the prevalence of aliphatic C-H
solar nebula were amorphous. The results obtained from bonds formation by H atom reactions on C grains over the
laboratory simulations indicate that amorphous-to-crystal- destruction by UV irradiation. In dense clouds, where grains
line transformations can only occur on timescales under are coated by an ice mantle, the C core is prevented from
106 yr if annealing temperatures above ~800 K are reached. reaction with H atoms and the C-H bonds are destroyed by
It is, therefore, unlikely that amorphous silicates were con- penetrating UV photons.
verted into crystalline materials in the outer nebula, where It is interesting to note that a complex of features in the
comets are supposed to have been formed, as the tempera- 3.3–3.4-µm range is evident in the emission spectra of com-
ture was too low (few tens of Kelvins) to thermally process ets. Most of these features are due to volatile coma mole-
grains before their incorporation in cometary bodies. A sub- cules (e.g., methanol, methane, and ethane). Excess emis-
sequent thermal processing at high temperatures would have sion, once the molecular contribution is accounted for, is
been necessary to crystallize them. attributed to a solid C component (Davies et al., 1993).
Two possible scenarios have been recently proposed to The applications reported above clearly evidence the
explain the presence of crystalline grains in comets: turbu- relevance of laboratory experiments on refractory materi-
lent radial mixing in the solar nebula (Bockelée-Morvan et als in the identification of cometary species. Despite the fact
al., 2002) and annealing of dust by nebular shocks (Harker that important results have already been obtained, many
and Desch, 2002). It has been demonstrated that a flash open points remain to be clarified and require further ex-
702 Comets II

perimental work. The genesis of the crystalline component, (3) their sizes. This Ar/Kr/Xe pattern in cold H2O-ice agrees
specifically concerning the cometary silicates, is still a well with the noble gas ratio in Earth’s atmosphere, sug-
matter of debate. Besides the interpretation reported above gesting that comets may have delivered most of these gases
about turbulent radial mixing and flash heating by shock, to the forming Earth (Melosh and Vickery, 1989; Chyba,
the possibility exists that amorphous silicate grains lie in 1987, 1990; Pepin, 1997; Owen and Bar-Nun, 1993, 1995;
an energetic metastable state, produced, e.g., by ion irra- Notesco et al., 2003), along with other cometary volatiles
diation. In this case, little energy would be required to al- such as CO, CO2, CH4, N2, NH3, HCN, and H2S.
low the amorphous-to-crystalline transition. Of course, the Moreover and most important, the high HDO/H2O ratio
validation of this scenario needs support from dedicated in Earth’s oceans, which could not have been obtained if the
laboratory experiments. As far as carbons are concerned, water was in chemical equilibrium with the H2 and HD in
the relations between the solid and the molecular phases in the solar nebula, suggests that comets rich in HDO/H2O
comets are still not well understood. Future experiments delivered a considerable fraction of Earth’s water and vola-
shall have to be oriented to clarify the chemistry related to tiles (Laufer et al., 1999). The high HDO/H2O and DCN/
energetic processes, such as UV irradiation and ion bom- HCN ratios in Comets Halley, Hyakutake, and Hale-Bopp
bardment, under conditions that are representative of comet (Eberhardt et al., 1995; Despois, 1997; Bockelée-Morvan et
environment, at different stages of their evolution. al., 1998; Meier et al., 1998) suggest that their water origi-
nated in the ISM, where ion-molecule reactions enriched
3. EXPERIMENTS ON THE PHYSICAL the amount of HDO over H2O, and also suggest that this
STRUCTURE OF COMETARY ICES water never equilibrated with the HD and H2 in the solar
nebula. A cold origin for ice grains is also inferred from the
Observations of cometary comae can reveal, although ~22–27 K required for the trapping of CO in ice, needed to
not completely, the composition of cometary ice, namely account both for the ~7% of CO/H2O in the comae of Com-
the gases trapped in the water ice in the nucleus and their ets Halley, Hyakutake, and Hale-Bopp (Irvine et al., 2000)
proportions relative to water. In turn this information can and the 25 K derived from the ortho-para spin ratio of H2O
tell us about the gas composition and temperature in the in Comets Halley (Mumma et al., 1988) and Hale-Bopp
region where ice grains formed, grains that later agglom- (Crovisier, 1999) and the ortho-para ratio of NH3 in Comet
erated to form comet nuclei. Ice grain formation may have LINEAR (Kawakita et al., 2001). It seems therefore that
occurred in the cold and dense IS cloud, which collapsed the ice grains that agglomerated to form these and other
to form the solar nebula or by water condensation on grains comets originated in very cold regions either in the collaps-
at the cold outskirts of the solar nebula itself. In both sce- ing dense interstellar cloud or in the very cold outskirts of
narios, water vapor adhered to mineral grains and formed the solar nebula.
H2O-ice in the presence of gases, which could be then Many experiments (e.g., Bar-Nun et al., 1985, 1987;
trapped in the ice itself. These trapped gases are released Laufer et al., 1987; Schmitt and Klinger, 1987; Sandford
from the ice during changes in its structure and not accord- and Allamandola, 1988; Schmitt et al., 1989a,b; Hudson
ing to their sublimation temperatures. This is evident from and Donn, 1991; Jenniskens et al., 1995; Notesco and Bar-
the simultaneous release of all the gases observed in the Nun, 1997) have shown that gases in the presence of con-
coma of Comet Hale-Bopp over many heliocentric distances densing water vapor can be trapped and distributed within
by Biver et al. (1999). the frozen H2O, and that they do not simply freeze out as
segregated molecules. More detailed studies were carried
3.1. Small-Scale Studies out by Jenniskens and Blake (1994) and Jenniskens et al.
(1995) on the structure of amorphous ice around 22–30 K.
When vapor-phase H2O molecules condense into ice Another mechanism by which gases can be trapped is
below ~120 K, they lack the energy to migrate and form a the formation of clathrate hydrates, in which H2O molecules
stable crystalline structure. Rather, they remain where they form cages around guest atoms or molecules. However,
strike, forming an amorphous ice structure with many open experiments have shown that while polar molecules, such as
pores. Any other gas molecules present can then enter these CH3OH, H2S, C4H8O (tetrahydrofurane), and C2H4O (oxi-
pores, adhere to the walls through Van der Waals forces, rene), can form clathrate hydrates (Blake et al., 1991; Rich-
and remain in the pores for a certain time. If additional H2O ardson et al., 1985; Bertie and Devlin, 1983), some of the
molecules arrive by then and condense, the pores can be most prominent cometary gases, such as CO, CO2, CH4, and
closed, trapping the gas inside the ice. Some molecules are NH3, do not. The latter molecules are not trapped as clath-
more readily trapped than others, which can lead to selec- rate hydrates even in the presence of a clathrate-hydrate-
tive trapping of the molecules from the gas-phase mixture, forming gas such as CH3OH (Notesco and Bar-Nun, 1997,
with important implications. For example, it has been shown 2000).
experimentally that among the heavy noble gases, the trap- When the H2O-ice is warmed, how do the trapped gases
ping preference is Kr > Xe > Ar (Owen et al., 1991, 1992) escape? Near 120 K (Schmitt et al., 1989a) H2O molecules in
due to (1) the different polarizabilities of these atoms and the amorphous ice acquire enough energy to move and re-
therefore different adherence to the walls of the ice pores, arrange into the more-stable cubic structure, although about
(2) differences in their masses (Notesco et al., 2003), and 70% of the ice remains in a “restrained amorphous” form,
 Colangeli et al.: Laboratory Experiments on Cometary Materials 703

Bar-Nun, 1992), using available experimental data on thin

(0.01–100-µm) ice samples. Yet, in order to study large-
scale phenomena, large ice samples have to be studied.

3.2. Large-Scale Studies

The first large-scale cometary ice experiment was the

Comet Simulation (KOSI) series of experiments carried out
at the German Aeronautic and Space Organization (DLR)
in Köln. A space simulator of 2.5-m diameter and 4.9-m
length, capable of reaching 10 –6 Torr and having an assem-
bly of Xe-arc lamps capable of illuminating a 30-cm-diam-
eter sample with 1–1.4 solar constants was used (Grün et
al., 1991). The comet analog, 30 cm in diameter and 15 cm
thick, was produced by spraying fine droplets of a slurry
Fig. 5. Gas evolution from a 0.1-µm amorphous gas-laden ice of minerals in liquid H2O into liquid N. Such ice was always
sample upon its warming up. The gas comes out when the amor- crystalline and not amorphous and so could not trap gases
phous ice transforms into its crystalline and “restrained amor- in it, as does amorphous cometary ice. In order to add gas
phous” forms.
to the solid mixture, CO2 was flowed into the mineral-crys-
talline ice mixture in liquid N and froze there. The canister
at 80 K, containing a mixture of ~10% minerals with traces
which is a viscous liquid at this temperature (Jenniskens and of C soot, crystalline ice, and 0–15% frozen CO2, all in
Blake, 1994, 1996; Jenniskens et al., 1995, 1997). This liquid N, was placed in the vacuum chamber, where the
movement opens pores in which the trapped gases reside, liquid N evaporated, leaving behind a porous sample with
and releases them (Fig. 5). Therefore, all the trapped gases a density of ~0.5 g cm–3. When the powerful “sun” was
come out together and not according to their sublimation turned on, a vigorous response from the 45° inclined sample
temperatures (Biver et al., 1999). was observed, in which water vapor from the surface and
When heat is applied to a collection of gas-laden ice frozen CO2 from both the surface and from deeper layers
grains, two gas-release steps occur (Fig. 5). First, near sublimated as the heat wave penetrated inward. Driven by
~120 K, each grain releases the gas trapped within by a dy- these gases, mineral grains were ejected. After a while, a
namic percolation process, in which channels in the ice open mineral dust layer free of ice accumulated on the surface,
up to the surface of the grain (Laufer et al., 1987). Next, a slowing down the activity, apparently due to its poor ther-
gas molecule leaving an individual grain must still pass near mal conductivity. These observations were accompanied by
other ice grains in order to emerge from the bulk of the ice. measurements of several types:
This involves another dynamic percolation process, in which 1. Heat was transported through the sample, illuminated
channels open between the grains up to the surface. The by 1–1.4 solar constants, with dark periods. A representa-
ejection of ice grains when a large flux of gas emanated tive data plot is shown in Fig. 6a. As expected, ice layers
from the ice was observed experimentally by Laufer et al. closer to the surface heat faster and the inner layers lag
(1987). These processes were modeled (e.g., Prialnik and behind. The same trend was observed when the heating was

Fig. 6. (a) Evolution of temperatures in KOSI-3 sample at different distances from the cold backplate. (b) H2O and CO2 gas flux
densities at the sample surface (KOSI-3).
704 Comets II

stopped and resumed. The thermal conductivity of various few seconds, apparently from pure ice grains, and much
KOSI samples was calculated from such measurements and broader ones, decaying over tens of seconds, apparently
found to be about 1–6 × 104 erg cm–1 K–1 s–1, depending from ice-containing porous mineral particles. The structure
on the ratios of minerals/hexagonal ice/frozen CO2. These of the collected grains was studied by SEM and found to
values are about an order of magnitude smaller than the be very fluffy (Fig. 7), with a density of about 0.1–1 g cm–3.
value for a block of hexagonal ice, 3.5–8 × 105 erg cm–2 They seemed to be an agglomerate of even smaller grains,
K–1 s–1 (Spohn et al., 1989), due to the porosity of the KOSI not unlike the interplanetary dust particles (IDPs) collected
samples. in the stratosphere (Brownlee et al., 1980). These agglom-
2. Gas emission was studied by the mass spectrometers erates of mineral particles were formed in the slurry of
(Fig. 6b) (Grün et al., 1991). Immediately when insolation water and minerals that was sprayed into the liquid N, but
began, a flux of H2O/CO2 ≈ 6 (the ratio in the original sam- it is possible that some could have formed in the ice dur-
ple was 5.6) was measured, decreasing to ~3 after 50 h of ing its sublimation. Occasionally, a dust grain still attached
illumination. When the insolation was interrupted, the H2O at one point to the mantle would vibrate violently for many
flux dropped immediately, whereas the CO2 flux lagged, de- minutes, driven by the gas flux, until finally it flew away.
creasing over 18 h. When the insolation was resumed, the Some dust bursts were observed when a larger chunk of ma-
H2O flux rose during about 2 h, whereas the CO2 took about terial fell back onto the surface.
5 h to rise. This is reasonable, because although the water After many hours of insolation, the chamber was opened
vapor came from the surface at the beginning and from just and the sample container was transferred to a bath of liq-
below the dust mantle, the frozen CO2 sublimated from uid N in a N purged glove-box. Its compressive strength
deeper layers that took longer to warm up. Generally, the was measured by driving a force meter into the sample. The
flux of both gases diminished by 2 orders of magnitude initial strength of 1–2 × 106 dynes cm–2 was increased af-
(from H2O 1018 to 1016 cm–2 s–1) after 50 h, due to the for- ter insolation to 0.4–5 × 107 dynes cm–2 just below the dust
mation of an insulating dust layer and the depletion of both mantle, probably due to the migration of some water vapor
volatiles from the upper layers of the ice. inward, and its freezing there. Reflectance spectra of the
3. During the sublimation of water and CO2, a very large surface between 500 and 2500 nm were measured and, as
flux of mineral and ice-coated mineral grains was ejected. expected, showed that the CO2 and H2O features diminished
The ejected material was photographed with a video cam- considerably.
era, grain impacts were monitored by microphones facing Similar large-scale experiments were carried out by
the sample, and particles were collected over a large sam- Green et al. (1999) and Green and Bruesch (2000) at the
pling area. The erratic flux of grains diminished by about Jet Propulsion Laboratory (JPL) in Pasadena, California. A
2 orders of magnitude during 10 h, along with the dimin- slurry of minerals in water was sprayed into liquid N, again
ishing flux of gas and water vapor. A median velocity of producing hexagonal ice, in a 200-cm-wide and 250-cm-
~100 m s–1 was obtained. This result is not far from the high cylindrical canister, with an insolation of 0.1–2.1 solar
value (≥167 m s–1) observed experimentally by Laufer et al. constants. The penetration of the heat wave was monitored
(1987) for ice grains ejected from a thin ice sample, when by thermocouples; the evolution of water vapor was meas-
a large flux of gas was released. ured by two mass spectrometers, and dust release by a video
In another experiment (Mauersberger et al., 1991), indi- camera. The mechanical properties were measured in the
vidual particles entered a tube with a pressure gauge, where closed chamber by a mechanical penetrator-scratcher and,
they were heated and their volatiles sublimated. Two types when the chamber was opened, measurements on compres-
of traces were measured: sharp spikes decaying within a sive strength, penetrability, porosity, and density were car-

Fig. 7. SEM micrographs of dust grains emitted during the KOSI-3 experiment.
 Colangeli et al.: Laboratory Experiments on Cometary Materials 705

ried out. The results of these measurements are not yet avail- chamber, were kept at 80 K by a controlled flow of liquid
able in the literature. N. This fully automatic, hydraulically controlled process was
Although the extensive and detailed KOSI and JPL proj- repeated at 10 –5 torr for 10–20 h until a large enough ice
ects opened a new field of large-scale comet simulation, sample accumulated, namely a 200-cm2 × 10-cm-high sam-
they suffered from a basic drawback due to the method of ple of an agglomerate of 200-µm particles of amorphous
sample preparation, namely spraying a slurry of ~10% dust gas-laden ice. The sample was then covered by the 80-K
in water into liquid N. This resulted in crystalline ice, which deposition plate while the dome was heated to ~330 K.
could not trap gases. The added CO2 (up to CO2/H2O ~0.2 When the plate was removed, the sample was illuminated
in the KOSI experiment) was frozen among the H2O-ice from above by the heated irradiation dome, made of a
particles and not actually trapped in amorphous H2O grains, roughly surfaced aluminum that behaves like a black body
which is the most relevant situation inferred from comet at 330 K, with a flux of 5 × 105 erg cm–2 s–1 at better than
observations (co-evolution of all gases and water vapor to- 3% uniformity. Since water is practically opaque to IR at
gether) and from the extensive small-scale laboratory stud- the 330-K blackbody spectrum, the energy input of the ir-
ies. These small-scale experiments have shown that trapping radiation dome was totally absorbed by the upper layers of
of ~10% CO in cometary H2O-ice grains at a very slow the ice sample.
deposition rate requires temperatures of ~22–27 K, where Ten thermocouples (types E and T) were embedded in
the ice formed by vapor deposition is amorphous and full the ice, recording the temperature profile of the sample. A
of pores. Yet amorphous ice can be produced even at 80 K, mass spectrometer recorded the emission of gas and H2O
with some structural differences from ice formed at ~30 K, vapor during heating, through a 2-cm hole in the dome right
but still well below the ~120-K transformation temperature above the center of the sample. The sensitivities to various
and gases can be trapped in it. gases provided by the manufacturer were checked by ana-
lyzing mixtures of gases with known compositions. The ice
3.3. Studies of Large Samples: Gas-Laden density was measured by collecting a small sample in a 1-
Amorphous Ice Samples cm2 × 5-cm glass vial simultaneously with the large ice
sample, and measuring its volume at 80 K and again when
The next step in large-scale comet simulation was to melted. The compressive strength was measured by insert-
produce a 200-cm2 × 10-cm-high sample of amorphous ice, ing a force-meter penetrator, cooled to 80 K, into the ice,
with gases trapped inside, although with no mineral dust immediately after the experiment was terminated and the
(Bar-Nun and Laufer, 2003). The main objective of this chamber was opened. A schematic drawing of the machine
study was to learn how much gas is released to the sample’s is presented in Fig. 8.
surface during the crystallization of the ice in deeper lay- To test whether indeed a sample of amorphous ice was
ers vs. the flux of water vapor released by sublimation on produced, Ar was flowed onto the 80-K cold plate by itself
the surface. The relevant cometary issue is the gas/water and, in a separate experiment, accompanied by H2O vapor.
vapor ratio in the coma vs. its ratio in the nucleus. Other As expected, Ar by itself did not freeze on the 80-K cold
ice properties, such as heat conductivity, which is of prime plate, but when accompanied by H2O vapor, it was trapped
importance to models, and compressive strength, which is in the amorphous H2O-ice that formed. As learned from
important for comet splitting and for landing on the nucleus, studies of thin ice samples, CO behaves like Ar (Bar-Nun
were also measured in this work. et al., 1987). In several experiments, 200-cm2 × 0.5-cm
Large samples of amorphous ice cannot be produced by thick and 200-cm2 × 6-cm-thick ice samples were produced.
depositing H2O vapor onto a cold plate, as is routinely done The density of the loose agglomerate of 200-µm ice grains
in small-scale experiments. With large samples the prob- was found to be 0.25 g cm–3. This should be compared with
lem of removing the water’s heat of condensation (2.7 × the densities of 0.3–0.7 and 0.29–0.83 g cm–3 calculated for
1010 erg g –1) is more severe, especially as amorphous ice Comets Halley (Rickman, 1989) and Borrelly (Farnham and
has a low thermal conductivity (<~104 erg cm–1 K–1). If one Cochran, 2002), respectively, which contain also mineral
grows too thick an ice layer, the heat of condensation can- particles.
not be removed by the underlying cold surface, so that the During the ice’s heating, the fluxes of sublimating water
newly deposited layers reach ~120 K and become crystal- vapor and Ar were monitored by a mass spectrometer until
line rather than amorphous. Consequently, even if a gas flow all the ice sample sublimated. The mass spectrometer record
accompanies ice formation, no gas trapping occurs. To solve of H2O and Ar during the entire experiment is shown in
these problems, thin ~200-µm ice layers were formed at Fig. 9a.
80 K (liquid N) on a cold plate, through which the heat of Several interesting results came out of this experiment:
condensation could still be transmitted to the cold surface, (1) As stated above, Ar was trapped in the 80-K ice, whereas
remain amorphous, and trap the accompanying gas. Once by itself it was not frozen on the cold plate. This showed
a thin amorphous gas-laden ice layer formed, it was scraped definitely that the ice made by this method was amorphous,
from the cold plate by a 80-K cold knife into the 80-K since only amorphous ice traps Ar in it, while being formed.
sample container, which was covered by an 80-K dome. All (2) The time-integrated mass spectrometer fluxes gave Ar/
these parts, as well as the heat shield surrounding the entire H2O = 1.01, in comparison with the 1 : 1 ratio in the flowed
706 Comets II

Fig. 8. A schematic drawing of the machine producing large (200 cm2 × 10 cm) gas-laden amorphous ice samples, as a “comet”
simulation: 1 = vacuum chamber, 2 = cold plate at 80 K, 3 = 200-µm amorphous gas-laden ice, 4 = homogeneous flow of water vapor
and gas, 5 = water vapor and gas pipes, 6 = 200-cm2 and 5–10-cm-thick ice sample, 7 = heating dome, 8 = 80-K cold knife, 9 = ther-
mocouples, 10 = density measurements, 11 = mass spectrometer, 12 = ionization gauge, 13 = heating tape, 14 = LN2 cooling pipes.

Fig. 9. (a) Evolution of Ar trapped in the ice and ice sublimation, upon heating from above of a 0.5-cm-thick sample. Note the early
rise of the Ar and its exhaustion before all the ice sublimates. (b) Temperature profiles of the thermocouples as a function of their
distance from the 80-K bottom plate in a 6-cm-thick ice deposit. Note also the sharp decrease and increase of the water flux vs. the
sluggish response of the Ar emanation, when the ice sample is covered by the cold plate and upon its removal.
 Colangeli et al.: Laboratory Experiments on Cometary Materials 707

Fig. 10. (a) Heat conductivity constant of various ice samples measured at different temperature ranges. (b) Compressive strength of
the studied ice samples as function of the penetration depth in the ice.

mixture. This result implies that all the Ar was trapped in derived was 3–6 × 104 erg cm–1 K–1 s–1 (Spohn et al., 1989;
the amorphous ice and was released upon warming up of Benkhoff and Spohn, 1991; Seiferlin et al., 1996).
the entire 0.5-cm-thick ice layer. (3) The timing and mag- From recent experiments (Fig. 10a) the heat conduction
nitude of Ar evolution from the ice, as seen in Fig. 9a, is of gas-free ice is 30 times smaller than Klinger’s value for a
of prime importance for the interpretation of comet observa- block of amorphous material [a very much lower thermal
tions. Even in a 0.5-cm-thick ice layer heated from above, conductivity value by a factor of 10 –4–10–5 was reported
the Ar flux rose to a level about seven times higher than by Kouchi et al. (1992), but was not measured in other ex-
that of the water vapor. This was because the Ar was re- periments]. This lower value is due to the fact that the
leased from the amorphous ice during the transformation sample is an agglomerate of ~200-µm ice particles, and the
into the cubic and “restrained amorphous” forms, as was heat conduction between the grains is poor. One cannot
found in numerous studies of thin ice samples. This pro- exclude the contribution of inward-flowing water vapor to
cess occurs in the interior of the sample, supplying gas to the thermal conductivity, but it should be noted that no
the experimental “coma,” whereas the water vapor emanates harder crust was detected below the surface, as would have
only from the ice surface. Eventually, the heated ice layer is been expected if a massive flow of water vapor froze in
exhausted of its gas, as can be seen in Fig. 9a. The Ar flux deeper layers. Nevertheless, the thermal conductivity of gas-
declines well before all the H2O-ice sublimates. This raises laden ice is much higher than that of pure H2O-ice, and even
the question of what the gas/H2O ratios in cometary comae more so when the gas content is even greater (Ar : H2O =
tell us about gas abundance ratios in cometary nuclei. 1 : 3 vs. 1 : 1). This shows the importance of trapped gas for
Figure 9b shows the thermal history of a 6-cm-thick ice the conduction of heat into the interior of comets.
sample, measured through five thermocouples, and the mass At this stage it is not possible to measure the effect of the
spectrometer records of water and Ar release. At 812 min exothermicity of the transformation amorphous to cubic ice
(after the beginning of ice formation) the sample was ex- on the temperature profile. Possibly, this process may be
posed to the 330-K heating dome. As expected, the ice tem- even somewhat endothermic in the presence of trapped gases
perature rose very steeply on the surface and more slug- (Kouchi and Sirono, 2001).
gishly below it. This allowed the thermal conductivity of the The measurement of mechanical properties is rather
ice to be determined. When the heating dome was blocked simple. Pressing a force-meter cooled to 80 K into the ex-
at 858 min, the surface temperature dropped immediately, tremely fluffy ice produced the results shown in Fig. 10b.
whereas the temperature of the deeper layers lagged. The As the ice was compressed, its compressive strength in-
thermal conductivity of the 0.25 g cm–3 agglomerate of 200- creased as its open spaces decreased. Pure ice is “stronger”
µm grains of amorphous ice can be calculated from the tem- whereas the Ar trapped in the ice “weakens” it, since the
perature profiles of the thermocouples embedded in the ice ice particles that form the sample are fluffier. The compres-
sample, and is shown in Fig. 10a. The heat conduction co- sive strength does, however, reach a finite limiting value.
efficients of amorphous and cubic water ice were calculated During heating, when the Ar left the ice, the fine ice struc-
by Klinger (1980) to be 2–3 × 10 4 and 2.8 × 105 erg cm–1 ture collapsed. A very low compressive strength of ~2 ×
K–1 s–1 respectively. In the KOSI experiments, on hexago- 105 dynes cm–2 can be deduced from the experiments. For
nal porous crystalline ice, the heat conduction coefficient comparison, in the KOSI experiments, in which mineral
708 Comets II

grains were mixed with hexagonal ice grains or were cov- 4. EXPERIMENTS ON CHEMICAL
ered by a layer of hexagonal ice, the compressive strength REACTIONS IN COMETARY ICES
was 3 × 105–2 × 107 dynes cm–2, depending on the mineral
content (Jessberger and Kotthaus, 1989). The previous Comets book (Wilkening, 1982) listed 35
chemical species observed in cometary spectra, but a mere
3.4. Summary and Implications of three stable molecules (CO, HCN, CH3CN). Since then, the
Large- and Small-Scale Studies cometary molecular list has grown to include about 20 rea-
sonably stable members. As comets are considered to be
By studying Ar : H2O (1 : 1) at 80 K in the large chamber, the solar system’s most primitive bodies, it is reasonable
it was proven that the ice is amorphous, since Ar does not to ask how they came to acquire molecules as complex as
freeze at 80 K but was trapped in the amorphous ice. Large ethane, methanol, and formamide. Laboratory investigations
samples of 200 cm2 × 6 cm, of an agglomerate of 200-µm can help with this question by revealing chemical reactions
ice particles of this amorphous gas-laden ice were produced and conditions that lead to observed cometary species.
and studied for the first time. These samples can represent It is generally accepted that at each stage of a comet’s
pristine cometary nuclei and their still-unprocessed interi- history, cosmic rays and energetic photons (UV or X-rays)
ors. Yet we should remember that the ice samples did not can drive chemistry in cometary ices. Although uncertain-
contain mineral and organic dust and, consequently, the ties remain in determining precise energy inputs, Table 4
buildup of an insulating dust layer and its subsequent effect shows values thought to be typical. We note that the chem-
on the penetration of the heat wave could not be studied. istry initiated by ionizing radiations, such as 1-MeV pro-
The most important finding was that the ratio of Ar/water tons or X-rays, results mostly from the secondary electrons
vapor in the experimental “coma” was between 7 and 10 generated. This means that the observed products, and their
(Fig. 9) times larger than the Ar/ice ratio in the experimen- abundances, are more dependent on the energy input than
tal “nucleus”. In the 0.5-cm-thick samples, the Ar was ex- the initial carrier of the energy. Since doses on the order of
hausted from the ice well before the ice sublimated com- 1 eV per molecule (Table 4) are attainable in the laboratory,
pletely but in the 6-cm-thick sample, Ar kept emanating experiments to mimic cometary ice chemistry can be per-
from deeper layers (Fig. 9b). This observation has direct formed. In most cases, the differences in photochemical and
bearing on the correlation between the gas/water vapor ob- radiation chemical effects are typically not in the nature of
served in cometary coma and the gas/ice ratio in the nu- the products made, but rather in product abundances or the
cleus: The ~10% of CO to water vapor seen in the comae depths at which products form in ice samples.
of Comets Halley, Hyakutake, and Hale-Bopp might well Goals motivating laboratory work on cometary chemistry
mean that the CO/ice in these nuclei could be closer to 1%. include the following: (1) Discovery of efficient reactions
In Comet Hale-Bopp (Biver et al., 1999), the CO flux leading from simple starting materials to more complex spe-
at 5.2 AU preperihelion was ~6 times larger than the water cies. This allows predictions of as yet unobserved cometary
flux, but became ~5 times smaller than water at perihelion. molecules. (2) Explanation of observed abundance and ra-
Apparently, the upper layers were exhausted and gases came tios, such as C2H6/CH4 and HNC/HCN. (3) Investigation of
out only, and more slowly, from deeper layers. A model low-albedo materials relevant for cometary nuclei (e.g.,
incorporating all new results is now being prepared. Halley and Borrelly). (4) Prediction of candidates for ex-
Finally, the low density and compressive strength, which tended sources of CO, CN, H2CO, and other molecules.
attest to the fluffy structure of the ice, can account for break- Here we describe some laboratory results related to the
ups of cometary nuclei and should be of concern for the chemistry of ices in cometary nuclei, leaving comae chemis-
Rosetta lander (Hilchenbach et al., 2000). However, incor- try for other chapters. The emphasis is on recent work,
porating about ~25% mineral dust and about 25% of or- especially that providing insight into molecular evolution
ganic “CHON” particles, as found for Comet Halley, may in comets.
harden the surface somewhat.
As for small-scale ice studies, much more has to be 4.1. Methods
learned about the preferential trapping of CO over N2, since
no N+2 was observed by Cochran et al. (2000, 2002) in vari- Figure 11 represents a laboratory setup used to investi-
ous recent comets where CO was observed. The enrichment gate cometary ice chemistry at the NASA Goddard Space
in Earth’s atmosphere of the heavier Xe isotopes is still an Flight Center (GSFC). Similar equipment exists in other
open problem, although the Ar and Kr isotopic enrichments, laboratories, with modifications made according to the in-
when trapped in ice according to their inverse square root terests of the investigators (e.g., Allamandola et al., 1988;
of the mass, account for their relative abundances (Notesco Gerakines et al., 1996; Demyk et al., 1998; Strazzulla et al.,
et al., 2003). A major problem remains as to how Jupiter 2001). In brief, the vacuum and temperature of outer space
obtained its abundances of C, N, O (?), S, P, etc., relative to are simulated with a high-vacuum chamber and a cryostat
H2, as these abundances are ~3 times the solar abundances. respectively. An ice sample is formed on a precooled sur-
It is possible that late bombardment by comets devoid of face, to a thickness of a few micrometers or less, by con-
H2 could have contributed these volatiles. densation of room-temperature gases. The sample is then
 Colangeli et al.: Laboratory Experiments on Cometary Materials 709

TABLE 4. Estimated fluxes for ice processing environments, compared to laboratory experiments.

Environment Ion Processing Photon Processing

(ice residence time Flux, 1 MeV p+ Energy absorbed Dose Flux Energy absorbed Dose
in years) (eV cm–2 s–1) (eV cm–2 s–1)* (eV molecule–1) (eV cm–2 s–1) (eV cm–2 s–1) (eV molecule–1)
Diffuse ISM 1 × 107 1.2 × 104 <1–30 9.6 × 108 5 × 108 104–106
(105–107)† at 10 eV† 0.02 µm ice

Dense cloud 1 × 106 1.2 × 103 <<1–3 1.4 × 104 1.7 × 103 <1–4
(105–107)† 0.02-µm ice at 10 eV 0.02 µm ice

Protoplanetary nebula 1 × 106 1.2 × 103 <<1–3 2 × 105 §5 ×104 2–240

(105–107)‡ 0.02-µm ice at 1–10 keV 0.02 µm ice

Oort cloud ϕ(E)** ** ~150 (0.1 m) 9.6 × 108 9.6 × 108 2.7 × 108
(4.6 × 109) ~55–5 (1–5 m) at 10 eV 0.1 µm ice
<10 (5–15 m)

Laboratory 8 × 10 16 2 × 1015 10 2.2 × 1015 2.2 × 1015 10

(4.6 × 10 –4)†† 1-µm ice at 7.4 eV 1 µm ice
* The absorbed energy dose from 1-MeV cosmic-ray protons assumes a 300-MeV cm2 g–1 stopping power and an H2O-ice density of
1 g cm–3. Protons deposit energy in both the entrance and exit ice layer of an ice-coated grain.
† 10 eV photons = 1200 Å, vacuum UV (UV-C). Jenniskens et al. (1993).
‡ Typical disk longevities (Lawson et al., 1996).
§ Typical flux at 0.1 pc, 1 keV photons = 12 Å, soft X-rays (Feigelson and Montmerle, 1999).
¶ Absorbed energy dose from 1-keV X-rays assumes a 1-keV electron production in 1 g cm–3 H O-ice with a 127-MeV cm2 g–1 stop-
2
ping power.
** An energy dependent flux, ϕ(E), was used to calculate the resulting energy dose at different depths in a comet nucleus for an H O-
2
ice density of 1 g cm–3. For details see Strazzulla and Johnson (1991) and references therein.
†† Typical proton and UV data from the Cosmic Ice Laboratory at NASA Goddard.

processed by positioning it before an ion beam to mimic

cosmic-ray bombardment or a UV lamp to simulate far-UV
exposure. The resulting ice chemistry can be followed by
IR spectroscopy (see Fig. 11) or other techniques [e.g., UV
(Mennella et al., 1997), Raman (Colangeli et al., 1992)].
At GSFC, a beam of ~1-MeV protons is generated by a Van
de Graaff accelerator, while vacuum-UV photolysis is done
with a flowing-H2 microwave-discharge lamp (mostly 100–
200-nm coverage).
To date, mid-IR spectroscopy (4000–400 cm−1, 2.5–
25 µm) has revealed more details of ice chemistry than any
other laboratory method. Spectra in this region are from
vibrations involving functional groups (groups of bonded
atoms), with certain functional groups having very diagnos-
tic absorbances. A disadvantage of IR spectroscopy is its
relatively low sensitivity. Reaction products with low abun-
dance can seldom be studied by IR alone, and often require
a combination of chromatography and mass spectrometry
for their identification during vaporization (e.g., Bernstein
et al., 1995).

4.2. Some Results and Case Histories

Fig. 11. Schematic of a laboratory setup for cometary ice experi- Of all cometary molecules, only H2O has been detected
ments. in both the solid and gas phases (Davies et al., 1997), all
710 Comets II

other species having been observed only in gas-phase coma

spectra. As H2O is the most abundant nuclear molecule, it
plays a particularly significant role in cometary ice chem-
istry. On exposure to either far-UV photons or high-energy
(keV, MeV) ions, H2O dissociates into H and OH radicals.
Even at cometary and interstellar temperatures, H and OH
can react with other molecules to produce many products.
Figure 12 summarizes an experiment in which an H2O +
CO (5 : 1) mixture was proton irradiated at 16 K (Hudson
and Moore, 1999). Before the irradiation, none of the bands
in the upper trace were present. The features shown were
produced by radiolysis and can be identified, among other
ways, by comparison to reference spectra. In each case,
fragments from H2O, either H or OH, form the products. For
example, H-atom addition to CO along the sequence

CO → HCO → H2CO → CH3O and/or Fig. 13. Molecular synthesis in an H2O + C2H2 (4 : 1) ice at 15 K
CH2OH → CH3OH after irradiation to a dose of 17 eV molecule–1. Spectra have been
offset for clarity.
leads to H2CO (formaldehyde) and CH3OH (methanol),
both being cometary molecules. Calculations of reaction
yields are possible from a knowledge of intrinsic IR band Figure 13 shows a related experiment, a proton irradia-
strengths, and show that energetic processing can account tion of an H2O + C2H2 ice (4 : 1) at ~15 K (Moore and Hud-
for the known abundance of many cometary organics. In son, 1998), work motivated by the discovery of C2H6 in
fact, radiolysis is presently the only process known to re- Comet Hyakutake by Mumma et al. (1996). The upper trace
produce many observed abundances. gives identifications and, again, H- and OH-addition reac-
Formic acid, HCOOH, in Fig. 12 is particularly interest- tions explain most of the products. A quantitative analysis
ing as this molecule arises from both H and OH adding to shows that this low-temperature ice chemistry can explain
CO, such as H-atom addition followed by OH reaction: C ≡ the unexpectedly high abundance of cometary C2H6.
O → HC = O → HC(=O)OH. Since H2O forms an isoelec- Products from low-temperature reactions of known
tronic series with NH3 and CH4, similar reactions will lead cometary molecules are summarized in Table 5 and repre-
to HC(=O)NH2, from NH3 + CO, and HC(=O)CH3, from sent work from various laboratories. The table is far from
CH4 + CO. These products are indeed observed in the labo- exhaustive [see Cottin et al. (1999) for a more complete
ratory, and both are known cometary molecules. listing]. Blanks in Table 5 indicate a lack of experimental
data.
Experiments have also revealed the radiolysis and photo-
lysis products of many single-component ices, and a sum-
mary is provided in Table 6, which is again far from ex-
haustive. Yields for some of these products may be low in
the H2O-rich ices of comets, but enrichment of the less-
volatile materials may occur as highly volatile species are
lost over many cometary apparitions. This effect is mani-
fested in the laboratory by a room-temperature residue that
remains after processed ices are warmed under vacuum.
These residues are the subject of much interest, as chro-
matographic analyses show that they contain high molecular
weight compounds. In residues from more complex ices,
biomolecules, such as certain amino acids, are found in
trace amounts (e.g., Bernstein et al., 2002). These materi-
als are thought to accumulate on cometary nuclei where
they may have been delivered to the early Earth. If such
molecules survived impact they could have significantly
enhanced the variety and volume of the Earth’s chemical
Fig. 12. New species formed in an H2O + CO (5 : 1) ice irradi- inventory. In both single- and multicomponent ice experi-
ated to 11 eV molecule–1 are identified by comparison with refer- ments, residual materials are also of interest as they could
ence spectra of dilute mixtures (H2O : molecule > 5 : 1) at ~16 K. explain the extended sources of H2CO, CN, CO, and other
Spectra have been offset for clarity. molecules seen in comae.
 Colangeli et al.: Laboratory Experiments on Cometary Materials 711

TABLE 5. Products from reactions of H2O-dominated two-component

ices at 10–20 K (references given in brackets).

Mixture Reaction Products Identified Processing

H2O + CO CO2, HCO, H2CO ( + CH3OH, HCOOH, Ion [1], UV [2]
HCOO –, H2CO3 from ion expts.)
H2O + CO2 CO, H2CO3, O3, H2O2 Ion [3,4], UV [4,5]
H2O + CH4 CH3OH, C2H5OH, C2H6, CO, CO2 Ion [6]
H2O + C2H2 C2H5OH, CH3OH, C2H6, C2H4, CO, CO2, Ion [6], UV [7]
CH4, C3H8, HC(=O)CH3, CH2CH(OH)
H2O + C2H6 CH4, C2H4, CH3CH2OH,CO, CO2, CH3OH Ion [8]
H2O + H2CO CO2, CO, CH3OH, HCO, HCOOH, CH4 Ion [1]
H2O + CH3OH CO, CO2, H2CO, HCO, CH4, ( + C2H4(OH)2, Ion [9,10], UV [2]
HCOO – from ion expts.)
H2O + NH3 [none reported] Ion [11]
H2O + HCN CN–, HNCO, OCN–, HC(=O)NH2, NH+4 (?), CO, CO2 Ion [8,12]
H2O + HNCO NH+4, OCN–, CO, CO2 UV [8]
H2O + HCOOH CO, CO2, H2CO Ion [8]
H2O + HC(=O)CH3 CO2, CO, CH4, CH3CH2OH Ion [8]
H2O + HC(=O)NH2 CO, CO2, HNCO, OCN– UV [8,12]
H2O + HC(=O)OCH3 CO2, CO, H2CO, CH3OH, CH4 Ion [8], UV [8]
H2O + SO2
H2O + H2S S2 UV [13]
H2O + OCS CO, CO2, SO2, H2CO (?), H2O2 (?) Ion [8]
H2O + CH3CN H2CCNH, CH4, OCN–, CN– Ion [8,12]
H2O + HCCCN
References: [1] Hudson and Moore (1999); [2] Allamandola et al. (1988); [3] Brucato et al. (1997); [4] Gerakines et
al. (2000); [5] Wu et al. (2003); [6] Moore and Hudson (1998); [7] Wu et al. (2002); [8] M. H. Moore et al. (unpub-
lished work, 2003); [9] Hudson and Moore (2000); [10] Palumbo et al. (1999); [11] Strazzulla and Palumbo (1998);
[12] Hudson et al. (2001); [13] Grim and Greenberg (1987a).

TABLE 6. Products from reactions of one-component ices at 10–20 K (references given in brackets).

Ice Reaction Products Identified Least-Volatile Species Processing Experiment

H2O H2O2, HO2 [2], OH [2] H2O2 Ion [1], UV [2]
CO CO2, C3O2, C2O C3O2 Ion [3], UV [2]
CO2 CO, O3, CO3 H2CO3 (from H+ implantation) [4] Ion [3,4], UV [1,2]
CH4 C2H2, C2H4, C2H6, PAHs [5] and high molecular Ion [5–7], UV [2]
C3H8, CH3, C2H5 weight hydrocarbons
C2H2 CH4 [6], polyacetylene [8] PAHs [5], polyacetylene [8] Ion [5,8]
C2H6
H2CO POM, CO, CO2, HCO POM Ion [8], UV [2]
CH3OH CH4, CO, CO2, H2CO, H2O, C2H4(OH)2 Ion [9,10], UV [2]
C2H4(OH)2, HCO, HCOO–
NH3 N2H4 [2], NH2 [2] N2H4 [2] Ion [12], UV [2]
HCN HCN oligomers HCN oligomers Ion [8], UV [8]
HNCO NH+4 , OCN–, CO, CO2 NH4OCN Ion [8], UV [8]
HCOOH
HC(=O)CH3
HC(=O)NH2
HC(=O)OCH3
SO2 SO3 S8 [12] Ion [12], UV [13]
H2S none reported UV [13]
OCS
CH3CN CH4, H2CCNH, CH3NC Ion [8], UV [8]
HCCCN
References: [1] Moore and Hudson (2000); [2] Gerakines et al. (1996); [3] Gerakines and Moore (2001); [4] Brucato
et al. (1997); [5] Kaiser and Roessler (1998); [6] Mulas et al. (1998); [7] Moore and Hudson (2003); [8] M. H. Moore et
al. (unpublished work, 2003); [9] Hudson and Moore (2000); [10] Palumbo et al. (1999); [11] Strazzulla and Palumbo
(1998); [12] Moore (1984); [13] Salama et al. (1990).
712 Comets II

Laboratory work also suggests ions as likely chemical Finally, we mention one of the most persistent puzzles
components of comets. Both radiolysis and photolysis of of cometary chemistry, the extraordinarily dark color of the
cometary ice analogs readily generate acids which, if NH3 nuclei of Comet Halley and Comet Borrelly. The most rea-
is present, undergo proton-transfer reactions of the type sonable explanation for low nuclear albedos is that radioly-
sis of cometary organics and CO produced a dark C-rich
HX + NH3 → X– + NH+4 material that accumulated over time (Johnson et al., 1987).
However, experiments showing progressive carbonization in
to produce stable ions. These ions would accumulate on the H2O-rich ices are lacking. More experiments and data-based
surface of a comet nucleus, or anywhere that sufficient ener- chemical models are needed.
getic processing occurs. Figure 14 illustrates this type of To summarize and conclude this section, laboratory ex-
acid-base chemistry, where the upper spectrum is from the periments have revealed efficient condensed-phase synthe-
irradiated H2O + CO (5 : 1) mixture of Fig. 12, while the ses for many cometary molecules such as H2CO, CH3OH,
lower spectrum is from an irradiated H2O + CO + NH3 (5 : 1 : 1) HCOOH, C2H6, HC(=O)NH2, and HC(=O)CH3 , as dis-
mixture (Hudson et al., 2001). The HCOO– (formate) and cussed. Reactions to make other molecules, such as CO2
NH4+ (ammonium) ion positions are indicated by arrows, and HNCO, have also been studied (Hudson et al., 2001).
and demonstrate that acid-base chemistry has occurred. Understanding the formation paths to other volatiles, and
Other ions that have been studied are OCN– (Grim and how they might relate to the dark nuclear surface, is work
Greenberg, 1987b; Hudson et al., 2001) and CN– (Moore in progress.
and Hudson, 2003). H3O + and OH– also are likely in
cometary nuclei, but difficult to detect by IR methods as 4.3. Future Steps
they lack strong unobscured bands.
Not only have changes in ice composition been investi- Little has been published on the ice chemistry of mol-
gated in the laboratory, but changes in ice phase have been ecules containing either a cyanide (CN) group or sulfur, two
studied (Baratta et al., 1991). Crystalline H2O-ice can be types of interest to astrobiologists. Cometary cyanides in-
converted into amorphous ice by either ionizing radiation or clude H-CN, H3C-CN, and HC ≡ C-CN. The correspond-
UV photons (Leto and Baratta, 2003). This amorphization ing isocyanides are known in the interstellar medium, but
is a general phenomenon and, at least for H2O and CH3OH, only H-NC has been reported in comets. Both the forma-
occurs with a rate that varies inversely with temperature tion and abundance of HCN and HNC, and their ratio of
(Hudson and Moore, 1995). Amorphization experiments HNC/HCN ~ 0.1, are of much interest, but lack a full ex-
also are related to the question of cometary clathrate hy- planation (Rodgers and Charnley, 2001). Cyanide isomer-
drates, crystalline cage-like solids. Laboratory work shows izations seen in the laboratory suggest new cometary mole-
that the H2O-CH3OH clathrate is readily destroyed by radia- cules awaiting detection, such as H3C-NC and HC ≡ C-NC
tion, raising serious questions about the stability of clath- from H3C-CN and HC ≡ C-CN, respectively, and H2C = C =
rates in cometary ice (Hudson and Moore, 1993). NH from H3C-CN. Also, a sequence similar to HC ≡ CH →
H2C = CH2 → H3C-CH3 may apply to HC ≡ C-CN, giving
cometary H2C = CH-CN and H3C-CH2-CN, but more labo-
ratory work is needed for a firmer prediction. As for sulfur,
it is present in comets as H2CS, H2S, OCS, SO2, and other
species. An observational search for CH3SH is suggested,
as CH3SH could be formed from H2CS in analogy with the
H2CO → CH3OH reaction. More laboratory work on com-
etary sulfur chemistry certainly is needed, as evidenced by
the gaps in Tables 5 and 6. For some early work on sulfur
ice chemistry, see Grim and Greenberg (1987a).
Other new molecules recommended for searches, based
on experiments, include ethanol (Moore and Hudson, 1998),
ethylene glycol (Hudson and Moore, 2000), and vinyl al-
cohol (Hudson and Moore, 2003), all readily formed by ice
processing. Acetic acid, glycolaldehyde, vinyl alcohol, and
ethylene oxide, all detected in the interstellar medium, are
probably cometary molecules as well, and isomers of each
Fig. 14. Infrared spectra of two irradiated laboratory ices at are seen in coma spectra.
16 K, showing the influence of acid-base chemistry. The upper Future laboratory work will undoubtedly include the
trace is an H2O + CO (5 : 1) ice and the lower trace is an H2O + roles of interstellar grains in ice chemistry. Do grains simply
CO + NH3 (5 : 1 :1) ice. Both were irradiated to about 25 eV mole- provide an inert reaction template or are they a catalytic
cule–1. surface? Much surface chemistry remains to be done on
 Colangeli et al.: Laboratory Experiments on Cometary Materials 713

cometary and interstellar molecules, and impressive experi- able way to understand and predict the actual behavior of
ments are already being published (Fraser et al., 2002). comets, pre- and postperihelion, appears to start with an
understanding of chemical reaction paths and to continue
5. CONCLUSIONS AND OUTLOOK on through the identification of phenomena that affect the
behavior of comet nuclei as a whole.
The results described in this chapter demonstrate the In conclusion, the aim of laboratory experiments is to
great value of laboratory simulations of cometary materi- increase our knowledge of how chemical species, at vari-
als and processes. Progress in laboratory experiments has ous levels and in different forms of arrangement, evolve in
grown in parallel to the increase of information from com- space. Laboratory scientists are encouraged to carry on their
etary observations and the reliability of models describing programs as the astrophysical community now recognizes
solar system formation and the role played by comets. This that interpretations of cosmic evolution, comets included,
chapter demonstrates that laboratory results are needed to cannot proceed without the firm reference frame offered by
understand the composition and evolution of both cometary laboratory results.
nuclei and comae, and to provide guidelines for future ex-
ploration and model development. This is true for both re- Acknowledgments. The experimental work at INAF – Osser-
fractory and ice components of comets. vatorio Astronomico di Capodimonte is partially supported by con-
Nevertheless, uncertainties remain and the field of re- tracts from ASI and MIUR. The research at Tel-Aviv University
search using laboratory experiments is rich with new tasks was supported by the Deutche Forschungs – Gemeinschaft, the
Israel Science foundation (Grant 194/93-2), and the United
to accomplish. Generally speaking, the characterization of
States – Israel Bi-national Science Foundation (Grant 2000005).
ice and dust analogs must continue to move in the direc-
Work at NASA Goddard Space Flight Center was supported
tion of using complementary techniques, mainly in situ through NASA’s Laboratory for Planetary Atmospheres and Space
methods, applied during or immediately after sample pro- Astrophysics Research and Analysis programs.
duction and/or treatment. Only in this way can information
on the different factors that characterize materials, and their
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718 Comets II
COLOR PLATES
Plate 1. Observable properties of a protoplanetary disk surround-
ing a T Tauri star, located at D = 150 pc. This montage presents
the information currently derivable from observations, and gives
the “apparent” sizes for optically thick and thin lines and thermal
dust emission observed at mm wavelengths with interferometers. Plate 2. A montage of the dust disk emission from the HST
(from Burrows et al., 1996) and its perpendicular jet. Contours
present 12CO J = 2–1 emission associated to the jet (black and
white) corresponding to the extreme velocity and the redshifted
and blueshifted integrated emission with respect to the systemic
velocity of 13CO J = 2–1 line coming from the disk (from J. Pety,
personal communication, 2003). Note that the velocity gradient
of the 13CO J = 2–1 emission is along the major disk axis, as ex-
pected for rotation. Both mm and optical images are tracing two
different aspects of the same physical object and contribute to give
a coherent outstanding of its physical properties.

Plate 3. This montage shows the HST image of HD 141569 at 0.5 µm

from Mouillet et al. (2001) and three channels (redshifted, systemic and
blueshifted velocity) of CO J = 2–1 map from the IRAM interferom-
eter. Note that, as expected for rotation the velocity gradient of the CO
emission is along the major disk axis. From J.-C. Augereau (unpublished
data, 2004).

Plate 4. This montage summarizes the observable properties of a protoplanetary disk encountered around a young main-sequence
star such as β Pictoris or HR 4796. A distance of 50 pc is assumed. The Gaussian gives an estimate of the angular resolution.
Plate 5. Scatter plot of osculating barycentric pericenter distance q vs. osculating barycentric semimajor axis (a) at various times in
the DLDW “cold” simulation of the formation of the Oort cloud. The points are color-coded to reflect the region in which the simu-
lated comets formed. (a) Initial conditions for the simulation (0 m.y.). (b) 1 m.y. into the simulation. (c) 10 m.y. into the simulation.
(d) 100 m.y. into the simulation. (e) 1000 m.y. into the simulation. (f) Final results for the simulation, at 4000 m.y., i.e., roughly the
present time. Note that in (f), there is a nearly empty gap for semimajor axes between about 200 and 1000 AU. Objects with a in this
range and q in the planetary region evolve rapidly in a at nearly constant q, thereby depleting this region, as discussed by DQT87.
Plate 6. Scatter plot of osculating inclination to the invariable plane vs. semimajor axis at various times in the DLDW “cold” simu-
lation of the formation of the Oort cloud. (a) Initial conditions for the simulation (0 m.y.). (b) 1 m.y. (c) 10 m.y. (d) 100 m.y. (e) 1000 m.y.
(f) Final results for the simulation, at 4000 m.y. The region in which each comet originated is labeled as in Plate 5. By the end of the
calculation, the inclination distribution is nearly isotropic, even in most of the inner Oort cloud.
Plate 7. The evolution of a representative particle originating in the Kuiper belt from the Plate 8. A contour plot of the relative distribution of ecliptic comets in the solar system as
integrations of LD97. Locations of the particle’s orbit in the q–Q (perihelion–aphelion) plane a function of aphelion (Q) and perihelion (q). The units are the fraction of comets per square
are joined by blue lines until the particle became “visible” (q < 2.5 AU) and are linked in AU in q–Q. Also shown are three lines of constant eccentricity at e = 0, 0.2, and 0.3. In
red thereafter. By definition, comets cannot have orbits with q > Q, so they cannot lie in addition, we plot two dashed curves of constant semimajor axis, one at Jupiter’s orbit and
the upper left of the diagram. The sampling interval was every 10 4 yr in the previsibility one at its 2:1 mean-motion resonances. They gray dot labeled “E” shows the location of
phase (q > 2.5 AU) and every 103 yr thereafter. Also shown are three lines of constant ec- Comet 2P/Encke. The label “1:2” indicates the location of Neptune’s 1:2 mean-motion reso-
centricity at e = 0, 0.2, and 0.3. In addition, we plot two dashed curves of constant semi- nance. From Levison and Duncan (1997).
major axis, one at Jupiter’s orbit and one at its 2:1 mean-motion resonance. From Levison
and Duncan (1997).
Plate 9. Different modes of light absorption on the cometary surface: (a) Surface absorption models; all radiation is absorbed at the
surface. (b) Volume absorption models; part of the radiation is absorbed in the interior and causes a “solid state greenhouse” effect.
 (a) (b)

κ = 0.00 κ = 0.025
(c) (d)

κ = 0.0275 κ = 0.050

Plate 10. Mach number distribution (color code) and velocity field (arrows) on the nightside of a homogeneous, spherical nucleus
(Crifo and Rodionov, 2000). The gas flow is computed from NSE for different values of the parameter κ, which controls the nightside
surface temperature. The arrows are proportional to the gas velocity vector. The Sun is on the horizontal axis, to the right.
 (a) (b)

(c) (d)

Plate 11. Inhomogeneous, spherical nuclei. (a) Gas density and (b) 30-µm grain radius dust density for one circular “Gaussian” ac-
tive area in a uniform background (Kitamura, 1986). (c) Gas density and (d) 30-µm grain radius dust density for one circular “Gaussian”
active ring in an anisotropic background (Knollenberg, 1994).
 (a) (b)

(c)

Plate 12. Spherical nucleus with one active ring: gas and dust distribution when the Sun is on-axis. (a) Gas density and velocity field
(Knollenberg, 1994); (b) 1.5-µm-radius grain density (Knollenberg, 1994); (c) enlarged gas density and velocity patterns; in this case,
the density isocontours are spaced by a factor 1.055 and the ticks on the horizontal axis are separated by 1 km; notice the whirl in the
upper-righthand corner of this panel [A. V. Rodionov (1998), unpublished recomputation of the result shown in (a)].
 (a) (b)

(c) (d)

(e) (f)

Plate 13. Spherical nucleus with the three unequal circular areas of Fig. 3c: gas and dust distribution when the Sun is in the direction
proposed by Keller et al. (1994). The three panels on the left give log10 of the H2O number density on nucleus-centered spheres with
radii 6.05 km (top), 17.49 km (middle), and 144.4 km ( bottom). The panels on the right give log10 of 9-µm-radius dust grain number
densities on the same spheres. The nucleus radius is 6.00 km (Crifo and Rodionov, 1998).
 (a)

(b) (c)

(d) (e)

Plate 14. Homogeneous vs. inhomogeneous nucleus (after Crifo et al., 2002b). The nucleus has the shape of P/Halley nucleus (Fig. 5)
smoothed by removal of the shape-spherical harmonics of degree >10. The middle and lowermost panels show isocontours of the
decimal logarithm of the gas number density, in the image planes of the Vega 2 flyby camera (image #90, center panels), and of the
Giotto HMC camera (lower panels). The projected Sun directions are to the angular graduations 198.6° (Vega 2) and 197° (Giotto).
The central blue area on the panels is the cross section of the nucleus in the image plane. On the lefthand panels, the nucleus is
assumed homogeneous (constant icy area fraction f). On the righthand panels, f has the random pattern shown on the nucleus shape
in the top panel.
 (a) (b)

q = 90° q = 75°

(c) (d)

q = 60° q = 45°

(e) (f)

q = 30° q = 15°

(g) (h)

q = 325° q = 270°

Plate 15. Deformation of the near-nucleus gas coma during the rotation of a bean-shaped, homogeneous nucleus (Crifo and Rodionov,
1999). Here, the Sun is rotated around the nucleus in the plane of the figure: q indicates its direction on the angular graduation. Notice
that the total gas production Qg varies during the rotation (from 6.3 to 8.7 × 1027 molecules per second).
Plate 16. A typical structureless dust tail: Comet Hale-Bopp 1995O1 on 1.84 UT May 1997. Plate 17. Striae observed in the dust tail of Comet Hale-Bopp 1995O1 on 16.15 UT March
The blue tail pointing to the left is the ion tail, while the whitish tail pointing to the top is 1997. The original image was filtered (unsharp masking) to enhance the striae in the whitish
the dust tail. Copyright by observer Marco Fulle. dust tail, which do not point toward the comet head. The blue tail on the left is the ion tail.
Copyright by observer Marco Fulle.
Plate 18. Colors of TNOs and Centaurs (108 objects) in the orbital eccentricity vs. semimajor axis plane. The sizes of the symbols are proportional to the corresponding object’s diameter.
A color palette has been adopted to scale the color spread from B-R = 1.0 (coded as dark blue) to B-R = 2.0 (coded as red). In comparison, B-R = 1.03 for the Sun and 1.97 for the Centaur
5145 Pholus (the reddest known object in the solar system). Resonances with Neptune [2:3 (a ~ 39.5 AU) and 1:2 (a ~ 48 AU)] are marked, as well as the q = 40 AU perihelion curve. The
advantage of this representation is that it offers to the eye the global color distribution of the TNOs. Interesting patterns clearly emerge from this color map. For instance, objects with
perihelion distances around and beyond 40 AU are mostly very red. Classical objects (mostly between the 2:3 and 1:2 resonances) with high eccentricity (and also inclination) are prefer-
entially neutral/slightly red. In contrast, no clear trend is obvious for scattered TNOs (a > 50 UA), nor for the Plutinos, which appear to lack any trends in their surface colors. Data ob-
tained from the Meudon multicolor survey (2MS, Doressoundiram et al., 2002) and the ESO Large Program (Boehnhardt et al., 2002; Peixinho et al., 2003).