View source for IK Pegasi

{{Short description|Star in the constellation Pegasus}}
{{pp-move}}
{{Starbox begin}}
{{Starbox image
 | image=[[File:Location of IK Pegasi.png|236px]]
 | caption=Location of IK Pegasi.
}}
{{Starbox observe
 | epoch=J2000
 | ra={{RA|21|26|26.66066}}<ref name=GaiaDR2/>
 | dec={{DEC| +19|22|32.3169}}<ref name=GaiaDR2/>
 | appmag_v=6.08<ref name=Anderson2012/>
 | constell=[[Pegasus (constellation)|Pegasus]]
}}
{{Starbox character
 | component1 = A
 | class=A8m:<ref name="apj221" /> or kA6hA9mF0<ref name=Skiff2014/>
 | b-v={{Val|0.235|0.009}}<ref name=Anderson2012/>
 | u-b=0.03<ref name="simbad" />
 | variable=[[Delta Scuti variable|Delta Scuti]]<ref name="apj221" />
 | component2 = B
 | class2 = DA<ref name="mnras270" />
}}
{{Starbox astrometry
 | radial_v={{Val|−9.7|0.2}}<ref name=Anderson2012/>
 | prop_mo_ra = +80.964<ref name=GaiaDR2/>
 | prop_mo_dec = +16.205<ref name=GaiaDR2/>
 | parallax = 21.1287
 | p_error = 0.1410
 | parallax_footnote = <ref name=GaiaDR2/>
 | absmag_v=2.75<ref name=Anderson2012/>
}}
{{Starbox detail
 | component1 = A
 | mass=1.65<ref name="mnras267" />
 | radius={{Val|1.47|0.07|0.09}}<ref name=GaiaDR2/>
 | luminosity={{Val|6.568|0.051}}<ref name=GaiaDR2/>
 | temperature={{Val|7624|237|181|fmt=commas}}<ref name=GaiaDR2/>
 | metal=117<ref name="mnras267" /><ref name="nras278" />
 | rotational_velocity=<&nbsp;32.5<ref name="nras278" />
 | gravity=4.25<ref name="mnras267" />
 | age_myr=50–600<ref name="mnras267" />
 | component2 = B
 | mass2 = 1.15<ref name="pasp105" />
 | radius2 = 0.006<ref name="mnras270" />
 | gravity2 = 8.95<ref name="mnras270" />
 | luminosity2 = 0.12<ref name="b" group="nb"/>
 | temperature2 = 35,500<ref name="pasp105" />
}}
{{Starbox catalog
 | component1=AB
 | names1={{odlist|V=IK Peg|HR=8210|BD=+18° 4794|HD=204188|SAO=107138|HIP=105860}}.<ref name="simbad" />
 | component2=B
 | names2=WD&nbsp;2124+191, EUVE&nbsp;J2126+193.<ref name="apj502"/><ref name=apj497_2_77/>
}}
{{Starbox reference
 | Simbad=IK+Peg
}}
{{Starbox end}}

'''IK Pegasi''' (or '''HR 8210''') is a [[binary star]] [[star system|system]] in the [[constellation]] [[Pegasus (constellation)|Pegasus]]. It is just luminous enough to be seen with the unaided eye, at a distance of about 154&nbsp;[[light year]]s from the [[Solar System]].

The primary (IK Pegasi A) is an [[A-type main-sequence star]] that displays minor pulsations in [[luminosity]]. It is categorized as a [[Delta Scuti variable]] star and it has a periodic cycle of luminosity variation that repeats itself about 22.9 times per day.<ref name="mnras267"/> Its companion (IK Pegasi B) is a massive [[white dwarf]]—a star that has evolved past the main sequence and is no longer generating energy through [[nuclear fusion]]. They orbit each other every 21.7 days with an average separation of about 31&nbsp;million kilometres, or 19&nbsp;million miles, or 0.21&nbsp;[[astronomical unit]]s (AU). This is smaller than the orbit of [[Mercury (planet)|Mercury]] around the [[Sun]].

IK Pegasi B is the [[Near-Earth supernova|nearest known]] [[supernova]] progenitor candidate. When the primary begins to evolve into a [[red giant]], it is expected to grow to a radius where the white dwarf can [[Accretion (astrophysics)|accrete]] matter from the expanded gaseous envelope. When the white dwarf approaches the [[Chandrasekhar limit]] of 1.4&nbsp;[[solar mass]]es ({{Solar mass|link=y}}),<ref>{{Cite journal | last1 = Mazzali | first1 = P. A. | last2 = Röpke | first2 = F. K. | last3 = Benetti | first3 = S. | last4 = Hillebrandt | first4 = W. | title = A Common Explosion Mechanism for Type Ia Supernovae | doi = 10.1126/science.1136259 | journal = Science | volume = 315 | issue = 5813 | pages = 825–828 | year = 2007 | pmid =  17289993| arxiv = astro-ph/0702351v1 | type = PDF|bibcode = 2007Sci...315..825M | s2cid = 16408991 }}</ref> it may explode as a [[Type Ia supernova]].<ref name="mnras262"/>

==Observation==
This star system was catalogued in the 1862 ''[[Durchmusterung|Bonner Durchmusterung]]'' ("Bonn astrometric Survey") as BD&nbsp;+18°4794B. It later appeared in [[Edward Charles Pickering|Pickering's]] 1908 ''[[Bright Star Catalogue|Harvard Revised Photometry Catalogue]]'' as HR 8210.<ref name=Pickering1908/> The designation "IK Pegasi" follows the expanded form of the [[variable star designation|variable star nomenclature]] introduced by [[Friedrich Wilhelm Argelander|Friedrich W. Argelander]].<ref name=rabinowitz_vogel2009/>

Examination of the [[spectrograph]]ic features of this star showed the characteristic [[absorption line]] shift of a binary star system. This shift is created when their orbit carries the member stars toward and then away from the observer, producing a [[doppler effect|doppler shift]] in the wavelength of the line features. The measurement of this shift allows astronomers to determine the relative orbital velocity of at least one of the stars even though they are unable to resolve the individual components.<ref name=sb/>

In 1927, the Canadian astronomer [[William Edmund Harper|William E. Harper]] used this technique to measure the period of this single-line spectroscopic binary and determined it to be 21.724&nbsp;days. He also initially estimated the [[orbital eccentricity]] as 0.027. (Later estimates gave an eccentricity of essentially zero, which is the value for a circular orbit.)<ref name="mnras262" /> The velocity amplitude was measured as 41.5&nbsp;km/s, which is the maximum velocity of the primary component along the line of sight to the Solar System.<ref name=pdao4_161/>

The distance to the IK Pegasi system can be measured directly by observing the tiny [[parallax]] shifts of this system (against the more distant stellar background) as the [[Earth]] orbits around the Sun. This shift was measured to high precision by the [[Hipparcos]] spacecraft, yielding a distance estimate of 150&nbsp;[[light year]]s (with an accuracy of ±5&nbsp;light years).<ref name=aaa323_L49/> The same spacecraft also measured the [[proper motion]] of this system. This is the small angular motion of IK Pegasi across the sky because of its motion through space.

The combination of the distance and proper motion of this system can be used to compute the transverse velocity of IK Pegasi as 16.9&nbsp;km/s.<ref name="c" group="nb"/> The third component, the heliocentric [[radial velocity]], can be measured by the average [[red-shift]] (or blue-shift) of the stellar spectrum. The ''General Catalogue of Stellar Radial Velocities'' lists a radial velocity of −11.4&nbsp;km/s for this system.<ref name=wilson1953/> The combination of these two motions gives a [[space velocity (astronomy)|space velocity]] of 20.4&nbsp;km/s relative to the Sun.<ref name=Anderson2012/>

An attempt was made to photograph the individual components of this binary using the [[Hubble Space Telescope]], but the stars proved too close to resolve.<ref name=p12ewwd/> Recent measurements with the [[Extreme Ultraviolet Explorer]] [[space telescope]] gave a more accurate orbital period of {{nowrap|21.72168 ± 0.00009 days}}.<ref name="apj502"/> The [[inclination]] of this system's [[Orbital plane (astronomy)|orbital plane]] is believed to be nearly edge-on (90°) as seen from the Earth. If so it may be possible to observe an [[eclipse]].<ref name="pasp105" />

==IK Pegasi A==
[[File:IKPegLightCurve.png|thumb|left|A [[light curve]] for IK Pegasi, plotted from ''[[Transiting Exoplanet Survey Satellite|TESS]]'' data<ref name=MAST/>]]
The [[Hertzsprung–Russell diagram]] (HR diagram) is a plot of [[luminosity]] versus a [[color index]] for a set of stars. IK Pegasi A is currently a [[main sequence]] star—a term that is used to describe a nearly linear grouping of core hydrogen-fusing stars based on their position on the HR diagram. However, IK Pegasi A lies in a narrow, nearly vertical band of the HR diagram that is known as the [[instability strip]]. Stars in this band oscillate in a coherent manner, resulting in periodic pulsations in the star's luminosity.<ref name="araa33"/>

The pulsations result from a process called the [[κ-mechanism]]. A part of the star's outer [[atmosphere]] becomes [[Optical density|optically thick]] due to partial [[ionization]] of certain elements. When these atoms lose an [[electron]], the likelihood that they will absorb energy increases. This results in an increase in temperature that causes the atmosphere to expand. The inflated atmosphere becomes less ionized and loses energy, causing it to cool and shrink back down again. The result of this cycle is a periodic pulsation of the atmosphere and a matching variation of the luminosity.<ref name="araa33" />

[[File:Size IK Peg.png|right|320px|thumb|The relative dimensions of IK Pegasi A (left), B (lower center) and the Sun (right).<ref>For an explanation of the star colors, see: {{cite web
 |date        = December 21, 2004
 |url         = http://outreach.atnf.csiro.au/education/senior/astrophysics/photometry_colour.html
 |title       = The Colour of Stars
 |publisher   = Australia Telescope Outreach and Education
 |access-date  = 2007-09-26
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20120318151427/http://outreach.atnf.csiro.au/education/senior/astrophysics/photometry_colour.html
 |archive-date = March 18, 2012
}}</ref>]]
Stars within the portion of the instability strip that crosses the main sequence are called [[Delta Scuti variable]]s. These are named after the prototypical star for such variables: [[Delta Scuti]]. Delta Scuti variables typically range from [[spectral class]] A2 to F8, and a stellar luminosity class of III ([[Giant star|giants]]) to V ([[main sequence]] stars). They are short-period variables that have a regular pulsation rate between 0.025 and 0.25&nbsp;days. Delta Scuti stars have an abundance of elements similar to the Sun's (see [[Population I]] stars) and between 1.5 and {{Solar mass|2.5|link=y}}.<ref name=templeton2004/> The pulsation rate of IK Pegasi A has been measured at 22.9 cycles per day, or once every 0.044 days.<ref name="mnras267" />

Astronomers define the [[metallicity]] of a star as the abundance of [[chemical element]]s that have a higher [[atomic number]] than helium. This is measured by a [[spectroscopic]] analysis of the atmosphere, followed by a comparison with the results expected from computed stellar models. In the case of IK Pegasus A, the estimated metal abundance is [M/H]&nbsp;=&nbsp;+0.07&nbsp;±&nbsp;0.20. This notation gives the [[logarithm]] of the ratio of metal elements (M) to hydrogen (H), minus the logarithm of the Sun's metal ratio. (Thus if the star matches the metal abundance of the Sun, this value will be zero.) A logarithmic value of 0.07 is equivalent to an actual metallicity ratio of 1.17, so the star is about 17% richer in metallic elements than the Sun.<ref name="mnras267" /> However the margin of error for this result is relatively large.

The spectrum of A-class stars such as IK Pegasi A show strong [[Balmer line]]s of hydrogen along with absorption lines of ionized metals, including the K&nbsp;line of ionized [[calcium]] (Ca&nbsp;II) at a wavelength of 393.3&nbsp;[[nanometre|nm]].<ref name=saha2007/> The spectrum of IK Pegasi A is classified as marginal [[Am star|Am]] (or "Am:"), which means it displays the characteristics of a spectral class A but is marginally metallic-lined. That is, this star's atmosphere displays slightly (but anomalously) higher than normal absorption line strengths for metallic isotopes.<ref name="apj221"/> Stars of spectral type Am are often members of close binaries with a companion of about the same mass, as is the case for IK Pegasi.<ref name=baas26_868/>

Spectral class-A stars are hotter and more massive than the Sun. But, in consequence, their life span on the main sequence is correspondingly shorter. For a star with a mass similar to IK Pegasi A (1.65 {{Solar mass}}), the expected lifetime on the main sequence is 2–3{{nowrap| × 10<sup>9</sup> years}}, which is about half the current age of the Sun.<ref name=gsu2005/>

In terms of mass, the relatively young [[Altair]] is the nearest star to the Sun that is a stellar analogue of component A—it has an estimated 1.7 {{Solar mass}}. The binary system as a whole has some similarities to the nearby system of [[Sirius]], which has a class-A primary and a white dwarf companion. However, Sirius A is more massive than IK Pegasi A and the orbit of its companion is much larger, with a semimajor axis of 20&nbsp;AU.

==IK Pegasi B==
The companion star is a dense [[white dwarf]] star. This category of stellar object has reached the end of its evolutionary life span and is no longer generating energy through [[nuclear fusion]]. Instead, under normal circumstances, a white dwarf will steadily radiate away its excess energy, mainly stored heat, growing cooler and dimmer over the course of many billions of years.<ref name=chandra1/>

===Evolution===
Nearly all small and intermediate-mass stars (below about 8~9 {{Solar mass}}) will end up as white dwarfs once they have exhausted their supply of [[thermonuclear]] fuel.<ref name=apj591_1_288/> Such stars spend most of their energy-producing life span as a [[main sequence|main-sequence]] star. The time that a star spends on the main sequence depends primarily on its mass, with the lifespan decreasing with increasing mass.<ref name=seligman2007/> Thus, for IK Pegasi B to have become a white dwarf before component A, it must once have been more massive than component A. In fact, the progenitor of IK Pegasi B is thought to have had a mass between 5 and {{Solar mass|8}}.<ref name="mnras262" />

As the hydrogen fuel at the core of the progenitor of IK Pegasi B was consumed, it evolved into a [[red giant]]. The inner core contracted until hydrogen burning commenced in a shell surrounding the helium core. To compensate for the temperature increase, the outer envelope expanded to many times the radius it possessed as a main sequence star. When the core reached a temperature and density where helium could start to undergo fusion this star contracted and became what is termed a [[horizontal branch]] star. That is, it belonged to a group of stars that fall upon a roughly horizontal line on the H-R diagram. The fusion of helium formed an inert core of carbon and oxygen. When helium was exhausted in the core a helium-burning shell formed in addition to the hydrogen-burning one and the star moved to what astronomers term the [[asymptotic giant branch]], or AGB. (This is a track leading to the upper-right corner of the H-R diagram.) If the star had sufficient mass, in time [[Carbon burning process|carbon fusion]] could begin in the core, producing [[oxygen]], [[neon]] and [[magnesium]].<ref name="evolution"/><ref name=richmond20061005/><ref name=darling/>

The outer envelope of a red giant or AGB star can expand to several hundred times the radius of the Sun, occupying a radius of about {{nowrap|5 × 10<sup>8</sup> km}} (3 AU) in the case of the pulsating AGB star [[Mira]].<ref name=hubble19970806/> This is well beyond the current average separation between the two stars in IK Pegasi, so during this time period the two stars shared a common envelope. As a result, the outer atmosphere of IK Pegasi A may have received an isotope enhancement.<ref name="pasp105"/>

[[File:NGC7293 (2004).jpg|right|thumb|The [[Helix Nebula]] is being created by a star evolving into a white dwarf. ''[[NASA]] & [[ESA]] image.'']]
Some time after an inert oxygen-carbon (or oxygen-magnesium-neon) core formed, thermonuclear fusion began to occur along two shells concentric with the core region; hydrogen was burned along the outermost shell, while helium fusion took place around the inert core. However, this double-shell phase is unstable, so it produced thermal pulses that caused large-scale mass ejections from the star's outer envelope.<ref name=science289_5476_88/> This ejected material formed an immense cloud of material called a [[planetary nebula]].  All but a small fraction of the hydrogen envelope was driven away from the star, leaving behind a white dwarf remnant composed primarily of the inert core.<ref name="apjs76"/>

===Composition and structure===
The interior of IK Pegasi B may be composed wholly of carbon and oxygen; alternatively, if its progenitor underwent [[carbon burning]], it may have a core of oxygen and neon, surrounded by a mantle enriched with carbon and oxygen.<ref name=aaa375_1_87/><ref name=rmp74_4_1015/> In either case, the exterior of IK Pegasi B is covered by an atmosphere of almost pure hydrogen, which gives this star its [[stellar classification]] of DA. Due to higher [[atomic mass]], any helium in the envelope will have sunk beneath the hydrogen layer.<ref name="mnras270"/> The entire mass of the star is supported by [[electron degeneracy pressure]]—a [[quantum mechanics|quantum mechanical]] effect that limits the amount of matter that can be squeezed into a given volume.

[[File:ChandrasekharLimitGraph.svg|left|280px|thumb|This graph shows the theoretical radius of a white dwarf, given its mass. The green curve is for a [[Special relativity|relativistic]] electron gas model.]]
At an estimated {{Solar mass|1.15}}, IK Pegasi B is considered to be a high-mass white dwarf.<ref name="e" group="nb"/> Although its radius has not been observed directly, it can be estimated from known theoretical relationships between the mass and radius of white dwarfs,<ref name=sb_se/> giving a value of about 0.60% of the [[solar radius|Sun's radius]].<ref name="mnras270" /> (A different source gives a value of 0.72%, so there remains some uncertainty in this result.)<ref name="mnras267" /> Thus this star packs a mass greater than the Sun into a volume roughly the size of the Earth, giving an indication of this object's extreme [[density]].<ref name="f" group="nb"/>

The massive, compact nature of a white dwarf produces a strong [[surface gravity]]. Astronomers denote this value by the decimal [[logarithm]] of the [[gravitational force]] in [[Centimeter gram second system of units|cgs units]], or log ''g''. For IK Pegasi B, log ''g'' is 8.95.<ref name="mnras270" /> By comparison, log ''g'' for the Earth is 2.99. Thus the surface gravity on IK Pegasi is over 900,000 times the gravitational force on the Earth.<ref name="g" group="nb"/>

The effective surface temperature of IK Pegasi B is estimated to be about {{nowrap|35,500 ± 1,500 K}},<ref name="pasp105" /> making it a strong source of [[ultraviolet]] radiation.<ref name="mnras270" /><ref name="h" group="nb"/> Under normal conditions this white dwarf would continue to cool for more than a billion years, while its radius would remain essentially unchanged.<ref name=imamura19950224/>

==Future evolution==
In a 1993 paper, David Wonnacott, Barry J. Kellett and David J. Stickland identified this system as a candidate to evolve into a [[Type Ia supernova]] or a [[Cataclysmic variable star|cataclysmic variable]].<ref name="mnras262" /> At a distance of 150&nbsp;light years, this makes it the nearest known candidate supernova progenitor to the [[Earth]]. However, in the time it will take for the system to evolve to a state where a supernova could occur, it will have moved a considerable distance from Earth but may still pose a threat.

At some point in the future, IK Pegasi A will consume the hydrogen fuel at its core and start to evolve away from the main sequence to form a red giant. The envelope of a red giant can grow to significant dimensions, extending up to a hundred times its previous radius (or larger). Once IK Pegasi A expands to the point where its outer envelope overflows the [[Roche lobe]] of its companion, a gaseous [[accretion disk]] will form around the white dwarf. This gas, composed primarily of hydrogen and helium, will then accrete onto the surface of the companion. This mass transfer between the stars will also cause their mutual orbit to shrink.<ref name=lrr2006/>

On the surface of the white dwarf, the accreted gas will become compressed and heated. At some point the accumulated gas can reach the conditions necessary for hydrogen fusion to occur, producing a [[thermal runaway|runaway]] reaction that will drive a portion of the gas from the surface. This would result in a (recurrent) [[nova]] explosion—a cataclysmic variable star—and the luminosity of the white dwarf would rapidly increase by several [[Apparent magnitude|magnitudes]] for a period of several days or months.<ref name=aavso200105/> An example of such a star system is [[RS Ophiuchi]], a binary system consisting of a red giant and a white dwarf companion. RS Ophiuchi has flared into a (recurrent) nova on at least six occasions, each time accreting the critical mass of hydrogen needed to produce a runaway explosion.<ref name="vsom0501"/><ref name=hendrix20070720/>

It is possible that IK Pegasi B will follow a similar pattern.<ref name="vsom0501" /> In order to accumulate mass, however, only a portion of the accreted gas can be ejected, so that with each cycle the white dwarf would steadily increase in mass. Thus, even should it behave as a recurring nova, IK Pegasus B could continue to accumulate a growing envelope.<ref name=aaa362_1046/>

An alternate model that allows the white dwarf to steadily accumulate mass without erupting as a nova is called the close-binary [[supersoft x-ray source]] (CBSS). In this scenario, the mass transfer rate to the close white dwarf binary is such that a steady fusion burn can be maintained on the surface as the arriving hydrogen is consumed in thermonuclear fusion to produce helium. This category of super-soft sources consist of high-mass white dwarfs with very high surface temperatures ({{nowrap|0.5 × 10<sup>6</sup>}} to {{nowrap|1 × 10<sup>6</sup> K}}<ref name=asp2002/>).<ref name=di_stefano_greiner1996/>

Should the white dwarf's mass approach the [[Chandrasekhar limit]] of 1.4 {{Solar mass|}} it will no longer be supported by [[electron degeneracy pressure]] and it will undergo a collapse. For a core primarily composed of oxygen, neon and magnesium, the collapsing white dwarf is likely to form a [[neutron star]]. In this case, only a fraction of star's mass will be ejected as a result.<ref name=lr20060124/> If the core is instead made of carbon-oxygen, however, increasing pressure and temperature will initiate carbon fusion in the center prior to attainment of the Chandrasekhar limit. The dramatic result is a runaway nuclear fusion reaction that consumes a substantial fraction of the star within a short time. This will be sufficient to unbind the star in a cataclysmic, Type Ia supernova explosion.<ref name=chandra2/>

Such a supernova event may pose some threat to life on the Earth. It is thought that the white dwarf, IK Pegasi B, is unlikely to detonate as a supernova for 1.9 billion years.<ref name=beech2011/> As shown previously, the space velocity of this star relative to the Sun is {{convert|20.4|km/s|mi/s|abbr=on}}. This is equivalent to moving a distance of one light year every 14,700&nbsp;years. After 5&nbsp;million years, for example, this star will be separated from the Sun by more than 500&nbsp;light years. A Type&nbsp;Ia supernova within a thousand parsecs (3,300&nbsp;light-years) is thought to be able to affect the Earth,<ref name=richmond20050408/> but it must be closer than about 10 parsecs (around thirty light-years) to cause a major harm to the terrestrial biosphere.<ref name=beech2011/>

Following a supernova explosion, the remnant of the donor star (IK Pegasus A) would continue with the final velocity it possessed when it was a member of a close orbiting binary system. The resulting relative velocity could be as high as {{convert|100–200|km/s|mi/s|abbr=on}}, which would place it among the [[High-velocity star|high-velocity members]] of the [[Milky Way|galaxy]]. The companion will also have lost some mass during the explosion, and its presence may create a gap in the expanding debris. From that point forward it will evolve into a single white dwarf star.<ref name=apj582_2_915/><ref name=apjss128_2_615/> The supernova explosion will create a [[Supernova remnant|remnant]] of expanding material that will eventually merge with the surrounding [[interstellar medium]].<ref name=nasa20060907/>

==See also==
*[[Lists of stars]]

==Notes==
{{Reflist|group="nb"|refs=

<ref name="b">Based upon:
:<math>\begin{smallmatrix} \frac{L}{L_{sun}} = \left ( \frac{R}{R_{sun}} \right )^2 \left ( \frac{T_{eff}}{T_{sun}} \right )^4 \end{smallmatrix}</math>
where ''L'' is luminosity, ''R'' is radius and ''T<sub>eff</sub>'' is the effective temperature. See:<br />{{cite web | last=Krimm | first=Hans | date=August 19, 1997 | url=http://ceres.hsc.edu/homepages/classes/astronomy/spring99/Mathematics/sec20.html | title=Luminosity, Radius and Temperature | publisher=Hampden-Sydney College | access-date=2007-05-16 | url-status=dead | archive-url=https://web.archive.org/web/20030508233052/http://ceres.hsc.edu/homepages/classes/astronomy/spring99/Mathematics/sec20.html | archive-date=May 8, 2003 }}
</ref>

<ref name="c">The net proper motion is given by:
:<math>\begin{smallmatrix} \mu = \sqrt{ {\mu_\delta}^2 + {\mu_\alpha}^2 \cdot \cos^2 \delta } = 77.63\, \end{smallmatrix}</math>&nbsp;mas/y.
where <math>\mu_\alpha</math> and <math>\mu_\delta</math> are the components of proper motion in the RA and Dec., respectively. The resulting transverse velocity is:
:''V<sub>t</sub>'' = μ • 4.74 ''d'' (pc) = 16.9&nbsp;km.
where ''d''(pc) is the distance in parsecs. See:<br />{{cite web | last=Majewski | first=Steven R. | date=2006 | url=http://www.astro.virginia.edu/class/majewski/astr551/lectures/VELOCITIES/velocities.html | title=Stellar Motions | publisher=University of Virginia | access-date=2007-05-14 | url-status=dead | archive-url=https://archive.today/20120125061201/http://www.astro.virginia.edu/class/majewski/astr551/lectures/VELOCITIES/velocities.html | archive-date=2012-01-25 }}
</ref>

<ref name="e">The white-dwarf population is narrowly distributed around the mean mass of {{Solar mass|0.58}}, and only 2%. See:<br />{{cite journal | author=Holberg, J. B. | display-authors=4 | author2=Barstow, M. A. | author3=Bruhweiler, F. C. | author4=Cruise, A. M. | author5=Penny, A. J. | title=Sirius B: A New, More Accurate View | journal=The Astrophysical Journal | date=1998 | volume=497 | issue=2 | pages=935–942 | doi=10.1086/305489 | bibcode=1998ApJ...497..935H| doi-access=free }} of all white dwarfs have at least one solar mass.
</ref>

<ref name="f">R<sub>*</sub> = 0.006 • (6.96 × 10<sup>8</sup>) ≈ 4,200&nbsp;km.</ref>

<ref name="g">The surface gravity of the Earth is 9.780 m/s<sup>2</sup>, or 978.0 cm/s<sup>2</sup> in cgs units. Thus:
:<math>\begin{smallmatrix} \log\ \operatorname{g}=\log\ 978.0=2.99 \end{smallmatrix}</math>
The log of the gravitational force ratios is 8.95 - 2.99 = 5.96. So:
:<math>\begin{smallmatrix} 10^{5.96} \approx 912,000 \end{smallmatrix}</math>
</ref>

<ref name="h">From [[Wien's displacement law]], the peak emission of a [[black body]] at this temperature would be at a [[wavelength]] of:
:<math>\begin{smallmatrix} \lambda_b = (2.898 \times 10^6 \operatorname{nm\ K})/(35,500\ \operatorname{K}) \approx 82\, \end{smallmatrix}</math>&nbsp;nm
which lies in the far ultraviolet part of the [[electromagnetic spectrum]].
</ref>

}}

==References==
{{Reflist|refs=

<ref name=MAST>{{cite web |title=MAST: Barbara A. Mikulski Archive for Space Telescopes |url=https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html |publisher=Space Telescope Science Institute |access-date=30 November 2022}}</ref>

<ref name=GaiaDR2>{{Cite Gaia DR2|1787127787263968640}}</ref>

<ref name="simbad">{{cite simbad | title=HD 12139 | access-date=2019-11-13}} — ''Note:'' some results were queried via the "Display all measurements" function on the web page.</ref>

<ref name=Anderson2012>{{citation
 | title=XHIP: An extended hipparcos compilation
 | last1=Anderson | first1=E. | last2=Francis | first2=Ch.
 | journal=Astronomy Letters | volume=38
 | issue=5 | pages=331 | year=2012
 | bibcode=2012AstL...38..331A | arxiv=1108.4971
 | doi=10.1134/S1063773712050015 | s2cid=119257644 | postscript=. }}</ref>

<ref name=Skiff2014>{{citation
 | title=Catalogue of Stellar Spectral Classifications
 | last=Skiff | first=B. A.
 | series=VizieR On-line Data Catalog: B/mk
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}}

==External links==
{{Commons category|IK Pegasi}}
* {{citation | last=Davies | first=Ben | date=2006 | url=http://ben.davies.net/supernovae2.htm | title=Supernova events | access-date = 2007-06-01 }}
* {{citation|last=Richmond |first=Michael |date=April 8, 2005 |url=http://www.tass-survey.org/richmond/answers/snrisks.txt |title=Will a Nearby Supernova Endanger Life on Earth? |publisher=The Amateur Sky Survey |access-date=2007-06-07 |url-status=dead |archive-url=https://web.archive.org/web/20070306114344/http://www.tass-survey.org/richmond/answers/snrisks.txt |archive-date=March 6, 2007 }}
* {{citation | last=Tzekova | first=Svetlana Yordanova | date=2004 | url=http://www.eso.org/public/outreach/eduoff/cas/cas2004/casreports-2004/rep-310/#2.%20The%20main%20star%20-%20IK%20Peg%20A | title=IK Pegasi (HR 8210) | publisher=ESO (European Organisation for Astronomical Research in the Southern Hemisphere) | access-date=2007-09-30 | archive-date=2012-05-20 | archive-url=https://web.archive.org/web/20120520195016/http://www.eso.org/public/outreach/eduoff/cas/cas2004/casreports-2004/rep-310/#2.%20The%20main%20star%20-%20IK%20Peg%20A | url-status=dead }}

{{Featured article}}
{{Stars of Pegasus}}
{{Portal bar|Astronomy|Stars|Spaceflight|Outer space|Solar System}}

{{DEFAULTSORT:IK Pegasi}}
[[Category:A-type main-sequence stars]]
[[Category:Am stars]]
[[Category:White dwarfs]]
[[Category:Spectroscopic binaries]]
[[Category:Supernovae]]
[[Category:Astronomical objects discovered in 1862|?]]
[[Category:Pegasus (constellation)]]
[[Category:Durchmusterung objects]]
[[Category:Henry Draper Catalogue objects|204188]]
[[Category:Hipparcos objects|105860]]
[[Category:Bright Star Catalogue objects|8210]]
[[Category:Objects with variable star designations|Pegasi, IK]]