Chapter 15
Surveying the Stars
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15.1 Properties of Stars
Our goals for learning:
• How do we measure stellar luminosities?
• How do we measure stellar temperatures?
• How do we measure stellar masses?
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How do we measure stellar
luminosities?
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The brightness of a star depends on both distance and luminosity.
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Luminosity:
Amount of power a star
radiates
(energy per second = watts)
Apparent brightness:
Amount of starlight that
reaches Earth
(energy per second per
square meter)
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Thought Question
Alpha Centauri and the Sun have about the same
luminosity. Which one appears brighter?
A. Alpha Centauri
B. The Sun
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Thought Question
Alpha Centauri and the Sun have about the same luminosity.
Which one appears brighter?
A. Alpha Centauri
B. The Sun
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The amount of
luminosity passing
through each sphere is
the same.
Area of sphere:
4π (radius)2
Divide luminosity by
area to get brightness.
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The relationship between apparent brightness and
luminosity depends on distance:
Luminosity
Brightness =
4π (distance)2
We can determine a star’s luminosity if we can measure
its distance and apparent brightness:
Luminosity = 4π (distance)2 × (brightness)
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Thought Question
How would the apparent brightness of Alpha
Centauri change if it were three times
farther away?
A. It would be only 1/3 as bright.
B. It would be only 1/6 as bright.
C. It would be only 1/9 as bright.
D. It would be three times brighter.
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Thought Question
How would the apparent brightness of Alpha
Centauri change if it were three times
farther away?
A. It would be only 1/3 as bright.
B. It would be only 1/6 as bright.
C. It would be only 1/9 as bright.
D. It would be three times brighter.
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So how far away are these stars?
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Parallax
is the apparent
shift in
position of a
nearby object
against a
background of
more distant
objects.
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Apparent
positions of
nearest
stars shift
by about an
arcsecond
as Earth
orbits Sun.
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Parallax
angle
depends on
distance.
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Parallax is
measured by
comparing
snapshots
taken at
different
times and
measuring
the shift in
angle to star.
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Parallax and Distance
p = parallax angle
d (in parsecs) = 1
p (in arcseconds)
d (in light-years) = 3.26 × 1
p (in arcseconds)
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Most luminous
stars:
106 LSun
Least luminous
stars:
10–4LSun
(LSun is luminosity
of Sun)
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The Magnitude Scale
m = apparent magnitude, M = absolute magnitude
Apparent brightness of star 1 = 1/ 5 m1 − m 2
(100 )
Apparent brightness of star 2
Luminosity of star 1 = 1/ 5 M 1 − M 2
(100 )
Luminosity of star 2
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How do we measure stellar
temperatures?
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Every object emits thermal radiation with a
spectrum that depends on its temperature.
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An object of
fixed size
grows more
luminous as its
temperature
rises.
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Properties of Thermal Radiation
1. Hotter objects emit more light per unit area at all
frequencies.
2. Hotter objects emit photons with a higher average
energy.
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Hottest stars:
50,000 K
Coolest stars:
3000 K
(Sun’s surface
is 5800 K.)
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Level of ionization
also reveals a star’s
temperature.
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Absorption lines in star’s spectrum tell us its ionization level.
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Lines in a star’s spectrum correspond to a spectral type that
reveals its temperature.
(Hottest) O B A F G K M (Coolest)
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Remembering Spectral Types
(Hottest) O B A F G K M (Coolest)
• Oh, Be A Fine Girl, Kiss Me
• Only Boys Accepting Feminism Get Kissed
Meaningfully
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Thought Question
Which kind of star is hottest?
A. M star
B. F star
C. A star
D. K star
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Thought Question
Which kind of star is hottest?
A. M star
B. F star
C. A star
D. K star
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Pioneers of Stellar Classification
• Annie Jump
Cannon and the
“calculators” at
Harvard laid the
foundation of
modern stellar
classification.
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How do we measure stellar
masses?
Insert TCP 6e Figure 15.7 unannotated
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The orbit of a binary star system depends on strength of gravity.
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Types of Binary Star Systems
• Visual binary
• Eclipsing binary
• Spectroscopic binary
About half of all stars are in binary systems.
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Visual Binary
We can directly observe the orbital motions of these
stars.
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Eclipsing Binary
We can measure periodic eclipses.
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Spectroscopic Binary
We determine the orbit by measuring Doppler shifts.
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We measure mass using gravity.
Direct mass measurements are possible only for
stars in binary star systems.
4π2
p2 = a3
G (M1 + M2)
p = period
a = average separation
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Need two out of three
observables to measure mass:
1) Orbital period (p)
2) Orbital separation (a or r = radius)
v
3) Orbital velocity (v)
r M
For circular orbits, v = 2πr/p.
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Most massive
stars:
100MSun
Least massive
stars:
0.08MSun
(MSun is the mass
of the Sun.)
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What have we learned?
• How do we measure stellar luminosities?
– If we measure a star’s apparent brightness and
distance, we can compute its luminosity with
the inverse square law for light.
– Parallax tells us distances to the nearest stars.
• How do we measure stellar temperatures?
– A star’s color and spectral type both reflect its
temperature.
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What have we learned?
• How do we measure stellar masses?
– Newton’s version of Kepler’s third law tells us
the total mass of a binary system, if we can
measure the orbital period (p) and average
orbital separation of the system (a).
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15.2 Patterns Among Stars
Our goals for learning:
• What is a Hertzsprung-Russell diagram?
• What is the significance of the main
sequence?
• What are giants, supergiants, and white
dwarfs?
• Why do the properties of some stars vary?
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What is a Hertzsprung-Russell
diagram?
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An H-R
diagram plots
the luminosity
and
Luminosity
temperature of
stars.
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Temperature
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Most stars fall
somewhere
on the main
sequence of
the H-R
diagram.
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Stars with lower
T and higher L
than main-
sequence stars
must have larger
radii. These stars
are called giants
and supergiants.
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Stars with higher
T and lower L
than main-
sequence stars
must have
smaller radii.
These stars are
called white
dwarfs.
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A star’s full classification includes spectral
type (line identities) and luminosity class (line
shapes, related to the size of the star):
I - supergiant
II - bright giant
III - giant
IV - subgiant
V - main sequence
Examples: Sun - G2 V
Sirius - A1 V
Proxima Centauri - M5.5 V
Betelgeuse - M2 I
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H-R diagram
depicts:
Temperature
Luminosity
Color
Spectral type
Luminosity
Radius
Temperature
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Which
star is the
hottest?
Luminosity
Temperature
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Which
star is the
hottest?
Luminosity
Temperature
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Which star
is the most
luminous?
Luminosity
Temperature
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Which star
is the most
luminous?
C
Lumiosity
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Temperature
Which star
is a main-
sequence
star?
Luminosity
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Temperature
Which star
is a main-
sequence
star?
Luminosity
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Temperature
Which star
has the
largest
radius?
Luminosity
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Temperature
Which star
has the
largest
radius?
Luminosity
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Temperature
What is the significance of the
main sequence?
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Main-sequence
stars are fusing
hydrogen into
helium in their
cores like the Sun.
Luminous main-
sequence stars are
hot (blue).
Less luminous
ones are cooler
(yellow or red).
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Mass
measurements of
main-sequence
stars show that the
hot, blue stars are
much more
massive than the
cool, red ones.
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The mass of a
normal,
hydrogen-burning
star determines its
luminosity and
spectral type.
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Core pressure and
temperature of a
higher-mass star
need to be larger
in order to
balance gravity.
Higher core
temperature
boosts fusion rate,
leading to larger
luminosity.
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Stellar Properties Review
Luminosity: from brightness and distance
10–4LSun–106LSun
Temperature: from color and spectral type
3000 K–50,000 K
Mass: from period (p) and average separation (a)
of binary star orbit
0.08MSun – 100MSun
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Stellar Properties Review
Luminosity: from brightness and distance
(0.08MSun) 10–4LSun–106LSun (100MSun)
Temperature: from color and spectral type
(0.08MSun) 3000 K–50,000 K (100MSun)
Mass: from period (p) and average separation (a)
of binary star orbit
0.08MSun–100MSun
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Mass and Lifetime
Sun’s life expectancy: 10 billion years
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Mass and Lifetime Until core hydrogen
(10% of total) is
used up
Sun’s life expectancy: 10 billion years
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Mass and Lifetime Until core hydrogen
(10% of total) is
used up
Sun’s life expectancy: 10 billion years
Life expectancy of 10MSun star:
10 times as much fuel, uses it 104 times as fast
10 million years ~ 10 billion years × 10/104
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Mass and Lifetime Until core hydrogen
(10% of total) is
used up
Sun’s life expectancy: 10 billion years
Life expectancy of 10MSun star:
10 times as much fuel, uses it 104 times as fast
10 million years ~ 10 billion years × 10/104
Life expectancy of 0.1MSun star:
0.1 times as much fuel, uses it 0.01 times as fast
100 billion years ~ 10 billion years × 0.1/0.01
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Main-Sequence Star Summary
High-Mass Star:
• High luminosity
• Short-lived
• Larger radius
• Blue
Low-Mass Star:
• Low luminosity
• Long-lived
• Small radius
• Red
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What are giants, supergiants, and
white dwarfs?
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Sizes of Giants and Supergiants
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Off the Main Sequence
• Stellar properties depend on both mass and age: Those that
have finished fusing H to He in their cores are no longer
on the main sequence.
• All stars become larger and redder after exhausting their
core hydrogen: giants and supergiants.
• Most stars end up small and white after fusion has ceased:
white dwarfs.
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Which star
is most like
our Sun?
Luminosity
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Temperature
Which star is
most like our
Sun?
B
Luminosity
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Temperature
Which of
these stars
will have
changed the
least 10
billion years
Luminosity
from now?
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Temperature
Which of
these stars
will have
changed the
least 10
Luminosity
billion years
from now?
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Temperature
Which of
these stars
can be no
more than
10 million
Luminosity
years old?
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Temperature
Which of
these stars
can be no
more than
10 million
Luminosity
years old?
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Temperature
Why do the properties of some
stars vary?
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Variable Stars
• Any star that varies significantly in brightness
with time is called a variable star.
• Some stars vary in brightness because they cannot
achieve proper balance between power welling up
from the core and power radiated from the surface.
• Such a star alternately expands and contracts,
varying in brightness as it tries to find a balance.
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Pulsating Variable Stars
• The light curve of this pulsating variable star shows
that its brightness alternately rises and falls over a
50-day period.
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Cepheid Variable Stars
• Most pulsating
variable stars inhabit
an instability strip
on the H-R diagram.
• The most luminous
ones are known as
Cepheid variables.
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What have we learned?
• What is a Hertzsprung-Russell diagram?
– An H-R diagram plots stellar luminosity of
stars versus surface temperature (or color or
spectral type).
• What is the significance of the main
sequence?
– Normal stars that fuse H to He in their cores fall
on the main sequence of an H-R diagram.
– A star’s mass determines its position along the
main sequence (high-mass: luminous and blue;
low-mass: faint and red).
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What have we learned?
• What are giants, supergiants, and white
dwarfs?
– All stars become larger and redder after core
hydrogen burning is exhausted: giants and
supergiants.
– Most stars end up as tiny white dwarfs after
fusion has ceased.
• Why do the properties of some stars vary?
– Some stars fail to achieve balance between
power generated in the core and power radiated
from the surface.
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15.3 Star Clusters
Our goals for learning:
• What are the two types of star clusters?
• How do we measure the age of a star
cluster?
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What are the two types of star
clusters?
Insert TCP 6e Figure 15.16
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Open cluster: A few thousand loosely packed stars
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Globular cluster: Up to a million or more stars in a dense ball bound
together by gravity
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How do we measure the age of a
star cluster?
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Massive blue
stars die first,
followed by
white, yellow,
orange, and
red stars.
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The Pleiades
cluster now
has no stars
with life
expectancy
less than
around 100
million years.
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The main-
sequence
turnoff point
of a cluster
tells us its
age.
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To determine
accurate ages,
we compare
models of
stellar
evolution to
the cluster
data.
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Detailed
modeling of
the oldest
globular
clusters
reveals that
they are
about 13
billion years
old.
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What have we learned?
• What are the two types of star clusters?
– Open clusters are loosely packed and contain
up to a few thousand stars.
– Globular clusters are densely packed and
contain hundreds of thousands of stars.
• How do we measure the age of a star
cluster?
– A star cluster’s age roughly equals the life
expectancy of its most massive stars still on the
main sequence.
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