Chapter 17:
The Stars:
A Celestial
Census
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The Lives of Stars
Stars live for a very long time, 100 million years
and up.
We can’t possibly observe a star this long!
How can we learn about the stages in a star’s
life?
We perform a census, getting a snapshot of many
stars at different stages of their life.
We infer the stages a star goes through from the
data we assemble in the census.
Cuidado! We can be misled if the star sample in
the census is biased. (Like political surveys.)
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A Stellar Census
We measure distances in light years (LY).
More details in Ch. 18
Small stars are less luminous, and therefore harder to
see.
If not corrected for, we will have a biased sample of stars.
Careful observation reveals that small stars (brown
dwarfs) are more common than large stars.
While less numerous, large stars are easier to see at
large distances. Most of the stars visible to the naked
eye are large.
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All Stars are Different
colors: blue-white to red
brightness: bright to very
faint
Orion: Constellation with
many different star types
Betelgeuse: orange-red
supergiant
Rigel: blue-white
supergiant
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Key Properties of Stars
color = surface
temperature
luminosity
Rigel (blue) 10,000 K
Sun (yellow) 6000 K
Betelgeuse (orange-red)
3,000 K
spectrum = chemical
composition
Rigel 60,000 LSun
Betelgeuse 50,000 LSun
mass
Rigel 16 solar masses
Betelgeuse 20 MSun
diameter
Rigel 7 solar diameters
Betelgeuse 1000 DSun
Rigel B
Sun G
Betelgeuse M
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17.2 Measuring Stellar Masses
Mass is one the key parameters of stars
Determines the behavior and life cycle of the star
Determined for binary stars – most common
case: spectroscopic binary stars
orbit depends on
mass of two stars
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Orbit of Binary Stars  Masses
Kepler's third law: (modified)
orbital period P and semimajor axis D
of ellipse related to masses M1 and
M2
D
D3 = (M1+M2)P2
D in AU, P in years, M1 and M2 in
solar masses (Msun)
each star orbits a common point –
the center of mass
Star’s distance from center of
mass determines the star’s
individual mass.
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center of mass
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Visual Binary: Sirius A and B
Visual Binaries: Wobbling Motion
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Sirius A and B
Sirius A normal star (class A main sequence)
Sirius B white dwarf companion
orbits are drawn to scale
exaggerated sizes of the two stars
Sirius A is considerably larger than the Sun while the
white dwarf Sirius B is about the size of the Earth.
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Spectroscopic Binary Stars
most known binaries are
spectroscopic binaries
distance too great to
resolve the two stars
individually
binary nature is
indicated in the periodic
shift of their spectral
lines as they orbit
around each other
can measure their
speeds from the Doppler
shifted lines
speed determines the
mass
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17.2.3The Range of Stellar Masses
How large and small can stars be?
Stars with 100 solar masses are known, and we
believe there may be stars up to about 200
solar masses (200 Msun).
True stars must be heavier than 1/12 Msun.
Objects between 1/100 Msun and 1/12 Msun may
produce energy by fusion for a short time and
are called brown dwarfs.
Objects less than 1/100 Msun are planets.
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17.2.4 The Mass-Luminosity
Relation
As shown in Fig. 17.8, there is a correlation
between mass and luminosity.
More massive stars are more luminous (give off
more energy).
For a few stars this relation is violated. These
exceptions are the white dwarfs.
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Mass vs. Luminosity
each point on this
plot represents the
absolute magnitude
(luminosity) and
color (temperature)
of a main sequence
star
Sun:
•luminosity 1.0
•mass 1.0
17.3 Diameters of Stars
Moon crosses in front of star – eclipse
brightness of the star decreases gradually
during the eclipse
time for decrease depends on size of star
Eclipsing binary stars
Time
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Eclipsing Binary System
Stars orbiting each other in a plane parallel to the line of sight:
orbit is seen edge-on.
One star periodically eclipses the other:
total brightness of the combined stars decreases during the eclipse.
The reduction in brightness depends on the luminosity and relative
size of the two stars.
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Interferometry
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Combine the light from two or more telescopes in a
special way that yields the resolution of a much larger
telescope.
Regularly done with radio waves, very difficult to do
with light.
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H-R Diagram
Relationship between temperature (color) and
luminosity (absolute magnitude) for 90% of the stars
90% of stars lie along a band called the main
sequence
Plot of luminosity vs. temperature is called the
Hertzsprung-Russell diagram
or just H-R diagram for short.
The following slides show different examples of H-R
diagrams.
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HR Diagram
each point on this
plot represents the
absolute magnitude
(luminosity) and
color (temperature)
of a star
Sun:
•+4.8 magnitude
•B-V color index 0.62
luminosity (solar units)
classes: familiar starsspectral class
temperature (Kelvin)
H-R Diagram
classes:
main sequence
90% of stars
large blue stars
medium yellow stars
small red stars
supergiants
giants
white dwarfs
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17.4.2 Main Sequence Stars
mass
Rigel (blue giant) ~ 16x Sun
Proxima Centauri (red dwarf) ~ 0.4x Sun
size
Rigel ~ 7x Sun, Proxima ~ 0.6x Sun
color = surface temperature
Rigel (blue) 28,000 K, Sun (yellow) 6000 K, Proxima (red)
3,500 K
spectrum = chemical composition
Rigel B, Sun G, Proxima Centauri M
luminosity
Rigel 27,000x Sun, Proxima 0.05x Sun
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Main Sequence Star Properties
solar
size
Temperature
(K)
example
prominent lines
color
class
solar
mass
bluest
O
20 –
100
12 - 25
40,000
10 Lacertae
ionized helium
bluish
B
4 - 20
4 - 12
18,000
Rigel, Spica
neutral helium, neutral
hydrogen
bluewhite
A
2-4
1.5 - 4
10,000
Sirius
neutral hydrogen
white
F
1.05 2
1.1 - 1.5
7,000
Canopus
neutral hydrogen, ionized
calcium
yellowwhite
G
0.8 1.05
0.85 1.1
5,500
Sun,
-Centauri
neutral hydrogen,
strongest ionized calcium
orange
K
0.5 0.8
0.6 0.85
4,000
Tau Ceti
neutral metals (calcium,
iron), ionized calcium
red
M
0.08 0.5
0.1 - 0.6
3,000
Proxima
Centauri
molecules and neutral
metals
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Color-Magnitude
H-R diagram also called a
color-magnitude diagram
All stars visible to the naked
eye (magnitude =< +5) & all
stars within 25 parsecs.
Luminous stars
easier to observe
rarer in the galaxy.
Mostly in top half of the H-R
diagram.
Faint stars
harder to see
more common in the galaxy.
Mostly in bottom half of the
H-R diagram.
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The Other 10% of Stars
About 10% of stars
Betelgeuse
don't follow the mass-luminosity
relationship
don't lie on the main sequence
Giant and Supergiant stars
upper right of the HR diagram.
large in diameter because very
luminous even though they are cool.
White dwarfs
lower left of the HR diagram.
small diameter (Earth-sized)
hot but dim
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Main Sequence: Typical Stars
Is the Sun an "average'' or "typical''?
The meaning of "average'' depends on how
one chooses the sample!
Compared to the nearby stars, the Sun is
luminous, hot, and big.
Compared to the apparently bright stars, the Sun
is dim, cool, and small.
Compared to the stars in globular clusters, the Sun
is very young.
Compared to the stars in open (galactic) clusters,
the Sun is very old.
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Our Sun compared to…
the 100 (apparent) brightest stars in our sky
and the 100 nearest stars.
From Hipparcus survey.
Most stars that appear
bright in our sky are also
intrinsically luminous
Near stars are all within
7.63 parsecs of the Sun.
Near stars are mostly
cool and faint.
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More comparisons…
Proportions of the spectral types for each group.
Bright Stars:
Most of the apparently
bright stars are hot and
luminous A and B-type
stars.
Includes a few of the
very hot O-type stars.
All but one of the K-type
stars in the bright star
sample are giants or
supergiant stars.
All of the M-type stars
are giants or
supergiants.
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More comparisons…


Proportions of the
spectral types for each
group.
Near Stars
 Look different from
bright stars.
 Majority of near stars
are cool and faint K
and M-type stars.
 Only one star in the
entire sample is a
giant star.
 Rest are main
sequence stars.
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Representative Sample
Which of these samples is more representative
of the entire population of stars in our galaxy?
A representative sample includes all parts of the
population of the objects your are investigating in
their proper proportions.
The relative proportion of common things will be
greater than the relative proportions of rare things.
In fact, the uncommon things may not be found in a
small representative sample because they are so
rare!
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Summary
A careful census of stars leads to a number of
conclusions:
Stars have a wide range of masses, luminosities,
temperatures, and sizes.
The most common stars are smaller and less luminous than
the Sun.
The stars organize into an understandable pattern on the HR diagram.
Binary star systems are common and useful for
measuring masses.
Several techniques exist for measuring diameters of
stars.
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