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Chapter 12
Stellar Evolution
Guidepost
This chapter is the heart of any discussion of
astronomy. Previous chapters showed how astronomers
make observations with telescopes and how they
analyze their observations to find the luminosity,
diameter, and mass of stars. All of that aims at
understanding what stars are.
This is the middle of three chapters that tell the story of
stars. The preceding chapter told us how stars form,
and the next chapter tells us how stars die. This chapter
is the heart of the story—how stars live.
As always, we accept nothing at face value. We expect
theory to be supported by evidence. We expect carefully
constructed models to help us understand the structure
inside stars. In short, we exercise our critical faculties
Guidepost (continued)
and analyze the story of stellar evolution rather than
merely accepting it.
After this chapter, we will know how stars work, and we
will be ready to study the rest of the universe, from
galaxies that contain billions of stars to the planets that
form around individual stars.
Outline
I. Main-Sequence Stars
A. Stellar Models
B. Why There Is a Main Sequence
C. The Ends of the Main Sequence
D. The Life of a Main-Sequence Star
E. The Life Expectancies of Stars
II. Post-Main-Sequence Evolution
A. Expansion into a Giant
B. Degenerate Matter
C. Helium Fusion
D. Fusing Elements Heavier than Helium
Outline (continued)
III. Evidence of Evolution: Star Clusters
A. Observing Star Clusters
B. The Evolution of Star Clusters
IV. Evidence of Evolution: Variable Stars
A. Cepheid and RR Lyrae Variable Stars
B. Pulsating Stars
C. Period Changes in Variable Stars
Main Sequence Stars
The structure and evolution of a star is determined by
the laws of
• Hydrostatic equilibrium
• Energy transport
• Conservation of mass
• Conservation of energy
A star’s mass (and chemical
composition) completely
determines its properties.
That’s why stars initially all line up along the main sequence.
Maximum Masses of Main-Sequence Stars
Mmax
~ 100 solar masses
a) More massive clouds fragment into
smaller pieces during star formation.
b) Very massive stars lose mass in
strong stellar winds
h Carinae
(Eta Carinae)
Example: h Carinae: Binary system of a 60 Msun and 70 Msun star.
Dramatic mass loss; major eruption in 1843 created double lobes.
Minimum Mass of Main-Sequence Stars
Mmin = 0.08 Msun
Gliese 229B
At masses below
0.08 Msun, stellar
progenitors do not
get hot enough to
ignite thermonuclear
fusion.
 Brown Dwarfs
Brown Dwarfs
Hard to find because they are very faint
and cool; emit mostly in the infrared.
Many have been detected in star forming
regions like the Orion Nebula.
Evolution on the Main Sequence (1)
Main-Sequence
stars live by
fusing H to He.
Zero-Age
Main
Sequence
(ZAMS)
MS evolution
Finite supply of H
=> finite life time.
Future of the Sun
(SLIDESHOW MODE ONLY)
Evolution on the Main Sequence (2)
A star’s life time T ~ energy reservoir / luminosity
Energy
reservoir ~ M
Luminosity
L ~ M3.5
T ~ M/L ~ 1/M2.5
Massive stars
have short
lives!
Evolution off the Main Sequence:
Expansion into a Red Giant
Hydrogen in the core
completely converted
into He:
 “Hydrogen burning”
(i.e. fusion of H into He)
ceases in the core.
H burning continues in a
shell around the core.
He Core + H-burning
shell produce more
energy than needed for
pressure support
Expansion and cooling of
the outer layers of the
star 
Red Giant
Expansion onto the Giant Branch
Expansion and
surface cooling during
the phase of an
inactive He core and
a H- burning shell
Sun will expand
beyond Earth’s orbit!
Degenerate Matter
Matter in the He core has
no energy source left.
 Not enough thermal
pressure to resist and
balance gravity
 Matter assumes a
new state, called
degenerate
matter:
Pressure in degenerate
core is due to the fact that
electrons can not be
packed arbitrarily close
together and have small
energies.
Red Giant Evolution
H-burning shell
keeps dumping He
onto the core.
4 H → He
He
He-core gets denser
and hotter until the
next stage of nuclear
burning can begin in
the core:
He fusion
through the
“Triple-Alpha
Process”
4He
+ 4He  8Be + g
8Be
+ 4He  12C + g
Helium Fusion
He nuclei can fuse to
build heavier elements:
When pressure and
temperature in the He core
become high enough,
Red Giant Evolution
(5 solar-mass star)
C, O
Inactive He
Fusion Into Heavier Elements
Fusion into heavier
elements than C, O:
requires very high
temperatures; occurs only
in very massive stars (more
than 8 solar masses).
The Life “Clock” of a Massive Star
(> 8 Msun)
Let’s compress a massive star’s life into one day…
H  He
11 12 1
Life on the Main Sequence
+ Expansion to Red Giant:
22 h, 24 min.
2
10
9
3
4
8
H burning
7
6
5
H  He
He  C,
O
11 12 1
2
10
He burning:
(Red Giant Phase)
1 h, 35 min, 53 s
9
3
4
8
7
6
5
The Life “Clock” of a Massive Star (2)
H
He
He  C, O
C  Ne, Na, Mg,
O
10
9
2
3
C burning:
8
4
6.99 s
H
HeO
He  C,
11 12 1
7
6
5
C  Ne, Na, Mg, O
Ne  O, Mg
Ne burning:
6 ms
23:59:59.996
The Life “Clock” of a Massive Star (3)
H
HeO
He  C,
C  Ne, Na, Mg, O
Ne  O, Mg
O  Si, S, P
O burning:
3.97 ms
H
HeO
He  C,
23:59:59.99997
C  Ne, Na, Mg, O
Ne  O, Mg
O  Si, S, P
Si  Fe, Co, Ni
Si burning:
0.03 ms
The final
0.03 msec!!
Summary of Post Main-Sequence
Evolution of Stars
Supernova
Fusion
proceeds;
formation
of Fe core.
M>8
Msun
Evolution of
4 - 8 Msun
stars is still
uncertain.
Mass loss in
stellar winds
may reduce
them all to <
4 Msun stars.
Fusion
stops at
formation of
C,O core.
M<4
Msun
M < 0.4 Msun
Red dwarfs:
He burning
never
ignites
Evidence for Stellar Evolution: Star
Clusters
Stars in a star cluster all have
approximately the same age!
More massive stars evolve more quickly
than less massive ones.
If you put all the stars of a star cluster on a
HR diagram, the most massive stars
(upper left) will be missing!
HR Diagram of a Star Cluster
Cluster Turnoff
(SLIDESHOW MODE ONLY)
Example: HR diagram of the star cluster M 55
High-mass stars
evolved onto the
giant branch
Turn-off point
Low-mass stars
still on the main
sequence
Estimating the Age of a Cluster
The lower
on the MS
the turn-off
point, the
older the
cluster.
Evidence for Stellar Evolution:
Variable Stars
Some stars show intrinsic
brightness variations not caused
by eclipsing in binary systems.
Most important example:
d Cephei
Light curve of d Cephei
Cepheid Variables:
The Period-Luminosity Relation
The variability period of
a Cepheid variable is
correlated with its
luminosity.
The more luminous it
is, the more slowly it
pulsates.
=> Measuring a
Cepheid’s period, we
can determine its
absolute magnitude!
Cepheid Distance Measurements
Comparing absolute and apparent magnitudes of Cepheids,
we can measure their distances (using the 1/d2 law)!
The Cepheid distance
measurements were
the first distance
determinations that
worked out to
distances beyond our
Milky Way!
Cepheids are up to
~ 40,000 times more
luminous than our sun
=> can be identified in
other galaxies.
Pulsating Variables: The Instability Strip
For specific
combinations of radius
and temperature, stars
can maintain periodic
oscillations.
Those combinations
correspond to locations
in the Instability Strip
Cepheids pulsate
with radius changes
of ~ 5 – 10 %.
Pulsating Variables: The Valve Mechanism
Partial He ionization zone is opaque and
absorbs more energy than necessary to
balance the weight from higher layers.
=> Expansion
Upon expansion,
partial He ionization
zone becomes more
transparent, absorbs
less energy => weight
from higher layers
pushes it back inward.
=> Contraction.
Upon compression, partial He ionization zone
becomes more opaque again, absorbs more
energy than needed for equilibrium => Expansion
Period Changes in Variable Stars
Periods of some Variables are not constant over time
because of stellar evolution.
 Another piece of evidence for stellar evolution.
New Terms
conservation of mass law
conservation of energy
law
stellar model
brown dwarf
zero-age main sequence
(ZAMS)
degenerate matter
triple alpha process
helium flash
open cluster
globular cluster
turnoff point
horizontal branch
variable star
intrinsic variable
Cepheid variable star
RR Lyrae variable star
period–luminosity relation
instability strip
Discussion Questions
1. How do we know that the helium flash occurs if it
cannot be observed? Can we accept an event as real if
we can never observe it?
2. Can you think of ways that chemical differences could
arise in stars in a single star cluster? Consider the
mechanism that triggered their formation.
Quiz Questions
1. Which of the following is NOT considered in making a simple
stellar model?
a. Hydrostatic equilibrium.
b. Energy transport.
c. Magnetic field.
d. Conservation of mass.
e. Conservation of energy.
Quiz Questions
2. According to Figure 12-1, what is the approximate radius of
the Sun's nuclear fusion zone?
a. 0.10 solar radii
b. 0.30 solar radii
c. 0.50 solar radii
d. 0.70 solar radii
e. 0.90 solar radii
Quiz Questions
3. Why is there a lower mass limit of 0.08 solar masses for
main sequence stars?
a. This is an unsolved astronomical mystery.
b. Objects below this mass can only form in HI clouds.
c. Objects below this mass are not hot enough to fuse normal
hydrogen.
d. They form too slowly and hot stars nearby clear the gas and
dust quickly.
e. Our telescopes do not have enough light gathering power to
detect dim objects.
Quiz Questions
4. Why is there an upper mass limit for main sequence stars of
about 100 solar masses?
a. Giant molecular clouds do not contain enough material.
b. General relativity does not allow such massive objects to
exist.
c. The rotation rate is so high that such an object splits into a
pair of stars.
d. Objects above this mass fuse hydrogen too rapidly and
cannot stay together.
e. Objects above this mass do form in molecular clouds;
however, they emit no light and are not considered stars.
Quiz Questions
5. Why are lower main sequence stars more abundant than
upper main sequence stars?
a. More low-mass main sequence stars are formed in
molecular clouds.
b. Lower main sequence stars have much longer lifetimes than
upper main sequence stars.
c. High-mass main sequence stars lose mass and become
lower main sequence stars.
d. Both a and b above.
e. All of the above.
Quiz Questions
6. Why does a star's life expectancy depend on mass?
a. Mass determines the amount of fuel a star has for fusion.
b. More massive stars can fuse hydrogen for a longer time.
c. Mass determines the rate of fuel consumption for a star.
d. Both a and b above.
e. Both a and c above.
Quiz Questions
7. Which of the following observable properties of a main
sequence star is a direct indication of the rate at which energy
is produced inside that star?
a. Surface temperature.
b. Luminosity.
c. Diameter.
d. Distance.
e. Age.
Quiz Questions
8. Why does an expanding giant star become cooler?
a. Less energy is produced in the star's interior.
b. More energy is produced in the star's interior.
c. Thermal energy is converted into gravitational energy.
d. Both a and b above.
e. Both a and c above.
Quiz Questions
9. Of the following, which main sequence star has a longer life
expectancy than the Sun?
a. Spectral type B9.
b. Spectral type K2.
c. Spectral type A7.
d. Spectral type O5.
e. Spectral type F4.
Quiz Questions
10. How does the main sequence lifetime of a star compare to
its entire fusion lifetime?
a. Stars spend about 10% of their fusion lifetimes on the main
sequence.
b. Stars spend about 30% of their fusion lifetimes on the main
sequence.
c. Stars spend about 50% of their fusion lifetimes on the main
sequence.
d. Stars spend about 70% of their fusion lifetimes on the main
sequence.
e. Stars spend about 90% of their fusion lifetimes on the main
sequence.
Quiz Questions
11. Why does an expanding giant star become more luminous?
a. Less energy is produced in the interior.
b. More energy is produced in the interior.
c. Thermal energy is converted into gravitational energy.
d. Both a and b above.
e. Both a and c above.
Quiz Questions
12. What increases the temperature of an inert helium core
inside a giant star?
a. Hydrogen shell fusion.
b. Helium shell fusion.
c. Gravitational contraction.
d. The triple-alpha process.
e. Both a and b above.
Quiz Questions
13. Twice during the late stages of the Sun's life it will move
upward and ascend the giant branch on the H-R diagram.
What will be going on in the Sun's core while it is climbing the
giant branch?
a. The Sun's core will fuse hydrogen to make helium during both
ascents of the giant branch.
b. The Sun's core will fuse helium to make carbon and oxygen
during both ascents of the giant branch.
c. The Sun's core will fuse hydrogen to make helium during the
first ascent, and fuse helium to make carbon and oxygen during
the second ascent of the giant branch.
d. The Sun's core will fuse helium to make carbon and oxygen
during the first ascent, and is inert during the second ascent of the
giant branch.
e. The Sun's core will be inert during both ascents of the giant
branch.
Quiz Questions
14. Why will a helium flash never occur in some stars?
a. Some stars will never leave the main sequence.
b. Some stars do not develop degenerate helium cores.
c. Some stars have a hydrogen flash in place of a helium flash.
d. Some stars contain no helium.
e. All of the above.
Quiz Questions
15. Why are lower-mass stars unable to ignite more massive
nuclear fuels such as carbon?
a. They never get hot enough.
b. They did not accumulate enough carbon when they formed.
c. Beryllium is highly unstable.
d. Carbon has too many neutrons in its nucleus.
e. Both a and d above.
Quiz Questions
16. How do star clusters confirm that stars are evolving?
a. The H-R diagram of a star cluster is missing the upper part
of the main sequence.
b. The H-R diagram of a star cluster is missing the lower part of
the main sequence.
c. The relative motion of stars in a cluster can be estimated by
their Doppler shifts.
d. Pulsating variable stars in globular clusters display a periodluminosity relationship.
e. Star clusters occasionally lose members.
Quiz Questions
17. How are the ages of star clusters related to their turn-off
points?
a. The age of a cluster is the life expectancy of stars at its turnoff point.
b. The higher the turn-off point, the older the star cluster.
c. The lower the turn-off point, the older the star cluster
d. Both a and b above.
e. Both a and c above.
Quiz Questions
18. What is the general trend in the ages of the two types of
star clusters?
a. Globular clusters are young and open clusters are old.
b. Globular clusters are old, and open clusters are both young
and old.
c. All star clusters are very young
d. All star clusters are very old.
e. The two types of star clusters have both very young and very
old members.
Quiz Questions
19. From Figure 12-13, what is the absolute magnitude of a
Type II Cepheid with a period of 30 days?
a. -5
b. -4
c. -3
d. -2
e. -1
Quiz Questions
20. The period of a Cepheid variable star and the time of one
recent maximum can be used to predict the time of a future
maximum. Suppose that you calculate the time of future
maximum brightness and then make measurements to observe
this maximum. After the correction for Earth's orbital position
has been made, you find that the maximum occurred a few
minutes later than predicted. What does this tell you about this
star?
a. The star is moving toward Earth.
b. The star is moving away from Earth.
c. The star is slowly contracting.
d. The star is slowly expanding.
e. The star is not a Cepheid variable.
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
c
b
c
d
d
e
b
c
b
e
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
b
c
e
b
a
a
d
b
d
d
Evolution of Stars
(SLIDESHOW MODE ONLY)