Astronomy Assignment #9: Stellar Evolution I Solutions
Review Questions from the first half of Chapter 13: Lives and Deaths of Stars
1. What fundamental property of stars determines their evolution?
Mass is the fundamental property of stars that determines their evolution because mass sets the central pressure,
temperature and density that controls the fusion rates and fusion rates determine luminosity, and lifetime.
2. Why do massive stars last for a short time as main sequence stars but low-mass stars last a long time in the main
sequence stage?
Massive stars last for a short time as main sequence stars because their higher central pressures, temperatures
and densities establish a higher fusion rate in their cores. The higher fusion rates (i.e. luminosities) burn
through the core hydrogen faster; thus shortening the high mass star’s lifetime. Low-mass stars last a long time
in the main sequence stage because their lower central pressures, temperatures and densities establish a lower
fusion rate in their cores. The lower fusion rates (i.e. luminosities) burn through the core hydrogen slower; thus
extending the low mass star’s lifetime.
3. How can you detect protostars if the surrounding gas and dust blocks visible light?
Protostars emit mostly IR thermal radiation as they generate energy by converting gravitational potential energy
into heat during collapse. The IR thermal radiation can pass through significant amounts of dust without
attenuation. Thus, the dust is transparent to IR radiation and we can “see” the stars within or behind the dust
clouds in the IR.
4. How do T-Tauri stars get rid of the surrounding gas and dust from which they formed?
T-Tauri stars are a class of very young (not quite main sequence) protostars that exhibit a very strong stellar
wind that is believed to be an effect of the young star’s magnetic field. The effect is to propel material away from
the star’s photosphere at speeds up to 100 km/s. It is this strong stellar wind the sweeps away the surrounding
gas and dust from which the star formed.
5. Define an OB Association and an HII region and describe the relationship between them.
An OB Association is a small group (10’s to 100’s)
of newly formed O and B main sequence stars.
These are the first types of stars to form from a
collapsing Giant Molecular Cloud (GMC). If the
process of star formation was like a train emerging
from a tunnel in a mountain, then the OB
Association would be the engine while the cooler
spectral types would be the cars behind the engine
with the main sequence M stars being the caboose.
The GMC would be the mountain that the stars are
emerging from.
OB Association
HII Region
An HII region is a large cloud of ionized
hydrogen gas (i.e. one electron is removed). As
HII Region
Rosette Nebula is a fine example of an OB Association and an associated HII Region
the freed electron recombines with the hydrogen nucleus it emits a characteristic red light as it cascades through
the energy levels to the ground state. High energy is required to ionize the hydrogen and this energy is supplied
by the newly formed OB Association stars that emit most of their energy as high-energy short-wavelength hardUV photons. The photons from the OB Association stars “power up” the HII region and keep it fluorescing.
Thus the OB Association forms first and then the HII region is created around the vicinity of the OB Association.
6. What is happening in the core of a main sequence star and why is it so stable?
In the core of a main sequence stars core h-burning is happening…that is the fusion of hydrogen into helium
through the p-p chain in the core. The main sequence stars are so stable, only very slowly changing their
luminosity, radius and temperature while on the main sequence, because of the natural thermostat mechanism in
main sequence stars. The thermostat mechanism acts to return the core fusion rates back to an equilibrium rate
in the event of fluctuations in the core fusion rate. This is known as a negative feedback cycle. For example, if
core fusion rates momentarily increase, then the excess energy generated will increase the temperature of the
core and cause the core to expand slightly. The resulting expansion then acts to reduce core fusion rates because
of a drop in core density that lowers the chances of the nuclear collisions needed to maintain the fusion rate.
Thus a small departure from the equilibrium fusion rate results in tiny changes in the cores physical
characteristics that act to restore the equilibrium fusion rate.
7. What happens to a main sequence star that has stopped fusing hydrogen in its core?
When a main sequence stars has stopped fusing hydrogen in this core then the balance maintained by hydrostatic
equilibrium between the outward thermal pressure from the core and the inward gravitational pressure from the
envelope cannot be maintained. The unbalanced gravitational pressure causes the core of the star to collapse
and heat. However, even though no hydrogen fusion is possible in the collapsing core (since there is no
hydrogen in the core anymore, it being all converted into helium) a thin shell of hydrogen in a shell around the
collapsing core is pushed deeper into the star as the core collapses and can now fuse for the first time. Shell Hburning begins. The shell H-burning releases gamma rays that do not have to thermalize out of the core so they
hit the envelope with more energy that core gamma rays would and, in effect, cause the envelope to swell to many
times its previous radius. Thus when a main sequence star that has stopped fusing hydrogen in its core, energy
production shifts to a shell around the collapsing core and causes the star to become a giant star.
8. What is the “Faint Young Sun” paradox? How has it been resolved?
Wikipedia states that “The faint young Sun paradox or problem describes the apparent contradiction between
observations of liquid water early in Earth's history and the astrophysical expectation that the Sun's output would
be only 70 percent as intense during that epoch as it is during the modern epoch. The issue was raised by
astronomers Carl Sagan and George Mullen in 1972. Explanations of this paradox have taken into account
greenhouse effects, astrophysical influences, or a combination of the two.”
So the paradox is that the Sun was 30% less luminous early in the Earth’s history about 4 billion years ago and
that is expected to lower the temperature of the Earth to below the freezing point of water so that liquid water
(i.e. oceans) could not exist on the Earth at that time. However, there is clear evidence that oceans did exist on
the Earth even 4 billion years ago. The geologic formations known as banded iron formations are rocks that
were formed under seawater at least 3.8 billion years ago.
The paradox has been resolved by postulating that the carbon dioxide content of the Earth’s atmosphere was
much higher early in the Earth’s history compared to know. The higher CO2 concentration would have led to an
increased greenhouse effect that could have kept the oceans liquid in spite of the lower energy flux from the Sun.
9. How do astronomers know the mass of stars?
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Astronomers can determine the mass of stars by analyzing the orbits of binary stars. If an astronomer observes a
binary star’s orbital period P and orbital radius R, then the combined mass of the binary system is given by the
R3
relation m1  m2  2 where the combined mass is expressed in solar masses if R is in AU and P in years.
P
If the combined masses of very many binary star systems are known, then, by suitable combinations, subtractions
and other algebraic techniques, the masses of individual spectral types can be determined.
10. What are the types of binary stars and how are they different from each other?
Type of
Binary Star
Description
Optical
Double or
Apparent
Binary Star
Two stars that appear next
to each other in the sky but,
in fact, are a vastly different
distances from each other
and are not really
physically associated with
each other. They are not
true binary stars.
True Visual
Binary Star
Two stars that are
physically bound to orbit
each other. A visual binary
star is a binary star for
which the angular
separation between the two
components is great enough
to permit them to be
observed as a double star in
a telescope, or even highpowered binoculars.
Spectroscopic
Binary Star
Eclipsing
Binary Star
Spectroscopic binary star
systems are a true binary
system but the stars are so
close together that they
appear as one star even
through a telescope.
These true binary stars have
their orbital plane aligned
with the Earth so that one
star appears to pass in front
of and then the other star.
Comments
Alpha Capricorni (α Cap, α Capricorni) is an optical double
star in the constellation Capricornus. It has the traditional
names Algiedi, Al Giedi, Algedi or Giedi; however, Giedi is
sometimes also associated with β Capricorni.
The two unassociated star systems in the optical double are:
 α¹ Capricorni, also called Prima Giedi at 690 ly
 α² Capricorni, also called Secunda Giedi at 109 ly
They are separated by 0.11° on the sky, and resolvable with
the naked eye, similar to Mizar and Alcor.
61 Cygni is a binary star system in the constellation
Cygnus, consisting of a pair of K-type dwarf stars that
orbit each other in a period of about 659 years. Of
apparent magnitude 5.20 and 6.05 respectively, they
can be seen with binoculars in city skies or with the
naked eye in rural areas without light pollution. In
1838, Friedrich Wilhelm Bessel measured its distance
from Earth at about 10.3 light years, very close to the
actual value of about 11.4 light years; this was the
first distance estimate for any star other than the Sun,
and first star to have its stellar parallax measured.
A typical spectroscopic binary star will have a separation of
about 1.0AU and an orbital period of less than 2 years. (from
Pedoussaut+ 1989) and an average combined mass of 2 solar
masses.
The diameter of each star can be deduced from the light curve of
the eclipsing pair.
11. Three binary star systems are listed below. What are the masses of each of the six stars? Show your work.
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Binary
Star
System
A
B
C
Spectral Types
Orbital Period,
yrs
G2V & K0V
K0V & K5V
M2III & K5V
80
88.3
10,180
Orbital Semimajor axis,
AU
24
23
650
a3
in
P2
Solar mass units
2.16
1.56
2.65
Combined mass =
a. We know that a G2V star (identical to the Sun) has a mass of 1 solar mass. Therefore the mass of the
KOV star in star system A must be 1.16 solar masses.
b. Now that we know the mass of a KOV star is 1.16 solar masses, the mass of the K5V star in star
system B must be 0.4 solar masses.
c. Now that we know the mass of a K5V star is 0.4 solar masses, the mass of the M2III star in star
system C must be 2.25 solar masses.
12. What happens to a main sequence star that has stopped fusing hydrogen in its core?
When a star stops fusing hydrogen in its core several things happen. First the star leaves the main sequence.
The core of the star collapses because it can no longer support the weight of the envelope. As the core collapses
a thin shell of hydrogen around the collapsing core is dragged deeper into the star and is under greater pressure
so the hydrogen in the shell is heated and its density increases so that the p-p chain can begin in this thin shell –
Shell H-burning begins. With the initiation of shell H-burning, the gamma rays from the p-p chain in the shell hit
the envelope with more energy than when core H-burning was occurring (because these shell gamma rays do
not have to “thermalize” out of the core) and the shell gamma rays deposit more energy into the star’s e3nvelope
causing it to swell in radius and become a giant star. Whenever energy production in a star occurs in a shell, the
star will swell in radius. Eventually, the core collapses sufficiently for the temperature and density to increase to
where core He-burning begins through the triple alpha process. The core stops collapsing. It supports the
envelope through hydrostatic equilibrium again. Shell H-burning ceases and the envelope shrinks slightly. The
star is now a horizontal branch star.
13. Are all red giants or supergiants very massive stars? Why are red giants so big and red? What is going on inside
the giants?
All red giants or supergiants are NOT very massive stars. In fact, our own Sun will become a red giant and a red
supergiant as it evolves through its final sequence of energy production mechanisms. Giant stars are not
necessarily giants in mass, but are giants in radius. Inside all giant stars energy is being produced in shells and
it is the shell gamma rays that inflate the envelope of the stars. The inflated envelope cools more efficiently due
to its lower density and thus appears redder in color (corresponding to the cooler temperatures).
14. If Giant stars are numerically so rare in the galaxy due to their short lifetimes, how is that over half the bright
stars in the night sky are giant stars?
Giant stars are indeed very rare. The figure to the right displays the
frequency of stellar types in a typical million cubic parsec cube of space.
Giants and Super Giants are so rare that they do not even warrant a
vertical bar to display their abundance. The most common stellar types, as
you can clearly see in the figure, are main sequence M stars (a.k.a Red
dwarfs).
Recall that even though the red dwarfs are the most common stars and they
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are the closest stars to the Sun, they are mostly invisible due to their exceedingly low luminosity. Invisible, even
though they are right next door.
The giant and super giant stars are just the opposite in that they have exceedingly high luminosities that allow
them to be seen to very great distances. So even though these stars are numerically rare, they are so luminous
that we can see them to great distances so much so that our night sky appears to be dominated by these rare
distant giant stars.
Another way of expressing why our night sky appears to contain mostly giant and super giant stars is that when
we look at giant stars we are samp0ling a much greater volume of space. A super giant star with an absolute
magnitude of -5 would be visible to the naked eye even if it were 1,000 parsecs (3,326 ly) distant, whereas Red
dwarf stars with an absolute magnitude of +12 would be invisible to the naked eye if they were beyond 1 parsec
from the Sun.
15. What is the evolution sequence for stars around the mass of our Sun? How long is the Sun's main sequence
lifetime?
The evolution sequence for stars around the mass of our Sun is a follows; GMC, Bok Globule, Protostar, Main
Sequence Star, Red Giant, Horizontal Branch Star, Red Super Giant, Planetary Nebula, White Dwarf Stellar
Remnant. The Sun’s main sequence lifetime is about 10 Billion years (10×109 years)
16. What are the mechanisms of energy production that the Sun will utilize over its lifetime? What stage of stellar
evolution is associated with each (e.g. core H-burning occurs in Main Sequence Stars)?
Stage of stellar evolution
Proto-Star
Main Sequence Star
Red Giant
Horizontal Branch Star
Red Super Giant
Planetary Nebula
White Dwarf Stellar Remnant
Mechanism of energy production
Conversion of gravitational potential
energy into thermal energy
Core H-burning
Shell H-burning
Core He-burning
Shell He-burning in Helium Flashes
None
None
17. What is a planetary nebula? What are its typical dimensions and lifetime?
A planetary nebula is the ejected envelope of a star of mass less than 9 solar masses that is excited to
luminescence by the high energy photons radiated from the exposed very hot – but very dead – carbon core of the
star. The planetary nebula may have a very symmetrical spherical shape or may be exhibit a bipolar symmetry
(usually attributed to planetary nebula forming in a tight binary system) or a completely chaotic morphology.
See examples below. Planetary nebulae are typically 1 light year in diameter and remain visible for about
10,000 years. The formation of a planetary nebula signals the death of these lower mass stars.
M57 Ring Nebula Planetary Nebula
Butterfly Planetary Nebula
Planetary Nebula NGC 2440
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18. What is a white dwarf stellar remnant? What is its typical dimensions, temperature and lifetime?
A white dwarf stellar remnant is the “tombstone” of a former stars whose mass was less than 9 solar masses.
The white dwarf stellar remnant is the dead core of the star after it has shed its envelope via a planetary nebula
and has a radius of about the same as the Earth, about 0.1 solar radii, a mass of less than 1.4 solar masses and a
very high temperature, equivalent to B & A stars. In spite of the high temperature of the white dwarf stellar
remnant, it produces no new energy but simply radiates the heat it has stored in its interior. Since white dwarfs
have such small surface area they require very long time to cool off – perhaps longer than the Universe is old.
19. What are Type II Supernova? What types of stars experience a Type II Supernova?
A Type II Supernova is the explosive destruction of a main sequence star with mass greater than 9 solar masses
that occurs at the end of the stars lifetime. The stars that supernova are principally O and B main sequence
stars that have evolved off the main sequence to a supergiant phase and then catastrophically explode as a Type
II Supernova.
20. What is the interior of a star like just before the Type II Supernova?
Just before a Type II supernova the interior of the star has an iron core surrounded by many layers of shell
fusion. The deep interior of the star resembles and onion-layer structure with different elements fusing in
different shells each interior shell fusing the “ashes” of the fusion in the next shell outward. The iron core cannot
fuse and produce energy, so it is the “last stop” in the fusion cycle of stars.
21. Why are Type II Supernovas important for the chemical evolution of the Universe?
During the Type II Supernova (i.e. the explosive death of a star with mass greater than about 9 solar masses –
mostly O & B main sequence stars), during the approximate hour it takes for the shock wave created by the
combined effects of the sudden burst of neutrinos when the iron core turned into neutrons and the core rebound
when the collapsing core reaches nuclear density and stiffens, during that hour fusion occurs in the exploding
envelope where fusion never before occurred. Every element in the Periodic Table of Elements is created in the
fusing envelope. These brand new heavy elements (heavier than hydrogen and helium) are then dispersed into
the interstellar medium to chemically enrich the next round of star formation.
Since planets form from the debris left over after star formation, newer planets will have a richer and more
diverse reservoir of chemical elements to form from. Without supernovas, the chemical composition of the
Universe would remain almost solely hydrogen and helium making life impossible anywhere in the Universe.
22. What do astronomers use Type II Supernova’s for?
Type II Supernova’s are useful as standard candles to astronomers. A standard candle is any astronomical
object whose luminosity is known “a priori” (i.e. ahead of time). Once a standard candle is observed in the sky,
its distance can be determined by comparing its apparent and absolute magnitudes (M is known ahead of time for
standard candles). Thus, standard candles are used to determine distances. Type II Supernova’s are especially
useful standard candles because they are of uniform peak luminosity and that peak luminosity is VERY luminous.
The peak luminosity of a Type II supernova corresponds to an absolute magnitude of -17! Thus these supernova
and be seen when they are very far away – even to the horizon of the Universe - and they can tell astronomers
much about the very distant and early universe.
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Instructor Assigned Topic
Complete an evolutionary track for the Sun on the blank HR diagram attached using the data in the table attached.
Label each section of the sun’s post-main sequence evolutionary track with the sun’s current method of energy
production as well as the name of the phase at the endpoint of each segment.
Post-Main Sequence Evolution of the Sun
Stage
Energy
Production
Method
Main
Sequence
Core
Hydrogen
Burning
Red Giant
Shell
Hydrogen
Burning
Horizontal
Branch
Core
Helium
Burning
Red Super
Giant
Shell
Helium
Burning
Planetary
Nebula
None
3,000 K
White
Dwarf
None
50,000 K
Spectral
Type
M
G2
+4.8
(1 L)
M3
-3.6
(2,350
L)
K1
0
(100 L)
M3
-3.9
(3,000
L)
Surface
Temperature
Radius
in Solar
Radii
Core
Temperature
Lifetime
15 Million K
10
Billion
Years
166
50 Million K
100
Million
Years
5,000 K
10
200 Million
K
50
Million
Years
3,000 K
180
250 Million
K
10,000
years
300 Million
K
Short
100 Million
K
Very
Long
5,800 K
3,500 K
1
0.01
7
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