Download HW #8 Stellar Evolution I Solutions

Astronomy Assignment #8: Stellar Nomenclature I
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Complete the assigned problems from the text listed below and address the Instructor Assigned Topic.
Mathematical problems may be hand written. Write out the problem, show your work in solving the problem
and state your answer in a complete sentence. Failure to complete all three of these tasks will result in less
than full credit awarded. The Instructor assigned topic must be typed.
Review Questions
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. 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.
6. 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 H-burning 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.
7. 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).
8. 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)
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What will happen to a hot, blue star (> 10 solar masses) during its entire lifetime?
What will happen to a cool, red star (< 0.5 solar masses) during its entire lifetime?
In which stage is most of a star's mass lost?
How is a planetary nebula formed? What is formed at the center of the planetary nebula? Which main
sequence stars will eventually form planetary nebulae?
5. What happens in a supernova explosion? Which main sequence stars will eventually go supernova?
6. How can you distinguish planetary nebulae and supernovae from each other and from ordinary H II
regions?
7. About how often does a supernova occur in a typical galaxy? Why is it better to look for supernovae in
other galaxies?
8. How does the concept of stellar nucleosynthesis explain where all of the elements on the Earth came
from?
9. Why is iron the limit for stellar nucleosynthesis in red giants? Where did heavier elements than iron
come from?
10. How do cluster H-R diagrams confirm the stellar evolution models?
11. How can you use a cluster's H-R diagram to find the age of the cluster? What can the main sequence
turnoff (MST) tell you?
12. What assumptions are made in the age-dating method of the main sequence turnoff?
13. How do you know that a cluster with a MST of 3 solar masses is younger than a cluster with a MST of
2.8 solar masses and older than a cluster with a MST of 3.2 solar masses?