Due: Friday, March 8
STAPLE your homework.
At the top, include your name, GSI's name, and Section # and time.
For each math-based question, please show your calculations (equations
used, values put into the equations, unit conversions, final answer, etc.).
Please put a box or circle around your final answer (if the answer is a
number).
Chapter 16: "STAR STUFF"
1a. What is degeneracy pressure (as in electron degeneracy pressure
or neutron degeneracy pressure)?
Degeneracy pressure is when the electrons (or neutrons) are so closely
packed together that they cannot get any closer, due to the exclusion principle.
1b. List the events or stages in a stars evolution in which degeneracy
pressure plays a role. Some or all of the following objects might
be on your list:
white dwarf;
neutron star;
helium flash;
brown dwarf;
a star on the main sequence;
a 2 solar mass, double shell burning, red giant star.
brown dwarf
helium flash
a 2 M_Sun, double shell burning, red giant star
white dwarf
neutron star
1c. For the events/stages on your list, describe the kind of
degeneracy pressure at issue and the relevance of degeneracy pressure for
this event/stage. (1-2 SPECIFIC sentences per item.)
brown dwarf - Electron degeneracy halts the gravitational contraction
of a brown dwarf before it gets hot enough for hydrogen fusion to occur.
A brown dwarf never gets hot enough for fusion reactions to occur.
helium flash - When the inert helium core is supported by electron
degeneracy pressure, and helium fusion occurs, the rate of helium fusion
increases rapidly because the temperature of the core is increasing, but
the core is not expanding. A helium flash is the result of this quick
release of energy.
2 M_Sun, double shell burning, red giant star - the two burning
shells are a hydrogen burning, and underneath, a helium-burning shell.
The core is inert carbon, and is supported by electron degeneracy.
The degeneracy pressure will halt its gravitational collapse before it
gets hot enough to being fusing carbon.
white dwarf - White dwarfs are the remaining cores of dying stars,
and are supported against gravitational collapse by electron degeneracy.
neutron star - A supernova leaves behind a dense ball of neutrons,
supported by neutron degeneracy.
1d. For the events/stages listed in 1b where degeneracy pressure
is not relevant, describe what kind of pressure is counter-acting gravity
in this case.
A star on the main sequence is supported by thermal pressure.
1e. Explain in general terms why degeneracy pressure can support
a stellar core against gravity even when the core becomes very cold.
(If you did not attend lecture, Chapter S4 contains a discussion of the
physics of degeneracy pressure.)
Unlike thermal pressure, which increases with temperature, degeneracy
pressure does not depend on temperature. No matter the temperature,
the electrons will be in the excited energy states because they cannot all
occupy ground states. The movement of the electrons in the excited states
exerts a pressure.
2a. Explain what happens to the core of a star when it exhausts
its hydrogen supply?
I'm looking for a 4-sentence
answer stating what happens to the following and why:
fusion rate in core, source,
core temperature, core pressure, core radius
When a star exhausts its hydrogen in the core, the core begins to
shrink because it is no longer supported by thermal pressure.
As it contracts, core temperature increases due to the release of
gravitational energy.
There
is no fusion occuring in the core at this moment. The core contraction
continues until it reaches electron degeneracy, and electron degeneracy
pressure is then supporting the core.
2b. Why does hydrogen shell burning begin around the inert core?
Again, I want a very short
answer stating what has happened to the following and why:
pressure and temperature
outside the core, fusion rate
As the core contracts, it releases gravitational energy that heats
up the shell to the point where hydrogen burning begins in the shell.
Because of the high temperatures, the thermal pressure increases, causing
the expansion of the envelope of the star. The fusion rate also increases
with temperature.
3. Consider the following objects:
10 solar mass star
flare star
carbon star
1.5 solar mass red giant
star
1 solar mass horizontal
branch star
red super giant.
a.) Write down the
luminosity & radius of these objects (be accurate to a factor of 10
or so).
10 M_Sun star: Luminosity = 10^5 L_Sun, Radius = 10 R_Sun
flare star: Lum = 10^-3 L_Sun, Radius = 0.1 R_Sun
carbon star: Lum = 10^4 L_Sun, Radius = 100 R_Sun
1.5 M_Sun red giant star: Lum = 10^4 L_Sun, Radius = 100 R_Sun
1 M_Sun horizontal branch star: 10^2 L_Sun, Radius = 10 R_Sun
red supergiant: Lum = 10^5 L_Sun, Radius = 1000 R_Sun
b.) Write down one
sentence describing how the star would look if you were orbiting the star
at 10 AU.
10 M_Sun star: It would look extremely bright and very whitish-bluish.
flare star: It would look very dim and very red, and you would see
the flares.
carbon star: It would look very bright and very red.
1.5 M_Sun red giant star: It would look very bright and very
red
1 M_Sun horizontal branch star: It would look bright and reddish-yellowish.
red supergiant: It would look extremely bright and very red.
c.) Do you think any
of these stars would have planetary systems which
support advanced life?
Probably not. A 10 M_Sun mass would
not have had time for advanced life to develop on a planetary system.
A flare star emits too many X-rays for advanced life to survive.
The other stars are all in later stages of evolution, when the star has
had large increases in luminosity and radius within a relatively short
time. Of course, never doubt the ingenuity of an extremely advanced
life form!