Download Astronomy 328 Midterm Exam - Department of Physics and Astronomy

Astronomy 328 Midterm Exam #1
16 October 2007
Exam rules: You may consult your sheet of formulas during the exam. This sheet can
contain any formulas or values for constants that you think you need but it cannot contain
worked out problems or concepts. You must turn in your formula sheet with the exam.
Calculators are permitted. Good luck.
Note:
 The number of points for each part of each problem is indicated. . Don't spend
half the allotted time for a question on a section only worth 10% of the marks.

Work first on the problems you find easiest, and come back to harder or less
familiar material later. Don’t get stuck.

Please write out complete solutions, with all steps filled in to allow me to give
you credit even if you get the final answer incorrect. For conceptual questions,
please write out a complete explanation, several sentences long so I understand
your reasoning.

Check the plausibility of your answers. Are the numbers sensible? Have you
converted units correctly? Is the equation dimensionally correct? Even if you
don't have time to re-work a question, at least write down that you recognize there
is a problem, so you can obtain some credit.

The amount of space left for each problem is not necessarily an indication of the
amount of writing it takes to solve it.
Name: ________________________
1. Stellar Structure and Hydrostatic Equilibrium
Suppose the density of a star is given by
 0

2
  r0 
 (r )   0  
 r
 0

r  r0
r0  r  R
Rr
(a) Find an expression for M(r). (10 pts)
(b) If the mass of the star is 1 M and R=R and r0=0.1R , what is the value of 0?
(5 pts)
(c) Find expressions for the pressure distribution, P(r) assuming hydrostatic
equilibrium. (15 pts)
2.
Binary Star Systems
The Hlines (=656.3 nm) from two stars in a binary system are observed to have
Doppler shifts of 0.022 and 0.044 nm, respectively. The period of the system is 20yr.
The eclipse minima are flat bottomed and 200 days long. It takes 10 hours from first
contact to reach the eclipse minimum.
a) What are the radial velocities of the two stars? (4 pts)
b) What is the orbital inclination? (2 pts)
c) What are the orbital radii of the two stars? (4 pts.)
d) What are the masses of the two stars? (10 pts)
e) What are the radii of the two stars? (10 pts)
3. Stellar Structure and Evolution
a) Here are a few questions to test your general understanding of stellar structure and
evolution
i)
Explain briefly why fusion rates are a strong function of temperature. Why is
higher temperature required for fusion of heavier nuclei? (3 pts)
ii)
Once a star’s core is composed entirely of iron, it can no longer replenish its
energy losses (from radiating) through fusion. Explain why this is the case. (3
pts)
iii)
Why is hydrogen left in a shell around the core after it has been used in the
core? (3 pts)
iv)
At a given density, for equal numbers of electrons and neutrons, electrons will
exert a greater degeneracy pressure. Explain why this is the case. Why then
are the more massive stars (neutron stars) supported by neutron degeneracy
pressure? (3 pts)
v)
Explain the physical reason why there is a limit to the mass of a white dwarf –
i.e., a star that is supported by electron degeneracy pressure (3 pts)
vi)
In the core of a white dwarf, nuclear fusion is no longer taking place. This
means that the white dwarf will radiate away its energy and cool with time.
Explain why this will not affect the radius of the star (3 pts)
b) Estimate the energy available and the lifetime for the helium burning phase in a 1
M star:
i.
 12C in the triple alpha
Calculate the energy released per net reaction 3 4 He 
process (Note: The atomic weight of 4He is 4.0026, and the weight of 12C is
12.0000) (5 pts)
ii.
If 10% of the original mass of the star is in the form of 4He in the stellar core
during the helium burning phase, estimate the total energy available from the
triple alpha process. (5 pts)
iii.
During the helium-core-burning phase, some hydrogen burning is also occurring
in a shell. Thus the star’s luminosity is not due to helium burning alone. Keeping
this in mind, assume that the typical luminosity from helium burning is 102 L .
Estimate the lifetime of the helium-core-burning phase. (5 pts)