Most Problems are from An Introduction to Stellar Astrophysics

HOMEWORK ASSIGNMENTS

**1. From CH.1::** Problems 1.4, 1.5, 1.7, 1.12, 1.13

**Problem 6:**
Examine Vega and Arcturus by eye. Note their colors. Estimate the surface temperatures of those two stars, based on their colors and use of the Wien Law.

**2. Due Sept. 17, From CH.2::** Problems 2.1, 2.3, 2.6, 2.8

**Problem 5:**
Suppose you squeeze the Sun by 1%. Keep T the same during the compression, but the density goes up of course. Estimate within a factor of 2 the period, P, of oscillation of the Sun as it rebounds, overshoots, and falls back, and overshoots again.

**Problem 6:**
Due Sept. 24.
Consider a box, 1m x 1m x 1m, at T = 5870K (=Teff of the Sun), containing both 10^20 H atoms and
Fe atoms in their relative cosmic abundance (see appendix E).

Determine n_e, and the ratio of the ionized to neutral numbers of H and Fe. Also determine the total pressure, P.

Adopt these partition functions: U(H) = 2, U(H+)=1, U(Fe) = 10^1.9, U(Fe+) = 10^1.9 (same). For ionization energies see Appendix D. Hint: Start with an assumption for ne (1/2 N(H)?). Write code to iterate.

If you've never written code, see www.learnpython.org
Download python from www.enthought.com/products/canopy/academic

**3. Due Sept. 24, From CH.3::** Problems 3.2, 3.4, 3.5, 3.7

For 3.2, the problem statement should say, S(tau) = a + b*tau^2 . (Be sure tau is squared.)

For 3.4, use tau = 2/3.

**Problem 5:**
At noon, the sun is overhead (at zenith) and 1% of the ultraviolet UV(B) photons reach the ground, to give you a great tan (and skin cancer).
At 3pm, the Sun is 45 deg from zenith. What fraction of the UVB photons reach the ground?

**3. Due October 1, From CH.3::** Problems 3.8, 3.9 and Extra problem handed out in class.

Hint: For 3.8, define x = I - S.

Hint: For 3.9: substitute: u = cos(theta) and use the solution to the eqn. of transfer.

Extra Problem:
A star of mass, M* and radius, R*, has a density profile:

rho(r) = rho_0 * (1 - r/R*)

where rho_0 is given. Assuming that the opacity is independent of frequency, find an expression for the frequency at which a distant observer would record a peak in energy flux from this star. You may treat the gas inside the star as ideal, and assume the gas is composed of pure atomic hydrogen gas. This is a rather involved problem. Here are a few hints to help you along. In no particular order: Hint 1: The part of the sun that an observer sees is at the radius such that a photon is more likely to make it out of the star than to be scattered or absorbed. Think about what this would correspond to in terms of optical depth.

Hint 2: Use the ideal gas law to find the temperature as a function of R. You might need to rewrite it in terms of the variables you have.

Hint 3: Use the hydrostatic equilibrium equation to find P(R), you may assume g is constant.

Hint 4: Factor the numerator of the T(R) expression that you get in order to save yourself from having a huge algebraic mess later.

Hint 5: Ask Jesse for help in Discussion Section, Office Hours, or by email.

Jesse Nims: jwnims@berkeley.edu

**4. Due October 15, From CH.4::** Problems 4.3, 4.7, 4.8, 4.11, 4.12, Separate problem: read two papers by Allard et al. on brown dwarfs.

**5. Due October 22, From CH.4::** Problems 4.5, 4.6, and handout: prob_ch4.ps.

**6. Due October 29, From CH.5:** Problems 5.3, 5.4, 5.7 (must read about conduction), 5.10,

Extra Problem:

Write the four eqns of stellar structure as "difference equations", assuming a grid of points labelled i = 1, 2, 3, ... N_pts. Include both radiative and convective trasnport.

Example: dM/dr = M_(i+1) - M_(i) / (r(i+1) - r(i))

**7. Due November 19
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**8. Due November 26, From CH.6::** Problems 6.2, 6.5, 6.7

**9. Due December 5, From CH.6::** Problem 6.16 - Hint:You may want to use eqns 6.111 and 6.113 at equilibrium.
Assume that the helium abundance is solar and the 3He is present in trace amounts.

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