Homework assignment 5

Please show all your work, written as neatly as possible. Hand in your papers to me directly or place them into the plastic mail folder outside my office door, anytime up to and including the class meeting on Friday, Feb 13.

This week's problems deal with stellar atmospheres.

Carroll and Ostlie, Prob 8.6
Consider a gas of neutral hydrogen atoms.
1. At what temperature will equal numbers of atoms have electrons in the ground state (n=1) and n=3 state?
2. At a temperature of 85,400 K, when an equal number, N, of atoms have electrons in n=1 and n=2, how many atoms are in the n=3 state? Express answer in terms of N.
3. As temperature goes to infinity, how will electrons in H atoms be distributed according to Boltzmann equation? Will this be ACTUAL distribution? Explain.
Carroll and Ostlie, Prob 8.7
I said in class that at T=10,000 K, "nearly all of the HI atoms are in the ground state, so that the partition function simplifies to Z_I = g1 = 2(1)^2 = 2." Check this statement by evaluating the first three terms in equation 8.5 for the partition function.
Carroll and Ostlie, Prob 8.11
Follow the procedure described in problem 8.10 to find the temperature at the middle of the He II partial ionization zone, where half the He II atoms have been ionized. This zone occurs deep inside most stars, so the electron pressure is larger than we used in class: use P_e = 10,000 dyne/cm^2. Examine temperatures in the range T = 10,000 to 60,000 K. This zone is especially important in certain pulsing stars....
Carroll and Ostlie, Prob. 8.14
A giant star and a dwarf star of the SAME spectral type do not have exactly the same temperature (look very closely at the first figure in the luminosity class lecture). Because it has a lower atmospheric density, the giant star will have a slightly lower temperature than a main-sequence star with the same spectral type. Use the Saha equation to explain this.
This difference in temperature at the same spectral class has been known for quite some time. Take a look at this paper by Adams and Russell , published in 1928. On page 25, you can see a table showing different temperatures for stars of similar spectral class, and a comment by the authors about this "well-known difference."
Make a table which provides for each of the seven stars in the Big Dipper (you may ignore Alcor),
1. the apparent V magnitude (look this up)
2. the spectral type (look this up)
3. a "spectroscopic parallax" distance -- which you must calculate yourself. Please write explicitly your assumed values for absolute magnitude
4. a true parallax distance, if you can find one, together with uncertainties
5. a comment -- does the spectroscopic distance agree with the trigonometric distance?
You will probably find SIMBAD to be very handy...