1) Even though most stars have very similar abundances of Hydrogen, the absorption line strengths of Hydrogen can differ from star to star depending upon the surface temperature.

a) (6 pts) Explain why very cool stars tend to have very few Hydrogen absorption lines.

b) (6 pts) Explain why very hot stars tend to have very few Hydrogen absorption lines.

2) Star A and star B have identical surface temperatures and compositions, and neither star has a significant rotation speed. The absorption lines from star A, however, are much broader than the absorption lines from star B.

a) (3 pts) Which star is probably larger in size? (A, B, same size, can't determine)

b) (9 pts) Explain your answer to part (a).

3) Two interstellar clouds (X and Y) are located at identical distances from us, but we know from emission line spectra that cloud X is much warmer than cloud Y. Assume for this question that stars are distributed uniformly across the sky.

a) (3 pts) In the direction of which cloud are you probably going to be able to observe a higher density of stars on the sky? (X or Y)

b) (9 pts) Explain your answer to part A.

4) Below are the light curves for two eclipsing binary systems:

a) (6 pts) Which system's companion star has a larger orbital distance? (left, right) Justify your answer.

b) (6 pts) Which system's parent star is more massive? Justify your answer (either mathematically or in words).

5) In a face-on binary system, we can easily measure the angular separation between the binary pair. From parallax measurements, we also know the distance from the Earth to the system. Assuming the companion star orbit is circular...

a) (5 pts) Is it possible to measure the orbital velocity of this system directly via Doppler shifting? Explain.

b) (7 pts) Explain how we could find the orbital distance of the companion star from the central star. A diagram may help but is not required.

6) We estimate the main-sequence lifetime of the star Alpha Centauri to be about 12 billion years. The star Procyon has a mass of about twice the mass of Alpha Centauri. The lifetime of a star depends inversely on its mass squared.

a) (6 pts) What is your estimate of the main sequence lifetime of Procyon? Show your work.

b) (6 pts) Explain (with words or equations) why the mass of a star has anything to do with that star's lifetime.

7) Imagine a spherical volume of space with a radius of about 200 parsecs (the maximum distance out to which we can make reliable parallax-based distance estimates) centered on the Sun. Explain why this volume of space will contain more low mass stars (masses < 1 solar mass) than high mass stars (masses > 1 solar mass).

8) The nucleus of Hydrogen consists of simply one proton. An isotope of Hydrogen called "Deuterium" has a nucleus containing one proton and one neutron (so the nucleus has the same charge as Hydrogen but twice the mass).

Suppose you want to try to fuse Deuterium, but you want to maintain the same density as the gas in which Hydrogen fusion has successfully occured. Explain how and why (just one reason) the temperature in the Deuterium gas will need to be different in order for fusion to occur.

9) At the end of the Hydrogen burning phase (the main sequence) part of a solar-mass star's lifetime, several changes occur in the star.

a) (6 pts) Use hydrostatic equilibrium to explain why the star shrinks when Hydrogen fusion ceases in the core.

b) (6 pts) After Helium fusion begins, the star expands and its surface appears red. Explain this red color.

10) We know that the absolute luminosity of a star can be written as follows:

Our own Sun has a temperature of 6000 K.

a) (6 pts) The star Aldebaran has a surface temperature of 3000 K and a radius four times as large as the Sun's. How does the absolute luminosity of Aldebaran compare to that of the Sun? Show work and state your answer as a sentence (e.g. "Aldebaran is 3 times more luminous.")

b) (6 pts) The star Canopus has a mass of 4 solar masses, and a radius half as large as the Sun. How does the density of Canopus compare to that of the Sun? Show your work and state your answer as a sentence.