1) The temperature of the Sun's photosphere is hotter the deeper one looks below the surface, resulting in limb darkening.

a) (8 pts) Explain what causes limb darkening (you may wish to include a diagram, but it is not required). Just saying "limb darkening occurs because the temperature gets hotter the deeper one looks" simply repeats the given information and will get no credit.

b) (6 pts) Suppose instead the temperature of the photosphere were constant throughout. Would we still see limb darkening? Explain.

2) In the constellation Orion, the star Rigel has a surface temperature (12,000 K) about twice as hot as the surface temperature of our Sun (6,000 K).

a) (2 pts) We expect the continuous radiation spectrum of Rigel to peak at (longer, shorter, the same) wavelength relative to our Sun.

b) (12 pts) Justify your answer to part (a).

3) Below is an energy level diagram for an atom of some unknown element, X:

State below (yes or no) which of these energies can be absorbed by this atom of element X with the electron in level 2. No explanations needed.

		E = 1  ________________		E = 6  ________________

		E = 3  ________________		E = 8  ________________

		E = 5  ________________		E = 11  ________________

4) The diagram below represents an observer on Earth viewing an edge-on binary star system. The central star of this system is at rest relative to the Earth. No explanations needed for this problem.

a) (3 pts) At A, companion's light will be (redshifted, blueshifted, unshifted)

b) (3 pts) At B, companion's light will be (redshifted, blueshifted, unshifted)

c) (2 pts) At C, companion's light will be (redshifted, blueshifted, unshifted)

d) (3 pts) If the central star's mass were doubled, how would your answer to (a) change? (more blueshift, less blueshift, no change, more redshift, less redshift).

e) (3 pts) If the central star's mass were doubled, how would your answer to (b) change? (more blueshift, less blueshift, no change, more redshift, less redshift)

5) Star X has only half the mass of our Sun. The radius of star X is about 200,000 miles. The radius of our Sun is about 400,000 miles.

a) (11 pts) How does the density of star X compare to the density of our Sun? Show your work.

b) (3 pts) Given that star X and the Sun have the same temperature and neither has a significant rotation speed, which one will show broader absorption lines? (The Sun, Star X, same line width for both). No explanation needed, just circle one.

6) We know that our Sun generates energy using nuclear fusion in the core rather than other proposed methods, so it is important to understand exactly how fusion works.

a) (8 pts) An alternate theory for the Sun's energy generation stated that the Sun's shrinking caused it to give off heat. State in a sentence why a shrinking Sun would give off heat, then state briefly why this theory was discarded.

b) (6 pts) Nuclear fusion in the core converts mass into energy by combining Hydrogen nuclei (protons) together to form Helium. Why does this nuclear reaction require incredibly high temperatures to occur? Explain.

7) The corona is the outer part of the Sun's atmosphere and can generally be observed easily during total solar eclipses, when the photosphere of the Sun is obscured by the Earth's Moon.

a) (7 pts) Explain how emission line widths show the temperature of the corona increases the further one looks from the surface of the Sun. As part of your answer, explain why line widths are related to temperature.

b) (7 pts) Although temperatures in the corona are often greater than temperatures in the Sun's core. No fusion occurs there. Explain why. As part of your answer, explain why this "missing property" of the corona is so important for fusion.

8) Suppose we construct a catalog of about 1,000 stars. In this catalog, we include only stars that have parallax angles that are large enough to be measured. Will this catalog be a representative sample of the stars in the Milky Way galaxy? Explain your answer.