1) A common emission line seen in interstellar nebulae corresponds to a particular electron transition in singly-ionized Oxygen (also called O II). Because this transition is extremely unlikely to occur at any given time, this kind of emission line is often referred to by astronomers as a "forbidden line".

a) (3 pts) Forbidden lines are more likely to be seen in regions of (higher density, lower density, either kind of density...density isnšt relevant to this problem).

b) (8 pts) Explain your answer to part (a).

2) In some binary star systems, the two stars are so close together than one of them will actually transfer its mass to the other. Suppose a given star loses some of its mass in this fashion. Use Hydrostatic Equilibrium to explain how the core temperature of that star will change as a result.

3) A black hole is also known as a "singularity" because the entire mass of the object is thought to be concentrated in a single infinitesimal point. Gravitational force can be calculated using the following equation:

a) (6 pts) Kate feels a certain gravitational force (called "weight") when standing on the surface of the Earth, about 4,000 miles away from the center of the Earth. Suppose Teresa is located 4,000 miles away from a black hole with a mass precisely equal to the mass of the Earth. Who feels a stronger gravitational force: Kate, Teresa, or do both feel the same force? Explain your answer.

b) (5 pts) Suppose Kate is instead located 30 feet away from the center of the Earth while Teresa is located 30 feet away from the black hole singularity. Who feels a stronger gravitational force: Kate, Teresa, or do both feel the same force? Explain.

4) Astronomers tell us that the absolute luminosity of a star is directly proportional to that staršs mass cubed (i.e. a star twice as massive as the Sun would be eight times more luminous). We also know that the self-gravity of a star is directly proportional to the staršs mass (i.e. a star twice as massive as the Sun would hold itself together with a self-gravity twice as strong).

A careful study of the main sequence in the H-R diagram reveals that the sizes of main sequence stars are proportional to the masses of the stars. In other words, the more massive a main sequence star, the larger we expect it to be. Explain why.

5) For this question, you may wish to refer to the inverse square law, given elsewhere in this exam. The Cepheid Period-Luminosity relationship tells us that the period of a Cepheid is directly proportional to its absolute luminosity. Suppose we observe Cepheids in two different nearby galaxies with no intervening interstellar material interfering with our observations. In both galaxies, the apparent luminosities of the Cepheids are identical. In galaxy A, the period of the Cepheid is much longer than the period of the Cepheid in galaxy B.

a) (3 pts) Which Cepheid has the higher absolute luminosity (A, B, same, can't determine just from the period)?

b) (3 pts) Based on your answer to (a), which galaxy is closer (A, B, same distance, can't determine).

c) (5 pts) Explain your answer to part (b), using the inverse square law to help (you may express your answer mathematically with a brief sentence if you wish).

6) As a star evolves from the main sequence into the red giant phase of its lifetime, you may assume that angular momentum (mass * size * rotation speed) is conserved. Since the mass of the star remains the same while the size increases by a large factor, what can you conclude happens to the staršs rate of rotation? Explain your answer.

7) We often use the inverse square law to determine the distances to stars:

where the absolute luminosity is defined to be:

However, the effects of the interstellar medium (extinction and reddening) often cause errors in our distance estimates.

a) (5 pts) Does interstellar reddening make our estimates of the distance to a star too high or too low? Justify your answer (in words or equations).

b) (6 pts) Does interstellar extinction make our estimates of the distance to a star too high or too low? Justify your answer (in words or equations).

8) Suppose as a student project, you decide to determine the sizes, temperatures and masses of all of the stars visible in the sky tonight.

a) (6 pts) Your final sample will show that most of your measured stars have masses greater than or equal to the mass of the Sun. Explain why.

b) (5 pts) Is this sample representative? Explain.

9) At the end of a star's main sequence, after hydrogen fusion ends, there is a brief period of time in the staršs development between the end of hydrogen fusion and (if the star is massive enough) the onset of Helium fusion.

a) (6 pts) What happens to the overall size of the star during this time? Use hydrostatic equilibrium to help explain your answer.

b) (5 pts) What happens to the density of the interior of the star during this time? Use the definition of density to help explain your answer.

10) Globular clusters are distributed uniformly around the center of our Milky Way Galaxy, and they can be used to deduce the age and size of our galaxy.

a) (6 pts) How does the distribution of globular clusters in the night sky lead us to believe that we are not at the center of the Milky Way galaxy?

b) (5 pts) Suppose you had a catalog with the distances to a random sample of globular clusters in our galaxy. How you would use this information to deduce the distance to the center of the Milky Way?