1) Below is a side view of the situation in which an observer on the Earth is observing a binary star system (with a stationary central star) that is tilted a bit with respect to the observer's line of sight. There are no eclipses in the light curve, so both stars are always visible, but they are so far away that they appear as a single blob of unresolved light. We only know it is a binary by observing its spectrum over time.

a) (8 pts) At point A, the companion star is moving across our line of sight. Would you expect the spectral lines for this system to be merged or split here? What about at point B? Explain both answers with a single sentence each.

b) (6 pts) At point B, the companion star's Doppler shift is measured. Based on this and the orbital distance (known accurately through some other method), will our estimate of the central star's mass be higher or lower than the true value? Explain.

2) Why weren't scientists able to categorize "nebulium" lines with the appropriate element originally, and why must atoms be in an extremely low density gas in order to emit forbidden spectral lines?

3) This question deals with two apparent paradoxes that we discussed in this section of the course.

a) (7 pts) What is the Fermi paradox, and what is one possible resolution of it?

b) (7 pts) What is the Faint Sun paradox, and what is the probable resolution of it?

4) Suppose the light from a distant star must pass through a molecular cloud on its way to the Earth. When the light arrives, we find that we must correct for the effect of the intervening material by analyzing the spectral lines associated with it (but we must be careful not to confuse the ISM lines with lines from the original star).

a) (7 pts) Explain how and why ISM lines differ from stellar lines.

b) (7 pts) Molecular clouds are so named because sometimes complex molecules can form there. In particular, we know that many complex organic molecules (even basic amino acids) are found in these clouds. Explain how these molecules might have formed in molecular clouds and the role in this process of UV light from newly forming stars deep within the cloud.

5) Suppose we wanted to observe some stars in the constellation Cepheus. We'd need to know where to point our telescope, and we'd also need to figure out how to correct for interstellar gas and dust along our line of sight to some of the stars there.

a) (8 pts) Draw a simple star chart of Cepheus (and name one of the bright stars in the constellation), then state an altitude and azimuth where it can be located at about 10pm tonight.

b) (6 pts) The gas and dust along the line of sight to Cepheus affects the apparent luminosity of the stars we are observing. If we know the absolute luminosity of these stars accurately (based on, say, spectral line analysis independent of ISM effects) and we try to estimate the distance based on the measured apparent luminosity, will our estimate be higher or lower than the true distance? Explain your answer.

6) A certain kind of cosmic ray called a "fastball" is thought to originate fairly close to us (in terms of galactic distances anyway).

a) (8 pts) Why do we think "fastballs" must be from relatively nearby sources, and why do they seem to come from all directions (even though it may only be a few sources nearby that are responsible for them)? Explain both answers briefly.

b) (6 pts) Suppose we try to find out more about fastballs by undertaking a study of nearby objects, say the nearest 1000 stars. Would this sample be representative of stars in the galaxy as a whole? Why or why not?

7) Two stellar outbursts we've studied in this part of the course are novae and supernovae. While supernovae can occur in single stars and binary systems, novae can only occur in binaries.

a) (6 pts) Explain the mechanism that causes a nova explosion in a binary system.

b) (8 pts) Explain the two possible mechanisms that cause a supernova (for both, explain briefly where the energy comes from for the explosion) in a solitary massive star and in a binary system (they must be different mechanisms).

8) One property of stars we have learned how to estimate recently is their ages. We often do this by analyzing the composition, or metallicity, of the star. Another way to do it (sometimes) is using the star's color as an indicator.

a) (7 pts) Suppose some star X has a mass 10 times that of our Sun. Would you predict it to have a higher or lower metallicity than the Sun (or would you not be able to predict better than a random guess)? Explain. As part of your answer, explain how and why metallicity should be related to a star's age.

b) (7 pts) Suppose star Y is a red main sequence star, somewhat less massive than the Sun. Would you predict it to have a higher or lower metallicity than the Sun (or would you not be able to predict better than a random guess). Explain. As part of your answer, explain how and why color should be related to a star's age.