1) Probably the most significant difference between spirals and ellipticals that is easy to discern from any distance is the difference in color.

a) (7 pts) Explain why spiral galaxies tend to have a blue color. Note well that not all newly formed stars are blue. Some are red. Be sure to deal with this issue explicitly in your answer.

b) (7 pts) Explain how the merger hypothesis is consistent with the red color of elliptical galaxies.

2) One distance determination technique that has been somewhat reliable in decades past has been the Tully-Fisher relation, which relies on the correlation between the rotation speed of a galaxy and its absolute luminosity.

a) (8 pts) Suppose we are observing a spiral galaxy that is nearly face-on (so that we measure almost no radial motion due to rotation). How will our estimate of its rotation speed (based on Doppler shifting) compare to the true rotation speed of the galaxy, if we do not correct for the inclination? How will this in turn affect our estimate of the distance? Briefly explain both answers.

b) (6 pts) For galaxies with very large redshifts (due to the Hubble expansion), the TF relation is nearly useless for accurately determining their distances. Explain why.

3) One popular method of distance determination is the Standard Candle method, which requires accurate knowledge of the absolute luminosity of a "standard" object as well as confidence that some distant object that looks similar to the standard object has the same absolute luminosity as the standard object.

a) (10 pts) Explain why the brightest galaxy in a given cluster is likely to have a similar absolute luminosity compared to the brightest galaxy in some other cluster.

b) (4 pts) Despite this predictability, these galaxies are not very widely used as standard candles anymore. Briefly explain why.

4) The ultimate fate of the Universe may well rest upon whether gravity is strong enough to halt the current expansion and force the Universe to collapse.

a) (6 pts) Define the critical density by stating what would happen to the Universe in the end of the total mass density were less than or greater than the critical density.

b) (8 pts) In order to properly estimate the mass density of the Universe, one major part that needs to be studied is Low Surface Brightness (LSB) galaxies. What evidence exists that makes us believe LSB galaxies are far more numerous than ordinary spirals and ellipticals? Explain your answer.

5) Read very carefully, please! Suppose *all* of the visible matter and dark matter in our galaxy were concentrated at a single point in the center of the galaxy except for a few stars with very small masses sprinkled throughout the disk (assume the masses of these stars are zero compared to the mass of the galaxy).

a) (8 pts) If you were to plot a rotation curve, showing the relationship of the orbital velocity of these stars vs distance from the center of the galaxy, would it more closely resemble (a) a solid body rotation curve, (b) a flat rotation curve, (c) a Keplerian rotation curve or (d) a curve with velocities slightly higher than the Keplerian curve? Justify your answer (you do not need to explain the shape of the curve, just why you picked the one you did).

b) (6 pts) In a solid-body rotation curve, the orbital (or rotational) velocity is directly proportional to the distance from the center of motion (or axis of rotation). Briefly explain why this relationship exists for a solid body (a simple diagram may help but is not required). In other words, explain the shape of the solid body rotation curve.

6) Despite the fact that, until recently, white dwarfs have been exceedingly difficult to detect, they play an important role is both the search for dark matter and in cosmological studies based on standard candles.

a) (7 pts) Supernovae from white dwarf explosions are thought to be excellent standard candles. Why are these sorts of supernovae thought to have very predictable absolute luminosities while supernovae from other types of stars do not?

b) (7 pts) Recent studies have shown that white dwarfs may well account for a large fraction of the previously unseen mass in the galactic halo. These objects had been unobservable in the past due to their faint apparent luminosity and their strange color. Why did Astronomers expect these white dwarfs to appear red? What causes them to appear blue?

7) Hubble's relation today is assumed to be a perfectly straight line if you assume that the motions of galaxies in the Universe have been constant since the beginning, as shown below. Assume for this problem that the Hubble constant implies that the age of the Universe is 10 billion years.

a) (7 pts) On the graph below, sketch how you think the Hubble relation looks based on current observations of galaxies. Explain why this evidence points to the conclusion that the expansion of the Universe is accelerating.

b) (7 pts) The Cosmological Constant was originally proposed by Einstein as some sort of large-scale repulsion force (the kind we think today may be causing the acceleration of the expansion of the Universe). Explain briefly why Einstein proposed this idea and why later observations convinced him to abandon it.

8) A stunning discovery made by radio astronomers in the past few decades has been that an extremely massive black hole lurks at the very center of our galaxy.

a) (4 pts) Why can the region around the black hole only be observed via radio wavelengths rather than other wavelengths, such as visible light?

b) (5 pts) Despite the fact that radio telescopes are often 1000 times (or more) larger than optical telescopes, they tend to have very poor resolution compared to optical telescopes. Briefly explain why.

c) (5 pts) One way to overcome the intrinsically poor resolution of radio telescopes is to use interferometry, a technique that improves resolution by correlating the signals from several linked radio telescopes. Briefly explain why this is not yet feasible to do for optical telescopes.