1) The Tully-Fisher technique is a method of distance determination used with spiral galaxies. In order for the distance estimate to be reliable, we must accurately measure the rotation speed of the galaxy.

a) (10 pts) If the galaxy is inclined with respect to our line of sight (instead of edge-on) and we do not take this inclination into account, we will underestimate the distance to the galaxy. Explain why.

b) (4 pts) Explain why the Tully-Fisher relation is only considered to be reliable within a certain distance from our own galaxy.

2) The Standard Candle technique is a very common method of distance determination. Suppose we find a Type Ia supernova in a distant galaxy and assume it has the same absolute luminosity as other Type Ia supernovae that have been studied.

a) (6 pts) Explain what we could then do to estimate the distance to the galaxy using this information.

b) (8 pts) Explain why Type Ia supernovae have such predictable absolute luminosities, so that we can trust the estimated distances derived from this information.

3) The Drake equation attempts to predict how successful we will be when we search the sky for extraterrestrial signals. Among the factors in the equation is f(L), the fraction of earth-like planets on which life will develop.

a) (8 pts) One strategy used while searching is a targeted search, in which Astronomers use very long intergration times to very sensitively search in the direction of sun-like stars in the hopes of finding signals. What is the potential weakness of this strategy? Also, can you describe an alternate strategy and its potential weakness?

b) (6 pts) Explain how and why current research on Jupiterąs moon Europa and the planet Mars will affect our estimate of f(L).

4) For this particular problem, you may assume that there is no acceleration or deceleration of the expansion of the Universe due to gravity or any kind of cosmological constant (just trying to keep it simple). Today, when the Universe has an age of about 12 billion years, we can draw a Hubble relation as below. Suppose Astronomers are alive 12 billion years in the future (so age of the U at that time would be 24 billion years) and draw a Hubble diagram based on the data they observe at that time. Would it look different? If so, show on the diagram how it would change. If it wouldnąt look different, just write "no change" on the diagram. In either case, justify your answer in 2-3 sentences.

(Helpful hint: Think about the diagram of the car race...how does it look after 1 hour? After 2 hours?)

5) The problem of dark matter is important, as we saw in the previous section, for helping to explain the rotation curve of spiral galaxies, among other things. It turns out that the dark matter is also important for determining the ultimate fate of the Universe, so our studies have taken on new importance in recent decades.

a) (10 pts) One effort to find dark matter has been the search for Low Surface Brightness (LSB) galaxies. Though we have discovered some of these galaxies, many Astronomers believe there are lots more to be found. Explain why.

b) (4 pts) Why do we need measure the amount of dark matter in the Universe in order to accurately predict the ultimate fate of the Universe?

6) In the past five years or so, many Astronomers have come to accept the observations that show the Universe apparently contains some sort of "Cosmological Constant" (CC), or repulsive force that pushes galaxies apart.

a) (7 pts) Briefly describe the evidence in favor of a CC in the most accurate Hubble diagrams.

b) (7 pts) If there were no CC in the Universe, no repulsive force, would the Hubble diagram look linear, or would it have some sort of up or down curvature? Justify your answer.

7) One of the more remarkable facts about the Cosmic Background Radiation (CBR) is that it has a spectrum that is almost identical in all directions on the sky, that of a continuous radiator with a characteristic temperature of about 2.7 degrees Kelvin.

a) (7 pts) Explain why the identical appearance of the CBR in all directions is difficult to explain using the "standard" laws of Physics.

b) (7 pts) Explain how the theory of inflation "solves" this problem and explains the appearance of the CBR.

8) Quasars have the highest absolute luminosities of any object in the visible Universe, and we use them to study conditions during the early Universe, a few billion years after the Big Bang.

a) (6 pts) Explain how we know that quasars have such high absolute luminosities.

b) (8 pts) Explain the evidence that leads us to believe that quasars have very small sizes, much smaller than typical galaxies.