1) Though very massive stars can be extremely luminous, they aren't nearly as bright as the recently discovered Gamma Ray Bursters (GRB's).

a) (6 pts) Explain the Eddington Limit. In other words, why do stars have a maximum mass?

b) (8 pts) GRB's are extremely luminous, perhaps much brighter than entire galaxies for a brief time. Name and briefly explain two pieces of evidence that tell us GRB's are extremely far away (and therefore extremely luminous).

2) A powerful (but imprecise) method of distance determination is called the Standard Ruler (SR) method.

a) (7 pts) Describe how we use the SR method to find the distance to galaxies. As part of your answer, describe the equation we use, what we assume, what we measure and how we solve for the distance.

b) (7 pts) Why is the SR method considered to be unreliable, and what statistical method do Astronomers use to improve the precision of this technique?

3) Although we had hoped to learn the density of the Universe by a careful analysis of Hubble's Law, we learned instead that the Universe's expansion is being accelerated by some sort of "Cosmological Constant" (CC). We later were able to estimate the density by analyzing the abundances of elements left over after the era of nucleosynthesis ended in the first few minutes of the Universe.

a) (6 pts) Briefly explain why no complex elements were formed in the Universe prior to a time of about 1 second and why no complex elements were formed (on a Universal scale) after a time of about 3 minutes.

b) (8 pts) Why did Einstein originally introduce the idea of a CC into his theory of cosmology? Why did he later withdraw it?

4) Quasars are very luminous objects that appeared throughout the Universe during the first few billion years of its existence. They are thought to be related to the extremely bright and mysterious blazars.

a) (8 pts) Explain how we know quasars are very bright (high absolute luminosity) and also how we know that they are relatively small in size, comparable to our solar system.

b) (6 pts) Quasars and blazars are thought to originate from the same type of object. Briefly explain what that object looks like and why the difference in appearance between quasars and blazars.

5) Among the seemingly paradoxical issues we discussed in cosmology are the so-called "age crisis", which was recently resolved, and also the darkness of the night sky.

a) (4 pts) What is the "age crisis" and how was it resolved?

b) (4 pts) Explain why metallicity affects how quickly a star burns its nuclear fuel (which in turn affects our age estimate of the star).

c) (6 pts) Explain why a dark night sky is consistent in part with a finite age for the Universe.

6) Two bright constellations that are visible in the night sky during April are Canis Minor and Hercules

a) (8 pts) Give the approximate location (altitude and azimuth) for these two constellations along with the name of one bright star in each constellation.

b) (6 pts) Suppose the bright star in Hercules is a Cepheid variable. Describe how you could find the distance to that star using the Period-L(abs) relation, step-by-step.

7) The very distant (early) Universe looks very different than the Universe today, and we can use this information to figure out how the Universe has evolved over time.

a) (4 pts) If you look at galaxies very distant (several billion light years) from our own, would you expect the metallicity of these galaxies to be higher or lower than our own galaxy? Explain your answer.

b) (10 pts) Draw a simple Hubble graph in the space below (along with the linear version of Hubble's Law, sketch the trend shown by the recent observations of galaxies based on type Ia supernova distances), and use it to help explain why Astronomers have concluded that the expansion of the Universe is accelerating.

8) The Cosmic Background Radiation (CBR) can potentially teach us a lot about the nature of the early Universe, even the fractions of a second after the Big Bang.

a) (8 pts) Explain why small "lumps" (or anisotropies) in the CBR were predicted by cosmologists.

b) (6 pts) Explain the "horizon problem" and how the theory of inflation resolves it.