1) One famous binary star pair in our sky is Sirius and its companion (Sirius B), which is a white dwarf star, the remnant of a planetary nebula. We assume that the two stars in this binary pair formed at the same time.

a) (6 pts) Which of these two stars was initially more massive when both formed, Sirius or its companion white dwarf, Sirius B? Justify your answer completely (stating a simple equation or relation without justifying how it is used is insufficient).

b) (8 pts) Suppose instead that Siriusı companion were a black hole with a rotating accretion disk of material surrounding it. How could you prove that this companion is a black hole?

2) Suppose a globular cluster of stars contains a main sequence star of the same mass, color and composition as Sirius. Further, suppose this Sirius-like star is at the main-sequence turnoff point for this cluster, as indicated below. How would you expect the metallicity of stars in this cluster to compare with the Sun? Explain.

3) Below is the Period-Luminosity relation for Cepheid variables. Next to it is a light curve for a Cepheid variable star with 10 times the luminosity of the Sun.

a) (6 pts) On the light curve graph just above the light curve of the first Cepheid, sketch the light curve for a Cepheid variable star with a luminosity of 20 times the luminosity of the Sun. No explanation needed here.

b) (8 pts) Suppose these two stars have the same apparent luminosity as viewed from Earth. Which one is closer (assume there is no intervening material along your line of sight to affect measurements)? Justify your answer.

4) A significant difference between spiral galaxies and elliptical galaxies is that spiral galaxies tend to contain a lot more gas and dust. Explain why this fact leads to spiral galaxies having a much bluer color compared to ellipticals.

5) Answer the following two questions about brown dwarf stars based on your research:

a) (7 pts) Why do brown dwarf stars show evidence of Lithium absorption lines while very low mass red stars do not show such evidence?

b) (7 pts) What is the ³brown dwarf desert²?

6) The existence of dark matter in our galaxy is revealed by a close examination of the rotation curve of our galaxy.

a) (7 pts) On the graph below, a Keplerian rotation curve has been drawn for reference. Assuming our galaxy contains *NO* dark matter, graph what you think the average rotation velocity of our galaxy would look like in this case. If you think the graph would be exactly the same, just write ³no change² below the curve. In either case, label your answer with an (a) and explain it in the space below.

b) (7 pts) Draw in the graph of the true rotation curve of the galaxy, which takes into account the presence of dark matter. If you think the graph would be the same as the Keplerian curve, just write ³no change² below the curve. Label this graph (b). In the space below, explain the shape of this graph.

7) Assume for this problem that spiral galaxies and elliptical galaxies are equally common in our local region of the Universe. Suppose we do a representative survey of all galaxies at some very high distance (several billion light years away) and we estimate the ratio of spirals vs ellipticals. How would you expect this high redshift ratio to compare to the local ratio (more spirals, more ellipticals, same as locally)? Explain your answer (be sure to explain why you would expect the ratio to depend on distance or if you donıt think it would depend on distance, explain why).

8) Explain how the distribution of gamma-ray bursters (GRBıs) on the sky is used as evidence by scientists who argue GRBıs are not located in our Milky Way galaxy or its halo but instead are at enormous distances.