1) Stars can end their lifetimes in a variety of ways. Low mass stars typically end up as planetary nebulae, while high mass stars typically end up as supernovae.

a) (8 pts) Explain what causes planetary nebulae and why only low mass stars end up this way.

b) (6 pts) High mass stars typically end up as supernovae. Explain what causes these incredibly energetic explosions.

2) Cepheid variables undergo periods of expansion and contraction. These changes can be understood through the mechanism of hydrostatic equilibrium (HSE).

a) (6 pts) During the contraction phase of a Cepheidıs pulsation, state and explain what is happening to the temperature and outward-pushing pressure of the star.

b) (8 pts) Suppose Cepheids are observed in two clusters, Kappa and Theta. The Cepheid in cluster Theta shows a period twice as long as the other Cepheid, and both stars have the same apparent luminosity. Explain why the period and absolute luminosity of Cepheids are related, then explain which cluster is further away from us (and how we know it).

3) One of the key concepts in any scientific survey is that of a representative sample. Suppose an astronomer wants to put together a representative sample of 1,000 stars to study the relationship between size and temperature.

a) (7 pts) If the astronomer picks the 1,000 nearest stars to the Earth (out of the 100 billion in our galaxy), would this sample be representative? Use the Copernican Principle to help explain why or why not.

b) (7 pts) A recent search for brown dwarfs observed binary systems in which one of the stars was similar to the Sun. Astronomers hoped to use the motion of the sun-like star to reveal the presence of a brown dwarf companion, but it turns out this wasnıt a representative sample of binary systems. It was biased against finding brown dwarfs. Explain why.

4) Suppose our galaxy had no dark matter. What would the rotation curve for the disk of the galaxy look like? Draw in what you think it would look like on the graph below. The Keplerian curve (which we see in our solar system) is included for reference. If the galaxyıs rotation curve would exactly match this, just write "no change" on the graph below. After drawing in your curve, explain why you drew it the way you did (or wrote "no change").

5) Deep inside a cold, dense interstellar cloud, a new massive star is formed. This star gives off a tremendous amount of ultraviolet light as well as light in other regions of the spectrum. Due to the dimming of light from interstellar extinction, the star is barely visible from the Earth.

a) (7 pts) Assume the ISM has done little to change the apparent color of the new star (no reddening). If we do not take into account the effects of extinction, our distance estimate to this star will be incorrect. Will our estimate be higher or lower than the true distance? Justify your answer.

b) (7 pts) Inside the cloud, the ultraviolet light is helping to create complex organic molecules. Briefly explain how this happens and why is this process important in the study of life on other worlds.

6) Two face-on binary systems, Alpha and Beta, have companion stars with identical orbital periods. The two systems also have the same angular size as seen from Earth. Parallax measurements show that system Beta is further away. Based on this information, which system has the more massive central star, Alpha or Beta? Justify your answer fully.

7) One of the only indicators Astronomers have for the age of a star is its composition, or metallicity. Color is sometimes an indicator of age, too.

a) (7 pts) Suppose we observe two main sequence stars, one blue and one red. Can we say with confidence which of these two stars has a higher metallicity? If yes, which one has a higher metallicity and why? If no, why can't we tell?

b) (7 pts) Suppose we observe two clusters of main sequence stars. The light from one cluster is predominantly blue and the other is predominantly red. Can we say with confidence which of these two clusters is younger? If yes, which one is younger and how do we know? If no, why can't we tell?

8) Two candidates for dark matter in our galaxy are very low mass (VLM) stars and solitary black holes. Both are extremely difficult, but not impossible, to detect.

a) (8 pts) Explain how Astronomers determined that VLM stars do not make up the dark matter. As part of your answer, explain why it is difficult to observe VLM stars that are relatively close to Earth to make up a representative sample.

b) (6 pts) Explain how Astronomers can detect solitary black holes and why we cannot yet determine whether they constitute a significant fraction of the dark matter.