1) Stars Alpha and Beta have the same apparent luminosity, but star Alpha shows evidence of higher ionization species in its spectrum. Both stars have the same spectral line widths. Which star is closer to the Earth? If the information given isn't conclusive, state that. Justify your answer fully.

2) At the end of the main sequence part of its lifetime, the Sun will swell to become a red giant star.

a) (4 pts) During the Sun's red giant phase, the core is more hotter, yet the surface of the star is red, indicating cooler temperatures. Why is this?

b) (4 pts) Name and explain two reasons why the core must be at a higher temperature in order for Helium fusion to occur (as opposed to main sequence Hydrogen burning).

3) Today, according to Hubble's Law, we estimate the age of the Universe to be about 12 billion years. Hubble's Law can be drawn as below for a Universe expanding at a constant rate (which, for simplicity, we will assume in this question). On the graph below, sketch how the Hubble Law will look when the Universe's age is about 24 billion years. If the graph will be unchanged, just write "no change" across the graph. Explain your answer fully.

4) Two important pieces of evidence that support the Big Bang theory are the dark night sky and the cosmic background radiation. Explain how each of these two observations support the Big Bang theory.

5) Some spectral lines in the Sun are also called Fraunhofer lines. Other lines seen in the Sun's corona and some hot, low density interstellar gas are called forbidden lines.

a) (4 pts) What are Fraunhofer lines, and under what conditions do we see these kinds of lines? Explain.

b) (4 pts) We only see forbidden lines when the gas density is extremely low. Explain why low density is required in order for us to see forbidden lines.

6) The temperature structure of the Sun's photosphere has been determined through a variety of observations, including limb darkening and spectral line analysis.

a) (4 pts) Explain limb darkening and what it tells us about the temperature structure of the Sun's photosphere.

b) (4 pts) Explain why the color of a gas and the temperature of a gas are related (not *how* they are related but *why* they are related).

7) The study of molecular clouds has recently been linked the SETI, the search for extra-terrestrial intelligence.

a) (4 pts) Scientists have noticed that some complex molecules, possibly leading to the development of life, form deep inside molecular clouds near regions of star formation. Explain why star formation contributes to the formation of complex molecules in clouds.

b) (4 pts) The fact that these complex molecules are found everywhere leads us to a consideration of Fermi's paradox (related to SETI). Explain Fermi's paradox, and briefly explain one possible resolution of this paradox.

8) The HIPPARCOS mission collected parallax information on about 100,000 stars (all the stars with parallax angles large enough to be measured by its sensitive equipment). If we were to compile the 10,000 stars with the largest parallax angles into a catalog, would this catalog be a representative sample of stars in the galaxy? Explain your answer.

9) The only way Astronomers have been able to find stellar masses has been to analyze binary star systems, particularly eclipsing systems in which many of the important unknown variables can be determined.

a) (5 pts) Suppose we observe an unresolved binary system, and we watch the spectral lines from this system split, merge, split, merge, etc. What would we have to measure, and how would we use this information to solve for the central mass in the system?

b) (3 pts) Suppose the companion stars in systems A and B show the same line shifts, but star A's companion takes longer to complete a cycle of shifting. Which central star is more massive? Explain your answer.

10) The study of black holes, which are virtually impossible to detect directly, has been central to our study of both stellar and galactic evolution.

a) (4 pts) How do we "prove" the existence of black holes in binary star systems?

b) (4 pts) How can we detect solitary black holes, in theory (they are thought to be a dark matter candidate)?

11) An important distance determination technique for our galaxy and other nearby galaxy is the use of the Cepheid Period-Absolute Luminosity relation.

a) (5 pts) Suppose Cepheid Gamma has a period twice as long as that of Cepheid Delta. If both stars have the same apparent luminosity, which star is further away? Explain.

b) (3 pts) Why is the Cepheid P-L technique limited to only nearby galaxies instead of much more distant galaxies?

12) If we were to observe the metallicity of galaxies with respect to distance (on a cosmological scale, looking at galaxies from here all the way out as far as we can see, several billion light years away), how would this graph look? Sketch the graph below and then explain why you drew the graph the way you did.

13) Two of the most energetic and mysterious objects we've studied this semester are cosmic rays and quasars.

a) (4 pts) Even though we believe cosmic rays originate from supernovae and other energetic explosions in our galaxy, cosmic rays seem to come from all directions, not just the disk of the Milky Way. Explain why.

b) (4 pts) Quasars and blazars are thought to be the same kind of object, but blazars give off lots of gamma rays compared to quasars. Why do these objects look so different if their source is essentially the same kind of object?

14) Recently, the cosmological constant has been at the center of debate in the Astronomical community thanks to new distance measurements of galaxies with type Ia supernovae.

a) (4 pts) Why did Einstein first propose the existence of the cosmological constant?

b) (4 pts) Explain the evidence from Hubble's Law and lookback time that supports the existence of a cosmological constant (a diagram may help).