1) Suppose star X is at the main sequence turnoff point in the H-R diagram for the Alpha Cluster of stars. Based on spectroscopic observations, Astronomers have deduced that star X is twice as massive as the Sun, which has a main sequence lifetime of 10 billion years. No explanations needed for a or b, but show work for partial credit.

a) (2 pts) What is the luminosity of star X relative to the Sun (answer with a value, such as "X is 3 times fainter than the Sun.")?

b) (2 pts) What is the main sequence lifetime of star X relative to the Sun (longer, shorter, about the same)?

c) (10 pts) We know that the age of the Alpha Cluster is equal to the current age of star X. State in a single sentence why this is true, then explain how we know that the current age of star X is equal to its main sequence lifetime.

2) If a star is massive enough, at the end of the Hydrogen-burning portion of its lifetime, the core will actually *heat up* until it gets hot enough for Helium fusion to take place.

a) (6 pts) Explain what happens to a star after Hydrogen fusion ends and before Helium fusion begins to cause its core temperature to increase.

b) (8 pts) Name and explain two reasons why Helium fusion requires a higher temperature and density than Hydrogen fusion.

3) Below is the spectrum showing the absorption pattern of Nitrogen gas in the spectrum of a star with an intervening interstellar cloud along the line of sight to the star (the cloud also contains some Nitrogen)

a) (2 pts) Which set of lines represents the absorption of the interstellar cloud (wider lines or narrower lines)?

b) (8 pts) Explain your answer to part (a). Just saying something like "because interstellar cloud lines are wider than stellar lines" is circular...you must explain why line widths are wider or narrower for interstellar clouds).

c) (4 pts) Assuming the star is stationary with respect to the Earth, how is the gas cloud moving with respect to the Earth (toward, away, not moving radially)? No explanation needed here.

4) Suppose we know the angular size of a planetary nebula, the distance of this nebula from the Earth and the velocity of the expanding gas at the edge of the nebula (via Doppler shift measurements). Explain how we can use these three pieces of information to deduce the age of the nebula (the time since the nebula first exploded).

5) Two of the most interesting puzzles that Astronomers have attempted to solve in the last decade involve gamma-ray bursters and dark matter.

a) (7 pts) Explain why Astronomers can say with confidence that gamma-ray bursters are not located within the Milky Way galaxy.

b) (7 pts) Explain how the rotation curve of our galaxy is evidence for the existence of dark matter.

6) For this question, assume that we are using the inverse square law without the "X" correction for interstellar reddening and extinction.

a) (7 pts) Star A and star B have the same absolute luminosity and the same distance from the Earth, but star A is suffering from interstellar extinction (no reddening). Explain how this affects our estimate of star A's apparent luminosity and our estimate of star A's distance. Will we estimate that star A is closer or further away?

b) (7 pts) Star A and star B have the same apparent luminosity and the same absolute luminosity, but star A is suffering from interstellar reddening (no extinction). Explain how this affects our estimate of star A's absolute luminosity and our estimate of star A's distance. Will we estimate that star A is closer or further away?

7) Although light itself cannot escape from black holes, these strange objects have some tell-tale signs that allow Astronomers to deduce their existence.

a) (7 pts) Explain how accretion disks of material falling into black holes generate energy (heat and light) that allow us to "see" the black hole system.

b) (7 pts) Explain how we use accretion disk properties (such as deduced orbital distance and orbital velocity of the edge of the disk) to justify the existence of a black hole (as opposed to, say, just a massive central star).

8) The radioactive isotope Aluminum-26 (Al-26) is a kind of atom that is only formed naturally during supernova explosions, and it decays a more stable atom within an astronomically short timescale (about a million years).

a) (7 pts) Explain why the presence of Al-26 decay traces in meteorites that have landed on Earth is seen as evidence a supernova caused the initial collapse of the solar nebula into our solar system.

b) (7 pts) Suppose the decay timescale (or half-life) of Al-26 were 10 billion years instead of just 1 million years. Would the Al-26 decay traces still be seen as evidence of a link between supernova and solar system formation? Explain.