Answer any 7 of the following 8 questions. All relevant equations have been given on the cover page (not visible in WWW version). Each is worth 14 points.
1) The Tully-Fisher (TF) relation and the Cepheid Period-Luminosity (PL) relation are two useful observed correlations that help us determine the distance to other galaxies. Explain why each of them is limited to galaxies relatively nearby.
2) Below is a graph representing the Hubble relation if the Universe's expansion has been completely constant over time, without any deceleration or acceleration. Suppose that the Universe is observed to be accelerating, due to a cosmological constant effect.
3) An observed quasar spectrum contains two equally strong Lyman-alpha absorption lines (marked A and B in the spectrum below), caused by the disks of spiral galaxies along the line of sight to the quasar. Which of these two lines represents a galaxy that is further from Earth? Justify your answer in 2-3 sentences.
4) In the space below, draw and label two graphs (7 pts each). Each graph should have the radial velocity of galaxies on the vertical axis and the distance to the galaxies on the horizontal axis. On the left, draw the graph of how the Universe would look if it weren't expanding. On the right, how it would look if the Universe were contracting. No explanations are necessary for this problem.
Universe not expanding Universe contracting
5) First, state in 1-2 sentences one version of the Anthropic Principle (and identify which version you are summarizing). Next, the fact that the density of the Universe is very close to the "critical density" is seen by many philosophers to be an "Anthropic coincidence". Explain why.
6) Suppose we were to compile a catalog of all the galaxies with apparent luminosity brighter than some threshold. Would you expect the average rotation velocity of this sample of galaxies to be greater than, less than or about the same as the true average rotation velocity of all galaxies? Justify your answer in 2-3 sentences.
Hint: Consider the Malmquist bias...what do stars/galaxies in a brightness-limited distribution tend to have in common? (This is a rhetorical question. You do not need to answer the hint in the space below, just the question above it).
7) Suppose you observe the abundance of Hydrogen (*not* the isotope of Hydrogen known as Deuterium...just simple Hydrogen) in galaxies at a variety of redshifts based on the strength of the Lyman-Alpha absorption lines in quasar spectra. On the graph below, plot how you would expect the abundance of Hydrogen to change (or not change) with increasing distance from the Earth. Justify your answer in 2-3 sentences.
8) Astronomers have wide-ranging opinions on the existence of extraterrestrial intelligent life. One major factor in determining whether or not our search for such life will be successful is how long civilizations can be expected to survive.