Question

2. Mass versus Light One of the primary goals of every galaxy survey is to measure the distribution of the luminosities of galaxies, which has been found to be well parameterized by the luminosity function L/L- where φ(L)dL is the number density of galaxies with luminosity between L and L + dL, and φ*, L*, and a are parameters to be determined from galaxy surveys (a) Show that the luminosity density of galaxies, J, is related to ф*, L*, and by a simple algebraic expression. Derive this expression. (Hint: If your answer contains an integral, you haven't tried hard enough For all your answers below, don't assume a specific value for h; instead, make sure to keep track of factors of h. (b) A recent galaxy survey measures ф.-00165h3 Mpc-3, Ф--1, 13, and L.-1.26 >< 1010h-2L0. Calculate j. What fraction of this luminosity density is contributed by galaxies fainter than L^? (c) The classical technique for quantifying the amount of dark vs. luminous matter is to determine the mass-to-light ratio, M/L (in units of solar Mo/Lo). Assuming the luminosity density from part (b) is representative for the universe (current galaxy surveys cover a large volume, so this should be an OK assumption), calculate the value of M/L (in units of Mo/Lo) required to close the universe The value of M/L is typically measured to be a few 10s in individual galaxies and a few 100s in galaxy clusters. Is there enough dark matter to make (m-1?

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