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# hw2 - Ph 444 Problem Set 2 Due Tuesday 1 A simple model for...

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Unformatted text preview: Ph 444 Problem Set 2 Due: Tuesday, September 21, 2010 1. A simple model for the lumpiness of the universe is that all of the matter is collected into clumps, each of mass m c , with a number density n c . These clumps could represent galaxies, clusters of galaxies, or even superclusters (clusters of galaxy clusters). In this problem we will focus on the simple situation where just one kind of clump is present and see what this implies for the typical departure from homogeneity in spherical volumes of increasing size. a. Assume that the clumps are placed at random such that each small volume of space, dV , has a uniform probability, n c dV , of containing the center of a clump. Then the number of clumps seen in a volume V has a Poisson distribution. What is the average number of clumps, N , expected in volume V ? In a sample of many different spheres, what will be the standard deviation of N , σ N , about its mean? b. If the clusters are the only mass in the universe, how does the average fractional deviation of the mass in a sphere, σ M /M , vary with M ? You should get a power-law dependence on M . How does your result compare to the observed....
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hw2 - Ph 444 Problem Set 2 Due Tuesday 1 A simple model for...

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