set6-06-sol - Astro 346 Spring Semester 2006 Homework 6th...

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Astro 346, Spring Semester 2006 Homework, 6th set, solutions. Problem 1: The relaxation problem in galaxy cannibalism (10 P) In problem 9.11 the last expression is derived using the result of problem 9.10, namely that the stellar orbits are virialized. Then the average kinetic energy of stars is half their average potential energy, so V 2 = G M 2 R That assumption should not be made in problem 14.3, because we look at the interaction between two galaxies whose stars are not yet on virialized orbits. So, you should start with the second-to-last equation of problem 9.11, after correction that now we are not dealing with star-star interactions, but star vs. galaxy core ( m * vs. m ). t relax = V 3 4 π G 2 m m * n ln(2 R/r ) ( X ) Here r is the impact parameter (closest separation along trajectory) for strong deflection as determined in 9.11, so the logarithmic term can be modified to the form given in 14.3. 1 r = V 2 2 G m 2 R r = R V 2 G m Note that the cluster core radius was denoted with an upper case R in 9.11, but the galaxy core radius in 14.3 is written as lower case
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