Phys/Astro 228: Extragalactic Astronomy and CosmologyOctober 27 2006C.–P. MaProblem Set 6Due Friday November 3Readings: (1) James Grahms notes on “Dynamics of Ideal Fluids” linked at coursewebsite; (2) Ch 7.1 of Dodelson.1.Validity of Non-Interacting Electron GasNo one in class has questioned why we can treat the electrons in the early universe as a non-interactingthermal gas despite their Coulomb interactions.Give a heuristic argument (i.e.don’t worry aboutnumerical factors of order 1) for why this is okay. (Hint: Compare the relevant energies.)2.Sound Waves and Jeans Length(based on Binney & Tremaine 5.1)At typical sea-level conditions, the density of air is 1.23×10-3g cm-3and the speed of sound is3.4×104cm sec-1. Find (a) the Jeans length and comment on how it compares with the thickness ofthe atmosphere and if you expect Jeans instabilities to occur; (b) the fractional change in frequencydue to the self-gravityof the air, for a sound wave with wavelength 1 meter.
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