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ps6 - Phys/Astro 228 Extragalactic Astronomy and Cosmology...

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Phys/Astro 228: Extragalactic Astronomy and Cosmology October 27 2006 C.–P. Ma Problem Set 6 Due Friday November 3 Readings: (1) James Grahms notes on “Dynamics of Ideal Fluids” linked at course website; (2) Ch 7.1 of Dodelson. 1. Validity of Non-Interacting Electron Gas No one in class has questioned why we can treat the electrons in the early universe as a non-interacting thermal gas despite their Coulomb interactions. Give a heuristic argument (i.e. don’t worry about numerical 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 - 3 g cm - 3 and the speed of sound is 3 . 4 × 10 4 cm sec - 1 . Find (a) the Jeans length and comment on how it compares with the thickness of the atmosphere and if you expect Jeans instabilities to occur; (b) the fractional change in frequency due to the self-gravity of the air, for a sound wave with wavelength 1 meter.
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