ps8 - Phys/Astro 228: Extragalactic Astronomy and Cosmology...

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Phys/Astro 228: Extragalactic Astronomy and Cosmology November 17 2006 C.–P. Ma Problem Set 8 Due in class Friday December 1 Readings: Ch 4 and 8.1-8.3 of Dodelson 1. When did Recombination Occur? (a) A precise calculation of the time evolution of the electron ionization fraction requires integration of the rate equations for atomic transitions. We can nonetheless estimate the redshift of recombination fairly accurately using the equilibrium distributions derived in class when we discussed the thermal history of the universe. Using the equilibrium distributions, write down an expression for the ratio, n p n e /n H , where n p , n e , and n H are the physical number densities of protons, electrons and neutral H atoms that are in thermal equilibrium with photons at temperature T . (Assume k B T m e c 2 , H atoms are in the ground states, and ignore He and heavier elements for simplicity.) (b) Using part (a), write down an expression for x 2 e / (1 x e ), where x e n e /n B
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ps8 - Phys/Astro 228: Extragalactic Astronomy and Cosmology...

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