Solving the system of atomic rate equations during recombination

Abstract

The recombination of hydrogen at z ~ 800 - 1800 induces distortions to the Cosmic Microwave Background (CMB) spectrum. We present a careful calculation and analysis of all of the main transitions occurring during this period in order to find the electron density throughout recombination and its dependence on each process. Our original motivation was to analyze the effects that Thomson scattering and resonance scattering will have on recombination. However, while working on the project, we found that first we had to thoroughly account for all of the atomic transitions. We present a new method for solving the system of equations throughout the period of recombination. This method allows us to show the effect of individual processes on the total ionization fraction.