The time development of a resonance line in the expanding universe

Abstract

The time-dependent spectral profile of a resonance line in a homogeneous expanding medium is studied by numerically solving an improved Fokker-Planck diffusion equation. The solutions are used to determine the time required to reach a quasi-static solution near the line center. A simple scaling law for this relaxation time is derived and is fitted to the numerical results. The results are applied to the case of Lyman alpha scattering during primordial recombination of hydrogen. For a wide range of cosmological models, it is found that the relaxation times are smaller than the recombination timescale, although not by a very large factor. Thus the standard assumption of a quasi-static solution in cosmological recombination calculations is reasonably valid and should not cause substantial errors in the solutions.