Lyman-alpha scattering in the intergalactic medium during the epoch of reionisation
We examine resonant scattering of Lyα (Lyman-alpha) photons in the neutral hydrogen Intergalactic Medium (IGM) at high redshift. Lyα scattering plays a key role in the 21cm emission/absorption against the Cosmic Microwave Background via the 'Wouthuysen-Field Effect' Knowledge of the strength of Lyα scattering induced by the first sources will constitute a significant step in predicting and understanding the eventual observations of the impact of these objects on the signal from the IGM during the Epoch of Reionisation (EoR), using planned facilities such as the Square Kilometre Array. A quantitative analysis of the scattering rate requires formulation and solution of the radiative transfer equation for the system. We consider radiative transfer of Lyα scattering far from a source in the homogeneous expanding IGM for photons that free stream until scattering in the blue wing of the local line profile: we describe an approximation that ignores spatial diffusion of photons and assumes a locally homogeneous scattering medium, allowing the calculation of simple analytic solutions to examine the dependence of the local scattering rate on various physical effects such as local expansion/contraction, and extend our approach to determine time-dependent solutions. The more complex problem of Lyα photons scattering in both frequency and space within a spherically symmetric medium is subsequently solved for several test problems using both Monte Carlo methods and a method based on the ray and moment radiative transfer equations following an approach due to Mihalas et al. [1975, 1976]. We examine local Lyα scattering around a continuum source in the homogeneous expanding IGM using both methods and compare our results with an analytic solution in the zero-temperature diffusion regime derived from an analogous solution for a monochromatic source found by Loeb and Rybicki . Our results are used to make estimates of the resulting size of the spherical region around the source that is rendered detectable via 21cm observations against the CMB background. We also examine cases with different density and velocity profiles and determine the effect on the scattering rate.