The scattering of LyA radiation in the intergalactic medium: numerical methods and solutions

Abstract

Two methods are developed for solving the steady-state spherically symmetric radiative transfer equation for resonance line radiation emitted by a point source in the Intergalactic Medium. One method is based on solving the ray and moment equations using finite differences. The second uses a Monte Carlo approach incorporating methods that greatly improve the accuracy compared with previous approaches in this context. Several applications are presented serving as test problems for both a static medium and an expanding medium, including inhomogeneities in the density and velocity fields. Solutions are obtained in the coherent scattering limit and for Doppler RII redistribution with and without recoils. We find generally that the radiation intensity is linear in the cosine of the azimuthal angle with respect to radius to high accuracy over a broad frequency region across the line centre for both linear and perturbed velocity fields, yielding the Eddington factors f(nu) = 1/3 and g(nu) = 3/5. We show the radiation field produced by a point source divides into three spatial regimes for a uniformly expanding homogeneous medium: at radii r small compared with a characteristic radius r*, the mean intensity near line centre varies as 1/ r^(7/3), while at r > r* it approaches 1/ r^2; for r << r* it is modified by frequency redistribution. Before the reionization epoch, r* takes on the universal value 1.1 Mpc, independent of redshift. The mean intensity and scattering rate are found to be very sensitive to the gradient of the velocity field, growing exponentially with the amplitude of the perturbation as the limit of a vanishing velocity gradient is approached near the source. We expect the 21cm signal from the Epoch of Reionization to thus be a sensitive probe of both the density and the peculiar velocity fields.