Radiative transfer effects in primordial hydrogen recombination

TL;DR

This paper investigates various radiative transfer effects in primordial hydrogen recombination, finding that many previously ignored effects are negligible, and develops a generalized formalism for line overlap, concluding no hydrogen maser occurs.

Contribution

The paper introduces a generalized Sobolev approximation for high-lying Lyman line overlap and evaluates several radiative effects, confirming their negligible impact on recombination history.

Findings

Thomson scattering near Lyman-alpha is negligible.

Feedback from deuterium Lyman-alpha distortions is negligible.

Line overlap effects are negligible for recombination accuracy.

Abstract

The calculation of a highly accurate cosmological recombination history has been the object of particular attention recently, as it constitutes the major theoretical uncertainty when predicting the angular power spectrum of Cosmic Microwave Background anisotropies. Lyman transitions, in particular the Lyman-alpha line, have long been recognized as one of the bottlenecks of recombination, due to their very low escape probabilities. The Sobolev approximation does not describe radiative transfer in the vicinity of Lyman lines to a sufficient degree of accuracy, and several corrections have already been computed in other works. In this paper, the impact of some previously ignored radiative transfer effects is calculated. First, the effect of Thomson scattering in the vicinity of the Lyman-alpha line is evaluated, using a full redistribution kernel incorporated into a radiative transfer code. The effect of feedback of distortions generated by the optically thick deuterium Lyman-alpha line blueward of the hydrogen line is investigated with an analytic approximation. It is shown that both effects are negligible during cosmological hydrogen recombination. Secondly, the importance of high-lying, non overlapping Lyman transitions is assessed. It is shown that escape from lines above Ly-gamma and frequency diffusion in Ly-beta and higher lines can be neglected without loss of accuracy. Thirdly, a formalism generalizing the Sobolev approximation is developed to account for the overlap of the high-lying Lyman lines, which is shown to lead to negligible changes to the recombination history. Finally, the possibility of a cosmological hydrogen recombination maser is investigated. It is shown that there is no such maser in the purely radiative treatment presented here.