Absorption effects in the expanding Universe: spectral transmittance functions of the intergalactic medium for distant sources

Abstract

We construct two self-consistent analytic approximations to the neutral hydrogen fraction, $x_{\rm HI}(z)$, and the helium ionization fractions, $x_{\rm HeI}(z)$, $x_{\rm HeII}(z)$, and $x_{\rm HeIII}(z)$, that are consistent with current constraints inferred from quasar spectra, galaxy surveys, and CMB polarization measurements. These approximations describe observationally motivated early- and late-reionization scenarios. Using these histories, we analyse the formation of broad absorption troughs in the continuum spectra of high-redshift sources over $1\leq z_{\rm s}\leq15$. We assume that neutral hydrogen and helium in a homogeneous diffuse intergalactic medium reside predominantly in their ground states and absorb radiation through the Lyman-series lines and continua of HI, HeI, and HeII. We compute the wavelength-dependent optical depths for the first 39 Lyman-series lines of HI and HeII, the first 10 lines of HeI, and the corresponding continua, and use them to derive spectral transmittance functions, $T(\lambda;z_{\rm s})$. As illustrative applications, we calculate the spectra of starless virialized Cloud9-type haloes and dwarf galaxies and demonstrate how intergalactic absorption modifies their intrinsic emission. Spectral features in sources at $5\lesssim z_{\rm s}\lesssim7$ are found to be particularly sensitive to the adopted hydrogen and helium ionization histories