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

TL;DR

This work analyzes how absorption by neutral hydrogen and helium in the expanding IGM shapes the continuous spectra of distant sources during Cosmic Dawn and the Reionization era. It develops analytic models for HI and He absorption in Lyman-series lines and continua, as well as HeI/HeII lines, then combines these with thermal free-free/free-bound emission from virialized halos to compute spectral transmittance functions S(λ;z) for sources at redshifts z≈5–15. Central contributions include closed-form optical-depth expressions for HI Lyα and Ly-continuum, HeI/HeII lines and continua, and the construction of S(λ;z) showing deep, redshift-dependent Gunn-Peterson troughs; the study also quantifies how variations in hydrogen and helium reionization histories alter the spectra and the Thomson depth, informing JWST-era observational planning. The results demonstrate that HI, HeI, and HeII absorptions collectively impose broad troughs whose widths grow with source redshift, and that the precise reionization history can notably affect spectra around z≈5.5–6.5, with practical guidance for interpreting distant galaxy and quasar spectra.

Abstract

We analyse the formation of troughs in the continuous spectra of sources in redshift range $5-15$ for two reionization histories followed from the distant galaxy spectra and CMB anisotropy. We supposed that neutral hydrogen and helium atoms of homogeneous intergalactic medium are mainly in ground state and absorb the light of distant sources in the lines of Lyman series and continuums of HI, HeI and HeII. The frequency dependence of optical depths in the 40 lines of Lyman series of HI and HeII, and in 10 lines of HeI, as well as in their continuums were computed in order to estimate the spectral flux of radiation from halos virialized during Cosmic Dawn and Reionization epochs. Assuming the thermal continuous spectra with virialized temperature of halos with dwarf galaxy mass $\sim10^9$ M$_\odot$, we compute the spectral fluxes from such halos in the vicinity of our galaxy taking into account the cosmological distances, redshifts and absorptions by each absorber and all together. The obtained spectral transmittance functions of intergalactic medium, $S(λ;z)$, are analysed on the subject which absorber systems of HI, HeI and HeII are corresponding for formation of troughs in the continuous spectra of sources at redshift range $5-15$ and how it depends on reionization history. It is shown, that spectral features in the continuous spectra of sources in redshift range $5-7$ are very sensitive to the reionization histories of both elements, hydrogen and helium.

Figures (9)

• Figure 1: Evolution of the neutral fraction of hydrogen and helium atoms following from the observational data.
• Figure 2: Optical depth in the $Ly_\alpha$ line (left panel) and superposition of the first 39 lines of Lyman series of HI (right panel) for the sources at different redshifts.
• Figure 3: The frequency dependences of the effective cross-section of absorption in the Lyman-continuum in the rest frame of Earth observer transferred from the source reference system at different redshifts (left) and optical depth for distant sources at different redshift (right) for both approximations of $x_{\rm HI}$ (1 - solid line, 2 -dotted one).
• Figure 4: Optical depth in the $Ly_\beta$ line (left panel) and superposition of the first 10 lines of Lyman series of HeI (right panel) for the sources at different redshifts.
• Figure 5: The frequency dependences of the effective cross-section of absorption in the HeI Lyman-continuum in the rest frame of Earth observer transferred from the source reference system at different redshifts (left) and optical depth in the HeI Lyman-continuum for distant sources at different redshift (right).