A covariant formulation for cosmological radiative transfer of the 21-cm line

TL;DR

This paper develops a covariant radiative transfer formulation for the 21-cm line, improving accuracy in modeling signals from the early universe and highlighting potential errors in previous simplified methods.

Contribution

It introduces a covariant 21-cm radiative transfer equation that accurately accounts for local emission, absorption, and line-continuum interactions in an expanding universe.

Findings

Simplified optical depth summation can cause up to 5% error at redshifts 12-35.

Errors exceed 10% for redshifts below 8.

Proper covariant formulation is essential for accurate cosmological 21-cm signal modeling.

Abstract

The 21-cm hyperfine line of neutral hydrogen is a useful tool to probe the conditions of the Universe during the Dark Ages, Cosmic Dawn, and the Epoch of Reionisation. In most of the current calculations, the 21-cm line signals at given frequencies are computed, using an integrated line-of-sight line opacity, with the correction for cosmological expansion. These calculations have not fully captured the line and continuum interactions in the radiative transfer, in response to evolution of the radiation field and the variations of thermal and dynamic properties of the line-of-sight medium. We construct a covariant formulation for the radiative transfer of the 21-cm line and derive the cosmological 21-cm line radiative transfer (C21LRT) equation. The formulation properly accounts for local emission and absorption processes and the interaction between the line and continuum when the radiation propagates across the expanding Universe to the present observer. Our C21LRT calculations show that methods simply summing the line optical depth could lead to error of $5\%$ in the 21-cm signals for redshift $z \sim 12-35$ and of $>10\%$ for redshift $z \lesssim 8$. Proper covariant radiative transfer is therefore necessary for producing correct theoretical templates for extracting information of the structural evolution of the Universe through the Epoch of Reionisation from the 21-cm tomographic data.