A method to determine the evolution history of the mean neutral Hydrogen fraction

Abstract

The light-cone (LC) effect imprints the cosmological evolution of the redshifted 21-cm signal Tb(n^,ν) along the frequency axis that is the line-of-sight (LoS) direction of an observer. The effect is particularly pronounced during the epoch of reionization (EoR) when the mean hydrogen neutral fraction x¯HI(ν) falls rapidly as the universe evolves. The multifrequency angular power spectrum Cℓ(ν1,ν2) quantifies the entire second-order statistics of Tb(n^,ν) considering both the systematic variation along ν due to the cosmological evolution and also the statistically homogeneous and isotropic fluctuations along all the three spatial directions encoded in n^ and ν. Here, we propose a simple model where the systematic frequency (ν1, ν2) dependence of Cℓ(ν1,ν2) arises entirely due to the evolution of x¯HI(ν)⁠. This provides a new method to observationally determine the reionization history. Considering an LC simulation of the EoR 21-cm signal, we use the diagonal elements ν1 = ν2 of Cℓ(ν1,ν2) to validate our model. We demonstrate that it is possible to recover the reionization history across the entire observational bandwidth provided we have the value x¯HI at a single frequency as an external input.