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 T-rm b (hatboldsymbol n, nu) 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 barx-rm rmH,small I(nu) falls rapidly as the universe evolves. The multifrequency angular power spectrum mathcal C-ell (nu -1,nu -2) quantifies the entire second-order statistics of T-rm b(hatboldsymbol n,nu) considering both the systematic variation along 1/2 due to the cosmological evolution and also the statistically homogeneous and isotropic fluctuations along all the three spatial directions encoded in hatboldsymbol n and 1/2. Here, we propose a simple model where the systematic frequency (1/2 1, 1/2 2) dependence of mathcal C-ell (nu -1,nu -2) arises entirely due to the evolution of barx-rm rmH,small I(nu). 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 1/2 1 = 1/2 2 of mathcal C-ell (nu -1,nu -2) 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 barx-rm rmH,small I at a single frequency as an external input.