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

TL;DR

This paper introduces a new method to determine the evolution history of the mean neutral hydrogen fraction during the Epoch of Reionization by analyzing the frequency dependence of the multi-frequency angular power spectrum of the 21-cm signal.

Contribution

The authors propose a simple model linking the frequency dependence of the MAPS to the evolution of the neutral hydrogen fraction, enabling reionization history reconstruction from observational data.

Findings

Model accurately recovers the reionization history from simulated data.

Single-frequency neutral fraction input suffices for full history reconstruction.

Method validated using a light-cone simulation of the EoR 21-cm signal.

Abstract

The light-cone (LC) effect imprints the cosmological evolution of the redshifted 21-cm signal $T_{\rm b} ({\hat{\bf{n}}}, \nu)$ along the frequency axis which 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 ${\bar{x}_{\rm HI}}(\nu)$ falls rapidly as the universe evolves. The multi-frequency angular power spectrum (MAPS) ${{\mathcal C}_{\ell}}(\nu_1,\nu_2)$ quantifies the entire second-order statistics of $T_{\rm b} ({\hat{\bf{n}}}, \nu)$ considering both the systematic variation along $\nu$ due to the cosmological evolution and also the statistically homogeneous and isotropic fluctuations along all the three spatial directions encoded in ${\hat{\bf{n}}}$ and $\nu$. Here we propose a simple model where the systematic frequency $(\nu_1,\nu_2)$ dependence of ${{\mathcal C}_{\ell}}(\nu_1,\nu_2)$ arises entirely due to the evolution of ${\bar{x}_{\rm HI}}(\nu)$. This provides a new method to observationally determine the reionization history. Considering a LC simulation of the EoR 21-cm signal, we use the diagonal elements $\nu_1=\nu_2$ 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 ${\bar{x}_{\rm HI}}$ at a single frequency as an external input.