Large HI optical depth and Redshifted 21-cm signal from cosmic dawn

TL;DR

This paper investigates the impact of large HI 21-cm optical depths during cosmic dawn on signal estimation, revealing that common linear approximations overestimate temperatures and statistical measures, especially under excess-cooling scenarios.

Contribution

It critically assesses the validity of the linearized equation for HI 21-cm brightness temperature and quantifies the effects of large optical depth on various signal statistics using simulations.

Findings

Linearized equation overestimates spin temperature by ~5-10%.

Variance, skewness, kurtosis are over-predicted by up to 90%.

Power spectrum is overpredicted by up to 80%.

Abstract

The HI 21-cm optical depth ($\tau_b$) can be considerably large as the kinetic and spin temperature of the inter-galactic medium (IGM) is expected to be very low during cosmic dawn. It will be particularly higher at regions with HI over-density. We revisit the validity of the widely used linearized equation for estimating the HI 21-cm differential brightness temperature ($T_b$) which assumes $\tau_b << 1$ and approximates $[1-\exp({-\tau_b})]$ as $\tau_b$. We consider two scenarios, one without any additional cooling mechanism or radio background (referred as the standard scenario) and the other (referred as the excess-cooling} scenario) assumes the EDGES-like absorption profile and an excess cooling mechanism. We find that given a measured global absorption signal, consistent with the standard (excess-cooling) scenario, the linearized equation overestimates the spin temperature by $\sim 5\%(10\%)$. Further, using numerical simulations, we study the impact that the large optical depth has on various signal statistics. We observe that the variance, skewness and kurtosis, calculated at simulation resolution ($\sim 0.5 h^{-1} \, {\rm Mpc}$), are over-predicted up to $\sim 30\%$, $30\%$ and $15\%$ respectively for the standard and up to $\sim 90\%$, $50\%$ and $50\%$ respectively for the excess-cooling scenario. Moreover, we find that the probability distribution function of $T_b$ is squeezed and becomes more Gaussian in shape if no approximation is made. The spherically averaged HI power spectrum is overpredicted by up to $\sim 25 \%$ and $80\%$ at all scales for the standard and excess-cooling scenarios respectively.