Large H i optical depth and redshifted 21-cm signal from cosmic dawn

Abstract

ABSTRACT The atomic neutral hydrogen (H i) 21-cm optical depth (τb) can be considerably large as the kinetic and spin temperature of the intergalactic medium is expected to be very low during cosmic dawn. It will be particularly higher at regions with H i overdensity. We revisit the validity of the widely used linearized equation for estimating the H i 21-cm differential brightness temperature (Tb) which assumes τb ≪ 1 and approximates [1 − exp (− τb)] as τb. We consider two scenarios, one without any additional cooling mechanism or radio background (referred as standard scenario) and the other (referred as 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 $\sim\!{5}\,\mathrm{ per}\,\mathrm{ cent}\ (10\,\mathrm{ per}\,\mathrm{ cent})$. Further, using numerical simulations, we study 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 overpredicted up to $\sim\!{30}$, $30$, and $15\,\mathrm{ per}\,\mathrm{ cent}$, respectively, for the standard and up to $\sim\!90$, $50$, and $50\,\mathrm{ per}\,\mathrm{ cent}$, respectively, for the excess-cooling scenario. Moreover, we find that the probability distribution function of Tb is squeezed and becomes more Gaussian in shape if no approximation is made. The spherically averaged H i power spectrum is overpredicted by up to $\sim\!25$ and $80\,\mathrm{ per}\,\mathrm{ cent}$ at all scales for the standard and excess-cooling scenarios, respectively.