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