Large HI optical depth and Redshifted 21-cm signal from cosmic dawn. (arXiv:2110.06925v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Datta_K/0/1/0/all/0/1">Kanan K. Datta</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Ghara_R/0/1/0/all/0/1">Raghunath Ghara</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Hoque_A/0/1/0/all/0/1">Ariful Hoque</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Majumdar_S/0/1/0/all/0/1">Suman Majumdar</a>

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.

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.

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