A halo model approach for the 21-cm power spectrum at cosmic dawn
  Prior to the epoch of reionisation, the 21-cm signal of the cosmic dawn is
dominated by the Lyman-$\alpha$ coupling and gas temperature fluctuations
caused by the first sources of radiation. While early efforts to model this
epoch relied on analytical techniques, the community quickly transitioned to
more expensive semi-numerical models. Here, we re-assess the viability of
simpler approaches that allow for rapid explorations of the vast astrophysical
parameter space. We propose a new analytical method to calculate the 21-cm
power spectrum based on the framework of the halo model. Both the
Lyman-$\alpha$ coupling and temperature fluctuations are described by
overlapping radiation flux profiles that include spectral red-shifting and
source attenuation due to look-back (light-cone) effects. The 21-cm halo model
is compared to the semi-numerical code 21cmFAST exhibiting generally good
agreement, i.e., the power spectra differ by less than a factor of three over a
large range of $k$-modes and redshifts. We show that the remaining differences
between the two methods are comparable to the expected variations from
modelling uncertainties associated with the abundance, bias, and accretion
rates of haloes. While these current uncertainties must be reduced in the
future, our work suggests that inference at acceptable accuracy will become
feasible with very efficient halo models of the cosmic dawn.
