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.