Extending Semi-numeric Reionisation Models to the First Stars and   Galaxies
  Semi-numeric methods have made it possible to efficiently model the epoch of reionisation (EoR). While most implementations involve a reduction to a simple three-parameter model, we introduce a new mass-dependent ionising efficiency parameter that folds in physical parameters that are constrained by the latest numerical simulations. This new parameterization enables the effective modeling of a broad range of host halo masses containing ionising sources, extending from the smallest Population III host halos with $M \sim 10^6 M_\odot$, which are often ignored, to the rarest cosmic peaks with $M \sim 10^{12} M_\odot$ during EoR. We compare the resulting ionising histories with a typical three-parameter model and also compare with the latest constraints from the Planck mission. Our model results in a optical depth due to Thomson scattering, $\tau_{\mathrm{e}}$ = 0.057, that is consistent with Planck. The largest difference in our model is shown in the resulting bubble size distributions which peak at lower characteristic sizes and are broadened. We also consider the uncertainties of the various physical parameters and comparing the resulting ionising histories broadly disfavors a small contribution from galaxies. As the smallest haloes cease a meaningful contribution to the ionising photon budget after $z = 10$, implying they play a role in determining the start of EoR and little else. 
Daegene Koh and John H. Wise
astro-ph.CO