Minihalo photoevaporation during cosmic reionization: evaporation times and photon consumption rates

The weak, R-type ionization fronts (I-fronts) which swept across the intergalactic medium during the reionization of the Universe often found their paths blocked by cosmological minihaloes (haloes with virial temperatures T_vir<= 10⁴ K). When this happened, the neutral gas which filled each minihalo was photoevaporated. In a cold dark matter universe, minihaloes formed in abundance before and during reionization and, thus, their photoevaporation is an important, possibly dominant, feature of reionization, which slowed it down and cost it many ionizing photons. In a previous paper, we described this process and presented our results of the first simulations of it by numerical gas dynamics with radiation transport in detail. In view of the importance of minihalo photoevaporation, both as a feedback mechanism on the minihaloes and as an effect on cosmic reionization, we have now performed a larger set of high-resolution simulations to determine and quantify the dependence of minihalo photoevaporation times and photon consumption rates on halo mass, redshift, ionizing flux level and spectrum. We use these results to derive simple expressions for the dependence of the evaporation time and photon consumption rate on these halo and external flux parameters. These can be conveniently applied to estimate the effects of minihaloes on the global reionization process in both semi-analytical calculations and larger-scale, lower-resolution numerical simulations, which cannot adequately resolve the minihaloes and their photoevaporation. We find that the average number of ionizing photons each minihalo atom absorbs during its photoevaporation is typically in the range 2-10. For the collapsed fraction in minihaloes expected during reionization, this can add about one photon per total atom to the requirements for completing reionization, potentially doubling the minimum number of photons required to reionize the Universe.