Non-equilibrium temperature evolution of ionization fronts during the Epoch of Reionization

The epoch of reionization (EoR) marks the end of the Cosmic Dawn and the beginning of large-scale structure formation in the universe. The impulsive ionization fronts (I-fronts) heat and ionize the gas within the reionization bubbles in the intergalactic medium (IGM). The temperature during this process is a key yet uncertain ingredient in current models. Typically, reionization simulations assume that all baryonic species are in instantaneous thermal equilibrium with each other during the passage of an I-front. Here we present a new model of the temperature evolution for the ionization front by studying non-equilibrium effects. In particular, we include the energy transfer between major baryon species ($e^{-}$, \HI, \HII, \HeI, and \HeII) and investigate their impacts on the post-ionization front temperature $T_{\mathrm{re}}$. For a better step-size control when solving the stiff equations, we implement an implicit method and construct an energy transfer rate matrix. We find that the assumption of equilibration is valid for a low-speed ionization front ($\lessapprox\ 10^9~\mathrm{cm}/\mathrm{s}$), but deviations from equilibrium occur for faster fronts. The post-front temperature $T_{\mathrm{re}}$ is lower by up to 19.7\% (at $3\times 10^9$ cm/s) or 30.8\% (at $10^{10}$ cm/s) relative to the equilibrium case.