Impact of the reduced speed of light approximation on ionization front velocities in cosmological simulations of the epoch of reionization

Context. Coupled radiative-hydrodynamics simulations of the epoch of reionization aim to reproduce the propagation of ionization fronts during the transition before the overlap of HII regions. Many of these simulations use moment-based methods to track radiative transfer processes using explicit solvers and are therefore subject to strict stability conditions regarding the speed of light, which implies a great computational cost. The cost can be reduced by assuming a reduced speed of light, and this approximation is now widely used to produce large-scale simulations of reionization.
Aims: We measure how ionization fronts propagate in simulations of the epoch of reionization. In particular, we want to distinguish between the different stages of the fronts' progression into the intergalactic medium. We also investigate how these stages and their properties are impacted by the choice of a reduced speed of light.
Methods: We introduce a new method for estimating and comparing the ionization front speeds based on maps of the reionization redshifts. We applied it to a set of cosmological simulations of the reionization using a set of reduced speeds of light, and measured the evolution of the ionization front speeds during the reionization process. We only considered models where the reionization is driven by the sources created within the simulations, without potential contributions of an external homogeneous ionizing background.
Results: We find that ionization fronts progress via a two-stage process, the first stage at low velocity as the fronts emerge from high density regions and a second later stage just before the overlap, during which front speeds increase close to the speed of light. For example, using a set of small 8 Mpc h^-3 simulations, we find that a minimal velocity of 0.3c is able to model these two stages in this specific context without significant impact. Values as low as 0.05c can model the first low velocity stage, but limit the acceleration at later times. Lower values modify the distribution of front speeds at all times. Using another set of simulations with larger 64 Mpc h^-3 volumes that better account for distant sources, we find that reduced speed of light has a greater impact on reionization times and front speeds in underdense regions that are reionized at late times and swept by radiation produced by distant sources. Conversely, the same quantities measured in dense regions with slow fronts are less sensitive to c∼ values. While the discrepancies introduced by reduced speed of light could be reduced by the inclusion of an additional UV background, we expect these conclusions to be robust in the case of simulations with reionizations driven by inner sources.