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

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. It can be reduced by assuming a reduced speed of light, and this approximation is now widely used to produce large-scale simulations of reionization. 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 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. Using a set of small 8Mpc/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 larger 64Mpc/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. The same quantities measured in dense regions with slow fronts are less sensitive to c values.