The impact of the reduced speed of light approximation on the post-overlap neutral hydrogen fraction in numerical simulations of the epoch of reionization

Context: The reduced speed of light approximation is used in a variety of simulations of the epoch of reionization and galaxy formation. Its popularity stems from its ability to drastically reduce the computing cost of a simulation, by allowing the use of larger, and therefore fewer timesteps to reach a solution. It is physically motivated by the fact that ionization fronts rarely propagate faster than some fraction of the speed of light. However, no global proof of the physical validity of this approach is available, and possible artefacts resulting from this approximation therefore need to be identifited and characterized to allow its proper use. Aims: In this paper we investigate the impact of the reduced speed of light approximation on the predicted properties of the intergalactic medium. Methods: To this end we use fully coupled radiation-hydrodynamics RAMSES-CUDATON simulations of the epoch of reionization. Results: We find that reducing the speed of light by a factor 5 (20, 100) leads to overestimating the post-reionization average volume-weighted neutral hydrogen fraction by a similar factor ~5 (20, 100) with respect to full speed of light simulations. We show that the error is driven by the hydrogen - photon chemistry by considering the analytical solution for a strongly ionized hydrogen gas in photo-ionization equilibrium. In this regime, reducing the speed of light has the same effect as artificially reducing the photon density or the reaction cross-section and leads to an underestimated ionizing flux. We confirm this interpretation by running additional simulations using a reduced speed of light in the photon propagation module, but keeping this time the true speed of light in the chemistry module. With this setup, the post-reionization neutral hydrogen fractions converge to the true value, which validates our explanation.