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

TL;DR

This study examines how the reduced speed of light approximation affects the accuracy of simulated hydrogen ionization during the epoch of reionization, revealing significant overestimations linked to hydrogen-photon chemistry.

Contribution

It demonstrates that the reduced speed of light approximation can cause substantial overestimations of neutral hydrogen, and clarifies the underlying physical cause through targeted simulations.

Findings

Reducing the speed of light by a factor of 5 to 100 overestimates neutral hydrogen by similar factors.

The error stems from the hydrogen-photon chemistry, mimicking reduced photon density effects.

Using full chemistry in photon propagation with reduced light speed aligns results with full speed simulations.

Abstract

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. In this paper we investigate the impact of the reduced speed of light approximation on the predicted properties of the intergalactic medium. To this end we use fully coupled radiation-hydrodynamics RAMSES-CUDATON simulations of the epoch of reionization. We find that reducing the speed of light by a factor 5 (20, 100) leads to overestimating the post-reionization volume-weighted $x_{HI}$ 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. In photo-ionization equilibrium, 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 full speed of light in the chemistry module. With this setup, the post-reionization neutral hydrogen fractions converge to the full speed of light value, which validates our explanation. Increasing spatial resolution beyond a cell size of 1 kpc physical, so as to better resolve Lyman-limit systems, does not significantly affect our conclusions.