Photon (Non)Conservation in the Reduced Speed of Light Approximation and How to (Almost) Fix It

TL;DR

This paper investigates photon non-conservation caused by the Reduced Speed of Light approximation in cosmological simulations, proposes a method to count missing photons exactly, and demonstrates the challenges of correcting these errors in realistic scenarios.

Contribution

It introduces a scheme to exactly count missing photons in RSL simulations and evaluates its effectiveness and limitations in simple and complex reionization models.

Findings

Missing photons can be exactly counted in some schemes.

Adding back missing photons improves accuracy in simple tests.

The correction scheme performs poorly in realistic reionization simulations.

Abstract

The "Reduced Speed of Light" (RSL) approximation is commonly used to speed up radiative transfer calculations in cosmological simulations. However, it has been shown previously that the RSL approximation leads to photon non-conservation in some regimes. I show that these missing photons can be counted exactly for some numerical schemes. Adding them back into a simulation, however, is a much harder task. I show one example of such a scheme, which achieves sub-percent accuracy on simple tests. Unfortunately, the scheme performs much worse on semi-realistic simulations of cosmic reionization, leading to a faster overlap and significant errors in the point-to-point comparison of the RSL radiation field with the reference simulation that maintains the full speed of light for the radiative transfer.