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

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 \rr{when the radiation field is rapidly evolving in time}. 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-wise comparison of the RSL radiation field with the reference simulation that maintains the full speed of light for the radiative transfer.