On the Proper Use of the Reduced Speed of Light Approximation

I show that the reduced speed of light (RSL) approximation, when used properly (I.e., as originally designed—only for local sources but not for the cosmic background), remains a highly accurate numerical method for modeling cosmic reionization. Simulated ionization and star formation histories from the “Cosmic Reionization on Computers” project are insensitive to the adopted value of the RSL for as long as that value does not fall below about 10% of the true speed of light. A recent claim of the failure of the RSL approximation in the Illustris reionization model appears to be due to the effective speed of light being reduced in the equation for the cosmic background too and hence illustrates the importance of maintaining the correct speed of light in modeling the cosmic background.