Towards an accurate treatment of the reduced speed of light approximation in parameterized radiative transfer simulations of reionization

Abstract

The reduced speed of light approximation (RSLA) has been employed to speed up radiative transfer simulations of reionization by a factor of $\gtrsim 5-10$. However, it has been shown to cause significant errors in the HI-ionizing background near reionization's end in simulations of representative cosmological volumes. We show that using the RSLA is, to a good approximation, equivalent to re-scaling the global ionizing emissivity in a redshift-dependent way. We derive this re-scaling and show that it can be used to ``correct'' the emissivity in RSLA simulations. This method requires the emissivity to be re-scaled after the simulation has been run, which limits its applicability to situations where the emissivity is set ``by hand'' or determined by free parameters. We test our method by running full speed of light simulations using these re-scaled emissivities and comparing them with their RSLA counterparts. We find that for reduced speeds of light $\tilde{c} \geq 0.2$, the 21 cm power spectrum at $0.1 \leq k /[h{\rm Mpc}^{-1}] \leq 0.2$ and key Ly$\alpha$ forest observables agree to within $20\%$, and often within $10\%$, throughout reionization. Position-dependent time-delay effects cause inaccuracies in reionization's morphology on large scales at the factor of $2$ level for $\tilde{c} \leq 0.1$. Our method allows for up to a factor of $5$ speedup in studies that express the emissivity in terms of free parameters, including efforts to constrain the emissivity using observations. This is a crucial step towards constraining the ionizing properties of high-redshift galaxies using efficient radiative transfer simulations.