Improved treatments of the ionizing photon mean free path in semi-numerical simulations of reionization

Efficient and accurate simulations of the reionization epoch are crucial to exploring the vast uncharted parameter space that will soon be constrained by measurements of the 21 cm power spectrum. One of these parameters, $R_{\rm max}$, is meant to characterize the absorption of photons by residual neutral gas inside of ionized regions, but has historically been implemented in a very simplistic fashion acting only as a maximum filtering scale. We leverage the correspondence between excursion set methods and the integrated flux from ionizing sources to define two physically-motivated prescriptions of the mean free path of ionizing photons that smoothly attenuate the contribution from distant sources. Implementation of these methods in semi-numerical reionization codes requires only modest additional computational effort due to the fact that spatial filtering is still performed on scales larger than the characteristic absorption distance. We find that our smoothly-defined mean free path prescriptions more effectively suppress large-scale structures in the ionization field in semi-numerical reionization simulations compared to the standard $R_{\rm max}$ approach, and the magnitude of the mean free path modulates the power spectrum in a much smoother manner. We show that this suppression of large-scale power is significant enough to be relevant for upcoming 21 cm power spectrum observations. Finally, we show that in our model the mean free path plays a larger role in regulating the reionization history than in models using $R_{\rm max}$.