Self-shielding of hydrogen in the IGM during the epoch of reionization

We investigate self-shielding of intergalactic hydrogen against ionizing radiation in radiative transfer simulations of cosmic reionization carefully calibrated with Lyman alpha forest data. While self-shielded regions manifest as Lyman-limit systems in the post-reionization Universe, here we focus on their evolution during reionization (redshifts z=6-10). At these redshifts, the spatial distribution of hydrogen-ionizing radiation is highly inhomogeneous, and some regions of the Universe are still neutral. After masking the neutral regions and ionizing sources in the simulation, we find that the hydrogen photoionization rate depends on the local hydrogen density in a manner very similar to that in the post-reionization Universe. The characteristic physical hydrogen density above which self-shielding becomes important at these redshifts is about $\mathrm{n_H \sim 3 \times 10^{-3} cm^{-3}}$, or $\sim$ 20 times the mean hydrogen density, reflecting the fact that during reionization photoionization rates are typically low enough that the filaments in the cosmic web are often self-shielded. The value of the typical self-shielding density decreases by a factor of 3 between redshifts z=3 and 10, and follows the evolution of the average photoionization rate in ionized regions in a simple fashion. We provide a simple parameterization of the photoionization rate as a function of density in self-shielded regions during the epoch of reionization.