We investigate self-shielding of intergalactic hydrogen against ionizing radiation in radiative transfer simulations of cosmic reionization carefully calibrated with Ly \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 n _ { \mathrm { 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 .