  We use the Aurora radiation-hydrodynamical simulations to study the mean free
path (MFP) for hydrogen ionizing photons during the epoch of reionization. We
directly measure the MFP by averaging the distance 1 Ry photons travel before
reaching an optical depth of unity along random lines-of-sight. During
reionization the free paths tend to end in neutral gas with densities near the
cosmic mean, while after reionizaton the end points tend to be overdense but
highly ionized. Despite the increasing importance of discrete, over-dense
systems, the cumulative contribution of systems with $N_{\rm{HI}} \lesssim
10^{16.5}~{\rm cm^{-2}}$ suffices to drive the MFP at $z \approx 6$, while at
earlier times higher column densities are more important. After reionization
the typical size of HI systems is close to the local Jeans length, but during
reionization it is much larger. The mean free path for photons originating
close to galaxies, $\rm{MFP_{gal}}$, is much smaller than the cosmic MFP. After
reionization this enhancement can remain significant up to starting distances
of $\sim 1$ comoving Mpc. During reionization, however, $\rm{MFP_{gal}}$ for
distances $\sim 10^2 - 10^3$ comoving kpc typically exceeds the cosmic MFP.
These findings have important consequences for models that interpret the
intergalactic MFP as the distance escaped ionizing photons can travel from
galaxies before being absorbed and may cause them to under-estimate the
required escape fraction from galaxies, and/or the required emissivity of
ionizing photons after reionization.
