A short mean free path at $z=6$ favors late and rapid reionization by faint galaxies

Recent measurements of the ionizing photon mean free path (${\lambda }_{912}^{\mathrm{m}\mathrm{f}\mathrm{p}}$) at $5<z<6$ suggest that the IGM was rapidly evolving at those times. We use radiative transfer simulations to explore the implications for reionization, with a focus on the short value of ${\lambda }_{912}^{\mathrm{m}\mathrm{f}\mathrm{p}}=3.57_{-2.14}^{+3.09}$ cMpc/$h$ at $z=6$. We introduce a model for sub-resolution ionizing photon sinks based on radiative hydrodynamics simulations of small-scale IGM clumping. We argue that the rapid evolution in ${\lambda }_{912}^{\mathrm{m}\mathrm{f}\mathrm{p}}$ at $z=5-6$, together with constraints on the metagalactic ionizing background, favors a late reionization process in which the neutral fraction evolved rapidly in the latter half. We also argue that the short ${\lambda }_{912}^{\mathrm{m}\mathrm{f}\mathrm{p}}(z=6)$ points to faint galaxies as the primary drivers of reionizaton. Our preferred model, with $\lambda_{912}^{\rm mfp}(z=6) = 6.5$Mpc\mathrm{/}$h$,hasamidpointof$z= 7.1$andendsat$z= 5.1$. It requires 3 ionizing photons per H atom to complete reionization and a LyC photon production efficiency of $\log(f^{\rm eff}{\rm esc} \xi{\rm ion}/[$\mathrm{e}\mathrm{r}\mathrm{g}$^{-1} $\mathrm{H}\mathrm{z}$]) = 24.8$at$z>6$\mathrm{.}Recovering$\lambda_{912}^{\rm mfp}(z=6)$ as low as the measured central value may require an increase in IGM clumpiness beyond predictions from simulations, with a commensurate increase in the photon budget.