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 ( ${\lambda }_{912}^{\mathrm{mfp}}$ ) 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 ${\lambda }_{912}^{\mathrm{mfp}}={3.57}_{-2.14}^{+3.09}$ cMpc h^-1 at z = 6. We introduce a model for subresolution ionizing photon sinks based on radiative hydrodynamics simulations of small-scale IGM clumping. We argue that the rapid evolution in ${\lambda }_{912}^{\mathrm{mfp}}$ 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 ${\lambda }_{912}^{\mathrm{mfp}}(z=6)$ points to faint galaxies as the primary drivers of reionizaton. Our preferred model, with ${\lambda }_{912}^{\mathrm{mfp}}(z=6)=6.5$ Mpc h^-1, has a midpoint of z = 7.1 and ends at z = 5.1. It requires three ionizing photons per H atom to complete reionization and a LyC photon production efficiency of $\mathrm{log}({f}_{\mathrm{esc}}^{\mathrm{eff}}{\xi }_{\mathrm{ion}}/[{\mathrm{erg}}^{-1}\mathrm{Hz}])=24.8$ at z > 6. Recovering ${\lambda }_{912}^{\mathrm{mfp}}(z=6)$ 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.