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 ($\lambda_{912}^{\rm mfp}$) at $5 6$. 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.