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The variations in Ly$\alpha$ forest opacity observed at $z>5.3$ between linesof sight to different background quasars are too strong to be caused byfluctuations in the density field alone. The leading hypothesis for the causeof this excess variance is a late, ongoing reionization process at redshiftsbelow six. Another model proposes strong ionizing background fluctuationscoupled to a short, spatially varying mean free path of ionizing photons,without explicitly invoking incomplete reionization. With recent observationssuggesting a short mean free path at $z\sim6$, and a dramatic improvement in$z>5$ Ly$\alpha$ forest data quality, we revisit this latter possibility. Herewe apply the likelihood-free inference technique of approximate Bayesiancomputation to jointly constrain the hydrogen photoionization rate $\Gamma_{\rmHI}$ and the mean free path of ionizing photons $\lambda_{\rm mfp}$ from theeffective optical depth distributions at $z=5.0$-$6.1$ from XQR-30. We findthat the observations are well-described by fluctuating mean free path modelswith average mean free paths that are consistent with the steep trend impliedby independent measurements at $z\sim5$-$6$, with a concomitant rapid evolutionof the photoionization rate.

Constraints on the Evolution of the Ionizing Background and Ionizing Photon Mean Free Path at the End of Reionization