The effect of reionization on direct measurements of the mean free path

Recent measurements of the ionizing photon mean free path (MFP) based on composite quasar spectra may point to reionization ending at $z<6$. These measurements are challenging because they rely on assumptions about the proximity zones of the quasars. For example, some quasars might have been close to neutral patches where reionization was still ongoing ("neutral islands"), and it is unclear how they would affect the measurements. We address this question with mock MFP measurements from radiative transfer simulations. We find that, even in the presence of neutral islands, our mock MFP measurements agree to within $30~\%$ with the true spatially averaged MFP in our simulations, which includes opacity from both the ionized medium and the islands. The inferred MFP is sensitive at the $<~50\%$ level to assumptions about quasar environments and lifetimes for realistic models. We demonstrate that future analyses with improved data may require explicitly modeling the effects of neutral islands on the composite spectra, and we outline a method for doing this. Lastly, we quantify the effects of neutral islands on Lyman-series transmission, which has been modeled with optically thin simulations in previous MFP analyses. Neutral islands can suppress transmission at $\lambda_{\rm rest}<912$ Angstroms significantly, up to a factor of 2 for $z_{\rm qso}=6$ in a plausible reionization scenario, owing to absorption by many closely spaced lines as quasar light redshifts into resonance. However, the suppression is almost entirely degenerate with the spectrum normalization and thus does not significantly bias the inferred MFP.