Constraints on the mean free path of ionising photons at $z\sim6$ using limits on individual free paths

TL;DR

This paper introduces a new method using quasar absorption data to better constrain the ionising mean free path at redshift 6, providing tighter bounds crucial for understanding the end of reionisation.

Contribution

The paper presents a novel approach to constrain the mean free path at z~6 using individual quasar free path limits, improving upon traditional stacking methods.

Findings

80% of bright quasars require free paths > 2 pMpc

Constraints on mp are tighter for lower 

New bounds on mp and  are crucial for reionisation studies

Abstract

The recent measurement of an ionising mean free path $\lambda_{\text{mfp}}<1$ pMpc at $z=6$ challenges our understanding of the small-scale structure of the intergalactic medium (IGM) at the end of reionisation. We introduce a new method to constrain \mfp at $z=6$ by using lower limits on the individual free paths of ionisation around quasars. Lyman-limit absorbers with a density sufficient to halt ionising photons produce strong absorption in the 6 lowest-energy Lyman transitions, in the absence of which a robust lower limit can be placed on the individual free path. Applying this method to a set of $26$ quasars at $5.5<z<6.5$, we find that $80\%$ of bright quasars ($M_{1450}<-26.5$) require individual free paths larger than $2$ pMpc. We model the relation between opacity $\kappa$ and photo-ionisation rate $\Gamma$ via the parameter $\xi$ such that $\kappa\propto\Gamma^{-\xi}$, and pose joint limits on \mfp and $\xi$. For the nominal value of $\xi=2/3$, we constrain $\lambda_{\text{mfp}}>0.31 \ (0.18)$ pMpc at $2\sigma \ (3\sigma)$: a much tighter lower bound than obtained through traditional stacking methods. Our constraints get significantly stronger for lower values of $\xi$. New constraints on \mfp and $\xi$ are crucial to our understanding of the reionisation-era IGM.