Measuring the IGM correlation length at 5<z<6.1: a fast change at the end of Reionization

The Lyman-$α$ forest of high redshift quasars is a powerful probe of the late stages of the Epoch of Reionization (EoR), particularly through the presence of Gunn-Peterson troughs. These troughs span a broad range of lengths (up to $\sim 100$ Mpc), suggesting large-scale coherent structures in the intergalactic medium. We aim to gain insight into the presence, extent, and magnitude of correlations in the Lyman-$α$ forest at $5<z<6.1$, and to quantify the scales over which correlations are significant to inform on the necessary volume for simulating the EoR. Using the extended XQR-30 dataset and accounting for the relevant systematics, we compute the flux correlation matrix and perform an MCMC analysis to quantify the extent and strength of the correlation. To interpret our results, we compare to $1.5^3,\mathrm{Gpc}^3$ lightcones of Lyman-$α$ transmission fluxes from several reionization scenarios, including a fiducial box employing SCRIPT. We detect strong correlations at $z > 5.3$, extending at least tens of Mpc and strongly increasing with redshift. Our results suggest a redshift-dependent correlation length, from $L \leq 26.53\, (68.47)$ Mpc at 1-$σ$ (2-$σ$) limit at $z = 5.0$ to $L = 252.72^{+272.61}_{-41.61}$ Mpc at $z = 6.1$. In contrast, all simulation models predict shorter correlation lengths ($< 60$ Mpc) and a slower redshift evolution. The presence and redshift-dependence of correlations in the Lyman-$α$ forest on $>200$ Mpc scales at $z=6$ indicates that cosmological simulations should be larger than this scale to adequately sample the Lyman-$α$ forest. Despite implementing a fluctuating UVB and numerous neutral islands at $z<6$, our fiducial SCRIPT-based simulation fails to reproduce the large-scale correlations. It may be that those ingredients are necessary, but not sufficient, to understanding the unfolding of the EoR.