Measuring the intergalactic medium correlation length at 5 < z < 6.1: A fast change at the end of reionization

¹ Institute for Theoretical Physics, Heidelberg University Philosophenweg 12 D–69120 Heidelberg, Germany
² Max-Planck-Institut für Astronomie Königstuhl 17 69117 Heidelberg, Germany

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Received: 16 July 2025
Accepted: 30 November 2025

Abstract

Context. The Lyman-α forest of high-redshift quasars is a powerful probe of the late stages of the epoch of reionization (EoR), in particular thanks to the presence of Gunn-Peterson troughs. These troughs exhibit a broad range of lengths, with some extending up to ∼100 cMpc, suggesting large-scale coherent structures in the intergalactic medium (IGM).

Aims. We aim to gain more insight into the presence, extent, and magnitude of correlations in the Lyman-α forest at the end of reionization, at 5 < z < 6.1. In particular, we want to quantify the scales over which correlations are significant in order to help inform the required size of cosmological simulations aiming to capture the evolution of the EoR.

Methods. We utilized the extended XQR-30 observational dataset over the redshift range 5 < z < 6.1 (Δz = 0.05) to explore large-scale correlations. After accounting for the relevant systematics, the flux correlation matrix proved to be a powerful tool for probing large-scale correlations across redshifts. We performed a Monte Carlo Markov chain analysis to quantify the extent and strength of the correlation, making use of several functional forms. We moreover employed new large-volume (1.5³ Gpc³) light cones of Lyman-α transmission implementing different reionization scenarios to interpret the observed signal, including a fiducial box employing SCRIPT.

Results. We detected strong correlations at redshifts z > 5.3, extending at least tens of megaparsecs and strongly increasing with redshift. Our results suggest a redshift-dependent correlation length, from L ≤ 26.53 (68.47) Mpc at 1σ (2σ) limit at redshift z = 5.0 to L = 252.72^+272.61_−41.61 Mpc at redshift z = 6.1. On the contrary, our simulations all demonstrate characteristic correlation scales < 60 Mpc with a very slow redshift evolution, in strong tension with our observations.

Conclusions. 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 ultraviolet background and numerous neutral islands at z < 6, and matching well the sightline scatter in the Lyman-α forest, our fiducial SCRIPT-based simulation fails to reproduce the large-scale correlations. It may be that those ingredients are necessary, but insufficient, to understand the unfolding of the EoR.