Damping wings in the Lyman-{\alpha} forest: a model-independent measurement of the neutral fraction at 5.4<z<6.1

Recent observations have positioned the endpoint of the Epoch of Reionisation (EoR) at redshift $z \sim 5.3$. However, observations of the Lyman-$\alpha$ forest have not yet been able to discern whether reionisation occurred slowly and late, with substantial neutral hydrogen persisting at redshift $\sim 6$, or rapidly and earlier, with the apparent late end driven by the fluctuating UV background. Gunn-Peterson (GP) absorption troughs are solid indicators that reionisation is not complete until $z=5.3$, but whether they contain significantly neutral gas has not yet been proven. We aim to answer this question by directly measuring, for the first time, the neutral hydrogen fraction ($x_\mathrm{HI}$) at the end of the EoR ($5 \lesssim z \lesssim 6$) in high-redshift quasars spectra. For high neutral fractions $x_\mathrm{HI}\gtrsim0.1$, GP troughs exhibit damping wing (DW) absorption extending over $1000$ km s$^{-1}$ beyond the troughs. While conclusively detected in Lyman-$\alpha$ emission lines of quasars at $z\geq7$, DWs are challenging to observe in the general Lyman-$\alpha$ forest due to absorption complexities and small-scale stochastic transmission features. We report the first successful identification of the stochastic DW signal adjacent to GP troughs at redshifts $z=5.6$ through careful stacking of the dark gaps in Lyman-$\alpha$ forest. We use the signal to present a measurement of the corresponding global $x_\mathrm{HI}=0.19\pm0.07$ $(_{-0.16}^{+0.11})$ at $1\sigma$ $(2\sigma)$ at $z=5.6$ and a limit $x_\mathrm{HI}<0.44$ at $z=5.9$. The detection of this signal demonstrates the existence of substantially neutral islands near the conclusion of the EoR, unequivocally signaling a late-and-slow reionization scenario.