IGM damping wing constraints on the tail end of reionisation from the enlarged XQR-30 sample

The attenuation of Ly$\alpha$ photons by neutral hydrogen in the intergalactic medium (IGM) at $z\gtrsim5$ continues to be a powerful probe for studying the epoch of reionisation. Given a framework to estimate the intrinsic (true) Ly$\alpha$ emission of high-$z$ sources, one can infer the ionisation state of the IGM during reionisation. In this work, we use the enlarged XQR-30 sample of 42 high-resolution and high-SNR QSO spectra between $5.8\lesssim\,z\lesssim\,6.6$ obtained with VLT/X-Shooter to place constraints on the IGM neutral fraction. This is achieved using our existing Bayesian QSO reconstruction framework which accounts for uncertainties such as the: (i) posterior distribution of predicted intrinsic Ly$\alpha$ emission profiles (obtained via covariance matrix reconstruction of the Ly$\alpha$ and N V emission lines from unattenuated high-ionisation emission line profiles; C IV, Si IV + O IV] and C III]) and (ii) distribution of ionised regions within the IGM using synthetic damping wing profiles drawn from a $1.6^3$ Gpc$^3$ reionisation simulation. Following careful quality control, we used 23 of the 42 available QSOs to obtain constraints/limits on the IGM neutral fraction during the tail-end of reionisation. Our median and 68th percentile constraints on the IGM neutral fraction are: $0.20\substack{+0.14\\-0.12}$ and $0.29\substack{+0.14\\-0.13}$ at $z = 6.15$~and 6.35. Further, we also report 68th percentile upper-limits of $\bar{x}_{\mathrm{H\,{\scriptscriptstyle I}}} < 0.21$, 0.20, 0.21 and 0.18 at $z = 5.8, 5.95, 6.05$~and 6.55. These results imply reionisation is still ongoing at $5.8\lesssim\,z\lesssim\,6.55$, consistent with previous results from XQR-30 (dark fraction and Ly$\alpha$ forest) along with other observational probes considered in the literature.