Constraints on reionisation from the z=7.5 QSO ULASJ1342+0928
  The recent detection of ULASJ1342+0928, a bright QSO at $z=7.54$, provides a
powerful probe of the ionisation state of the intervening intergalactic medium,
potentially allowing us to set strong constraints on the epoch of reionisation
(EoR). Here we quantify the presence of Ly$\alpha$ damping wing absorption from
the EoR in the spectrum of ULASJ1342+0928. Our Bayesian framework
simultaneously accounts for uncertainties on: (i) the intrinsic QSO emission
(obtained from reconstructing the Ly$\alpha$ profile from a covariance matrix
of emission lines) and (ii) the distribution of HII regions during reionisation
(obtained from three different 1.6$^3$ Gpc$^3$ simulations spanning the range
of plausible EoR morphologies). Our analysis is complementary to that in the
discovery paper (Ba\~nados et al.) and the accompanying method paper (Davies et
al.) as it focuses solely on the damping wing imprint redward of Ly$\alpha$
($1218 < \lambda < 1230$\AA), and uses a different methodology for (i) and
(ii). We recover weak evidence for damping wing absorption. Our intermediate
EoR model yields a volume-weighted neutral hydrogen fraction at $z=7.5$ of
$\bar{x}_{\rm HI} = 0.21\substack{+0.17 \\ -0.19}$ (68 per cent). The
constraints depend weakly on the EoR morphology. Our limits are lower than
those presented previously, though they are consistent at ~1-1.5$\sigma$. We
attribute this difference to: (i) a lower amplitude intrinsic Ly$\alpha$
profile obtained from our reconstruction pipeline, driven by correlations with
other high-ionisation lines in the spectrum which are relatively weak; and (ii)
only considering transmission redward of Ly$\alpha$ when computing the
likelihood, which reduces the available constraining power but makes the
results less model-dependent. Our results are consistent with previous
estimates of the EoR history, and support the picture of a moderately extended
EoR.
