Constraints on the <i>z</i>   ∼  6−13 intergalactic medium from JWST spectroscopy of Lyman-alpha damping wings in galaxies

Context. JWST provides a unique dataset for studying the earliest stages of reionisation at z &gt; 9, promising insights into the first galaxies. Many JWST/NIRSpec prism spectra of z &gt; 5 galaxies have revealed smooth Lyman-alpha breaks, implying damping wing scattering by neutral hydrogen. Aims. We investigate what current prism spectra imply about the intergalactic medium (IGM) at z &gt; 6 and how best to use NIRSpec spectra to recover IGM properties. We use a sample of 99 z ∼ 5.5 − 13 galaxies with high S/N prism spectra in the public archive, including 12 at z &gt; 10. Methods. We analyse these spectra using damping wing sightlines from inhomogeneous reionising IGM simulations, mapping between the distance of a source from the neutral IGM and the average IGM neutral fraction. We marginalise over absorption by local neutral hydrogen around the galaxies and Lyman-alpha emission. Results. We observe a decline in the median and variance of flux around the Ly α break with increasing redshift, consistent with an increasingly neutral IGM, as ionized regions become smaller and rarer. At z ≳ 9 the spectra become consistent with an almost fully neutral IGM. We find S/N &gt; 15 per pixel is required to robustly estimate IGM properties from prism spectra. We fit a sub-sample of high S/N spectra and infer mean IGM neutral fractions of x̄ H I = 0.33 −0.27 +0.18 , 0.64 −0.23 +0.17 (&gt; 0.70 excluding GNz11) at z ≈ 6.5, 9.3. We also investigate local HI absorption, finding a median column density of log 10 N H I ≈ 10 20.8 cm −2 , comparable to z ∼ 3 Lyman-break galaxies, with no significant redshift evolution z ≳ 5.5. We find galaxies showing the highest column density absorption are more likely to be in close associations of sources (≲500 pkpc), implying absorption is enhanced in massive dark matter halos. Future deep prism and grating spectroscopy of z &gt; 9 sources will provide tighter constraints on the earliest stages of reionisation, key for understanding the onset of star formation.