Probing patchy reionisation with JWST: IGM opacity constraints from the Lyman-$\alpha$ forest of galaxies in legacy extragalactic fields

We present the first characterization of the Gunn-Peterson trough in high-redshift galaxies using public JWST NIRSpec spectroscopy. This enables us to derive the first galaxy-based IGM opacity measurements at the end of reionisation. Using galaxy spectra has several advantages over quasar spectra: it enables measurements of the IGM opacity in any extragalactic field over a continuous redshift range $4\lesssim z\lesssim 7$, as well as measurements of the intrinsic Lyman-$\beta$ opacity. Our novel constraints are in good agreement with state-of-the-art ground-based quasar Lyman-$\alpha$ forest observations, and will become competitive as the number of JWST $z>5$ galaxy spectra rapidly increases. We also provide the first constraints on the uncontaminated Lyman-$\beta$ opacity at $5<z<6$. Finally, we demonstrate the power of JWST to connect the ionisation state of the IGM to the sources of reionisation in a single extragalactic field. We show that a previously reported galaxy overdensity and an excess of Lyman-$\alpha$ emitters detected with JWST in GOODS-South at $z=5.8-5.9$ coincides with an anomalously low IGM opacity to Lyman-$\alpha$ at this redshift. The local photo-ionisation rate excess can be fully accounted for by the cumulative ionising output of $M_{\rm{UV}}\lesssim -10$ galaxies in the overdensity, provided they have $\log_{10}\langle \xi_{\rm{ion}} f_{\rm{esc}} / \ [\rm{erg}^{-1}\rm{Hz}]\rangle \simeq 25$ (e.g. $\log_{10}\xi_{\rm{ion}} / \ [\rm{erg}^{-1}\rm{Hz}]=25.4$ and $f_{\rm{esc}}=40\%$). Overall, this breakthrough offers a new way to connect the galaxy large-scale structure to the state of the IGM, potentially enabling us to precisely identify the sources of reionisation.