We present a new flexible Bayesian framework for directly inferring the fraction of neutral hydrogen in the intergalactic medium ( IGM ) during the Epoch of Reionization ( EoR , z \sim 6 - 10 ) from detections and non-detections of Lyman Alpha ( \lya ) emission from Lyman Break galaxies ( LBGs ) .
Our framework combines sophisticated reionization simulations with empirical models of the interstellar medium ( ISM ) radiative transfer effects on \lya .
We assert that the \lya line profile emerging from the ISM has an important impact on the resulting transmission of photons through the IGM , and that these line profiles depend on galaxy properties .
We model this effect by considering the peak velocity offset of \lya lines from host galaxies ’ systemic redshifts which are empirically correlated with UV luminosity and redshift ( or halo mass at fixed redshift ) .
We use our framework on the sample of LBGs presented in ( ) and infer a global neutral fraction at z \sim 7 of { \overline { x } _ { \textrm { \scriptsize { H { i } } } } } = 0.59 _ { -0.15 } ^ { +0.11 } , consistent with other robust probes of the EoR and confirming reionization is on-going \sim 700 Myr after the Big Bang .
We show that using the full distribution of \lya equivalent width detections and upper limits from LBGs places tighter constraints on the evolving IGM than the standard \lya emitter fraction , and that larger samples are within reach of deep spectroscopic surveys of gravitationally lensed fields and JWST NIRSpec .