The Universe is Reionizing at z~7: Bayesian Inference of the IGM Neutral Fraction Using Ly$α$ Emission from Galaxies

Abstract: 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~6-10) from detections and non-detections of Lyman Alpha (Ly$\alpha$) emission from Lyman break galaxies (LBGs). Our framework combines sophisticated reionization simulations with empirical models of the interstellar medium (ISM) radiative transfer effects on Ly$\alpha$. We assert that the Ly$\alpha$ 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 Ly$\alpha$ 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 Pentericci et al. (2014) and infer a global neutral fraction at z~7 of $\overline{x}\mathrm{HI} = 0.59{-0.15}^{+0.11}$, consistent with other robust probes of the EoR and confirming reionization is on-going ~700 Myr after the Big Bang. We show that using the full distribution of Ly$\alpha$ equivalent width detections and upper limits from LBGs places tighter constraints on the evolving IGM than the standard Ly$\alpha$ emitter fraction, and that larger samples are within reach of deep spectroscopic surveys of gravitationally lensed fields and JWST NIRSpec.