Probing the Reionization History and Bubble Sizes with JWST Lyman-$\alpha$ Fraction Measurements

Recent James Webb Space Telescope (JWST) measurements quantify the fraction of ultraviolet-selected galaxies showing detectable Lyman-alpha (Ly-$\alpha$) lines at $z\sim 6-14$. These Ly-$\alpha$ fractions are partly shaped by Ly-$\alpha$ scattering from neutral hydrogen in the surrounding intergalactic medium (IGM), and so the observed Ly-$\alpha$ fraction evolution can inform our understanding of the reionization history and the size distribution of ionized bubbles during reionization. We compare the JWST measurements with Ly-$\alpha$ transmission calculations based on both the THESAN reionization simulations and a flexible semi-analytic model. In each case, we calibrate a sub-grid model for the intrinsic Ly-$\alpha$ emission lines emerging from the interstellar medium (ISM) and circumgalactic medium (CGM) of the host galaxies using empirical estimates of the Ly-$\alpha$ equivalent width (EW) distributions at $z\sim 6$. We find that the reionization history and bubble sizes in THESAN yield good agreement with current JWST Ly-$\alpha$ fraction observations, with a reduced ${\chi }_{\nu }^2=0.4-1.2$. Our semi-analytic models and THESAN Ly-$\alpha$ transmission calculations agree well, allowing us to explore a wide range of reionization models. We derive $1\sigma$ bounds on the average mass-weighted neutral fractions of: $⟨x_{\mathrm{H}\mathrm{I}}⟩$ = $0.38_{-0.38}^{+0.14}$ ($0.52_{-0.21}^{+0.09}$), $0.57_{-0.57}^{+0.23}$ ($0.68_{-0.39}^{+0.12}$), and $0.93_{-0.17}^{+0.05}$ ($0.89_{-0.15}^{+0.11}$) at $z\sim$ 7, 8, and 11, based on the Ly-$\alpha$ fraction measurements with EW $>25\mathring{\mathrm{A}}$ ($>10\mathring{\mathrm{A}}$).