JWST Measurements of Neutral Hydrogen Fractions and Ionized Bubble Sizes at $z=7-12$ Obtained with Ly$\alpha$ Damping Wing Absorptions in 27 Bright Continuum Galaxies

We present volume-averaged neutral hydrogen fractions $x_{\rm \HI}$ and ionized bubble radii $R_{\rm b}$ measured with Ly$\alpha$ damping wing absorption of galaxies at the epoch of reionization. We combine JWST/NIRSpec spectra taken by CEERS, GO-1433, DDT-2750, and JADES programs, and obtain a sample containing 27 bright UV-continuum ($M_{\rm UV}<-18.5~{\rm mag}$) galaxies at $7<z<12$. We construct 4 composite spectra binned by redshift, and find the clear evolution of softening break towards high redshift at the rest-frame $1216$ {\AA}, suggesting the increase of Ly$\alpha$ damping wing absorption. We estimate Ly$\alpha$ damping wing absorption in the galaxy spectra with realistic templates including Ly$\alpha$ emission and circum-galactic medium absorptions. Assuming the standard inside-out reionization picture having an ionized bubble with radius $R_b$ around a galaxy embedded in the intergalactic medium with $x_{\rm \HI}$, we obtain $x_{\rm \HI}$ ($R_{\rm b}$) values generally increasing (decreasing) from $x_{\rm \HI}={0.53}^{+0.18}_{-0.47}$ to ${0.92}^{+0.08}_{-0.10}$ ($\log R_{\rm b}={1.67}^{+0.14}_{-0.16}$ to ${-0.69}^{+0.89}_{-0.24}$ comoving Mpc) at redshift $7.12^{+0.06}_{-0.08}$ to $9.91^{+1.49}_{-1.15}$. The redshift evolution of $x_{\rm \HI}$ indicates a moderately late reionization history consistent with the one previously suggested from the electron scattering of cosmic microwave background and the evolution of UV luminosity function with an escape fraction $f_{\rm esc}\sim 0.2$. Our ${R_{\rm b}}$ measurements suggest that bubble sizes could be up to a few dex larger than the cosmic average values estimated by analytic calculations for a given $x_{\rm \HI}$, while our $R_{\rm b}$ measurements are roughly comparable with the values for merged ionized bubbles around bright galaxies predicted by recent numerical simulations.
Comment: Accepted for publication in ApJ. We have added discussion comparing fitting for low-resolution spectra and high resolution spectra. We also modified the inference method based on Bayesian theory