Abstract
Recent observations of GN-z11 with JWST have revealed a Ly$\alpha$ emission
line with an equivalent width of 18$2$ angstroms. At z=10.6, this galaxy is
expected to lie in the heart of reionization. We use a series of inhomogeneous
reionization simulations to derive the distribution of the Ly$\alpha$ EW after
traveling through the neutral intergalactic medium with varying average neutral
gas fraction, $x_HI$. We use these distribution to place an upper limit of
$x_HI < $ 0.88 at z=10.6 at 95% confidence level. We compare our upper limit
to different reionization history models, which include the recently identified
enhancement at the bright end of the luminosity function at z>8. We find that
models in which faint galaxies have higher escape fraction compared to bright
galaxies are favored by the new data.
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