Abstract
The Ly$\alpha$ luminosity function (LF) of Ly$\alpha$ emitters (LAEs) has
been used to constrain the neutral hydrogen fraction in the intergalactic
medium (IGM) and thus the timeline of cosmic reionization. Here we present the
results of a new narrow-band imaging survey for $z=7.3$ LAEs in a large area of
$3\ deg^2$ with Subaru/Hyper Suprime-Cam. No LAEs are detected
down to $L_Ly\alpha10^43.2\ erg\ s^-1$ in an
effective cosmic volume of $210^6$ Mpc$^3$, placing an upper limit
to the bright part of the $z=7.3$ Ly$\alpha$ LF for the first time and
confirming a decrease in bright LAEs from $z=7.0$. By comparing this upper
limit with the Ly$\alpha$ LF in the case of the fully ionized IGM, which is
predicted using an observed $z=5.7$ Ly$\alpha$ LF on the assumption that the
intrinsic Ly$\alpha$ LF evolves in the same way as the UV LF, we obtain the
relative IGM transmission
$T^IGM_Ly\alpha(7.3)/T^IGM_Ly\alpha(5.7)<0.77$,
and then the volume-averaged neutral fraction $x_HI(7.3)>0.28$. Cosmic
reionization is thus still ongoing at $z=7.3$, being consistent with results
from other $x_HI$ estimation methods. A similar analysis using
literature Ly$\alpha$ LFs finds that at $z=6.6$ and 7.0 the observed Ly$\alpha$
LF agrees with the predicted one, consistent with full ionization.
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