Abstract
The large opacity fluctuations in the $z > 5.5$ Ly$\alpha$ forest may
indicate inhomogeneous progress of reionization. To explain the observed large
scatter of the effective Ly$\alpha$ optical depth ($\tau_eff$) of the
intergalactic medium (IGM), fluctuation of UV background ($\Gamma$ model) or
the IGM gas temperature ($T$ model) have been proposed, which predict opposite
correlations between $\tau_eff$ and galaxy density. In order to address
which model can explain the large scatter of $\tau_eff$, we search for
Ly$\alpha$ emitters (LAEs) around two (J1137+3549 and J1602+4228) quasar
sightlines with $\tau_eff\sim3$ and J1630+4012 sightline with $\tau_\rm
eff\sim5.5$. Using a narrowband imaging with Subaru/Hyper Suprime-Cam, we draw
LAE density maps to explore their spatial distributions. Overdensities are
found within 20 $h^-1$Mpc of the quasar sightlines in the low $\tau_\rm
eff$ regions, while a deficit of LAEs is found in the high $\tau_eff$
region. Although the $\tau_eff$ of the three quasar sightlines are
neither high nor low enough to clearly distinguish the two models, these
observed $\tau_eff$-galaxy density relations all consistently support the
$\Gamma$ model rather than the $T$ model in the three fields, along with the
previous studies. The observed overdensities near the low $\tau_eff$
sightlines may suggest that the relic temperature fluctuation does not affect
reionization that much. Otherwise, these overdensities could be attributed to
other factors besides the reionization process, such as the nature of LAEs as
poor tracers of underlying large-scale structures.
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