Lyα forest opacity, τeff, measured by the Gunn-Peterson (GP) trough at z>5.5 has a significant variation among different quasar lines of sight, indicating a spatially inhomogeneous reionizing process. A physical origin of such a significant variation has not yet been identified. Two contradictory models, incorporating either the ionizing background (Γ) fluctuations or the relic temperature (T) fluctuation, obviously have completely different predictions about the spatial distribution the Lyα opacity, and it may be possible to directly distinguish these two predictions through galaxy distributions at the same redshift. We propose HSC deep NB816 imaging to probe the Lyα emitters (LAEs) at z∼5.7 in five z>6 quasar fields. The main goal of the observation is to test whether τeff correlates positively or negatively with the LAE density and to distinguish the two contradicting scenario, either fluctuation in T or Γ, based on the carefully selected sample of z>6 quasars with extreme high τeff at the end of reionization. A large semi-numerical simulations demonstrated that our well-designed observation will clearly distinguish between the competing models. The observation will answer, for the first time, why there are large variation in GP trough at z=5.7.
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