Lyα opacity, τeff, measured by the Gunn-Peterson (GP) trough at z>5.5, has a significant variation among different quasar sightlines, indicating a spatially inhomogeneous reionizing process. A physical origin of such a significant variation has not yet been identified. Two contradictory models, incorporating additional fluctuations in either the ionizing background (Γ) or the relic temperature (T) fluctuation, have completely different predictions about the spatial distribution of the τeff, and it is thus possible to directly distinguish these two predictions through galaxy distributions at the same redshift. We conducted HSC NB816 imaging to probe the Lyα emitters (LAEs) in three regions, and the results suggested that Γ fluctuation causes the patchy reionization. However, since most of the galaxy searches so far have used LAEs, the results may depend on the nature of LAEs. To obtain more robust conclusion, independent validation using another galaxy population is required. We propose HSC imaging of NB872, HSC-I2, HSC-Z, and HSC-Y to probe the distribution of LAEs and Lyman Break Galaxies (LBGs) around the two high-τeff quasar sightlines. The main goal of the observation is to test τeff correlates positively or negatively with galaxy density to distinguish the two contradicting scenarios.
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