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Statistical correlation between the distribution of Ly$α$ emitters and IGM HI at $z\sim2.2$ mapped by Subaru/Hyper Suprime-Cam

The correlation between neutral Hydrogen (HI) in the intergalactic medium (IGM) and galaxies now attracts great interests. We select four fields which include several coherently strong Ly$α$ absorption systems at $z\sim2.2$ detected by using background quasars from the whole SDSS/(e)BOSS database. Deep narrow-band and $g$-band imaging are performed using the Hyper Suprime-Cam on the Subaru Telescope. We select out 2,642 Ly$α$ emitter (LAE) candidates at $z=2.177\pm0.023$ down to the Ly$α$ luminosity of $L_{\text{Ly}α}\approx 2 \times 10^{42} {\rm erg~s}^{-1}$ to construct the galaxy overdensity maps, covering an effective area of 5.39 deg$^2$. Combining the sample with the Ly$α$ absorption estimated from 64 (e)BOSS quasar spectra, we find a moderate to strong correlation between the LAE overdensity $δ_{\rm LAE}$ and the effective optical depth $τ_{\rm LoS}$ in line-of-sights, with $P$-value$=0.09\%$ ($<0.01\%$) when the field that contains a significant quasar overdensity is in(ex)cluded. The cross-correlation analysis also clearly suggests that up to $4\pm1$ pMpc, LAEs tend to cluster in the regions rich in HI gas, indicated by the high $τ_{\rm LoS}$, and avoid the low $τ_{\rm LoS}$ region where the HI gas is deficient. By averaging the $τ_{\rm LoS}$ as a function of the projected distance ($d$) to LAEs, we find a $30\%$ excess signal at $2σ$ level at $d<200$ pkpc, indicating the dense HI in circumgalactic medium, and a tentative excess at $400<d<600$ pkpc in IGM regime, corroborating the cross-correlation signal detected at about $0.5$ pMpc. These statistical analyses indicate that galaxy$-$IGM HI correlations exist on scales ranging from several hundred pkpc to several pMpc at $z\sim2.2$.