Statistical correlation between the distribution of Ly$\alpha$ 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$\alpha$ 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$\alpha$ emitter (LAE) candidates
at $z=2.177\pm0.023$ down to the Ly$\alpha$ luminosity of
$L_{\text{Ly}\alpha}\approx 2 \times 10^{42} {\rm erg~s}^{-1}$ to construct the
galaxy overdensity maps, covering an effective area of 5.39 deg$^2$. Combining
the sample with the Ly$\alpha$ absorption estimated from 64 (e)BOSS quasar
spectra, we find a moderate to strong correlation between the LAE overdensity
$\delta_{\rm LAE}$ and the effective optical depth $\tau_{\rm LoS}$ 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 $\tau_{\rm
LoS}$, and avoid the low $\tau_{\rm LoS}$ region where the HI gas is deficient.
By averaging the $\tau_{\rm LoS}$ as a function of the projected distance ($d$)
to LAEs, we find a $30\%$ excess signal at $2\sigma$ 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 $z\sim2.2$.
