  This paper systematically investigates comoving Mpc scale intergalactic
medium (IGM) environment around galaxies traced by the Ly$\alpha$ forest. Using
our cosmological hydrodynamic simulations, we investigate the IGM-galaxy
connection at $z=2$ by two methods: (I) cross-correlation analysis between
galaxies and the fluctuation of Ly$\alpha$ forest transmission
($\delta_\text{F}$); and (II) comparing the overdensity of neutral hydrogen
(HI) and galaxies. Our simulations reproduce observed cross-correlation
functions (CCF) between Ly$\alpha$ forest and Lyman-break galaxies. We further
investigate the variation of the CCF using subsamples divided by dark matter
halo mass ($M_\text{DH}$), galaxy stellar mass ($M_\star$), and star-formation
rate (SFR), and find that the CCF signal becomes stronger with increasing
$M_\text{DH}$, $M_\star$, and SFR. The CCFs between galaxies and gas-density
fluctuation are also found to have similar trends. Therefore, the variation of
the $\delta_\text{F}$-CCF depending on $M_\text{DH}$, $M_\star$, and SFR is due
to varying gas density around galaxies. We find that the correlation between
galaxies and the IGM HI distribution strongly depends on $M_\text{DH}$ as
expected from the linear theory. Our results support the $\Lambda$CDM paradigm,
finding a spatial correlation between galaxies and IGM HI, with more massive
galaxies being clustered in higher-density regions.
