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.
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