MOIRCS Deep Survey. II. Clustering Properties of $K$-Band Selected Galaxies in GOODS-North Region

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Abstract We present the first measurement of clustering properties of low-mass galaxies with a stellar mass down to $M_*\sim 10^9 M_{\odot}$ at 1$\lt z \lt $4 in 24.4 arcmin$^{2}$ of the GOODS-North region with a depth of $K_\mathrm{AB}\sim$25. Luminous galaxies in the $K$-band have a larger correlation length than faint galaxies. For color-selected samples at 2$\lt z \lt$4, distant red galaxies with $J-K \gt$1.3 show a large bias of $b\sim$7.2$\pm$1.3 on scales of up to $\theta\sim$100$^{\prime\prime}$ or 3.1 comoving Mpc, while blue galaxies with 0.5$\lt J-K \lt $1.3 have a weak clustering signal on large scales, but a possible strong small-scale excess at $\theta \lt $10$^{\prime\prime}$. For massive galaxies with $M_*\gtrsim 10^{10}M_{\odot}$, we estimate the correlation length and bias to be $r_0\sim$4.5$h^{-1}$Mpc and $b=$1.9–3.5, which are much larger than those of low-mass ($M_*\sim$10$^9-10^{10}M_{\odot}$) galaxies. The comparison of our measurements with analytic CDM models constrains the properties of hosting dark halos, and indicates that the low-mass galaxies would be progenitors of galaxies with a typical luminosity of $L\lesssim L_*$ in the local Universe. The blue galaxies in low-mass samples are more strongly clustered in more massive halos with higher occupation numbers than low-mass red galaxies. This fact suggests an environment effect due to the halo mass on the star-formation activity at high-$z$.