GOLDRUSH. II. Clustering of galaxies at z ∼ 4-6 revealed with the half-million dropouts over the 100 deg2 area corresponding to 1 Gpc3

We present clustering properties from 579492 Lyman-break galaxies (LBGs) at z similar to 4-6 over the 100 deg(2) sky (corresponding to a 1.4 Gpc(3) volume) identified in early data of the Hyper Suprime-Cam (HSC) Subaru Strategic Program survey. We derive angular correlation functions (ACFs) for the HSC LBGs with unprecedentedly high statistical accuracies at z similar to 4-6, and compare them with the halo occupation distribution (HOD) models. We clearly identify significant ACF excesses in 10 '' < theta < 90 '', the transition scale between one-and two-halo terms, suggestive of the existence of the non-linear halo bias effect. Combining the HOD models and previous clustering measurements of faint LBGs at z similar to 4-7, we investigate the dark matter halo mass (M-h) of the z similar to 4-7 LBGs and its correlation with various physical properties including the star formation rate (SFR), the stellar-to-halo mass ratio (SHMR), and the dark matter accretion rate (<(M)over dot>(h)) over a wide mass range of M-h/M-circle dot = 4 x 10(10)-4 x 10(12). We find that the SHMR increases from z similar to 4 to 7 by a factor of similar to 4 at Mh similar or equal to 1 x 10(11) M-circle dot, while the SHMR shows no strong evolution in the similar redshift range at M-h similar or equal to 1 x 10(12) M-circle dot. Interestingly, we identify a tight relation of SFR/<(M)over dot>(h)-M-h showing no significant evolution beyond 0.15 dex in this wide mass range over z similar to 4-7. This weak evolution suggests that the SFR/<(M)over dot>(h)-M-h relation is a fundamental relation in high-redshift galaxy formation whose star formation activities are regulated by the dark matter mass assembly. Assuming this fundamental relation, we calculate the cosmic star formation rate densities (SFRDs) over z = 0-10 (a. k. a. the Madau-Lilly plot). The cosmic SFRD evolution based on the fundamental relation agrees with the one obtained by observations, suggesting that the cosmic SFRD increase from z similar to 10 to 4 - 2 (decrease from z similar to 4-2 to 0) is mainly driven by the increase of the halo abundance (the decrease of the accretion rate).