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

Abstract

Abstract We present clustering properties from 579492 Lyman-break galaxies (LBGs) at z ∼ 4–6 over the 100 deg2 sky (corresponding to a 1.4 Gpc3 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 ∼ 4–6, and compare them with the halo occupation distribution (HOD) models. We clearly identify significant ACF excesses in 10″ < θ < 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 ∼ 4–7, we investigate the dark matter halo mass (Mh) of the z ∼ 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 ($\skew4\dot{M}_{\,\rm h}$) over a wide mass range of Mh/M⊙ = 4 × 1010–4 × 1012. We find that the SHMR increases from z ∼ 4 to 7 by a factor of ∼4 at Mh ≃ 1 × 1011 M⊙ , while the SHMR shows no strong evolution in the similar redshift range at Mh ≃ 1 × 1012 M⊙ . Interestingly, we identify a tight relation of SFR$/\skew4\dot{M}_{\,\rm h}$–Mh showing no significant evolution beyond 0.15 dex in this wide mass range over z ∼ 4–7. This weak evolution suggests that the SFR$/\skew4\dot{M}_{\,\rm h}$–Mh 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 ∼ 10 to 4 − 2 (decrease from z ∼ 4–2 to 0) is mainly driven by the increase of the halo abundance (the decrease of the accretion rate).