Measurement of Galaxy Clustering at z~7.2 and the Evolution of Galaxy Bias from 3.8<z<8 in the XDF, GOODS-S AND GOODS-N

Lyman-Break Galaxy (LBG) samples observed during reionization ($z\gtrsim 6$) with Hubble Space Telescope’s Wide Field Camera 3 are reaching sizes sufficient to characterize their clustering properties. Using a combined catalog from the Hubble eXtreme Deep Field and CANDELS surveys, containing $N=743$ LBG candidates at z>6.5 at a mean redshift of $z=7.2$, we detect a clear clustering signal in the angular correlation function (ACF) at $\sim 4\sigma$, corresponding to a real-space correlation length $r_0=6.7_{-1.0}^{+0.9}{h}^{-1}$cMpc. The derived galaxy bias $b=8.6_{-1.0}^{+0.9}$ is that of dark-matter halos of $M={10}^{11.1_{-0.3}^{+0.2}}$M${}_{\odot }$ at $z=7.2$, and highlights that galaxies below the current detection limit ($M_{AB}\sim -17.7$) are expected in lower-mass halos ($M\sim {10}^8-{10}^{10.5}$M${}_{\odot }$). We compute the ACF of LBGs at $z\sim 3.8-z\sim 5.9$ in the same surveys. A trend of increasing bias is found from $z=3.8$ ($b\sim 3.0$) to $z=7.2$ ($b\sim 8.6$), broadly consistent with galaxies at fixed luminosity being hosted in dark-matter halos of similar mass at $4<z<6$, followed by a slight rise in halo masses at $z\sim 7$ ($\sim 2\sigma$ confidence). Separating the data at the median luminosity of the $z=7.2$ sample ($M_{UV}=-19.4$) shows higher clustering at $z=5.9$ for bright galaxies ($r_0=5.5_{-1.5}^{+1.4}{h}^{-1}$cMpc, $b=6.2_{-1.5}^{+1.2}$) compared to faint galaxies ($r_0=1.9_{-1.0}^{+1.1}{h}^{-1}$cMpc, $b=2.7\pm 1.2$) implying a constant mass-to-light ratio $\frac{dlogM}{dlogL}\sim 1.2_{-0.8}^{+1.8}$. A similar trend is present in the $z=7.2$ sample with larger uncertainty. Finally, our bias measurements allow us to investigate the fraction of dark-matter halos hosting UV-bright galaxies (the duty-cycle, ${ϵ}_{DC}$). At $z=7.2$ values near unity are preferred, which may be explained by the shortened halo assembly time at high-redshift.