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

Abstract

Lyman-break galaxy (LBG) samples observed during reionization (z >~ 6) with the 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 \overline{z}=7.2, we detect a clear clustering signal in the angular correlation function (ACF) at >~ 4σ, corresponding to a real-space correlation length r_0=6.7^+0.9_-1.0h^-1cMpc. The derived galaxy bias b=8.6^+0.9_-1.0 is that of dark matter halos of M=10^{11.1^{+0.2}_-0.3} M_⊙ \hspace{2.84526pt}at z = 7.2, and highlights that galaxies below the current detection limit (M_AB ~ -17.7) are expected in lower-mass halos (M ~ 10⁸-10^10.5 M_⊙ \hspace{2.84526pt}). We compute the ACF of LBGs at z ~ 3.8 - z ~ 5.9 in the same surveys. A trend of increasing bias is found from \overline{z}=3.8 (b ~ 3.0) to \overline{z}=7.2 (b ~ 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 >~ 7 (~2σ confidence). Separating the data at the median luminosity of the \overline{z}=7.2 sample (M _UV = -19.4) shows higher clustering at \overline{z}=5.9 for bright galaxies (r_0=5.5^+1.4_-1.6h^-1cMpc, b=6.2^+1.2_-1.5) compared to faint galaxies (r_0=1.9^+1.1_-1.0h^-1cMpc, b=2.7^+1.2_-1.2) implying a constant mass-to-light ratio { ({dlogM}/{dlogL)}} ∼ 1.2^+1.8_-0.8. A similar trend is present in the \overline{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, epsilon_DC). At \overline{z}=7.2 values near unity are preferred, which may be explained by the shortened halo assembly time at high redshift.