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 ($z\gtrsim6$)
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 $\sim4\sigma$,
corresponding to a real-space correlation length
$r_{0}=6.7^{+0.9}_{-1.0}h^{-1}$cMpc. 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$_{\odot}$ at $z=7.2$, and highlights that galaxies
below the current detection limit ($M_{AB}\sim-17.7$) are expected in
lower-mass halos ($M\sim10^{8}-10^{10.5}$M$_{\odot}$). We compute the ACF of
LBGs at $z\sim3.8-z\sim5.9$ in the same surveys. A trend of increasing bias is
found from $z=3.8$ ($b\sim3.0$) to $z=7.2$ ($b\sim8.6$), 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 $z\sim7$
($\sim2\sigma$ 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 ($r_{0}=5.5^{+1.4}_{-1.5}h^{-1}$cMpc, $b=6.2^{+1.2}_{-1.5}$) compared
to faint galaxies ($r_{0}=1.9^{+1.1}_{-1.0}h^{-1}$cMpc, $b=2.7\pm1.2$) implying
a constant mass-to-light ratio $\frac{dlogM}{dlogL}\sim1.2^{+1.8}_{-0.8}$. 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, $\epsilon_{DC}$).
At $z=7.2$ values near unity are preferred, which may be explained by the
shortened halo assembly time at high-redshift.
