Lyman-Break Galaxy ( LBG ) samples observed during reionization ( z \gtrsim 6 ) with Hubble Space Telescope ’ s WideFieldCamera3 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 \geq 6.5 at a mean redshift of \overline { z } = 7.2 , we detect a clear clustering signal in the angular correlation function ( ACF ) at \gtrsim 4 \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 } \hskip { 2.845276 pt } 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 } \hskip { 2.845276 pt } ) .
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 \overline { z } = 3.8 ( b \sim 3.0 ) to \overline { 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 \lesssim z \lesssim 6 , followed by a slight rise in halo masses at z \gtrsim 7 ( \sim 2 \sigma 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 } _ { -1.6 } 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 ^ { +1.2 } _ { -1.2 } ) implying a constant mass-to-light ratio \frac { \textnormal { dlogM } } { \textnormal { dlogL } } \sim 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 _ { \textnormal { DC } } ) .
At \overline { z } = 7.2 values near unity are preferred , which may be explained by the shortened halo assembly time at high-redshift .