Strong Clustering of Lyman Break Galaxies around Luminous Quasars at z~4
  In the standard picture of structure formation, the first massive galaxies
are expected to form at the highest peaks of the density field, which
constitute the cores of massive proto-clusters. Luminous quasars (QSOs) at z~4
are the most strongly clustered population known, and should thus reside in
massive dark matter halos surrounded by large overdensities of galaxies,
implying a strong QSO-galaxy cross-correlation function. We observed six z~4
QSO fields with VLT/FORS exploiting a novel set of narrow band filters custom
designed to select Lyman Break Galaxies (LBGs) in a thin redshift slice of
Delta_z~0.3, mitigating the projection effects that have limited the
sensitivity of previous searches for galaxies around z>~4 QSOs. We find that
LBGs are strongly clustered around QSOs, and present the first measurement of
the QSO-LBG cross-correlation function at z~4, on scales of 0.1<~R<~9 Mpc/h
(comoving). Assuming a power law form for the cross-correlation function
xi=(r/r0_QG)^gamma, we measure r0_QG=8.83^{+1.39}_{-1.51} Mpc/h for a fixed
slope of gamma=2.0. This result is in agreement with the expected
cross-correlation length deduced from measurements of the QSO and LBG
auto-correlation function, and assuming a linear bias model. We also measure a
strong auto-correlation of LBGs in our QSO fields finding
r0_GG=21.59^{+1.72}_{-1.69} Mpc/h for a fixed slope of gamma=1.5, which is ~4
times larger than the LBG auto-correlation length in random fields, providing
further evidence that QSOs reside in overdensities of LBGs. Our results
qualitatively support a picture where luminous QSOs inhabit exceptionally
massive (M_halo>10^12 M_sun) dark matter halos at z~4.
