Are z~5 QSOs found in the most massive high redshift over-densities?
  Luminous high-redshift QSOs are thought to exist within the most massive dark
matter haloes in the young Universe. As a consequence they are likely to be
markers for biased, over-dense regions where early galaxies cluster, regions
that eventually grow into the groups and clusters seen in the lower redshift
universe. In this paper we explore the clustering of galaxies around z ~ 5 QSOs
as traced by Lyman Break Galaxies (LBGs). We target the fields of three QSOs
using the same optical imaging and spectroscopy techniques used in the ESO
Remote Galaxy Survey (ERGS, Douglas et al. 2009, 2010), which was successful in
identifying individual clustered structures of LBGs. We use the statistics of
the redshift clustering in ERGS to show that two of the three fields show
significant clustering of LBGs at the QSO redshifts. Neither of these fields is
obviously over-dense in LBGs from the imaging alone; a possible reason why
previous imaging-only studies of high-redshift QSO environments have given
ambiguous results. This result shows that luminous QSOs at z ~ 5 are typically
found in over-dense regions. The richest QSO field contains at least nine
spectroscopically confirmed objects at the same redshift including the QSO
itself, seven LBGs and a second fainter QSO. While this is a very strong
observational signal of clustering at z ~ 5, it is of similar strength to that
seen in two structures identified in the 'blank sky' ERGS fields. This
indicates that, while over-dense, the QSO environments are not more extreme
than other structures that can be identified at these redshifts. The three
richest structures discovered in this work and in ERGS have properties
consistent with that expected for proto-clusters and likely represent the early
stages in the build-up of massive current-day groups and clusters.
