The halo masses and galaxy environments of hyperluminous QSOs at z~2.7
  in the Keck Baryonic Structure Survey
  We present an analysis of the galaxy distribution surrounding 15 of the most
luminous (>10^{14} L_sun; M_1450 ~ -30) QSOs in the sky with z~2.7. Our data
are drawn from the Keck Baryonic Structure Survey (KBSS). In this work, we use
the positions and spectroscopic redshifts of 1558 galaxies that lie within ~3',
(4.2 h^{-1} comoving Mpc; cMpc) of the hyperluminous QSO (HLQSO) sightline in
one of 15 independent survey fields, together with new measurements of the
HLQSO systemic redshifts. We measure the galaxy-HLQSO cross-correlation
function, the galaxy-galaxy autocorrelation function, and the characteristic
scale of galaxy overdensities surrounding the sites of exceedingly rare,
extremely rapid, black hole accretion. On average, the HLQSOs lie within
significant galaxy overdensities, characterized by a velocity dispersion
sigma_v ~ 200 km s^{-1} and a transverse angular scale of ~25", (~200 physical
kpc). We argue that such scales are expected for small groups with
log(M_h/M_sun)~13. The galaxy-HLQSO cross-correlation function has a best-fit
correlation length r_0_GQ = (7.3 \pm 1.3) h^{-1} cMpc, while the galaxy
autocorrelation measured from the spectroscopic galaxy sample in the same
fields has r_0_GG = (6.0 \pm 0.5) h^{-1} cMpc. Based on a comparison with
simulations evaluated at z ~ 2.6, these values imply that a typical galaxy
lives in a host halo with log(M_h/M_sun) = 11.9\pm0.1, while HLQSOs inhabit
host halos of log(M_h/M_sun) = 12.3\pm0.5. In spite of the extremely large
black hole masses implied by their observed luminosities [log(M_BH/M_sun) >
9.7], it appears that HLQSOs do not require environments very different from
their much less luminous QSO counterparts. Evidently, the exceedingly low space
density of HLQSOs (< 10^{-9} cMpc^{-3}) results from a one-in-a-million event
on scales << 1 Mpc, and not from being hosted by rare dark matter halos.
