2012ApJ...752...39T

We present an analysis of the galaxy distribution surrounding 15 of the most luminous ( ≳ 10¹⁴ L_☉; M₁₄₅₀≃ -30) QSOs in the sky with z ≃ 2.7. Our data are drawn from the Keck Baryonic Structure Survey, which has been optimized to examine the small-scale interplay between galaxies and the intergalactic medium during the peak of the galaxy formation era at z ∼ 2-3. 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) sight line in 1 of 15 independent survey fields, together with new measurements of the HLQSO systemic redshifts. By combining the spatial and redshift distributions, 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 σ_v≃ 200 km/s 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 _☉) ≃ 13. The galaxy-HLQSO cross-correlation function has a best-fit correlation length r ^GQ₀= (7.3±1.3) h^–1 cMpc, while the galaxy autocorrelation measured from the spectroscopic galaxy sample in the same fields has r ^GG₀= (6.0±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_☉) = 11.9±0.1, while HLQSOs inhabit host halos of log (M_h/M_☉) = 12.3±0.5. In spite of the extremely large black hole masses implied by their observed luminosities [log (M_BH/M_☉) ≳ 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 c/Mpc3) results from a one-in-a-million event on scales {Lt}1 Mpc, and not from being hosted by rare dark matter halos.