The 2dF-SDSS LRG and QSO survey: QSO clustering and the L-z degeneracy

We combine the quasi-stellar object (QSO) samples from the 2dF QSO Redshift Survey (2QZ) and the 2dF-Sloan Digital Sky Survey luminous red galaxy (LRG) and QSO Survey (2dF-SDSS LRG and QSO, hereafter 2SLAQ) in order to investigate the clustering of z ~1.5 QSOs and measure the correlation function (ξ). The clustering signal in redshift-space and projected along the sky direction is similar to that previously obtained from the 2QZ sample alone. By fitting functional forms for ξ(σ, π), the correlation function measured along and across the line of sight, we find, as expected, that β, the dynamical infall parameter and Ω0m, the cosmological density parameter, are degenerate. However, this degeneracy can be lifted by using linear theory predictions under different cosmological scenarios. Using the combination of the 2QZ and 2SLAQ QSO data, we obtain: βQSO(z = 1.5) = 0.60+0.14−0.11, Ω0m = 0.25+0.09−0.07 which imply a value for the QSO bias, b(z = 1.4) = 1.5 ± 0.2. The combination of the 2QZ with the fainter 2SLAQ QSO sample further reveals that QSO clustering does not depend strongly on luminosity at fixed redshift. This result is inconsistent with the expectation of simple ‘high peaks’ biasing models where more luminous, rare QSOs are assumed to inhabit higher mass haloes. The data are more consistent with models which predict that QSOs of different luminosities reside in haloes of similar mass. By assuming ellipsoidal models for the collapse of density perturbations, we estimate the mass of the dark matter haloes which the QSOs inhabit as ~3 × 1012 h−1 Mo. We find that this halo mass does not evolve strongly with redshift nor depend on QSO luminosity. Assuming a range of relations which relate halo to black hole mass, we investigate how black hole mass correlates with luminosity and redshift, and ascertain the relation between Eddington efficiency and black hole mass. Our results suggest that QSOs of different luminosities may contain black holes of similar mass.