The 2dF QSO Redshift Survey - XIV. Structure and evolution from the two-point correlation function

In this paper we present a clustering analysis of quasi-stellar objects (QSOs) using over 20 000 objects from the final catalogue of the 2dF QSO Redshift Survey (2QZ), measuring the redshift-space two-point correlation function, ξ(s). When averaged over the redshift range 0.3 < z < 2.2 we find that ξ(s) is flat on small scales, steepening on scales above ∼25 h -1 Mpc. In a WMAP/2dF cosmology (Ω m = 0.27, Ω A = 0.73) we find a best-fitting power law with so = 5.48 +0.42 -0.48 h -1 Mpc and γ = 1.20 ± 0.10 on scales s = 1 to 25 h -1 Mpc. We demonstrate that non-linear redshift-space distortions have a significant effect on the QSO ξ(s) at scales less than ∼10 h -1 Mpc. A cold dark matter model assuming WMAP/2dF cosmological parameters is a good description of the QSO ξ(s) after accounting for non-linear clustering and redshift-space distortions, and allowing for a linear bias at the mean redshift of b Q (z = 1.35) = 2.02 ± 0.07. We subdivide the 2QZ into 10 redshift intervals with effective redshifts from z = 0.53 to 2.48. We find a significant increase in clustering amplitude at high redshift in the WMAP/2dF cosmology. The QSO clustering amplitude increases with redshift such that the integrated correlation function, ξ(s), within 20 h -1 Mpc is ξ(20, z = 0.53) = 0.26 ± 0.08 and ξ(20, z = 2.48) = 0.70 ± 0.17. We derive the QSO bias and find it to be a strong function of redshift with b Q (z = 0.53) = 1.13 ± 0.18 and b Q (z = 2.48) = 4.24 ± 0.53. We use these bias values to derive the mean dark matter halo (DMH) mass occupied by the QSOs. At all redshifts 2QZ QSOs inhabit approximately the same mass DMHs with M DH = (3.0 ± 1.6) × 10 12 h -1 M ○. , which is close to the characteristic mass in the Press-Schechter mass function, M*, at z = 0. These results imply that LQ QSOs at z ∼ 0 should be largely unbiased. If the relation between black hole (BH) mass and M DH or host velocity dispersion does not evolve, then we find that the accretion efficiency (L /L Edd ) for LQ QSOs is approximately constant with redshift. Thus the fading of the QSO population from z ∼ 2 to ∼0 appears to be due to less massive BHs being active at low redshift. We apply different methods to estimate, t Q , the active lifetime of QSOs and constrain t Q to be in the range 4 x 10 6 -6 x 10 8 yr at z ∼2. We test for any luminosity dependence of QSO clustering by measuring ξ(s) as a function of apparent magnitude (equivalent to luminosity relative to L* Q ). However, we find no significant evidence of luminosity-dependent clustering from this data set.