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 Λ = 0.73) we find a best‐fitting power law with s 0 = 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, , within 20  h −1 Mpc is and . 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 L * Q 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 L * Q 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 × 10 6 –6 × 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.