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, xi(s). When averaged over the redshift range 0.3 < z < 2.2 we find that xi(s) is flat on small scales, steepening on scales above similar to25 h(-1) Mpc. In a WMAP/2dF cosmology (Omega(m) = 0.27,Omega(Lambda) = 0.73) we find a best-fitting power law with s(0) = 5.48(-0.48)(+0.42) h(-1) Mpc and gamma = 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 xi(s) at scales less than similar to10 h(-1) Mpc. A cold dark matter model assuming WMAP/2dF cosmological parameters is a good description of the QSO xi(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, (xi) over bar (s), within 20 h(-1) Mpc is (xi) over bar (20 z = 0 53) = 0 26 +/- 0 08 and (xi) over bar (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) x 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 MDH 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 similar to 2 to similar to0 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 similar to 2. We test for any luminosity dependence of QSO clustering by measuring (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.