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 20000 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 ~25h^-1 Mpc. In a WMAP/2dF cosmology (Ω_m= 0.27, Ω_Λ= 0.73) we find a best-fitting power law with s₀= 5.48^+0.42_-0.48h^-1 Mpc and γ= 1.20 +/- 0.10 on scales s= 1 to 25h^-1 Mpc. We demonstrate that non-linear redshift-space distortions have a significant effect on the QSO ξ(s) at scales less than ~10h^-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 20h^-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) × 10¹²h^-1 M_solar, 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 × 10⁶-6 × 10⁸ 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.