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

*S. M. Croom, B. J. Boyle, T. Shanks, R. J. Smith, L. Miller, P. J. Outram, N. S. Loaring, F. Hoyle, J. da Ângela*

**Abstract**

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 s_{0}=
5.48^{+0.42}_{-0.48}h^{-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) ×
10^{12}h^{-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 × 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.

**Monthly Notices of the Royal Astronomical Society**

Volume 356, Page 415

January 2005