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

TL;DR

The paper measures the redshift-space two-point correlation function $\xi(s)$ for over $2\times10^4$ QSOs from the final 2QZ catalogue to test structure formation and QSO/host-halo evolution in a $\Lambda$CDM cosmology. Using a Landy–Szalay estimator and corrections for selection effects and redshift-space distortions (linear and non-linear), it compares the measurements to both simple power laws and CDM-based models, deriving a mean QSO bias $b_Q(z\approx1.35)=2.02\pm0.07$ and showing that QSOs inhabit dark-matter halos of mass $M_{DH}\approx(3.0\pm1.6)\times10^{12} h^{-1}M_\odot$ essentially independent of redshift. The analysis reveals strong redshift evolution of QSO bias (from $b_Q\sim1.1$ at $z\sim0.5$ to $b_Q\sim4.2$ at $z\sim2.5$) while the host halo mass grows little, implying high-redshift QSOs reside in progenitors of present-day clusters and that the QSO population fades mainly due to BH mass evolution rather than a change in fueling efficiency. The inferred QSO lifetimes are short, with $t_Q$ constrained to $\lesssim6\times10^8$ yr at high redshift, and the data favor modest or evolving BH accretion efficiencies consistent with BH growth scenarios, rather than a static $M_{BH}$–$\sigma$ relation across cosmic time. No strong luminosity dependence of clustering is detected within current uncertainties, suggesting a complex interplay between halo mass, black-hole growth, and accretion that governs QSO activity over $0.3<z<2.9$.

Abstract

We present a clustering analysis of QSOs using over 20000 objects from the final catalogue of the 2dF QSO Redshift Survey (2QZ), measuring the z-space correlation function, xi(s). When averaged over the range 0.3<z<2.2 we find that xi(s) is flat on small scales, steepening on scales above ~25h-1Mpc. In a WMAP/2dF cosmology we find a best fit power law with s_0=5.48+0.42-0.48h-1Mpc and gamma=1.20+-0.10 on scales s=1-25h-1Mpc. A CDM model assuming WMAP/2dF cosmological parameters is a good description of the QSO xi(s) after accounting for non-linear clustering and z-space distortions, and a linear bias of b_qso(z=1.35)=2.02+-0.07. We subdivide the 2QZ into 10 redshift intervals from z=0.53 to 2.48 and find a significant increase in clustering amplitude at high redshift in the WMAP/2dF cosmology. We derive the bias of the QSOs which is a strong function of redshift with b_qso(z=0.53)=1.13+-0.18 and b_qso(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)x10^12h-1M_sun, which is close to the characteristic mass in the Press-Schechter mass function, M*, at z=0. 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* 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_qso, the active lifetime of QSOs and constrain this to be in the range 4x10^6-6x10^8 years at z~2. (Abridged).

Figures (27)

• Figure 1: The distribution of 2QZ QSOs from the final catalogue. The SGP strip is on the left, the equatorial strip on the right. The rectangular regions show the distributions projected onto the sky. An EdS cosmology is assumed in calculating the comoving distances to each QSO.
• Figure 2: The completeness map of the 2QZ catalogue for the equatorial (top) and SGP (bottom) regions. The grey-scale indicates the percentage of all 2QZ targets that were both observed and positively identified (quality 1) over the two survey strips.
• Figure 3: QSO and simulation $n(z)$ distributions. a) The $n(z)$ distributions in the two 2QZ slices, SGP (solid line) and NGP (dotted line). The NGP has been renormalized to the number of QSOs in the SGP to aid comparison. Also shown is the 12th order polynomial fit to the combined $n(z)$ (dashed line). b) The $n(z)$ distribution of two Hubble Volume simulation slices each containing 12500 particles.
• Figure 4: Comparison of masking (filled points) and RA-Dec mixing (open points) methods for the Hubble Volume simulations. Beneath each plot we show the ratio of the two correlation function measures, $\xi(s)_{\rm mask}/\xi(s)_{\rm mixing}$. a) $\xi(s)$ measured over a broad redshift range, $z=0.3-2.2$. There is no significant difference between the two estimates. b) $\xi(s)$ measured over a narrow redshift range, $z=1.35-1.70$. In this case the RA-Dec mixing method produces a correlation function which is $\sim10-20$ per cent lower than the masking method.
• Figure 5: Comparison of simulated correlation functions with (open points) and without (filled points) zero-point errors for a) the full redshift range and b) a narrow redshift range with $z=1.35-1.70$. The ratio of the points with and without zero-point errors, $\xi(s,\sigma_{\rm zp}=0.05)/\xi(s,\sigma_{\rm zp}=0.000)$, is shown below each plot.