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Register a new userThe 2dF QSO Redshift Survey - XIV. Structure and evolution from the two-point correlation function
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Scott M. Croom
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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).
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We present a clustering analysis of QSOs over the redshift range z=0.3-2.9. We use a sample of 10558 QSOs taken from the preliminary catalogue of the 2dF QSO Redshift Survey (2QZ). The two-point redshift-space correlation function of QSOs is shown to follow a power law on scales s~1-35h-1Mpc. Fitting a power law to QSO clustering averaged over the redshift interval 0.3<z<2.9 we find s_0=3.99+0.28-0.34h-1Mpc and gamma=1.58+0.10-0.09 for an Einstein-de Sitter cosmology (EdS). With Omega_0=0.3 and lambda_0=0.7 the power law extends to s~60h-1Mpc with a best fit of s_0=5.69+0.42-0.50h-1Mpc and gamma=1.56+0.10-0.09. These values, measured at a mean redshift of z=1.49, are comparable to the clustering of local optically selected galaxies. We measure the evolution of QSO clustering as a function of redshift. For an EdS cosmology there is no evolution in comoving coordinates over the redshift range of the 2QZ. For Omega_0=0.3 and lambda_0=0.7 QSO clustering shows a marginal increase at high redshift. Although the clustering of QSOs is measured on large scales where linear theory should apply, the evolution of QSO clustering does not follow the linear theory predictions for growth via gravitational instability (rejected at the >99 per cent confidence level). A redshift dependent bias is required to reconcile QSO clustering observations with theory. A simple biasing model, in which QSOs have cosmologically long lifetimes (or alternatively form in peaks above a constant threshold in the density field) is acceptable in an EdS cosmology, but is only marginally acceptable if Omega_0=0.3 and lambda_0=0.7. Biasing models which assume QSOs form over a range in redshift, based on the Press-Schechter formalism are approximately consistent with QSO clustering evolution (abridged).
We present a clustering analysis of Luminous Red Galaxies (LRGs) using nearly 9 000 objects from the final catalogue of the 2dF-SDSS LRG And QSO (2SLAQ) Survey. We measure the redshift-space two-point correlation function, xi(s), at the mean LRG redshift of z=0.55. A single power-law fits the deprojected correlation function, xi(r), with a correlation length of r_0=7.45+-0.35 Mpc and a power-law slope of gamma=1.72+-0.06 in the 0.4<r<50 Mpc range. But it is in the LRG angular correlation function that the strongest evidence for non-power-law features is found where a slope of gamma=-2.17+-0.07 is seen at 1<r<10 Mpc with a flatter gamma=-1.67+-0.03 slope apparent at r<~1 Mpc scales. We use the simple power-law fit to the galaxy xi(r) to model the redshift space distortions in the 2-D redshift-space correlation function, xi(sigma,pi). We fit for the LRG velocity dispersion, w_z, Omega_m and beta, where beta=Omega_m^0.6/b and b is the linear bias parameter. We find values of w_z=330kms^-1, Omega_m= 0.10+0.35-0.10 and beta=0.40+-0.05. These high redshift results, which incorporate the Alcock-Paczynski effect and the effects of dynamical infall, start to break the degeneracy between Omega_m and beta found in low-redshift galaxy surveys. This degeneracy is further broken by introducing an additional external constraint, the value of beta(z=0.1)=0.45 from 2dFGRS, and then considering the evolution of clustering from z~0 to z_LRG~0.55. With these combined methods we find Omega_m(z=0)=0.30+-0.15 and beta(z=0.55)=0.45+-0.05. Assuming these values, we find a value for b(z=0.55)=1.66+-0.35. We show that this is consistent with a simple ``high peaks bias prescription which assumes that LRGs have a constant co-moving density and their clustering evolves purely under gravity. [ABRIDGED]
We analyse the redshift-space (z-space) distortions of QSO clustering in the 2dF QSO Redshift Survey (2QZ). To interpret the z-space correlation function, xi(sigma,pi), we require an accurate model for the QSO real-space correlation function, xi(r). Although a single power-law xi(r) model fits the projected correlation function (wp(sigma)) at small scales, it implies somewhat too shallow a slope for both wp(sigma) and the z-space correlation function, xi(s), at larger scales > 20 h^(-1) Mpc. Motivated by the form for xi(r) seen in the 2dF Galaxy Redshift Survey (2dFGRS) and in standard LCDM predictions, we use a double power-law model for xi(r) which gives a good fit to xi(s) and wp(sigma). The model is parametrized by a slope of gamma=1.45 for 1<r<10 h^(-1) Mpc and gamma=2.30 for 10<r<40 h^(-1) Mpc. As found for 2dFGRS, the value of beta determined from the ratio of xi(s)/xi(r) depends sensitively on the form of xi(r) assumed. With our double power-law form for xi(r), we measure beta(z=1.4)=0.32(+0.09)(-0.11). Assuming the same model for xi(r) we then analyse the z-space distortions in the 2QZ xi(sigma,pi) and put constraints on the values of Omega m and beta(z=1.4), using an improved version of the method of Hoyle et al. The constraints we derive are Omega m=0.35(+0.19)(-0.13), beta(z=1.4)=0.50(+0.13)(-0.15), in agreement with our xi(s)/xi(r) results at the ~1 sigma level.
We present the final catalogue of the 2dF QSO Redshift Survey (2QZ), based on Anglo-Australian Telescope 2dF spectroscopic observations of 44576 colour-selected (u b_J r) objects with 18.25<b_J<20.85 selected from APM scans of UK Schmidt Telescope (UKST) photographic plates. The 2QZ comprises 23338 QSOs, 12292 galactic stars (including 2071 white dwarfs) and 4558 compact narrow-emission-line galaxies. We obtained a reliable spectroscopic identification for 86 per cent of objects observed with 2dF. We also report on the 6dF QSO Redshift Survey (6QZ), based on UKST 6dF observations of 1564 brighter 16<b_J<18.25 sources selected from the same photographic input catalogue. In total, we identified 322 QSOs spectroscopically in the 6QZ. The completed 2QZ is, by more than a factor 50, the largest homogeneous QSO catalogue ever constructed at these faint limits (b_J<20.85) and high QSO surface densities (35 QSOs deg^-2). As such it represents an important resource in the study of the Universe at moderate-to-high redshifts. As an example of the results possible with the 2QZ, we also present our most recent analysis of the optical QSO luminosity function and its cosmological evolution with redshift. For a flat, Omega_m=0.3 and Omega_lam=0.7, Universe, we find that a double power law with luminosity evolution that is exponential in look-back time, t, of the form L*(z) exp(6.15t), equivalent to an e-folding time of 2Gyr, provides an acceptable fit to the redshift dependence of the QSO luminosity function over the range 0.4 < z < 2.1 and M_bJ<-22.5. Evolution described by a quadratic in redshift is also an acceptable fit, with L*(z)~10^(1.39z-0.29z^2).
The completed 2dF QSO Redshift (2QZ) Survey has been used to search for extreme large-scale cosmological structure (around 200 Mpc) over the redshift range 0<z<2.5. We demonstrate that statistically significant overdensities and underdensities do exist and hence represent the detection of cosmological fluctuations on comoving scales that correspond to those presently detected in the cosmic microwave background. However, the fractional overdensities on scales >100Mpc are in the linear or only weakly non-linear regime and do not represent collapsed non-linear structures. We compare the measurements with the expectation of a standard LCDM model by measuring the variance of counts in cells and find that, provided the distribution of QSOs on large scales exhibits a mild bias with respect to the distribution of dark matter, the observed fluctuations are found to be in good agreement with the model. There is no evidence on such scales for any extreme structures that might require, for example, departures from the assumption of Gaussian initial perturbations. Thus the power-spectrum derived from the 2QZ Survey appears to provide a complete description of the distribution of QSOs. The amount of bias and its redshift dependence that is required is consistent with that found from studying the clustering of 2QZ QSOs on 10 Mpc scales, and may be adequately described by an approximately redshift-invariant power spectrum with normalisation sigma_8=1.0 corresponding to a bias at z=0 of b=1.1 rising to b=2 at the surveys mean redshift z=1.5.
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