The 2dF-SDSS LRG and QSO Survey: the LRG 2-point correlation function and redshift-space distortions

We present a clustering analysis of luminous red galaxies (LRGs) using nearly 9000 objects from the final, three-year catalogue of the 2dF-SDSS LRG and QSO (2SLAQ) Survey. We measure the redshift-space two-point correlation function, ξ(s) and find that, at the mean LRG redshift of shows the characteristic downturn at small scales (1 h−1 Mpc) expected from line-of-sight velocity dispersion. We fit a double power law to ξ(s) and measure an amplitude and slope of s0 = 17.3+2.5−2.0 h−1 Mpc, γ = 1.03 ± 0.07 at small scales (s 4.5 h−1 Mpc). In the semiprojected correlation function, wp(σ), we find a simple power law with γ = 1.83 ± 0.05 and r0 = 7.30 ± 0.34 h−1 Mpc fits the data in the range 0.4 < σ < 50 h−1 Mpc, although there is evidence of a steeper power law at smaller scales. A single power law also fits the deprojected correlation function ξ(r), with a correlation length of r0 = 7.45 ± 0.35 h−1 Mpc and a power-law slope of γ = 1.72 ± 0.06 in the 0.4 < r < 50 h−1 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 γ = −2.17 ± 0.07 is seen at 1 < r < 10 h−1 Mpc with a flatter γ = −1.67 ± 0.07 slope apparent at r 1 h−1 Mpc scales. We use the simple power-law fit to the galaxy ξ(r), under the assumption of linear bias, to model the redshift-space distortions in the 2D redshift-space correlation function, ξ(σ, π). We fit for the LRG velocity dispersion, wz, the density parameter, Ωm and β(z), where β(z) = Ω0.6m/b and b is the linear bias parameter. We find values of wz = 330 km s−1, Ωm = 0.10+0.35−0.10 and β = 0.40 ± 0.05. The low values for wz and β reflect the high bias of the LRG sample. These high-redshift results, which incorporate the Alcock–Paczynski effect and the effects of dynamical infall, start to break the degeneracy between Ωm and β found in low-redshift galaxy surveys such as 2dFGRS. This degeneracy is further broken by introducing an additional external constraint, which is the value β(z = 0.1) = 0.45 from 2dFGRS, and then considering the evolution of clustering from z 0 to zLRG 0.55. With these combined methods we find Ωm(z = 0) = 0.30 ± 0.15 and β(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-peak’ bias prescription which assumes that LRGs have a constant comoving density and their clustering evolves purely under gravity.