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 (<~1h-1Mpc) 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+2.5-2.0h-1Mpc,γ = 1.03 +/- 0.07 at small scales (s < 4.5h-1Mpc) and s0 = 9.40 +/- 0.19h-1Mpc,γ = 2.02 +/- 0.07 at large scales (s > 4.5h-1Mpc). In the semiprojected correlation function, wp(σ), we find a simple power law with γ = 1.83 +/- 0.05 and r0 = 7.30 +/- 0.34h-1Mpc fits the data in the range 0.4 < σ < 50h-1Mpc, 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 +/- 0.35h-1Mpc and a power-law slope of γ = 1.72 +/- 0.06 in the 0.4 < r < 50h-1Mpc 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 < 10h-1Mpc with a flatter γ = -1.67 +/- 0.07 slope apparent at r <~ 1h-1Mpc 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 = 330kms-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.