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 s 0 = 17.3 +2.5 −2.0   h −1  Mpc, γ= 1.03 ± 0.07 at small scales ( s < 4.5  h −1  Mpc) and s 0 = 9.40 ± 0.19  h −1  Mpc, γ= 2.02 ± 0.07 at large scales ( s > 4.5  h −1  Mpc) . In the semiprojected correlation function, w p (σ), we find a simple power law with γ= 1.83 ± 0.05 and r 0 = 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 r 0 = 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, w z , the density parameter, Ω m and β( z ), where β( z ) =Ω 0.6 m / b and b is the linear bias parameter. We find values of w z = 330 km s −1 , Ω m = 0.10 +0.35 −0.10 and β= 0.40 ± 0.05 . The low values for w z 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 Ω m 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 z LRG ∼ 0.55 . With these combined methods we find Ω m ( 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.