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, xi (s) and find that, at the mean LRG redshift of z = 0.55, xi (s) shows the characteristic downturn at small scales (less than or similar to 1 h(-1) Mpc) expected from line-of-sight velocity dispersion. We fit a double power law to. ( s) and measure an amplitude and slope of s(0) = 17.3(-2.0)(+2.5) h-1 Mpc, gamma = 1.03 +/- 0.07 at small scales (s < 4.5 h(-1) Mpc) and s(0) = 9.40 +/- 0.19 h(-1) Mpc, gamma = 2.02 +/- 0.07 at large scales (s > 4.5 h(-1) Mpc). In the semiprojected correlation function, w(p)(sigma), we find a simple power law with gamma = 1.83 +/- 0.05 and r(0) = 7.30 +/- 0.34 h(-1) Mpc fits the data in the range 0.4 < s < 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 xi (r), with a correlation length of r0 = 7.45 +/- 0.35 h(-1) Mpc and a power-law slope of gamma = 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 gamma = -2.17 +/- 0.07 is seen at 1 < r < 10 h(-1) Mpc with a flatter. = -1.67 +/- 0.07 slope apparent at r less than or similar to 1 h(-1) Mpc scales. We use the simple power-law fit to the galaxy. (r), under the assumption of linear bias, to model the redshift-space distortions in the 2D redshift-space correlation function,. ( s, p). We fit for the LRG velocity dispersion, w(z), the density parameter, Omega(m) and beta(z), where beta(z) = Omega(0.6)(m)/b and b is the linear bias parameter. We find values of w(z) = 330 km s(-1), Omega(m) = 0.10(-0.10)(+ 0.35) and beta = 0.40 +/- 0.05. The low values for w(z) and beta 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 Omega(m) and beta found in low-redshift galaxy surveys such as 2dFGRS. This degeneracy is further broken by introducing an additional external constraint, which is the value beta(z = 0.1) = 0.45 from 2dFGRS, and then considering the evolution of clustering from z similar to 0 to z(LRG) similar to 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 'highpeak' bias prescription which assumes that LRGs have a constant comoving density and their clustering evolves purely under gravity.