The 2 dF-SDSS LRG and QSO Survey : The 2-Point Correlation Function and Redshift-Space Distortions

We present a clustering analysis of Luminous Red Galaxies (L RGs) using nearly 9 000 objects from the final, three year catalogue of the 2dF-SDSS LRG And QSO (2SLAQ) Survey. We measure the redshift-space two-point correlation f unction,ξ(s) and find that, at the mean LRG redshift of̄z = 0.55, ξ(s) shows the characteristic downturn at small scales ( ∼ <1 hMpc) expected from line-of-sight velocity dispersion. We fit a d ouble power-law to ξ(s) and measure an amplitude and slope of s0 = 17.6 hMpc, γ = 1.08 at small scales (s ∼ < 5 hMpc) ands0 = 9.4 hMpc, γ = 1.98 at large scales ( s∼>5 h Mpc). In the semi-projected correlation function, wp(σ), we find a simple power law with γ = 1.83±0.05 andr0 = 7.30 ± 0.34 hMpc fits the data in the range 0.4 < σ < 70 hMpc, 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 hMpc and a power-law slope of γ = 1.72 ± 0.06 in the0.4 < r < 70 hMpc range. But it is in the LRG angular correlation function that the strongest evi d nce for non-power-law features is found where a slope of γ = −2.17 ± 0.07 is seen at1 < r < 10 hMpc with a flatter γ = −1.67 ± 0.03 slope apparent at r ∼ < 1 hMpc 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 2-D redshift-sp ace correlation function, ξ(σ, π). We fit for the LRG velocity dispersion, wz , the density parameter, Ωm andβ(z), whereβ(z) = Ω m /b andb is the linear bias parameter. We find values of wz = 330kms , Ωm = 0.10 +0.35 −0.10 andβ = 0.40 ± 0.05. The low values forwz andβ reflect the high bias of the LRG sample. These high redshift results, which incorporate the AlcockPaczynski effect and the effects of dynamical infall, start to break the degeneracy between Ωm andβ found in low-redshift galaxy surveys such as 2dFGRS. This degeneracy is further broken by i troducing an additional external constraint, which is the value β(z = 0.1) = 0.45 from 2dFGRS, and then considering the evolution of clustering fromz ∼ 0 to zLRG ∼ 0.55. With these combined methods we find Ωm(z = 0) = 0.30 ± 0.15 andβ(z = 0.55) = 0.45 ± 0.05. Assuming these values, we find a value forb(z = 0.55) = 1.66 ± 0.35. We show that this is consistent with a simple “high-peaks” bias prescription which assumes that LRGs hav e a constant co-moving density and their clustering evolves purely under gravity.