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

Ross, N. P.; daAngela, J.; Shanks, T.; Wake, D.; Cannon, R. D.; Edge, A. C.; Nichol, R. C.; Outram, P. J.; Colless, M.; Couch, W. J.; Croom, S. M.; De Propris, R.; Drinkwater, M. J.; Eisenstein, D. J.; Loveday, J.; Pimbblet, K. A.; Roseboom, I. G.; Schneider, D. P.; Sharp, R. G. and Weilbacher, P. M. (2007). The 2dF-SDSS LRG and QSO Survey: the LRG 2-point correlation function and redshift-space distortions. Monthly Notices of the Royal Astronomical Society, 381(2) pp. 573–588.

DOI: https://doi.org/10.1111/j.1365-2966.2007.12289.x

Abstract

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 ¯z = 0.55, ξ(s) 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) and s0 =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, 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−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 ± 0.35 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) = Ω0.6 m /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 ‘highpeak’ bias prescription which assumes that LRGs have a constant comoving density and their clustering evolves purely under gravity.

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