The 2dF QSO Redshift Survey– XV. Correlation analysis of redshift‐space distortions

We analyse the redshift-space (z-space) distortions of quasi-stellar object (QSO) clustering in the 2-degree field instrument (2dF) QSO Redshift Survey (2QZ). To interpret the z-space correlation function, ξ(σ, π), we require an accurate model for the QSO real-space correlation function, ξ(r). Although a single power-law ξ(r) oc r -γ model fits the projected correlation function [ω p (σ)] at small scales, it implies somewhat too shallow a slope for both w p (σ) and the z-space correlation function, ξ(s), at larger scales (?20 h -1 Mpc). Motivated by the form for ξ(r) seen in the 2dF Galaxy Redshift Survey (2dFGRS) and in standard A cold dark matter (CDM) predictions, we use a double power-law model for ξ(r), which gives a good fit to ξ(s) and w p (σ). The model is parametrized by a slope of y = 1.45 for 1 < r < 10 h -1 Mpc and y = 2.30 for 10 < r < 40 h -1 Mpc. As found for the 2dFGRS, the value of β determined from the ratio of ξ(s)/ξ(r) depends sensitively on the form of ξ(r) assumed. With our double power-law form for ξ(r), we measure β(z = 1.4) = 0.32 +0.09 -0.11 . Assuming the same model for ξ(r), we then analyse the z-space distortions in the 2QZ ξ(σ, π) and put constraints on the values of Ω 0 m and β(z = 1.4), using an improved version of the method of Hoyle et al. The constraints we derive are Ω 0 m = 0.35 +0.19 -0.13 , β(z = 1.4) = 0.50 +0.13 -0.15 , in agreement with our ξ(s)/ξ(r) results at the ∼ 1σ level.