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 ) ∝ r −γ model fits the projected correlation function [ w 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 Λ 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 γ= 1.45 for 1 < r < 10  h −1  Mpc and γ= 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.