Correlation function of quasars in real and redshift space from the Sloan Digital Sky Survey Data Release 7

We analyse the quasar two-point correlation function (2pCF) within the redshift interval 0.8 < z < 2.2 using a sample of 52 303 quasars selected from the recent Sloan Digital Sky Survey Data Release 7. Our approach to the 2pCF uses the concept of a local Lorentz (Fermi) frame, for the determination of the distance between objects, and the permutation method of random catalogue generation. Assuming a spatially flat cosmological model with ΩΛ= 0.726, we have found that the real-space 2pCF is fitted well with the power-law model within the distance range 1 < σ < 35 h−1 Mpc with the correlation length r0= 5.85 ± 0.33 h−1 Mpc and the slope γ= 1.87 ± 0.07. The redshift-space 2pCF is approximated with s0= 6.43 ± 0.63 h−1 Mpc and γ= 1.21 ± 0.24 for 1 < s < 10 h−1 Mpc, and s0= 7.37 ± 0.81 h−1 Mpc and γ= 1.90 ± 0.24 for 10 < s < 35 h−1 Mpc. For distances s > 10 h−1 Mpc, the parameter describing the large-scale infall to density inhomogeneities is β= 0.63 ± 0.10 with the linear bias b = 1.44 ± 0.22, which marginally (within 2σ) agrees with the linear theory of cosmological perturbations. We discuss possibilities to obtain a statistical estimate of the random component of quasar velocities (different from the large-scale infall). We note a slight dependence of the quasar velocity dispersion upon the 2pCF parameters in the region r < 2 Mpc.