Clustering of low-redshift (z ≤ 2.2) quasars from the sloan digital sky survey

We present measurements of the quasar two-point correlation function, ξ_Q, over the redshift range 0.3 ≤ z ≤ 2.2 based upon data from the Sloan Digital Sky Survey (SDSS). Using a homogeneous sample of 30,239 quasars with spectroscopic redshifts from the Data Release 5 Quasar Catalog, our study represents the largest sample used for this type of investigation to date. With this redshift range and an areal coverage of 4000 deg², we sample over 25 h ^-3 Gpc³ (comoving) of the universe in volume, assuming the current Lambda Cold Dark Matter (ΛCDM) cosmology. Over this redshift range, we find that the redshift-space correlation function, ξ(s), is adequately fit by a single power law, with s ₀ = 5.95 0.45 h ^-1 Mpc and γ_s = 1.16^+0.11 _-0.16 when fit over 1.0 h ^-1 Mpc ≤ s ≤ 25.0 h ^-1 Mpc. We find no evidence for deviation from ξ(s) = 0 at scales of s>100 h ^-1 Mpc, but do observe redshift-space distortions in the two-dimensional ξ(r_p , π) measurement. Using the projected correlation function, w_p (r_p ), we calculate the real-space correlation length, r ₀ = 5.45^+0.35 _-0.45 h ^-1 Mpc and γ = 1.90^+0.04 _-0.03, over scales of 1.0 h ^-1 Mpc ≤ r_p ≤ 130.0 h ^-1 Mpc. Dividing the sample into redshift slices, we find very little, if any, evidence for the evolution of quasar clustering, with the redshift-space correlation length staying roughly constant at s ₀ 6-7 h ^-1 Mpc at z ≲ 2.2 (and only increasing at redshifts greater than this). We do, however, see tentative evidence for evolution in the real-space correlation length, r ₀, at z>1.7. Our results are consistent with those from the 2dF QSO Redshift Survey and previous SDSS quasar measurements using photometric redshifts. Comparing our clustering measurements to those reported for X-ray selected active galactic nucleus at z 0.5-1, we find reasonable agreement in some cases but significantly lower correlation lengths in others. Assuming a standard ΛCDM cosmology, we find that the linear bias evolves from b 1.4 at z = 0.5 to b 3 at z = 2.2, with b(z = 1.27) = 2.06 0.03 for the full sample. We compare our data to analytical models and infer that quasars inhabit dark matter halos of constant mass M _halo 2 × 10¹² h ^-1 M _⊙ from redshifts z 2.5 (the peak of quasar activity) to z 0; therefore, the ratio of the halo mass for a typical quasar to the mean halo mass at the same epoch drops with decreasing redshift. The measured evolution of the clustering amplitude is in reasonable agreement with recent theoretical models, although measurements to fainter limits will be needed to distinguish different scenarios for quasar feeding and black hole growth.