CLUSTERING OF LOW-REDSHIFT (z ≤ 2.2) QUASARS FROM THE SLOAN DIGITAL SKY SURVEY

We present measurements of the quasar two-point correlation function,xi(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 approximate to 4000 deg(2), we sample over 25 h(-3) Gpc(3) (comoving) of the universe in volume, assuming the current Lambda Cold Dark Matter (Lambda CDM) cosmology. Over this redshift range, we find that the redshift-space correlation function, xi(s), is adequately fit by a single power law, with s(0) = 5.95 +/- 0.45 h(-1) Mpc and gamma(s) = 1.16(-0.16)(+0.11) when fit over 1.0 h(-1) Mpc <= s <= 25.0 h(-1) Mpc. We find no evidence for deviation from xi(s) = 0 at scales of s > 100 h(-1) Mpc, but do observe redshiftspace distortions in the two-dimensional xi(r(p), pi) measurement. Using the projected correlation function, w(p)(r(p)), we calculate the real-space correlation length, r(0) = 5.45(-0.45)(+0.35) h(-1) Mpc and gamma = 1.90(-0.03)(+0.04) , 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) similar to 6-7 h(-1) Mpc at z less than or similar to 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 similar to 0.5-1, we find reasonable agreement in some cases but significantly lower correlation lengths in others. Assuming a standard Lambda CDM cosmology, we find that the linear bias evolves from b similar to 1.4 at z = 0.5 to b similar to 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 similar to 2 x 10(12) h(-1) M-circle dot from redshifts z similar to 2.5 (the peak of quasar activity) to z similar to 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.