We present measurements of the quasar two-point correlation function , \xi _ { Q } , over the redshift range 0.3 \leq z \leq 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 Catalogue , our study represents the largest sample used for this type of investigation to date .
With this redshift range and an areal coverage of \approx 4,000 deg ^ { 2 } , we sample over 25 h ^ { -3 } Gpc ^ { 3 } ( comoving ) of the Universe in volume , assuming the current \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 \pm 0.45 ~ { } h ^ { -1 } ~ { } { Mpc } and \gamma _ { s } = 1.16 ^ { +0.11 } _ { -0.16 } when fit over 1.0 \leq s \leq 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 redshift-space distortions in the 2-D \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 ^ { +0.35 } _ { -0.45 } ~ { } h ^ { -1 } ~ { } { Mpc } and \gamma = 1.90 ^ { +0.04 } _ { -0.03 } , over scales of 1.0 \leq r _ { p } \leq 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 } \sim 6 - 7 ~ { } h ^ { -1 } ~ { } { Mpc } at z \lesssim 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 2QZ survey and previous SDSS quasar measurements using photometric redshifts .
Comparing our clustering measurements to those reported for X-ray selected AGN at z \sim 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 \sim 1.4 at z = 0.5 to b \sim 3 at z = 2.2 , with b ( z = 1.27 ) = 2.06 \pm 0.03 for the full sample .
We compare our data to analytical models and infer that quasars inhabit dark matter haloes of constant mass M _ { halo } \sim 2 \times 10 ^ { 12 } h ^ { -1 } M _ { \odot } from redshifts z \sim 2.5 ( the peak of quasar activity ) to z \sim 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 .