Using \sim 300,000 photometrically classified quasars , by far the largest quasar sample ever used for such analyses , we study the redshift and luminosity evolution of quasar clustering on scales of \sim 50 ~ { } h ^ { -1 } ~ { } { kpc } to \sim 20 ~ { } h ^ { -1 } ~ { } { Mpc } from redshifts of \bar { z } \sim 0.75 to \bar { z } \sim 2.28 .
We parameterize our clustering amplitudes using realistic dark matter models , and find that a \Lambda CDMÂ power spectrum provides a superb fit to our data with a redshift-averaged quasar bias of b _ { Q } ^ { \bar { z } = 1.40 } = 2.41 \pm 0.08 ( P _ { < \chi ^ { 2 } } = 0.847 ) for \sigma _ { 8 } = 0.9 .
This represents a better fit than the best-fit power-law model ( \omega = 0.0493 \pm 0.0064 \theta ^ { -0.928 \pm 0.055 } ; P _ { < \chi ^ { 2 } } = 0.482 ) .
We find b _ { Q } increases with redshift .
This evolution is significant at > 99.6 % using our data set alone , increasing to > 99.9999 % if stellar contamination is not explicitly parameterized .
We measure the quasar classification efficiency across our full sample as a = 95.6 \pm ^ { 4.4 } _ { 1.9 } % , a star-quasar separation comparable with the star-galaxy separation in many photometric studies of galaxy clustering .
We derive the mean mass of the dark matter halos hosting quasars as M _ { DMH } = 5.2 \pm 0.6 \times 10 ^ { 12 } ~ { } { h ^ { -1 } } M _ { \sun } .
At \bar { z } \sim 1.9 we find a 1.5 \sigma deviation from luminosity-independent quasar clustering ; this suggests that increasing our sample size by a factor of \sim 1.8 could begin to constrain any luminosity dependence in quasar bias at z \sim 2 .
Our results agree with recent studies of quasar environments at z < 0.4 , which detected little luminosity dependence to quasar clustering on proper scales \sim > ~ { } 50 ~ { } h ^ { -1 } ~ { } { kpc } .
At z < 1.6 , our analysis suggests that b _ { Q } is constant with luminosity to within \Delta b _ { Q } \sim 0.6 , and that , for g < 21 , angular quasar autocorrelation measurements are unlikely to have sufficient statistical power at z~ { } \lower 3.139 pt \hbox { $ \sim$ } \hbox to 0.0 pt { \raise 1.72 pt \hbox { $ < $ } } ~ { } 1.6 to detect any luminosity dependence in quasars ’ clustering .