Cross-Correlation of SDSS DR7 Quasars and DR10 BOSS Galaxies: The Weak
  Luminosity Dependence of Quasar Clustering at z~0.5
  We present the measurement of the two-point cross-correlation function (CCF)
of 8,198 Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) quasars and
349,608 DR10 CMASS galaxies from the Baryonic Oscillation Spectroscopic Survey
(BOSS) at redshift <z>~0.5 (0.3<z<0.9). The cross-correlation function can be
reasonably well fit by a power-law model xi_QG(r)=(r/r_0)^(-gamma) on projected
scales of r_p=2-25 Mpc/h with r_0=6.61+-0.25 Mpc/h and gamma=1.69+-0.07. We
estimate a quasar linear bias of b_Q=1.38+-0.10 at <z>=0.53 from the CCF
measurements. This linear bias corresponds to a characteristic host halo mass
of ~4x10^12 M_sun/h, compared to ~10^13 M_sun/h characteristic host halo mass
for CMASS galaxies. We divide the quasar sample in luminosity and constrain the
luminosity dependence of quasar bias to be db_Q/dlogL=0.20+-0.34 or 0.11+-0.32
(depending on different luminosity divisions) for quasar luminosities
-23.5>M_i(z=2)>-25.5, implying a weak luminosity dependence of quasar
clustering for the bright end of the quasar population at <z>~0.5. We compare
our measurements with theoretical predictions, Halo Occupation Distribution
(HOD) models and mock catalogs. These comparisons suggest quasars reside in a
broad range of host halos, and the host halo mass distributions significantly
overlap with each other for quasars at different luminosities, implying a poor
correlation between halo mass and instantaneous quasar luminosity. We also find
that the quasar HOD parameterization is largely degenerate such that different
HODs can reproduce the CCF equally well, but with different outcomes such as
the satellite fraction and host halo mass distribution. These results highlight
the limitations and ambiguities in modeling the distribution of quasars with
the standard HOD approach and the need for additional information in populating
quasars in dark matter halos with HOD. [Abridged]
