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The Halo Occupation Distribution of SDSS Quasars

We present an estimate of the projected two-point correlation function (2PCF) of quasars in the Sloan Digital Sky Survey (SDSS) over the full range of one- and two-halo scales, 0.02-120 Mpc/h. This was achieved by combining data from SDSS DR7 on large scales and Hennawi et al. (2006; with appropriate statistical corrections) on small scales. Our combined clustering sample is the largest spectroscopic quasar clustering sample to date, containing ~48,000 quasars in the redshift range 0.4<z<2.5 with median redshift 1.4. We interpret these precise 2PCF measurements within the halo occupation distribution (HOD) framework and constrain the occupation functions of central and satellite quasars in dark matter halos. In order to explain the small-scale clustering, the HOD modeling requires that a small fraction of z~1.4 quasars, fsat=(7.4+/-1.4) 10^(-4), be satellites in dark matter halos. At z~1.4, the median masses of the host halos of central and satellite quasars are constrained to be Mcen=(4.1+0.3/-0.4) 10^12 Msun/h and Msat=(3.6+0.8/-1.0) 10^14 Msun/h, respectively. To investigate the redshift evolution of the quasar-halo relationship, we also perform HOD modeling of the projected 2PCF measured by Shen et al. (2007) for SDSS quasars with median redshift 3.2. We find tentative evidence for an increase in the mass scale of quasar host halos---the inferred median mass of halos hosting central quasars at z~3.2 is Mcen=(14.1+5.8/-6.9) 10^12 Msun/h. The cutoff profiles of the mean occupation functions of central quasars reveal that quasar luminosity is more tightly correlated with halo mass at higher redshifts. The average quasar duty cycle around the median host halo mass is inferred to be fq=(7.3+0.6/-1.5) 10^(-4) at z~1.4 and fq=(8.6+20.4/-7.2) 10^(-2) at z~3.2. We discuss the implications of our results for quasar evolution and quasar-galaxy co-evolution.