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Very small-scale clustering of quasars from a complete quasar lens survey

We measure the small-scale (comoving separation 10 kpc/h < r_p < 200 kpc/h) two-point correlation function of quasars using a sample of 26 spectroscopically confirmed binary quasars at 0.6<z<2.2 from the Sloan Digital Sky Survey Quasar Lens Search (SQLS). Thanks to careful candidate selections and extensive follow-up observations of the SQLS, which is aimed at constructing a complete quasar lens sample, our sample of binary quasars is also expected to be nearly complete within a specified range of angular separations and redshifts. The measured small-scale correlation function rises steeply toward smaller scales, which is consistent with earlier studies based on incomplete or smaller binary quasar samples. We find that the quasar correlation function can be fitted by a power-law reasonably well over 4 order of magnitudes, with the best-fit slope of xi(r)\propto r^{-1.92}. We interpret the measured correlation function within the framework of the Halo Occupation Distribution (HOD). We propose a simple model which assumes a constant fraction of quasars that appear as satellites in dark matter haloes, and find that measured small-scale clustering signals constrain the satellite fraction to f_sat=0.054_{-0.016}^{+0.017} for a singular isothermal sphere number density profile of satellites. We note that the HOD modelling appears to underpredict clustering signals at the smallest separations of r_p ~ 10 kpc/h unless we assume very steep number density profiles (such as an NFW profile with the concentration parameter c_vir > 30), which may be suggestive of enhanced quasar activities by direct interactions.