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.
