Binary quasars at high redshift. II. Sub-Mpc clustering at z ∼ 3-4

We present measurements of the small-scale (0.1 ≲ r ≲ 1 h ^-1 Mpc) quasar two-point correlation function at z > 2.9, for a flux-limited (i < 21) sample of 15 binary quasars compiled by Hennawi et al. The amplitude of the small-scale clustering increases from z ∼ 3 to z ∼ 4. The small-scale clustering amplitude is comparable to or lower than power-law extrapolations (assuming a fixed slope γ = 2) from the large-scale correlation function of the i < 20.2 quasar sample from the Sloan Digital Sky Survey. Using simple prescriptions relating quasars to dark matter halos, we model the observed small-scale clustering with halo occupation models. We found that the level of small-scale clustering favors an active fraction of black holes in (M ≳ 10¹³ h^-1 M_⊙) satellite halos f_s ≳ 0.1 at z ≳ 3.