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−1Mpc) 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. (2009). 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 (with 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. Reproducing the large-scale clustering amplitude requires that the active fraction of the black holes in the central galaxies of halos is near unity, but the level of small-scale clustering favors an active fraction of black holes in satellite galaxies 0.1 . fs . 0.5 at z & 3. Subject headings: black hole physics – galaxies: active – cosmology: observations – large-scale structure of universe – quasars: general – surveys