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We investigate the theoretical expectations for detections of supermassivebinary black holes that can be identified as sub-parsec luminous quasars.To-date, only two candidates have been selected in a sample comprising 17,500sources selected from the Sloan Digital Sky Survey (SDSS) Quasar Catalog atz<0.70 (Boroson & Lauer 2009) In this Letter, we use models of assembly andgrowth of supermassive black holes (SMBHs) in hierarchical cosmologies to studythe statistics and observability of binary quasars at sub-parsec separations.Our goal is twofold: (1) test if such a scarce number of binaries is consistentwith theoretical prediction of SMBH merger rates, and (2) provide additionalpredictions at higher redshifts, and at lower flux levels. We determine thecumulative number of expected binaries in a complete, volume limited sample.Motivated by Boroson & Lauer (2009), we apply the SDSS Quasar luminosity cut(M_i<-22) to our theoretical sample, deriving an upper limit to the observablebinary fraction. We find that sub-parsec quasar binaries are intrinsicallyrare. Our best models predict ~0.01 deg^-2 sub-parsec binary quasars withseparations below ~10^4 Schwarzschild radii (v_orb>2000 km/s) at z<0.7, whichrepresent a fraction ~6x10^-4 of unabsorbed quasars in our theoretical sample.In a complete sample of ~10,000 sources, we therefore predict an upper limit of~10 sub-parsec binary quasars. The number of binaries increases rapidly withincreasing redshift. The decreasing lifetime with SMBH binary mass suggeststhat lowering the luminosity threshold does not lead to a significant increasein the number of detectable sub-parsec binary quasars.

Sub-parsec supermassive Binary Quasars: expectations at z<1