  We investigate the theoretical expectations for detections of supermassive
binary black holes that can be identified as sub-parsec luminous quasars.
To-date, only two candidates have been selected in a sample comprising 17,500
sources selected from the Sloan Digital Sky Survey (SDSS) Quasar Catalog at
z<0.70 (Boroson & Lauer 2009) In this Letter, we use models of assembly and
growth of supermassive black holes (SMBHs) in hierarchical cosmologies to study
the statistics and observability of binary quasars at sub-parsec separations.
Our goal is twofold: (1) test if such a scarce number of binaries is consistent
with theoretical prediction of SMBH merger rates, and (2) provide additional
predictions at higher redshifts, and at lower flux levels. We determine the
cumulative 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 observable
binary fraction. We find that sub-parsec quasar binaries are intrinsically
rare. Our best models predict ~0.01 deg^-2 sub-parsec binary quasars with
separations below ~10^4 Schwarzschild radii (v_orb>2000 km/s) at z<0.7, which
represent 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 with
increasing redshift. The decreasing lifetime with SMBH binary mass suggests
that lowering the luminosity threshold does not lead to a significant increase
in the number of detectable sub-parsec binary quasars.
