Emission Signatures from Sub-parsec Binary Supermassive Black Holes III:
  Comparison of Models with Observations
  We present a method for comparing the H$\beta$ emission-line profiles of
observed supermassive black hole (SBHB) candidates and models of sub-parsec
SBHBs in circumbinary disks. Using the approach based on principal component
analysis we infer the values of the binary parameters for the spectroscopic
SBHB candidates and evaluate the parameter degeneracies, representative of the
uncertainties intrinsic to such measurements. We find that as a population, the
SBHB candidates favor the average value of the semimajor axis corresponding to
$\log(a/M) \approx 4.20\pm 0.42$ and comparable mass ratios, $q>0.5$. If the
SBHB candidates considered are true binaries, this result would suggest that
there is a physical process that allows initially unequal mass systems to
evolve toward comparable mass ratios (e.g., accretion that occurs
preferentially onto the smaller of the black holes) or point to some, yet
unspecified, selection bias. Our method also indicates that the SBHB candidates
equally favor configurations in which the mini-disks are coplanar or misaligned
with the binary orbital plane. If confirmed for true SBHBs, this finding would
indicate the presence of a physical mechanism that maintains misalignment of
the mini-disks down to sub-parsec binary separations (e.g., precession driven
by gravitational torques). The probability distributions of the SBHB parameters
inferred for the observed SBHB candidates and our control group of AGNs are
statistically indistinguishable, implying that this method can in principle be
used to interpret the observed emission-line profiles once a sample of
confirmed SBHBs is available but cannot be used as a conclusive test of
binarity.
