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 can not be used as a conclusive test of binarity .