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We present a method for comparing the H$\beta$ emission-line profiles ofobserved supermassive black hole (SBHB) candidates and models of sub-parsecSBHBs in circumbinary disks. Using the approach based on principal componentanalysis we infer the values of the binary parameters for the spectroscopicSBHB candidates and evaluate the parameter degeneracies, representative of theuncertainties intrinsic to such measurements. We find that as a population, theSBHB 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 theSBHB candidates considered are true binaries, this result would suggest thatthere is a physical process that allows initially unequal mass systems toevolve toward comparable mass ratios (e.g., accretion that occurspreferentially onto the smaller of the black holes) or point to some, yetunspecified, selection bias. Our method also indicates that the SBHB candidatesequally favor configurations in which the mini-disks are coplanar or misalignedwith the binary orbital plane. If confirmed for true SBHBs, this finding wouldindicate the presence of a physical mechanism that maintains misalignment ofthe mini-disks down to sub-parsec binary separations (e.g., precession drivenby gravitational torques). The probability distributions of the SBHB parametersinferred for the observed SBHB candidates and our control group of AGNs arestatistically indistinguishable, implying that this method can in principle beused to interpret the observed emission-line profiles once a sample ofconfirmed SBHBs is available but cannot be used as a conclusive test ofbinarity.

Emission Signatures from Sub-parsec Binary Supermassive Black Holes III: Comparison of Models with Observations