Motivated by advances in observational searches for sub-parsec supermassive black hole binaries (SBHBs) made in the past few years, we develop a semi-analytic model to describe spectral emission-line signatures of these systems. The goal of this study is to aid the interpretation of spectroscopic searches for binaries and tohelp test one of the leading models of binary accretion flows in the literature: SBHB in a circumbinary disk. In this work, we present the methodology and a comparison of the preliminary model with the data. We model SBHB accretion flows as a set of three accretion disks: two mini-disks that are gravitationally bound to the individual black holes and a circumbinary disk. Given a physically motivated parameter space occupied by sub-parsec SBHBs, we calculate a synthetic database of nearly 15 million broad optical emission-line profiles and explore the dependence of the profile shapes on characteristic properties of SBHBs. We find that the modeled profiles show distinct statistical properties as a function of the semimajor axis, mass ratio, eccentricity of the binary, and the degree of alignment of the triple disk system. This suggests that the broad emission-line profiles from SBHB systems can in principle be used to infer the distribution of these parameters and as such merit further investigation. Calculated profiles are more morphologically heterogeneous than the broad emission lines in observed SBHB candidates and we discuss improved treatment of radiative transfer effects, which will allow adirect statistical comparison of the two groups.

Motivated by observational searches for sub-parsec supermassive black hole binaries (SBHBs) we develop a modular analytic model to determine the likelihood for detection of SBHBs by ongoing spectroscopic surveys. The model combines the parametrized rate of orbital evolution of SBHBs in circumbinary disks with the selection effects of spectroscopic surveys and returns a multivariate likelihood for SBHB detection. Based on this model we find that in order to evolve into the detection window of the spectroscopic searches from larger separations in less than a Hubble time, 10 8 M SBHBs must, on average, experience angular momentum transport faster than that provided by a disk with accretion rate 0.06Ṁ E . Spectroscopic searches with yearly cadence of observations are in principle sensitive to binaries with orbital separations < few × 10 4 r g (r g = GM/c 2 and M is the binary mass), and for every one SBHB in this range there should be over 200 more gravitationally bound systems with similar properties, at larger separations. Furthermore, if spectra of all SBHBs in this separation range exhibit the AGN-like emission lines utilized by spectroscopic searches, the projection factors imply five undetected binaries for each observed 10 8 M SBHB with mass ratio 0.3 and orbital separation 10 4 r g (and more if some fraction of SBHBs is inactive). This model can be used to infer the most likely orbital parameters for observed SBHB candidates and to provide constraints on the rate of orbital evolution of SBHBs, if observed candidates are shown to be genuine binaries.

We present an improved semi-analytic model for calculation of the broad optical emission-line signatures from sub-parsec supermassive black hole binaries (SBHBs) in circumbinary disks. The secondgeneration model improves upon the treatment of radiative transfer by taking into account the effect of the radiation driven accretion disk wind on the properties of the emission-line profiles. Analysis of 42.5 million modeled emission-line profiles shows that correlations between the profile properties and SBHB parameters identified in the first-generation model are preserved, indicating that their diagnostic power is not diminished. The profile shapes are a more sensitive measure of the binary orbital separation and the degree of alignment of the black hole mini-disks, and are less sensitive to the SBHB mass ratio and orbital eccentricity. We also find that modeled profile shapes are more compatible with the observed sample of SBHB candidates than with our control sample of regular AGNs. Furthermore, if the observed sample of SBHBs is made up of genuine binaries, it must include compact systems with comparable masses, and misaligned mini-disks. We note that the model described in this paper can be used to interpret the observed emission-line profiles once a sample of confirmed SBHBs is available but cannot be used to prove that the observed SBHB candidates are true binaries.

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