Emission Signatures from Sub-parsec Binary Supermassive Black Holes I: Diagnostic Power of Broad Emission Lines

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 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 semi-major 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 direct statistical comparison of the two groups.