  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.
