We report on the properties of eclipsing binaries from the Kepler mission
with a newly developed photometric modeling code, which uses the light curve,
spectral energy distribution of each binary, and stellar evolution models to
infer stellar masses without the need for radial velocity measurements. We
present solutions and posteriors to orbital and stellar parameters for 728
systems, forming the largest homogeneous catalogue of full Kepler binary
parameter estimates to date. Using comparisons to published radial velocity
measurements, we demonstrate that the inferred properties (e.g., masses) are
reliable for well-detached main-sequence binaries, which make up the majority
of our sample. The fidelity of our inferred parameters degrades for a subset of
systems not well described by input isochrones, such as short-period binaries
that have undergone interactions, or binaries with post-main sequence
components. Additionally, we identify 35 new systems which show evidence of
eclipse timing variations, perhaps from apsidal motion due to binary tides or
tertiary companions. We plan to subsequently use these models to search for and
constrain the presence of circumbinary planets in Kepler eclipsing binary
systems.Comment: 36 pages, 16 figures; accepted 2019 July 30 to MNRA