Contact binary star systems represent the long-lived penultimate phase of binary evolution. Population statistics of their physical parameters inform an understanding of binary evolutionary pathways and end products. We use light curves and new optical spectroscopy to conduct a pilot study of ten (near) contact systems in the long-period (P>0.5d) tail of close binaries in the Kepler field. We use PHOEBE light-curve models to compute Bayesian probabilities on five principal system parameters. Mass ratios and third-light contributions measured from spectra agree well with those inferred from the light curves. Pilot study systems have extreme mass ratios q<0.32. Most are triples. Analysis of the unbiased sample of 783 0.15d0.8. There exists an empirical mass ratio lower limit q_min_(P)~0.05-0.15 below which contact systems are absent, supporting a new set of theoretical predictions obtained by modeling the evolution of contact systems under the constraints of mass and angular momentum conservation. Premerger systems should lie at long periods and near this mass ratio lower limit, which rises from q=0.044 for P=0.74d to q=0.15 at P=2.0d. These findings support a scenario whereby nuclear evolution of the primary (more massive) star drives mass transfer to the primary, thus moving systems toward extreme q and larger P until the onset of the Darwin instability at q_min_ precipitates a merger.

Cone search capability for table J/ApJS/262/12/systems (Best parameters (Table 3) and Bayesian percentile parameters (Table 4) for contact, detached, and ambiguous systems when modeled using contact configuration)