Light curve solutions of 12 eccentric Kepler binaries and analysis of their out-of-eclipse variability

The eccentricity, periastron angle, orbital inclination, mass ratio, stellar temperatures and relative stellar radii of 12 eclipsing eccentric binaries were determined on the basis of Kepler data. The analysis of their out-of-eclipse variability led to the following results: (i) KIC 10490980 exhibits rotational (spot-type) variability; (ii) Four new heartbeat stars were found: KIC 9344623 and KIC 10296163, which have wide tidally induced light humps and KIC 9119405 and KIC 9673173, which have narrow "W-shape" features; (iii) KIC 4932691 shows oscillations with approximately the 18th harmonic of the orbital period. We established that the eccentric Kepler binaries fall below the envelope P(1-e^2)^{3/2} = 5 days on the period-eccentricity diagram and that there is a surprising lack of eccentric binaries with periods of 25-35 days.