Tracking the stellar longitudes of starspots in short-period Kepler binaries

We report on a new method for tracking the phases of the orbital modulations in very short-period, near-contact, and contact binary systems in order to follow starspots. We apply this technique to Kepler light curves for 414 binary systems that were identified as having anticorrelated O−C curves for the mid-times of the primary and secondary eclipses, or in the case of non-eclipsing systems, their light-curve minima. This phase tracking approach extracts more information about starspot and binary system behaviour than may be easily obtained from the O−C curves. We confirm the hypothesis of Tran et al. that we can successfully follow the rotational motions of spots on the surfaces of the stars in these binaries. In ∼34 per cent of the systems, the spot rotation is retrograde as viewed in the frame rotating with the orbital motion, while ∼13 per cent show significant prograde spot rotation. The remaining systems show either little spot rotation or erratic behaviour, or sometimes include intervals of both types of behaviour. We discuss the possibility that the relative motions of spots are related to differential rotation of the stars. It is clear from this study that the motions of the starspots in at least 50 per cent of these short-period binaries are not exactly synchronized with the orbits.