We report on a study of eclipse timing variations in contact binary systems , using long-cadence lightcurves in the Kepler archive .
As a first step , ‘ observed minus calculated ’ ( O - C ) curves were produced for both the primary and secondary eclipses of some 2000 Kepler binaries .
We find \sim 390 short-period binaries with O - C curves that exhibit ( i ) random-walk like variations or quasi-periodicities , with typical amplitudes of \pm 200-300 seconds , and ( ii ) anticorrelations between the primary and secondary eclipse timing variations .
We present a detailed analysis and results for 32 of these binaries with orbital periods in the range of 0.35 \pm 0.05 days .
The anticorrelations observed in their O - C curves can not be explained by a model involving mass transfer , which among other things requires implausibly high rates of \sim 0.01 M _ { \odot } { yr } ^ { -1 } .
We show that the anticorrelated behavior , the amplitude of the O - C delays , and the overall random-walk like behavior can be explained by the presence of a starspot that is continuously visible around the orbit and slowly changes its longitude on timescales of weeks to months .
The quasi-periods of \sim 50 - 200 days observed in the O - C curves suggest values for k , the coefficient of the latitude dependence of the stellar differential rotation , of \sim 0.003 - 0.013 .