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In recent years it has been claimed that the length of stellar activitycycles is determined by the stellar rotation rate. It is observed that thecycle period increases with rotation period along the so-called active andinactive sequences. In this picture the Sun occupies a solitary position inbetween the two sequences. Our goal is to measure cyclic variations of thestellar light curve amplitude and the rotation period using four years ofKepler data. Periodic changes of the light curve amplitude or the stellarrotation period are associated with an underlying activity cycle. Using theMcQuillan et al. 2014 sample we compute the rotation period and the variabilityamplitude for each Kepler quarter and search for periodic variations of bothtime series. To test for periodicity in each stellar time series we considerLomb-Scargle periodograms and use a selection based on a False AlarmProbability (FAP). We detect amplitude periodicities in 3203 stars between0.5-6 years covering rotation periods between 1-40 days. Given our sample sizeof 23,601 stars and our selection criteria that the FAP is less than 5%, thisnumber is almost three times higher than that expected from pure noise. We donot detect periodicities in the rotation period beyond those expected fromnoise. Our measurements reveal that the cycle period shows a weak dependence onrotation rate, slightly increasing for longer rotation period. We further showthat the shape of the variability deviates from a pure sine curve, consistentwith observations of the solar cycle. Our measurements do not support theexistence of distinct sequences in the P_rot-P_cyc plane, although there issome evidence for the inactive sequence for rotation periods between 5-25 days.Unfortunately, the total observing time is too short to draw sound conclusionson activity cycles with similar length as the solar cycle.

Evidence for photometric activity cycles in 3203 Kepler stars