Evidence for photometric activity cycles in 3203 Kepler stars

Context. In recent years it has been claimed that the length of stellar activity cycles is determined by the stellar rotation rate. It has been observed that the cycle period increases with rotation period along two distinct sequences, known as the active and inactive sequences. In this picture the Sun occupies a solitary position between the two sequences. Whether the Sun might undergo a transitional evolutionary stage is currently under debate. Aims. Our goal is to measure cyclic variations of the stellar light curve amplitude and the rotation period using four years of Kepler data. Periodic changes in the light curve amplitude or the stellar rotation period are associated with an underlying activity cycle. Methods. Using a recent sample of active stars we compute the rotation period and the variability amplitude for each individual Kepler quarter and search for periodic variations of both time series. To test for periodicity in each stellar time series we consider Lomb-Scargle periodograms and use a selection based on a false alarm probability (FAP). Results. We detect amplitude periodicities in 3203 stars between 0 : 5 < P-cyc < 6 yr covering rotation periods between 1 < Prot < 40 days. Given our sample size of 23 601 stars and our selection criteria that the FAP is less than 5%, this number is almost three times higher than that expected from pure noise. We do not detect periodicities in the rotation period beyond those expected from noise. Our measurements reveal that the cycle period shows a weak dependence on rotation rate, slightly increasing for longer rotation periods. We further show that the shape of the variability deviates from a pure sine curve, consistent with observations of the solar cycle. The cycle shape does not show a statistically significant dependence on effective temperature. Conclusions. We detect activity cycles in more than 13% of our final sample with a FAP of 5% (calculated by randomly shuffling the measured 90-day variability measurements for each star). Our measurements do not support the existence of distinct sequences in the P-rot P-cyc plane, although there is some evidence for the inactive sequence for rotation periods between 5-25 days. Unfortunately, the total observing time is too short to draw sound conclusions on activity cycles with similar lengths to that of the solar cycle.