New rotation periods of 67163 Kepler stars

The maximum of the gradient corresponds to the position of the inflection point (IP), i.e., the point where the curvature of the high-frequency tail of the power spectrum changes its sign. It was shown previously that the stellar rotation period Prot is linked to the inflection point period P_IP_) by the simple equation Prot=P_IP_/alpha, where alpha is a calibration factor. The GPS method is superior to classical methods (such as auto-correlation functions (ACF)) because it does not require a repeatable variability pattern in the time series, making it an ideal tool for detecting periods of stars with very short-lived spots.

From the initial sample of 142168 stars with effective temperatures Teff<=6500K and logg>=4.0 in the Kepler archive, we could measure rotation periods for 67163 stars by combining the GPS and the ACF method. We further report the first determination of a rotation period for 20,397 stars. The GPS periods show good agreement with previous period measurements using classical methods, where these are available.

Furthermore, we show that the scaling factor alpha increases for very cool stars with effective temperatures below 4000K, which we interpret as spots located at higher latitudes. We conclude that new techniques (such as the GPS method) must be applied to detect rotation periods of stars with small and more irregular variabilities. Ignoring these stars will distort the overall picture of stellar activity and, in particular, solar-stellar comparison studies.