Context. The Kepler space telescope leaves a legacy of tens of thousands of stellar rotation period measurements. While many of these stars show strong periodicity, there is an even bigger fraction of stars with irregular variability for which rotation periods are rarely visible or in most cases unknown. As a consequence, many studies of stellar activity might be strongly biased toward the behavior of more active stars, for which rotation periods have been determined.
Aims: With the goal to at least partially lift this bias, we apply a new method capable of determining rotation periods of stars with irregular light curve variability. This effort greatly increases the number of stars with well-determined periods, especially for stars with small variabilities similar to that of the Sun.
Methods: We employed a novel method based on the gradient of the power spectrum (GPS). The maximum of the gradient corresponds to the position of the inflection point (IP), namely, the point where the curvature of the high-frequency tail of the power spectrum changes its sign. Previously, it was shown that the stellar rotation period, P
rot, is linked to the inflection point period, P
IP, by the simple equation P
rot = P
IP/α, where α 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.
Results: From the initial sample of 142 168 stars with effective temperatures T
eff < 6500 K and log g > 4.0 in the Kepler archive, we could measure rotation periods for 67 163 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, when available. Furthermore, we show that the scaling factor a increases for very cool stars with effective temperatures below 4000 K, which we interpret as spots located at higher latitudes.
Conclusions: We conclude that new techniques, such as the GPS method, ought to be applied in detecting the rotation periods of stars with small and more irregular variabilities. Ignoring these stars will distort the overall picture of stellar activity, particular with respect to solar-stellar comparison studies. <P />Full Tables B.1 and C.1 are available at the CDS via anonymous ftp to <A href="https://cdsarc.cds.unistra.fr">cdsarc.cds.unistra.fr</A> (ftp://130.79.128.5) or via <A href="https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/678/A24">https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/678/A24</A>
