Activity of low mass stars in the light of spot signature in the Fourier domain

Context. Magnetic fields exhibit a wide variety of behaviours in low mass stars and further characterization is required to understand these observations. Stellar photometry from space missions such as MOST, CoRoT, Kepler, and, in future PLATO, provide thousands of highly precise light curves (LC) that can shed new light upon stellar activity, in particular through the signature of transiting spots. Aims. We study the impact of star spots on light curves in the Fourier domain, reducing the degeneracies encountered by direct spot modelling in the temporal domain, and use this new formulation to explore the spot properties from the available data. Methods. We propose a model of LC power spectra at low frequency based on a description of spot transits that allows us to retrieve information about the amplitude of their photometric impact $\mathcal{H}$, and about the spot mean lifetime over the observation $\tau_{\rm life}$ when the power spectrum exibits rotation peaks. We first validate this method with simulated LCs and then apply it to the Kepler data to extract global trends over a set of more than 37 755 stars. Results. This analysis leads to a classification of the sample into "peakless" or "with peaks" spectra, and enables the identification of different activity regimes based on $\mathcal{H}$ and $\tau_{\rm life}$ for different ranges of Rossby number. More specifically, we observe an intense regime of activity between Ro = 0.7 and Ro = 1, for stars with masses under 1$M_\odot$. Conclusions. This new systematic method can be used to provide new observational constraints on stellar activity (and possibly a link with stellar magnetism) when applied to large photometric datasets, such as those from the future PLATO mission.