  The Kepler mission has been providing high-quality photometric data leading
to many breakthroughs in the exoplanet search and in stellar physics. Stellar
magnetic activity results from the interaction between rotation, convection,
and magnetic field. Constraining these processes is important if we want to
better understand stellar magnetic activity. Using the Sun, we want to test a
magnetic activity index based on the analysis of the photo- metric response and
then apply it to a sample of M dwarfs observed by Kepler. We estimate a global
stellar magnetic activity index by measuring the standard deviation of the
whole time series, Sph. Because stellar variability can be related to
convection, pulsations, or magnetism, we need to ensure that this index mostly
takes into account magnetic effects. We define another stellar magnetic
activity index as the average of the standard deviation of shorter subseries
which lengths are determined by the rotation period of the star. This way we
can ensure that the measured photometric variability is related to starspots
crossing the visible stellar disk. This new index combined with a
time-frequency analysis based on the Morlet wavelets allows us to determine the
existence of magnetic activity cycles. We measure magnetic indexes for the Sun
and for 34 M dwarfs observed by Kepler. As expected, we obtain that the sample
of M dwarfs studied in this work is much more active than the Sun. Moreover, we
find a small correlation between the rotation period and the magnetic index.
Finally, by combining a time-frequency analysis with phase diagrams, we
discover the presence of long-lived features suggesting the existence of active
longitudes on the surface of these stars.
