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We study the relation between stellar rotation and magnetic activity for asample of 134 bright, nearby M dwarfs observed in the Kepler Two-Wheel (K2)mission during campaigns C0 to C4. The K2 lightcurves yield photometricallyderived rotation periods for 97 stars (79 of which without previous periodmeasurement), as well as various measures for activity related to cool spotsand flares. We find a clear difference between fast and slow rotators with adividing line at a period of ~10d at which the activity level changes abruptly.All photometric diagnostics of activity (spot cycle amplitude, flare peakamplitude and residual variability after subtraction of spot and flarevariations) display the same dichotomy, pointing to a quick transition betweena high-activity mode for fast rotators and a low-activity mode for slowrotators. This unexplained behavior is reminiscent of a dynamo mode-change seenin numerical simulations that separates a dipolar from a multipolar regime. Asubstantial number of the fast rotators are visual binaries. A tentativeexplanation is accelerated disk evolution in binaries leading to higher initialrotation rates on the main-sequence and associated longer spin-down andactivity lifetimes. We combine the K2 rotation periods with archival X-ray andUV data. X-ray, FUV and NUV detections are found for 26, 41, and 11 stars fromour sample, respectively. Separating the fast from the slow rotators, wedetermine for the first time the X-ray saturation level separately for early-and for mid-M stars.

A path towards understanding the rotation-activity relation of M dwarfs with K2 mission, X-ray and UV data