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Rotation period measurements of stars observed with the Kepler mission haverevealed a lack of stars at intermediate rotation periods, accompanied by adecrease of photometric variability. Whether this so-called dearth region is apeculiarity of stars in the Kepler field, or reflects a general manifestationof stellar magnetic activity, is still under debate. Our goal is to measurestellar rotation periods and photometric variabilities for tens of thousands ofK2 stars, located in different fields along the ecliptic plane, to shed lighton the relation between stellar rotation and photometric variability. We useLomb-Scargle periodograms, auto-correlation and wavelet functions to determineconsistent rotation periods. Stellar brightness variability is assessed bycomputing the variability range from the light curve. We further apply Gaussianmixture models to search for bimodality in the rotation period distribution.Combining measurements from all K2 campaigns, we detect rotation periods in29,860 stars. For effective temperatures below 6000K, the variability rangeshows a local minimum at different periods, consistent with an isochrone age of750 Myr. Additionally, the K2 rotation period distribution shows evidence forbimodality, although the dearth region is less pronounced compared to theKepler field. The period at the dip of the bimodal distribution shows goodagreement with the period at the local variability minimum. We conclude thatthe period bimodality is present in different fields of the sky, and is hence ageneral manifestation of stellar magnetic activity. The reduced variability inthe dearth region is interpreted as a cancelation between dark spots and brightfaculae. Our results strongly advocate that the role of faculae has beenunderestimated so far, suggesting a more complex dependence of the brightnessvariability on the rotation period.

Stellar rotation periods from K2 Campaigns 0-18 -- Evidence for rotation period bimodality and simultaneous variability decrease