The stellar rotation-activity relationship in fully convective M dwarfs

The coronal activity-rotation relationship is considered to be a proxy for the underlying stellar dynamo responsible for magnetic activity in solar and late-type stars. While this has been studied in considerable detail for partly convective stars that are believed to operate an interface dynamo, it is poorly unconstrained in fully convective stars that lack the necessary shear layer between radiative core and the convective envelope. We present new X-ray observations of 19 slowly rotating fully convective stars with rotation periods from the MEarth Project. We use these to calculate X-ray luminosities (or upper limits for undetected sources) and combine these with existing measurements. We confirm the existence of fully convective stars in the X-ray unsaturated regime and find that these objects follow the same rotation-activity relationship seen for partly convective stars. We measure the power-law slope of the relationship between Rossby number (the ratio of the rotation period to the convective turnover time) and the fractional X-ray luminosity for X-ray unsaturated fully convective stars for the first time, and find it to be consistent with that found for partly convective stars. We discuss this implications of this result for our understanding of stellar magnetic dynamos in fully- and partly convective stars. Finally, we also use this data to improve empirical estimates of the convective turnover time for fully convective stars.