Evaluating Rotation Periods of M Dwarfs Across the Ages.

In this work we examine M dwarf rotation rates at a range of ages to establish benchmarks for Mdwarf gyrochronology. This work includes a sample of 713 spectroscopically-classified M0-M8 dwarfs with new rotation rates measured from K2 light curves. We analyzed data and recover rotation rates for 179 of these objects. We add these to rotation rates for members of clusters with known ages (5-700 Myr), as well as objects assumed to have field ages ($>$1 Gyr). We use Gaia DR2 parallax and (G-GRP) photometry to create color-magnitude diagrams to compare objects across samples. We use color-period plots to analyze the period distributions across age, as well as incorporate Halpha equivalent width and tangential velocity where possible to further comment on age dependence. We find that the age of transition from rapid to slow rotation in clusters, which we define as an elbow in the period-color plots, depends on spectral type. Later spectral types transition at older ages: M4 for Praesepe at 700 Myr, one of the oldest clusters for which M dwarf rotation rates have been measured. The transition from active to inactive Halpha equivalent width also occurs at this elbow, as objects transition from rapid rotation to the slowly rotating sequence. Redder or smaller stars remain active at older ages. Finally, using Gaia kinematics we find evidence for rotation stalling for late Ms in the field sample, suggesting the transition happens much later for mid to late-type M dwarfs.