Relation of X-ray activity and rotation in M dwarfs and predicted time-evolution of the X-ray luminosity

The relation of activity to rotation in M dwarfs is of high astrophysical interest because it provides observational evidence of the stellar dynamo, which is poorly understood for low-mass stars, especially in the fully convective regime. Previous studies have shown that the relation of X-ray activity to rotation consists of two different regimes: the saturated regime for fast-rotating stars and the unsaturated regime for slowly rotating stars. The transition between the two regimes lies at a rotation period of ∼10 d. We present here a sample of 14 M dwarf stars observed with XMM-Newton and Chandra, for which we also computed rotational periods from Kepler Two-Wheel (K2) Mission light curves. We compiled X-ray and rotation data from the literature and homogenized all data sets to provide the largest uniform sample of M dwarfs (302 stars) for X-ray activity and rotation studies to date. We then fit the relation between L_x − P_rot using three different mass bins to separate partially and fully convective stars. We found a steeper slope in the unsaturated regime for fully convective stars and a nonconstant L_x level in the saturated regime for all masses. In the L_x/L_bol − R_O space we discovered a remarkable double gap that might be related to a discontinuous period evolution. Then we combined the evolution of P_rot predicted by angular momentum evolution models with our new results on the empirical L_x − P_rot relation to provide an estimate for the age decay of X-ray luminosity. We compare predictions of this relationship with the actual X-ray luminosities of M stars with known ages from 100 Myr to a few billion years. We find remarkably good agreement between the predicted L_x and the observed values for partially convective stars. However, for fully convective stars at ages of a few billion years, the constructed L_x-age relation overpredicts the X-ray luminosity because the angular momentum evolution model underpredicts the rotation period of these stars. Finally, we examine the effect of different parameterizations for the Rossby number (R_O) on the shape of the activity-rotation relation in L_x/L_bol − R_O space, and we find that the slope in the unsaturated regime and the location of the break point of the dual power-law depend sensitively on the choice of R_O.