The Rotation–activity Correlations in K and M Dwarfs. II. New Constraints on the Dynamo Mechanisms in Late-K and M Dwarfs before and at the Transition to Complete Convection*

We study the rotation-activity correlations (RACs) in a sample stars from spectral type dK4 to dM4. We study RACs using chromospheric data and coronal data. We study the Ca\,{\sc ii} line surface fluxes-$P/\sin i$ RACs. We fit the RACs with linear homoscedastic and heteroscedastic regression models. We find that these RACs differ substantially from one spectral sub-type to another. For dM3 and dM4 stars, we find that the RACs cannot be described by a simple model, but instead that there may exist two distinct RAC behaviors for the low activity and the high activity stellar sub-samples respectively. Although these results are preliminary and will need confirmation, the data suggest that these distinct RACs may be associated with different dynamo regimes. We also study R'$_{HK}$ as a function of the Rossby number R$_{0}$. We find that: (i) For dK4 stars, we confirm R'$_{HK}$ as a function of R$_{0}$ agrees well with previous results for F-G-K stars. (ii) In dK6, dM2, dM3 and dM4 stars, we find that, at a given R$_{0}$, the values of R'$_{HK}$ lie a factor of 3, 10, 20 and 90 respectively below the F-G-K RAC. Our results suggest a significant decrease in the efficiency of the dynamo mechanism(s) as regards chromospheric heating before and at dM3, i.e. before and at the TTCC. We also show that the ratio of coronal heating to chromospheric heating $L_{X}/L_{HK}$ increases by a factor of 100 between dK4 and dM4 stars.