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We study the rotation-activity correlations (RACs) in a sample stars fromspectral type dK4 to dM4. We study RACs using chromospheric data and coronaldata. We study the Ca\,{\sc ii} line surface fluxes-$P/\sin i$ RACs. We fit theRACs with linear homoscedastic and heteroscedastic regression models. We findthat these RACs differ substantially from one spectral sub-type to another. FordM3 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 lowactivity and the high activity stellar sub-samples respectively. Although theseresults are preliminary and will need confirmation, the data suggest that thesedistinct RACs may be associated with different dynamo regimes.  We also study R'$_{HK}$ as a function of the Rossby number R$_{0}$. We findthat: (i) For dK4 stars, we confirm R'$_{HK}$ as a function of R$_{0}$ agreeswell with previous results for F-G-K stars. (ii) In dK6, dM2, dM3 and dM4stars, we find that, at a given R$_{0}$, the values of R'$_{HK}$ lie a factorof 3, 10, 20 and 90 respectively below the F-G-K RAC. Our results suggest asignificant decrease in the efficiency of the dynamo mechanism(s) as regardschromospheric 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.

astrophysical journal/the astrophysical journal

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