2017ApJ...837...96H

We study the rotation-activity correlations (RACs) in a sample of stars from spectral type dK4 to dM4. We study RACs using chromospheric data and coronal data. We study the Ca II line surface fluxes-P/sini 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 R₀. We find (i) for dK4 stars, R_HK^′^ as a function of R₀ agrees well with previous results for F-G-K stars and (ii) in dK6, dM2, dM3, and dM4 stars, at a given R₀, the values of R_HK^′^ lie at 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 transition to complete convection. 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.