A new look at the relationship between activity, dynamo number and Rossby number in late-type stars

The correlation between stellar activity, as measured by the indicator Delt aR(HK), and the Rossby number Ro in late-type stars is revisited in light o f recent developments in solar dynamo theory. Different stellar interior mo dels, based on both mixing-length theory and the full spectrum of turbulenc e, are used in order to see to what extent the correlation of activity with Rossby number is model dependent, or otherwise can be considered universal . Although we find some modest model dependence, we find that the correlati on of activity with Rossby number is significantly better than with rotatio n period alone for all the models we consider. Dynamo theory suggests that activity should scale with the dynamo number. A current model of the solar dynamo, the so-called interface dynamo, proposes that the amplification of the toroidal magnetic field by differential rotation (the omega -effect) an d the production of the poloidal magnetic field from toroidal by helical tu rbulence (the alpha -effect) take place in different, adjacent layers near the base of the convection zone. A new scale analysis based on the interfac e dynamo shows that the appropriate dynamo number does not depend on the Ro ssby number alone, but also depends on an additional dimensionless factor r elated to the differential rotation. This leads to a new interpretation of the correlation between activity and Rossby number, which in turn leads to some conclusions about the magnitude of differential rotation in the dynamo layers of late-type main-sequence stars.