A dynamo model of magnetic activity in solar-like stars with different rotational velocities

We attempt to provide a quantitative theoretical explanation for the observations that Ca II H/K emission and X-ray emission from solar-like stars increase with decreasing Rossby number (i.e., with faster rotation). Assuming that these emissions are caused by magnetic cycles similar to the sunspot cycle, we construct flux transport dynamo models of $1M_{\odot}$ stars rotating with different rotation periods. We first compute the differential rotation and the meridional circulation inside these stars from a mean-field hydrodynamics model. Then these are substituted in our dynamo code to produce periodic solutions. We find that the dimensionless amplitude $f_m$ of the toroidal flux through the star increases with decreasing rotation period. The observational data can be matched if we assume the emissions to go as the power 3-4 of $f_m$. Assuming that the Babcock-Leighton mechanism saturates with increasing rotation, we can provide an explanation for the observed saturation of emission at low Rossby numbers. The main failure of our model is that it predicts an increase of magnetic cycle period with increasing rotation rate, which is the opposite of what is found observationally. Much of our calculations are based on the assumption that the magnetic buoyancy makes the magnetic flux tubes to rise radially from the bottom of the convection zone. On taking account of the fact that the Coriolis force diverts the magnetic flux tubes to rise parallel to the rotation axis in rapidly rotating stars, the results do not change qualitatively.