  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.
