  Rapidly rotating stars show short-period oscillations in magnetic activity
and polar appearance of starspots. The aim of this paper is to study
large-scale shallow water waves in the tachoclines of rapidly rotating stars
and their connection to the periodicity and the formation of starspots at high
latitudes. Shallow-water magnetohydrodynamic equations were used to study the
dynamics of large-scale waves at the rapidly rotating stellar tachoclines in
the presence of toroidal magnetic field. Dispersion relations and latitudinal
distribution of wave modes were derived. We found that low-frequency magnetic
Rossby waves tend to be located at poles, but high-frequency magnetic Poincare
waves are concentrated near the equator in rapidly rotating stars. These
results have important implications for the evolution of the stellar wind in
young Sun-like stars. Unstable magnetic Rossby waves may lead to the local
enhancement of magnetic flux at high latitudes of tachoclines in rapidly
rotating stars. The enhanced magnetic flux may rise upwards owing to the
magnetic buoyancy in the form of tubes and appear as starspots at polar
regions. Magnetic Rossby waves may also cause observed short-term periodicity
in the stellar magnetic activity.
