α_θ waves in the tachoclines of Sun-like stars

Vertical gradient of mean turbulent electromotive force (expressed by the dynamo coefficient, $\alpha$) caused by the penetrating convection into the tachoclines of Sun-like stars leads to the non-propagating $\alpha$-mode patterns, which result in the periodic variations of magnetic field horizontal components. The aim of the paper is to study the influence of the latitudinal variation of the dynamo coefficient on the linear dynamics of large-scale waves in the overshoot layers of the tachoclines in Sun-like stars. We use the linear magnetohydrodynamic equations with the dynamo coefficient in a simple rectangular geometry. It is shown that the vertical gradient of the $\alpha$ coefficient has the same appearance in the induction equation as the Coriolis force in the momentum equation. Therefore, the latitudinal variation of $\alpha$ parameter excites new large-scale waves similar to the Rossby waves on a rotating sphere. The dispersion properties of the waves depend only on vertical and latitudinal gradients of the parameter, therefore the modes are basically different from the ordinary dynamo waves. The $\alpha _ heta$ waves may have either prograde or retrograde propagation depending on the signs of the gradients. The time-scales of the waves may vary from hundreds of days to tens of years in various parameters of the solar tachocline. These waves are coupled with the Rossby waves on a rotating sphere in the presence of the large-scale magnetic field, which may lead to the mutual transformation of convective and rotational energies.