A two-dimensional asymptotic solution for a dynamo wave in the light of the solar internal rotation

Abstract

The mean field dynamo equations for a two-dimensional (radius–latitude) αΩ model are solved in the leading order of asymptotic expansion by the use of a WKBJ method. The limiting case of short waves (large regeneration rate) is considered. The solution is shown to possess properties of travelling dynamo waves obeying Yoshimura's law. Indeed, the dynamo wave propagates along lines of constant angular velocity. This solution is compared with the one obtained for the one-dimensional model and with observational results for solar large-scale magnetic activity. The internal differential rotation, deduced from helioseismological data, is represented by an analytic fitting function. Specific locations of the dynamo wave maxima and reversals calculated in this approximation, using both the one-dimensional model and the paraboloidal approximation of the two-dimensional model, are shown to be close to each other. In our approach two non-overlapping independent dynamo waves are obtained. The first wave propagates equatorwards over low latitudes, while the second one propagates polewards over high latitudes. The wave maxima are located at the bottom of the convection zone.