Abstract
Many stars exhibit magnetic cycles typified by the butterfly diagram characterising our Sun’s 11 year solar activity cycle. Parker explained the phenomenon by an alpha-omega dynamo acting in the star’s convection zone causing the equatorial propagation of dynamo waves. In contrast, to the many continuing numerical investigations, we adopt a minimalist approach and expand on Parker’s original one-dimensional uniform plane layer model. To apply asymptotic methods, we suppose that the dynamo is confined to a thin shell with latitudinal variations of the alpha-omega sources, whose product the Dynamo number vanishes at the pole and equator. The ensuing linear stability problem is resolved by global stability criteria. Our new results concern the role of meridional circulation. They show that sufficiently large circulation halts the Parker travelling waves leading to non-oscillatory behaviour, a result only predicted previously from numerical integration of the full pde’s governing axisymmetric alpha-omega dynamos.