Magnetic field escape from a stellar convection zone and the dynamo-cycle period

Traditionally, dynamo theories have predicted periods for stellar activity cycles that are much shorter than is observed. We argue that this problem can be solved by allowing for the non-free escape of magnetic fields through the surface boundary. New boundary conditions are suggested that largely reduce magnetic Aux escape from the dynamo region compared to the traditional vacuum conditions. The effect of the new conditions is checked with a solar-type dynamo model in a spherical shell. The dynamo incorporates the helioseismologically-detected rotation law and prescribes all the key parameters in accord with the convection zone structure models. The cycle period increases by an order of magnitude and the critical dynamo number decreases in about the same proportion when the new boundary conditions are implemented. The observed 22-year period of the solar cycle can be reproduced. Also the ratio of toroidal-to-poloidal magnetic field is brought closer to observations in this way. Based on our dynamo model, an interpretation can be offered for the empirical relation between activity cycle period and rotation rate of the slowly rotating solar-type stars.