THE INFLUENCE OF BOUNDARY-CONDITIONS ON THE EXCITATION OF DISK DYNAMO MODES

Calculations of mean field dynamos for galaxies have largely been for two rather disparate models. The thin disk model treats the ratio of disk height to radius explicitly as a small parameter, and applies zero tangential field boundary conditions at the disk surface. In contrast, the embedded disk model calculates the magnetic field in a spherical volume, whose radius is the disk radius and with the magnetic field fitting smoothly on to a curl-free exterior field at the surface of the sphere. The disk geometry is imposed by a flat distribution of the alpha-effect (and maybe also of the diffusivity eta). For computational reasons this model has not been applied to very thin disks, so the regions of validity of the two models are almost disjoint. Comparison between their predictions is therefore difficult. In this paper we calculate, in linear theory, galactic dynamo modes according to both thin and embedded (or "thick") disk models for a simple underlying distribution of alpha-effect and differential rotation, using a common numerical scheme. For the smallest attainable ratio of disk height to radius, we find the critical dynamo numbers are similar, but that there are some significant differences in field topology.