Progress and Problems in Solar Dyanmo Theory

In the 1970's it was widely believed that an application of mean-field dynamo theory to the bulk of the solar convection zone had 'solved' the solar dynamo problem, but the advent of helioseismology provided measures of solar differential rotation within the convection zone that contradicted the required assumption of an angular velocity increasing inward. This and requirements for storage of magnetic flux while it amplified led to new theories focussed on the solar tachocline, a sharp shear layer seen at the base of the solar convection zone. Most recently, new bulk convection zone dynamo models, the so-called flux transport models, have shown considerable success in reproducing many features of the solar cycle, but such models still contain assumptions concerning processes that are not subject to observational test. A crucial improvement in the these models has been the inclusion of (measured) meridional circulation, which is now seen as determining the solar cycle period. Despite these successes, many uncertainties remain. Little is known about the global dynamics and MHD of the solar tachocline, where toroidal magnetic flux is likely stored while it amplifies enough to generate sunspots. Global convection theory still has not yielded a fully convincing theory of the maintenance of the differential rotation in the convection zone, though all such models rely on organized transport of angular momentum toward the equator to make it spin faster in the face of turbulent diffusion. The history of the solar dynamo problem makes it clear that observational constraints are crucial to developing a plausible, durable theory; presumably the same is also true for the geodynamo.