Magnetic Buoyancy, Vorticity, and Three-dimensional Flux-Tube Formation

Sunspots and other intense flux elements making up active regions are formed from loops of magnetic field that erupt through the Sun's surface; the field is believed to originate in the stable overshoot region below the convection zone. It is likely that these structures arise through magnetic buoyancy. We have conducted the first numerical simulations of the three-dimensional evolution of an unstable horizontal layer of magnetic field. The initial development is almost two-dimensional, with little variation along the field lines, but then the field becomes markedly three-dimensional, forming arched structures. A separate calculation with an isolated rising flux tube shows no such arching; the three-dimensional behavior of the layer is in fact due to a nonlinear interaction between adjacent but oppositely directed vortex tubes induced by the rising field. These vorticity-driven modes, absent from earlier flux-tube models, seem likely to be of importance in the process of sunspot formation.