Model for the Coupled Evolution of Subsurface and Coronal Magnetic Fields in Solar Active Regions

According to Babcock's theory of the solar dynamo, bipolar active regions are Omega-shaped loops emerging from a toroidal field located near the base of the convection zone. In this paper, a mean field model for the evolution of a twisted Omega-loop is developed. The model describes the coupled evolution of the magnetic field in the convection zone and the corona after the loop has fully emerged into the solar atmosphere. Such a coupled evolution is required to fully understand what happens to the coronal and subsurface fields as magnetic flux cancels at polarity inversion lines on the photosphere. The jump conditions for the magnetic field at the photosphere are derived from the magnetic stress balance between the convection zone and corona. The model reproduces the observed spreading of active region magnetic flux over the solar surface. At polarity inversion lines, magnetic flux submerges below the photosphere, but the component of magnetic field along the inversion line cannot submerge, because the field in the upper convection zone is nearly radial. Therefore, magnetic shear builds up in the corona above the inversion line, which eventually leads to a loss of equilibrium of the coronal fields and the "lift-off" of a coronal flux rope. Fields that submerge are transported back to the base of the convection zone, leading to the repair of the toroidal flux rope. Following Martens and Zwaan, interactions between bipoles are also considered.