We present our results of a hybrid model of sunspots and their overlying corona. The two-layer model considers both the nonlinear, compressible magnetoconvection beneath the photosphere and potential, or linear force-free, models of the coronal fields. Heating of the plasma along the field lines is then treated using quasi-static and steady-state models with the heating rate being specified by the dynamics of the magnetoconvection.
Two distinct magnetoconvection scenarios are considered. The first describes magnetoconvection in a 2D axisymmetric geometry and considers the time development of the overlying coronal field. The second describes a 3D cylindrical geometry with a static coronal field configuration. Both scenarios diverge from the standard practice of assuming constant temperature and vertical magnetic field conditions at the top surface. Instead, a radiative linear force-free field condition is adopted.
Extrapolation of the top surface boundary conditions results in a coronal field configuration which is assumed to be filled with plasma heated to coronal temperatures. The heating rate and thermodynamic behaviour of the plasma is related to the subsurface model by assuming that individual fluxtubes are heated uniformly with the necessary energy being generated from the dissipation of the Poynting flux entering the coronal volume. Radiation and conductive losses are included.
The combination of a sunspot model, whereby the surface field is completely specified, with a coronal heating model, in which the plasma parameters are specified for a given energy input, allows us to explore a broad class of heating paradigms.