Sunspot models with bright rings

A theoretical sunspot model is provided including magnetic suppression of the diffusivities and also a strong stratification of density and temperature. Heat diffusion alone with given magnetic field and zero mean flow only produces (after a very long relaxation time) dark spots without any bright ring. Models with full dynamics of both field and flow, however, provide rings and also the observed correlation of ring temperature excess and the spot size. The rings are formed as the result of heat transport by the resulting flow system and increased thermal diffusivity due to reduced magnetic quenching around spots.