Sunspot dynamics and coronal heating

Simultaneous observations of sunspots in the photosphere and in the coronal regions above them reveal a close coupling between the dynamics of the photospheric motion and structure and the heating of coronal loops. We investigate this relationship through detailed three-dimensional simulations of dynamic, small-scale structures in sunspot penumbra and umbra in conjunction with models of coronal excitation and emission. The numerical models incorporate a fully three-dimensional magnetoconvection calculation, potential field extrapolations from the sunspot model boundary conditions, steady-state and dynamic coronal loops powered by the convective motions at the surface, EUV and X-ray instrument response functions, and a fieldline rendering. The result is a simulated dynamical active region in three dimensions which can be compared directly with observations and enables us to explore coronal heating and its relationship to the dynamics of the photosphere and convection zone. We present results of recent calculations exploring the dynamics and structure of penumbrae and their possible influence on the overlying corona.