MHD simulations of penumbra fine structure

We present results of numerical 3D MHD simulations with radiative energy transfer of fine structure in a small sunspot of about 4 Mm width. The simulations show the development of filamentary structures and flow patterns that are, except for the lengths of the filaments, very similar to those observed. The filamentary structures consist of gaps with reduced field strength relative to their surroundings. Calculated synthetic images show dark cores like those seen in the observations; the dark cores are the result of a locally elevated $\tau=1$ surface. The magnetic field in these cores is weaker and more horizontal than for adjacent brighter structures, and the core support a systematic outflow. Movies show migration of the dark-cored structures towards the umbra, and fragments of magnetic flux that are carried away from the spot by a large scale `moat flow'. We conclude that the simulations are in qualitative agreement with observed penumbra filamentary structures, Evershed flows and moving magnetic features.