Convective flows around sunspot-like objects

Results are given for calculations of convective flows around objects in the outer layers of the Sun that have similar characteristics to small sunspots. These objects are allowed to radiatively (diffusively) exchange heat with their surroundings, but convective motions and exchange are absent. This assumption is based on the simple presumption that a sunspot magnetic field maintains pressure equilibrium with the surrounding medium and prevents convective exchange with that medium.The flow structure around the object, and the question of the overall balance or redistribution of the emerging heat flux as suggested by earlier empirical models, are studied and discussed.After a period of adjustment, shortly after the sunspot-like object is placed into the domain, the layer readjusts itself so that most of the heat flux actually reappears at the surface, although some fraction of the flux is carried horizontally far from the object. There is no indication of long term storage of the heat flux that would normally appear in the place where the object resides. Finally, when the object is removed, the surrounding medium responds very quickly and soon returns to the undisturbed state before the object was in place.The present numerical treatment includes restrictions that may influence aspects of the heat redistribution, convective flows and time scales. In particular, the shape of the object and its size (somewhat smaller than a sunspot) are important, as is the number of spatial dimensions and the treatment of some boundary conditions. Since all of these issues require further investigation, some discussion is presented regarding the applicability of our results to real sunspots.