Theoretical modelling of the fine structures in sunspots

Until a decade ago most solar physicists thought of a sunspot as the upper end of a giant flux tube floating vertically. The existence of umbral dots and penumbral grains has been known for several decades. On the basis of available observations, they seem to be regions of photospheric intensity with upflowing gas motion and magnetic fields much weaker than in the surrounding sunspot surface. It has also been suggested that the differences in the appearances of umbral dots and granular cells are caused by the highly nonlinear nature of the convection problem in the presense of strong magnetic fields. The main ideas are presented here without any equations. It can be shown that a pocket of field free gas surrounded by a vertical magnetic field in the presence of gravity takes up the shape of a tapering column ending at a vertex at the top. Some convection is expected to take place in the trapped field free gas, whereas the magnetic field around it makes those regions stable against convection. Eventually the apex of the tapering column reaches the photospheric surface where the bulging of the magnetic field makes the field no longer able to close on the field free gas and trap it underneath