Convection in sunspots and the origin of umbral dots

Recent studies of non-linear magnetoconvection are used to show that the observed properties of umbral dots can be explained if they are produced by oscillatory convection in the umbrae of sunspots. The overall magnetic field is assumed to be coherent within the flux tube underneath the sunspot. Individual convection cells are about 1500 km deep and 300 km in diameter. The oscillations are highly non-linear, with periods of around 6 hr, but the relatively vigorous upward motion that is responsible for umbral dots lasts for only a fraction of this lifetime. This model is compared with various alternative hypotheses. (author)