Cooling of a sunspot

Abstract

The question of whether a perturbed photospheric area can grow into a region of reduced temperature resembling a sunspot is investigated by considering whether instabilities exist that can lead to a growing temperature change and corresponding magnetic-field concentration in some region of the photosphere. After showing that Alfven cooling can lead to these instabilities, the effect of a heat sink on the temperature development of a perturbed portion of the photosphere is studied. A simple form of Alfven-wave cooling is postulated, and computations are performed to determine whether growing modes exist for physically relevant boundary conditions. The results indicate that simple inhibition of convection does not give growing modes, but Alfven-wave production can result in cooling that leads to growing field concentration. It is concluded that since growing instabilities can occur with strong enough cooling, it is quite possible that energy loss through Alfven waves gives rise to a self-generating temperature change and sunspot formation.