Overstability and cooling in sunspots

The role played by overstable Alfven modes in magnetic structures such as sunspots is considered in detail for a column of magnetic field. It is demonstrated explicitly that overstable Alfven waves cool the interior of the magnetic column. It is suggested that these waves account for the cooling in sunspot umbrae, and therefore, in concurrence with Parker, we conclude that a sunspot is a region of enhanced heat transport. The calculations indicate that sunspots have small regions at normal photospheric brightness, and we tentatively suggest that these regions are umbral dots. We also suggest that cooling by overstable Alfven waves may explain the existence of the intense small magnetic flux tubes that constitute the general solar magnetic field.