The cooling time scales of growing sunspots

The evolution of brightness and magnetic fields of growing sunspots is studied. Growing sunspots are found to be brighter (or less dark) than stable sunspots with the same magnetic field strength. From comparison of brightness and magnetic fields of a growing sunspot with those of stable sunspots, a dynamical parameter, the cooling time, of the growing sunspot is obtained. Ten growing sunspots are studied, and cooling times of 0.5 to 9 hr are found. Two models, the inhibition model and the Alfven wave model, give cooling times of about 0.05 hr, based on linear theory. The discrepancy between theory and observation may be due to the fact that the observed sunspots are in the nonlinear regime.