SUNSPOT MODELING AND SCALING LAWS

In an early paper Skumanich suggested the existence of a scaling law relating the mean sunspot magnetic field with the square-root of the photospheric pressure. This was derived from an analysis of a variety of theoretical spot models including those by Yun (1968). These were based on the Schliiter-Temesvary (S- T) similarity assumption. To answer criticisms that such modeling may have unphysical (non-axial maxima) solutions, the S-T model was revisited, Moon et al. (1998), with an improved vector potential function. We consider here the consequences of this work for the scaling relation. We show that by dimensionalizing the lateral force balance equation for the S- T model one finds that a single parameter enters as a characteristic value of the solution. This parameter yields Skumanich's scaling directly. Using an observed universal flux-radius relation for dark solar magnetic features (spots and pores) for comparison, we find good to fair agreement with Yun's characteristic value, however the Moon et al. values deviate significantly.