Making sense of sunspot decay - I. Parabolic decay law and Gnevyshev-Waldmeier relation

In a statistical study of the decay of individual sunspots based on DPR data we find that the mean instantaneous area decay rate is related to the spot radius r(0) and the maximum radius r(0) as D = C(D)r/r(0), C-D = 32.0 +/- 0.26 MSH day(-1). This implies that sunspots on the mean follow a parabolic decay law; the traditional linear decay law is excluded by the data. The validity of the Gnevyshev-Waldmeier relationship between the maximum area A(0) and lifetime T of a spot group, A(0)/T similar or equal to 10 MSH day(-1), is also demonstrated for individual sunspots. No evidence is found for a supposed supergranular 'quantization' of sunspot areas. Our results strongly support the recent turbulent erosion model of sunspot decay while all other models are excluded.