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 and the maximal radius r0 as D=C r/r0, C=32.0 +- 0.26 MSH/day. 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 maximal area A0 and lifetime T of a spot group, A0/T = 10 MSH/day, 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.