Making sense of sunspot decay - II. Deviations from the mean law and plageeffects

In a statistical analysis of Debrecen Photoheliographic Results sunspot are a data we find that the logarithmic deviation (log D)' of the area decay ra te D from the parabolic mean decay law (derived in the first paper in this series) follows a Gaussian probability distribution. As a consequence, the actual decay rate D and the time-averaged decay rate (D) over bar are also characterized by approximately lognormal distributions, as found in an earl ier work. The correlation time of (log D)' is about 3 days. We find a signi ficant physical anticorrelation between (log D)' and the amount of plage ma gnetic flux of the same polarity in an annulus around the spot on Kitt Peak magnetograms. The anticorrelation is interpreted in terms of a generalizat ion of the turbulent erosion model of sunspot decay to the case when the fl ux tube is embedded in a preexisting homogeneous 'plage' field. The decay r ate is found to depend inversely on the value of this plage field, the rela tion being very close to logarithmic, i.e., the plage field acts as multipl icative noise in the decay process. A Gaussian probability distribution of the field strength in the surrounding plage will then naturally lead to a l ognormal distribution of the decay rates, as observed. It is thus suggested that, beside other multiplicative noise sources, the environmental effect of surrounding plage fields is a major factor in the origin of lognormally distributed large random deviations from the mean law in the sunspot decay rates.