Applications of fractal geometry to dynamical evolution of sunspots*

A fractal model for sunspot dynamics is presented. Formation of a sunspot in the solar photosphere is considered from the viewpoint of aggregation of magnetic flux tubes on a fractal geometry. Fine structure of the magnetic flux tubes is analyzed for a broad class of non‐Maxwellian plasma distribution functions. The sunspot fractal dimension is proved to depend on the parameters of the plasma distribution function, enabling one to investigate intrinsic properties of the solar plasma by means of powerful geometrical methods. Magnetic field dissipation in the tubes is shown to result in effective sunspot decay. Sunspot formation and decay times as well as the diffusion constant K deduced by using the fractal model, are in a good agreement with observational data. Disappearance of umbras in decaying sunspots is interpreted as a second‐order phase transition reminiscent of the transition through the Curie point in ferromagnetics.