Geometrical properties of Sine-Gordon Abelian Higgs sunspots

We discuss a slightly modified Abelian Higgs model of sunspots in which the potential term V(Φ) has a ‘Sine-Gordon’-like form, . The model accounts not only for the observed diversity of the absolute dimensions of sunspots, but is also compatible with a more-or-less constant value of their penumbra-to-umbra radius ratios provided the parameter κ is close to unity.