Higgs Field Topology of a Pair of Sunspots and Its Observed Manifestations

Fundamental properties of both the phase and amplitude distributions of the Higgs field characterizing a pair of equally-quantized, Abelian Higgs sunspots are examined. Guided by symmetry principles one shows that in case of equal (opposite) orientation of the spots' magnetic field the lines of a constantphase represent a family of hyperbolae (circles) passing through the centers of sunspots, F₁ and F₂, whereas the curves of a fixedamplitude are in both cases the Cassini curves with the foci F₁ and F₂. Following the hypothesis that both spots' penumbral and spot-connected filaments are stretched out along the lines of constant phase these theoretical findings are shown to mimic remarkably well the data inferred from observations.