‘Quantized’ dimensions of sunspots and penumbra phenomenon

Abstract

Imposing the constraint that a penumbral filament of the Abelian Higgs sunspots is formed only in the case if an ‘angular’ gradient of the corresponding Higgs field distribution, ∇ _H , exceeds a certain value, ∇ _C , it is shown that the outer penumbral radius of ap-fold quantized sunspot must attain afixed value - ap-multiple of theelementary radiusR ₀. It is rather intriguing to observe that takingR ₀ ≈ 250 km one finds that the observed grouping of the dimensions of sunspots around values 20, 27, 36, 45, and 56 × 10³ km corresponds in our theory top =n(n + 1) withn = 6, 7, 8, 9, and 10, respectively. Finally, one argues that ∇ _C may be of such value that it is everywhere greater than ∇ _H for spots carryingp <p _t flux quanta, which would immediately explain why one does not observe penumbrae in case of pores.