Flux linkages of bipolar sunspot groups: A computer study

Past studies of the structure of solar magnetic fields have used magnetograph data to compute selected field lines for comparison with the morphology of structures seen in various spectral wavelengths. While those analyses examine one of the integral properties of magnetic fields (field lines), they are not complete since they fail to determine the other important integral property: the boundaries of the flux of field lines of given connectivity. In the present analysis we determine such a system of boundaries, called separatrices, for the current free field of two p-f spot pairs so as to exhibit the line of self-intersection, called the separator. The analysis is compared with previous analytical work. These computer results, confirming earlier studies carried out using iron fillings, show that the separatrix has the form of two intersecting ovoids, defining four flux cells. New features which have emerged from this study include the observation that the projections of the separatrix in a plane perpendicular to the separator at its highest point do not intersect at 90° as has been widely believed, but rather closer to 60° in the case studied. The separator is very nearly circular over most of its length. The two neutral points (B = 0) which appear at the photospheric ends of the separator have the mixed radial-hyperbolic form as expected, a feature requiring every field line lying on the separatrix to connect with at least one of the two neutral points. The rotation of line direction with height (shear) is graphically illustrated in the potential field case studied here. We also exhibit a magnetic arcade.