How skeletons turn into quasi-separatrix layers in source models

Context. In situations where there are no magnetic null points located above a reference photospheric plane, and when the photospheric magnetic field is modeled by discrete flux concentrations, the magnetic connectivity is defined by the magnetic skeleton of the configuration. For a continuous distribution of non-zero photospheric flux, the connectivity is defined by quasi-separatrix layers (QSLs). Both the magnetic skeleton and QSLs can account for current sheet formation and dissipation. Observationally, though, only some portions of the skeleton are found to be related to flare ribbons, which are generally associated with QSL footpoints. Aims. In potential magnetic source models, a transition from the skeleton to QSLs has been shown to occur when the sources are displaced below the photospheric plane. The objective of this paper is to understand the topological and geometrical nature of this transition, and to derive rules to predict which parts of a given skeleton will give rise to QSLs. Methods. We consider magnetic configurations, derived from potential magnetic sources, which possess no coronal null points. We have calculated their skeletons, composed of null points, spine field lines and separatrix (fan) surfaces. Choosing a reference photospheric plane above the sources, we have calculated their QSL footprints. Results. As already known, the latter mostly match with subphotospheric spine field lines since, above these lines, field lines tend to diverge as a result of approaching a null and lying either side of the separatrix surface extending out of from this null. However, many non-spine related QSL footprints are also found, which we call branches. They correspond to the intersection with the photosphere of portions of fan field lines which "branch" away from the sources and result in QSLs due to the inclination of the coronal field lines. Conclusions. Our findings allow a better geometrical understanding of the relations between QSLs and skeletons. We show that in the absence of coronal null points, spines, as well as specific portions of fans as calculated in standard potential source models, are good predictors for the location of QSL footprints and of flare ribbons.