Domain structures in complex 3D magnetic fields

The numerous magnetic fragments that populate the mixed-polarity, quiet-Sun photosphere give rise to many interesting topological features in the corona. In light of this, much recent work has gone into classifying the configurations that arise from simple, point-source potential-field models in efforts to determine the nature of the quiet-Sun magnetic field. These studies have ranged from systematic and detailed examinations of magnetic fields arising from only a handful of sources, involving classifying the configurations that arise (and how some states may bifurcate into other states), to statistical studies of the overall properties of fields arising from hundreds of magnetic sources. Such studies have greatly increased our understanding of what we might expect the magnetic field over the quiet Sun to behave like; the purpose of the study presented here is to extend this understanding further by examining the structure of the individual domains (the regions in space through which pairs of opposite-polarity sources are connected). In particular, the features of lesser-known domain structures that are absent from fields arising from only a few sources and overlooked by sweeping statistical studies are documented. In spite of the incredible complexity of the coronal field, previous studies have shown that there are only two types of building block in a potential field arising from coplanar point sources: namely, an isolated dome , bounded by a single unbroken separatrix surface, and a separator-ring domain , engirdled by a ring of separators. However, it is demonstrated here how both isolated domains and separator-ring domains may be categorised further depending upon their particular geometrical and topological traits. As many models predict coronal heating at topologically distinct features in magnetic fields such as null points, separators and separatrices, for any such models to be applied to general fields would require a scheme for identifying which topological features are related to a given domain. The study here explores some of the issues that would need to be taken into account by such a scheme, and in particular the problems associated with trying to deduce the properties of a general magnetic field from knowledge of domain footprints alone. Animated 3D-rotational views of some of the figures in this manuscript may be viewed in AVI, MPEG and animated-GIF formats by visiting http://www-solar.mcs.st-and.ac.uk/robertc/animations/blocks.html and following the desired link.