On Three-Dimensional Magnetic Skeleton Elements Due to Discrete Flux Sources

Abstract

The magnetic field in the solar corona plays an important role in coronal heating, flaring activity and many other phenomena studied on the Sun. Magnetic topology is frequently used to understand complicated coronal magnetic fields. By calculating the skeleton of a field, it is possible to build up a sophisticated representation of the key elements of a field's configuration. This paper determines a simple relation between the numbers of separators (X), coronal null points (N_c), flux domains (D) and flux sources (S) in such a configuration: D=X+S−N_c−1. This equation is used to explain the behaviour of some of the bifurcations found in Magnetic Charge Topology, and to show that a one-to-one relationship exists between the number of circuits in the domain graph and the augmented null graph. Finally, it is shown that in quiet-Sun regions, the number of separators is approximately proportional to the number of flux sources.