A Framework for Understanding the Topology of Complex Coronal Structures

The Sun's coronal magnetic field is highly complex and provides the driving force for many dynamical processes. The topology of this complex field is made up mainly of discrete topological building blocks produced by small numbers of magnetic fragments. In this work we develop a method for predicting the possible topologies due to a potential field produced by three photospheric sources, and describe how this model accurately predicts the results of Brown and Priest (1999). We then sketch how this idea may be extended to more general non-symmetric configurations. It is found that, for the case of positive total flux, a local separator bifurcation may take place with three positive sources or with one positive and two negative sources, but not for two positive sources and one negative.