A Topological Analysis of the Magnetic Breakout Model for an Eruptive Solar Flare

The magnetic breakout model gives an elegant explanation for the onset of an eruptive solar flare, involving magnetic reconnection at a coronal null point which leads to initially enclosed flux 'breaking out' to large distances. In this paper we take a topological approach to the study of the conditions required for this breakout phenomenon to occur. The evolution of a simple delta sunspot model, up to the point of breakout, is analysed through several sequences of potential and linear force-free quasi-static equilibria. We show that any new class of field lines, such as those connecting to large distances, must be created through a global topological bifurcation, and derive rules to predict the topological reconfiguration due to various types of bifurcation.