Magnetic topologies in the solar corona due to four discrete photospheric flux regions

Many dynamic phenomena in the solar corona are driven by the complex and ever-changing magnetic field. It is helpful, in trying to model these phenomena, to understand the structure of the magnetic field, i.e. the magnetic topology. We study here the topological structure of the coronal magnetic field arising from four discrete photospheric flux patches, for which we find that seven distinct, topologically stable states are possible; the changes between these are caused by six types of bifurcation. Two bifurcation diagrams are produced, showing how the changes occur as the relative positions and strengths of the flux patches are varied. A method for extending the analysis to higher numbers of sources is discussed.