Topological structure of the magnetic solar corona

Abstract

The solar corona is a highly complex and active plasma environment, containing many exotic phenomena such as solar flares, coronal mass ejections, prominences, coronal loops, and bright points. The fundamental element giving coherence to all this apparent diversity is the strong coronal magnetic field, the dominant force shaping the plasma there. In this thesis, I model the 3D magnetic fields of various coronal features using the techniques of magnetic charge topology (MCT) in a potential field. Often the real coronal field has departures from its potential state, but these are so small that the potential field method is accurate enough to pick out the essential information about the structure and evolution of the magnetic field. First I perform a topological analysis of the magnetic breakout model for an eruptive solar flare. Breakout is represented by a topological bifurcation that allows initially enclosed flux from the newly emerging region in my MCT model of a delta sunspot to reconnect out to large distances. I produce bifurcation diagrams showing how this behaviour can be caused by changing the strength or position of the emerging flux source, or the force-free parameter α. I also apply MCT techniques to observational data of a coronal bright point, and compare the results to 3D numerical MHD simulations of the effects of rotating the sources that underlie the bright point. The separatrix surfaces that surround each rotating source are found to correspond to locations of high parallel electric field in the simulations, which is a signature of magnetic reconnection. The large-scale topological structure of the magnetic field is robust to changes in the method of deriving point magnetic sources from the magnetogram. Next, I use a Green’s function expression for the magnetic field to relax the standard topological assumption of a flat photosphere and extend the concept of MCT into a spherical geometry, enabling it to be applied to the entire global coronal magnetic field. I perform a comprehensive study of quadrupolar topologies in this new geometry, producing several detailed bifurcation diagrams. These results are compared to the equivalent study for a flat photosphere. A new topological state is found on the sphere which has no flat photosphere analogue; it is named the dual intersecting state because of its twin separators joining a pair of magnetic null points. The new spherical techniques are then applied to develop a simple six-source topological model of global magnetic field reversal during the solar cycle. The evolution of the large-scale global magnetic field is modelled through one complete eleven-year cycle, beginning at solar minimum. Several distinct topological stages are exhibited: active region flux connecting across the equator to produce transequatorial loops; the dominance of first the leading and then the following polarities of the active regions; the magnetic isolation of the poles; the reversal of the polar field; the new polar field connecting back to the active regions; the polar flux regaining its dominance; and the disappearance of the transequatorial loops.