C. Beveridge

A quantitative, topological model of reconnection and flux rope formation in a two-ribbon flare

We present a topological model for energy storage and subsequent release in a sheared arcade of either infinite or finite extent. This provides a quantitative picture of a twisted flux rope produced through reconnection in a two-ribbon flare. It quantifies relationships between the initial shear, the amount of flux reconnected, and the total axial flux in the twisted rope. The model predicts reconnection occurring in a sequence that progresses upward even if the reconnection sites themselves do not move. While some of the field lines created through reconnection are shorter, and less sheared across the polarity inversion line, reconnection also produces a significant number of field lines with shear even greater than that imposed by the photospheric motion. The most highly sheared of these is the overlying flux rope. Since it is produced by a sequence of reconnections, the flux rope has twist far in excess of that introduced into the arcade through shear motions. The energy storage agrees well with previous calculations using the full equations of magnetohydrodynamics, and the agreement improves as the topology is defined using increasingly finer detail. This is the first comparative study of the application of a topological model to a continuous flux distribution. As such, it demonstrates how the coarseness with which the photospheric flux distribution is partitioned affects the accuracy of prediction in topological models.

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.

EFFECTS OF PARTITIONING AND EXTRAPOLATION ON THE CONNECTIVITY OF POTENTIAL MAGNETIC FIELDS

Coronal magnetic field may be characterized by how its field lines interconnect regions of opposing photospheric flux—its connectivity. Connectivity can be quantified as the net flux connecting pairs of opposing regions, once such regions are identified. One existing algorithm will partition a typical active region into a number of unipolar regions ranging from a few dozen to a few hundred, depending on algorithmic parameters. This work explores how the properties of the partitions depend on some algorithmic parameters, and how connectivity depends on the coarseness of partitioning for one particular active region magnetogram. We find the number of connections among them scales with the number of regions even as the number of possible connections scales with its square. There are several methods of generating a coronal field, even a potential field. The field may be computed inside conducting boundaries or over an infinite half-space. For computation of connectivity, the unipolar regions may be replaced by point sources or the exact magnetogram may be used as a lower boundary condition. Our investigation shows that the connectivities from these various fields differ only slightly—no more than 15%. The greatest difference is between fields within conducting walls and those in the half-space. Their connectivities grow more different as finer partitioning creates more source regions. This also gives a quantitative means of establishing how far away conducting boundaries must be placed in order not to significantly affect the extrapolation. For identical outer boundaries, the use of point sources instead of the exact magnetogram makes a smaller difference in connectivity: typically 6% independent of the number of source regions.

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 the 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.

A hierarchical application of the minimum current corona

We study the energy and helicity injected into the corona by the slow motion of photospheric source regions. A previous study compared these quantities in a simple quadrupolar configuration modeled by a quasi-static, line-tied MHD simulation and a minimum current corona (MCC). The MCC provides a lower bound for the coronal magnetic free energy by quantifying the coronal linkages (flux domains) between discrete photospheric source regions; the chosen configuration contains four flux domains and one separator. The MCC analysis can be extended by decomposing each source region into smaller ones, increasing the number of flux domains and separators. This creates a hierarchy of topological features that asymptotically approaches a line-tied model. We demonstrate the hierarchical approach using two octopolar decompositions of the previously studied quadrupole. One of these has helicity and free energy significantly closer to those of the line-tied experiment; this is primarily due to the interweaving of lower level flux domains approximating the self-helicity of a rotating region. The other decomposition does not allow such interweaving and has helicity and free energy comparable to the quadrupolar MCC configuration.