Observations of the large two-ribbon flare on 7 November 2004 made using SOHO and TRACE data are interpreted in terms of a three-dimensional magnetic field model. Photospheric flux evolution indicates that −1.4 × 10 43 Mx 2 of magnetic helicity was injected into the active region during the 40-hour buildup prior to the flare. The magnetic model places a lower bound of 8 × 10 31 ergs on the energy stored by this motion. It predicts that 5 × 10 21 Mx of flux would need to be reconnected during the flare to release the stored energy. This total reconnection compares favorably with the flux swept up by the flare ribbons, which we measure using high-time-cadence TRACE images in 1 600 Å. Reconnection in the model must occur in a specific sequence that would produce a twisted flux rope containing significantly less flux and helicity (10 21 Mx and −3 × 10 42 Mx 2 , respectively) than the active region as a whole. The predicted flux compares favorably with values inferred from the magnetic cloud observed by Wind. This combined analysis yields the first quantitative picture of the flux processed through a two-ribbon flare and coronal mass ejection.
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 toroidal flux in the twisted rope. The model predicts reconnection occurring in a sequence which 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.
2005). 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.
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