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 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. Subject headings: MHD — Sun: corona — Sun: magnetic fields — Sun: flares