Basic topology of twisted magnetic configurations in solar flares

It is accepted now that flare-like phenomena are the result of reconnection of topologically complex magnetic fields. Observations show that such fields are often characterized by a twisted structure. This is modeled here using a force-free flux tube whose arc-like body is embedded into an external potential magnetic field. We study how the topological structure of this configuration evolves when the flux tube emerges quasi-statically from below the photosphere to a certain height in the corona, where the tube becomes unstable and its eruption has to occur. During this evolution below the flux tube there appears a separator field line, along which two separatrix surfaces intersect. This separator is of generalized type because there are no magnetic nulls in the configuration. Both the separator and the separatrices are topological features, where the connectivity of magnetic field lines suffers a jump. We propose that the eruption of the flux tube has to stimulate the formation of strong current layers, in which the free magnetic energy of configuration is released in the form of a flare. The model predicts the formation of hot loops of two kinds during the reconnection phase: the long loops which make nearly one turn around the twisted flux tube, and short sheared loops below. The proposed model provides important clues to the mechanism of solar flares in twisted configurations.