A dynamic model of filament eruptions and two ribbon flares

Two basically different models for the filamentequilibrium by Kippenhahn and Schluter (1957) and Kuperus and Raadu (1974) have appeared in the literature. A further analyses by van Tend and Kuperus (1978) added the force due to the horizontal component of the background field to the Kuperus and Raadu model. In order to obtain a better model which actually describes these phenomena, the evolution of the filamenthas to be considered in detail. A first attempt was recently presented by Kaastra. Kaastra did not formulate the precise energy balanceequations for the problem, as is done in the present work. In the present model not only the force balance, but also the energy balanceof the filamentis taken into account. Thus a fully closed systemof equations is obtained, that describes the evolution of the filament, first in force equilibrium during the current build-up phase, then in the non-equilibrium phase before the eruption, and the eruption itself. A neutral point appears above the photosphericsurface in the non-equilibrium phase, but long before the eruption. It was found that although the filament itselfmay be in non-equilibrium, the evolution may still be slow up to the height where the eruption takes place. The eruption of the filament itselfcauses a large induced electric field at the neutral point which leads to the observed flare phenomena.