CATASTROPHIC EVOLUTION OF A FORCE-FREE FLUX ROPE - A MODEL FOR ERUPTIVE FLARES

We present a self-consistent, two-dimensional, magnetohydrodynamic model of an eruptive flare based on an ideal-MHD coronal magnetic field configuration which is line-tied at the photosphere and contains a force-free flux rope. If the flux rope is not too large, the gradual disappearance of the photospheric field causes the flux rope to lose equilibrium catastrophically and jump to a higher altitude, releasing magnetic energy in the process. During the jump, an extended current sheet forms below the flux rope, and subsequent reconnection of this current sheet allows the flux rope to escape into the outer corona. A critical flux-rope radius, which depends on the form of the photospheric field, divides configurations which undergo a catastrophic loss of equilibrium from those which do not. For a photospheric field equivalent to that produced by a submerged, two-dimensional magnetic quadrupole, the critical radius is 0.23 times the length scale of the photospheric field. This result shows that catastrophic eruptions can occur for flux ropes having plausible solar values. We identify the catastrophic loss of equilibrium with the impulsive phase of eruptive flares and the subsequent reconnection of the current sheet with the gradual phase.