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

We present a self-consistent, two-dimensional, magnetohydrodynamic mod el of an eruptive flare based on an ideal-MHD coronal magnetic field c onfiguration which is line-tied at the photosphere and contains a forc e-free flux rope. If the flux rope is not too large, the gradual disap pearance of the photospheric field causes the flux rope to lose equili brium catastrophically and jump to a higher altitude, releasing magnet ic energy in the process. During the jump, an extended current sheet f orms 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 equilibr ium from those which do not. For a photospheric field equivalent to th at produced by a submerged, two-dimensional magnetic quadrupole, the c ritical radius is 0.23 times the length scale of the photospheric fiel d. This result shows that catastrophic eruptions can occur for flux ro pes having plausible solar values. We identify the catastrophic loss o f equilibrium with the impulsive phase of eruptive flares and the subs equent reconnection of the current sheet with the gradual phase.