Magnetic instability of coronal arcades as the origin of two-ribbon flares

The generally accepted scenario for the events leading up to a two-ribbon flare is that a magnetic arcade responds to the slow photospheric motions of its footpoints by evolving passively through a series of force-free equilibria. At some critical amount of shear the configuration becomes unstable and erupts outwards. Subsequently, the field closes back down in the manner modelled by Kopp and Pneuman (1976). The present paper analyses the magnetohydrodynamic stability of several possible arcade configurations, including the dominant stabilizing effect of line-tying at the photospheric footpoints. One low-lying force-free structure is found to be stable regardless of the shear; also some of the arcades that lie on the upper branch of the equilibrium curves are shown to be stable. However, another force-free configuration appears more likely to represent the preflare structure. It consists of a large flux tube, anchored at its ends and surrounded by an arcade, so that the field transverse to the arcade axis contains a magnetic island. Such a configuration is found to become unstable when either the length of the structure, the twist of the flux tube, or the height of the island becomes too great.