Magnetic stability of coronal arcades relevant to two-ribbon flares

The dense photosphere provides an extremely efficient mechanism, called line-tying, for stabilising solar coronal magnetic fields. In this paper, we study the ideal magnetohydrodynamic (MHD) stability of cylindrically symmetric arcades, the field structure thought to be present prior to the onset of a large two-ribbon flare. It is found that, when the axis of symmetry lies on the photosphere, a wide range of force-free fields are completely stable to all possible perturbations. However, replacing the axial magnetic field by an equivalent gas pressure will produce a localised instability. Instability, the mechanism for the release of energy for a flare, will also occur if the symmetry axis, assumed to coincide with an active-region filament, is too high above the photosphere to benefit from its stabilising influence.