Magnetic shear and cross-field currents: Roles in the evolution of the pre-coronal mass ejection corona

A widely used approximation in modeling the solar corona is to assume that the magnetic field is force free, in which case all electric currents flow parallel to the magnetic field. However, observations of the large-scale corona show clearly the presence of nonradial density variations and thus, presumably, nonradial pressure gradients. In equilibrium, such pressure gradients must be balanced by magnetic forces arising from cross-field currents. It is possible that these deviations from force-free conditions play a significant role in the evolution of the corona, particularly in the evolution leading to the large-scale eruptions known as coronal mass ejections (CMEs). In this work we explore the role of cross-field currents in the evolution of a model corona involving a simple magnetic arcade in magnetostatic equilibrium, neglecting the solar wind flow. Our formalism builds on the generating-function approach used in some force-free modeling but transcends the limitation to force-free conditions by introducing a second generating function representing a nonhydrostatic pressure distribution and associated cross-field electric currents. The results show that the presence of cross-field currents makes our model corona more prone to eruptive behavior than a strictly force-free corona. This effect may be relevant to the onset of CMEs, suggesting that the coronal conditions most likely to result in mass ejections are those in which both held-aligned and cross-held currents are present.