Cross-field currents: An energy source for coronal mass ejections?

Eruptive solar events like flares and coronal mass ejections are thought to involve the release of energy stored in magnetic fields. In a mass ejection, the coronal magnetic field opens to interplanetary space and some 10(16) g of material are propelled outward along the open field lines at a speed of typically 350 km s(-1). A considerable body of research shows that the energy in force-free magnetic fields, in which electric currents how parallel to the field, may be sufficient to open the coronal magnetic field but not additionally to accelerate the ejected material nor to lift it against solar gravity. Thus a purely magnetic explanation for coronal mass ejections must involve cross-field currents-that is, currents with components perpendicular to the magnetic field direction. This paper explores the energetics of a family of simple solutions for an axisymmetric corona in magnetostatic equilibrium including cross-field currents. We extend previous treatments to show that it is possible to build up magnetic energy in excess of that in the presumed fully open state that follows a mass ejection, even if the latter still contains horizontal pressure gradients. We show further that energies in excess of the energy of a fully open state without horizontal pressure gradients are attainable over a wider range of parameters than previously reported. However, our results are tempered by our demonstration that excess mass associated with pressure gradients that balance the magnetic forces of cross-field currents always results in negative total energy. This is because the excess mass is great enough that its negative gravitational energy exceeds in magnitude the sum of the magnetic and thermal energies that also arise from the presence of excess mass. We suggest that nonlinear solutions, involving more realistic density distributions that model the helmet structure and cavity of coronal streamers, may overcome this problem of negative excess energy.