THE FREE-ENERGIES OF PARTIALLY OPEN CORONAL MAGNETIC-FIELDS

Analytical solutions are presented to describe the static equilibrium of polytropic atmospheres under the influence of solar gravity and in the presence of a global partially open magnetic field. These axisymmetric solutions serve to model the approximately static, lower region of the solar corona, where the solar wind may be neglected except for its influence as manifest in the partially open magnetic topology. The paper addresses the question of whether the corona can possess sufficient free magnetic energy to account for the work required to open up the closed part of its magnetic field, with a significant residue available for lifting the weight and driving the motion of the plasma during a coronal mass ejection. This question is discussed in relation to a magnetohydrodynamic limit due to Aly (1991) on the amount of energy which can be stored in force-free electric currents. The conclusion is drawn in this paper that electric currents flowing across the magnetic field in static equilibrium is viable in providing sufficient energy to exceed the minimum threshold, in particular, if these currents create a magnetic bubble in the corona. To the extent that the low-density prominence cavity commonly observed to initiate a coronal mass ejection can be identified with the magnetic bubble in the axisymmetric model, the calculations provide a theoretical basis for the popular idea that the source of energy for the mass ejection is magnetic in origin.