Energy of Force-Free Magnetic Fields in Relation to Coronal Mass Ejections

In typical observations of coronal mass ejections (CMEs), a magnetic structure of a helmet-shaped closed configuration bulges out and eventually opens up. In order for this transition of field configuration to occur spontaneously, the pre-eruption closed magnetic field must have more energy than the post-eruption open field. In force-free fields, however, such a possibility is denied by the Aly-Sturrock theorem. The theorem states that the maximum energy state of force-free fields with a given boundary normal field distribution is the open field. Here we note that the theorem implicitly assumes the existence of the maximum energy configuration. However, this may not be taken for granted because the limiting configuration of energy-increasing sequences of force-free fields does not necessarily have an energy equal to the energy supremum. In this study, we have constructed force-free fields containing tangential discontinuities in multiple flux systems. These force-free fields can be generated from a potential field by footpoint motions that do not conserve the boundary normal field distribution. Some of these force-free fields are found to have more magnetic energy than the corresponding open fields. The constructed force-free configurations are compared with observational features of CME-bearing active regions. Possible mechanisms of CMEs are also discussed.