Magnetic Field Confinement in the Corona: The Role of Magnetic Helicity Accumulation

A loss of magnetic field confinement is believed to be the cause of coronal mass ejections (CMEs), a major form of solar activity in the corona. The mechanisms for magnetic energy storage are crucial in understanding how a field may possess enough free energy to overcome the Aly limit and open up. Previously, we have pointed out that the accumulation of magnetic helicity in the corona plays a significant role in storing magnetic energy. In this paper, we investigate another hydromagnetic consequence of magnetic-helicity accumulation. We propose a conjecture that there is an upper bound on the total magnetic helicity that a force-free field can contain. This is directly related to the hydromagnetic property that force-free fields in unbounded space have to be self-confining. Although a mathematical proof of this conjecture for any field configuration is formidable, its plausibility can be demonstrated with the properties of several families of power-law, axisymmetric force-free fields. We put forth mathematical evidence, as well as numerical, indicating that an upper bound on the magnetic helicity may exist for such fields. Thus, the accumulation of magnetic helicity in excess of this upper bound would initiate a non-equilibrium situation, resulting in a CME expulsion as a natural product of coronal evolution. Subject headings: MHD — Sun: magnetic fields — Sun: corona — Sun: coronal mass ejections (CMEs) National Astronomical Observatory, Chinese Academy of Sciences, Datun Road A20, Chaoyang District, Beijing 100012, China High Altitude Observatory, National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307, USA Scientific Computing Division, National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307, USA