[Previous] | [Session 20] | [Next]
M.A. Weber, P.A. Sturrock (Center for Space Science and Astrophysics, Stanford University)
Aly conjectured that the energy of a closed magnetic-field configuration above the photosphere cannot exceed the energy of the corresponding open-field configuration with the same normal field distribution at the photosphere. This limitation, later proved by Aly for a planar geometry and by Sturrock for a curved geometry, has important consequences for modeling coronal dynamics, especially solar eruptions such as flares and CMEs, that involve the release of magnetic energy.
The above analyses were based on the assumption that all field lines are connected to the photosphere. However, one can conceive of a pre-eruption configuration involving magnetic flux that does not thread the photosphere. A toroidal current-carrying wire embedded in a dipolar arcade can have arbitrarily large magnetic energy relative to the potential configuration as its radius goes to zero, but this would be an unphysical model for the solar corona. We inquire into whether there exist force-free field solutions with ``disconnected'' flux and energy greater than the open-field energy.
We examine a magnetic-field model comprising a toroidal, force-free flux tube in the equatorial plane, restrained by an overlying arcade with dipole boundary conditions, analyzing the configuration by the generating-function (Grad-Shafranov) method. We solve the equations numerically by an iterative procedure, relaxing the flux-tube and the dipole field separately, alternately allowing their interface to adjust. We confirm that it is indeed possible for the energy of such a closed magnetic-field configuration to exceed the Aly-Sturrock limit. However, it requires such a large amount of twist that the flux-tube would be unstable in a full 3-D MHD treatment.
We gratefully acknowledge that this research was supported by NASA grants NAS 8-37334 and NAG 5-9784.
The author(s) of this abstract have provided an email address for comments about the abstract: mweber@stanford.edu
[Previous] | [Session 20] | [Next]
Bulletin of the American Astronomical Society, 34
© 2002. The American Astronomical Soceity.