Magnetohydrostatic equilibria, in which the Lorentz force, the plasma pressure force and the gravitational force balance out to zero, are widely adopted as the zeroth order states of many astrophysical plasma structures. A magnetic flux-current surface is a surface, in which both magnetic field lines and current lines lie. We for the first time derive the necessary and sufficient condition for existence of magnetic flux-current surfaces in magnetohydrostatic equilibria. It is also shown that the existence of flux-current surfaces is a necessary (but not sufficient) condition for the ratio of gravity-aligned components of current density and magnetic field to be constant along each field line. However, its necessary and sufficient condition is found to be very restrictive. This finding gives a significant constraint in modeling solar coronal magnetic fields as force-free fields using photospheric magnetic field observations.

Recently, Choe & Cheng (2002) have demonstrated that multiple magnetic flux systems with closed configurations can have more magnetic energy than the corresponding open magnetic fields. In relation to this issue, we have addressed two questions: (1) how much fraction of eruptive solar active regions shows multiple flux system features, and (2) what winding angle could be an eruption threshold. For this investigation, we have taken a sample of 105 front-side halo CMEs, which occurred from 1996 to 2001, and whose source regions were located near the disk center, for which magnetic polarities in SOHO/MDI magnetograms are clearly discernible. Examining their soft X-ray images taken by Yohkoh SXT in pre-eruption stages, we have classified these events into two groups: multiple flux system events and single flux system events. It is found that 74% (78/105) of the sample events show multiple flux system features. Comparing the field configuration of an active region with a numerical model, we have also found that the winding angle of the eruptive flux system is slightly above 1.5π.