Global budget for an eruptive active region - I. Equilibrium reconstruction approach

We present results on the magnetic structure of NOAA Active Region #7912 which was involved in a long duration flare on 14 October 1995, and was the source region for a magnetic cloud observed by the WIND spacecraft from October 18-20. Using vector magnetograms from the Imaging Vector Magnetograph ("IVM"), we reconstruct the magnetic field above this active region, assuming it is in a non-linear force-free state. This reconstruction is used to determine global properties of the active region magnetic field including topology, magnetic energy, and relative magnetic helicity. A comparison of some global quantities before and after the eruptive event is discussed. We show that the magnetic energy and relative helicity of the active region decreased after the eruption, consistent with the ejection of a large amount of helicity ( in the magnetic cloud). We also show that the relaxed post-flare state still contains nonlinearities and is not consistent with a linear force-free state as predicted by Taylor's theory of relaxation. These results agree with those of recent numerical simulations concerning plasmoid ejection and helicity redistribution in the disruption of magnetic configurations. We propose as an explanation that the anchoring of field lines in the photosphere prevents a full cascade to the Taylor state, and that a variational formulation in which the action functional would describe this constraint should be derived.