NONLINEAR EVOLUTION OF THE CORONAL MAGNETIC-FIELD UNDER RECONNECTIVE RELAXATION

Recently, Vekstein et al. (Vekstein, Priest, & Steele 1993) have devel oped a model for coronal heating in which the corona responds to photo spheric footpoint motions by small-scale reconnection events that brin g about a relaxed state while conserving magnetic helicity but not fie ld-line connectivity. Vekstein et al. consider a partially open field configuration in which magnetic helicity is ejected to infinity on ope n field lines but retained in the closed-field region. Under this sche me, they describe the evolution of an initially potential field, in re sponse to helicity injection, in the linear regime. The present work u ses numerical calculations to extend the model of Vekstein et al. into the fully nonlinear regime. The results show a rise and bulging of th e field lines of the closed-field region with increasing magnetic heli city, to a point where further solutions are impossible. We interpret these solution-sequence end-points as indicating a possible loss of eq uilibrium, in the sense that a relaxed equilibrium state may no longer be available to the corona when sufficient helicity has been injected . The rise and bulging behavior is reminiscent of what is observed in a helmet streamer just before the start of a coronal mass ejection (CM E), and so our model suggests that a catastrophic loss of magnetic equ ilibrium might be the initiation mechanism for CMEs. We also find that some choices of boundary conditions can result in qualitative changes in the magnetic topology, with the appearance of magnetic islands. Wh ether or not this behavior occurs depends on the relative strengths of the fields in the closed- and open-field regions; in particular, isla nd formation is most likely when the open field (which is potential) i s strong and thus acts to confine the force-free closed field. Finally , we show that the energy released through reconnective relaxation can be a substantial fraction of the magnetic energy injected into the co rona through footpoint motions and may be sufficient for heating the c orona above active regions.