A Simple Dynamical Model for Filament Formation in the Solar Corona

Abstract

Filament formation in the solar atmosphere is considered. In the limit of sub-Alfvénic but supersonic motion, plasma flow in the solar corona is driven via the induction equation by a slow evolution of force-free magnetic fields. Methods for solving the relevant magnetohydrodynamic equations are presented and applied to filament modeling in two and three dimensions. An illustrative two-dimensional example is given, which is based on a potential magnetic field with a dip. The example describes the formation of a normal filament between two bipolar regions on the Sun. Next a detailed three-dimensional calculation is presented, which uses linear force-free magnetic fields. The boundary conditions are chosen to resemble the qualitative ''head-to-tail'' linkage model for the formation of filaments, suggested by Martens & Zwaan. Consistent with this model, dense formations, reminiscent of filament pillars, are shown to appear in the corona above the region of converging and canceling magnetic bi-poles. The numerical results are consistent with the principal role of magnetic field in the dynamical processes of dense plasma accumulation and support in filaments, advocated by Martens & Zwaan.