Evolving force-free magnetic fields. I - The development of the preflare stage

Abstract

Two boundary value problems are solved analytically to obtain nonlinear force-free magnetic fields overlying given time-dependent distributions of bipolar photospheric magnetic fields. We follow the evolution in time of these two magnetic fields to show the development of conditions likely to lead to solar flares. For the first magnetic field, the photosphere moves as two almost rigid plates sliding past each other along the magnetic neutral line. For the second magnetic field, the photospheric velocity at large distances from the magnetic neutral line has a growing uniform shear. The preflare stage for each magnetic field is described. In particular, the model demonstrates that the presence of large horizontal photospheric velocity shear across the magnetic neutral line prior to a flare eruption is closely associated with either a parallel or a perpendicular horizontal magnetic field along the magnetic neutral line.