Analytical Three-dimensional Magnetohydrostatic Equilibrium Solutions for Magnetic Field Extrapolation Allowing a Transition from Non-force-free to Force-free Magnetic Fields

Abstract

For the extrapolation of magnetic fields into the solar corona from measurements taken in the photosphere (or chromosphere) force-free magnetic fields are typically used. This does not take into account that the lower layers of the solar atmosphere are not force-free. While some numerical extrapolation methods using magnetohydrostatic magnetic fields have been suggested, a complementary and numerically comparatively cheap method is to use analytical magnetohydrostatic equilibria to extrapolate the magnetic field. In this paper, we present a new family of solutions for a special class of analytical three-dimensional magnetohydrostatic equilibria, which can be of use for such magnetic field extrapolation. The new solutions allow for the more flexible modelling of a transition from non-force-free to (linear) force-free magnetic fields. In particular, the height and width of the region where this transition takes place can be specified by choosing appropriate model parameters.