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

TL;DR

This paper introduces a new family of analytical 3D magnetohydrostatic solutions that enable flexible modeling of the transition from non-force-free to force-free magnetic fields, improving solar magnetic field extrapolation.

Contribution

It presents a novel set of analytical solutions for magnetohydrostatic equilibria that facilitate more accurate magnetic field extrapolation in the solar atmosphere.

Findings

Allows modeling of transition height and width between non-force-free and force-free regions.

Provides a computationally efficient alternative to numerical methods.

Enhances the accuracy of magnetic field extrapolation in solar physics.

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.