An Optimization Principle for Computing Stationary MHD Equilibria With Solar Wind Flow

TL;DR

This paper introduces a numerical optimization method based on a nonlinear force-free principle to compute stationary MHD equilibria, enabling better modeling of the solar corona's magnetic field especially in regions where plasma and flow effects are significant.

Contribution

The paper presents a novel optimization-based code for stationary MHD equilibrium modeling that extends the magnetic field reconstruction further into the corona than previous models.

Findings

The method accurately models the solar corona's magnetic field up to two solar radii.

It captures deviations from force-free conditions where plasma and flow effects are strong.

The approach enhances the understanding of magnetic connectivity for solar observations.

Abstract

In this work we describe a numerical optimization method for computing stationary MHD-equilibria. The newly developed code is based on a nonlinear force-free optimization principle. We apply our code to model the solar corona using synoptic vector magnetograms as boundary condition. Below about two solar radii the plasma $\beta$ and Alfv\'en Mach number $M_A$ are small and the magnetic field configuration of stationary MHD is basically identical to a nonlinear force-free field, whereas higher up in the corona (where $\beta$ and $M_A$ are above unity) plasma and flow effects become important and stationary MHD and force-free configuration deviate significantly. The new method allows the reconstruction of the coronal magnetic field further outwards than with potential field, nonlinear force-free or magneto-static models. This way the model might help to provide the magnetic connectivity for joint observations of remote sensing and in-situ instruments on Solar Orbiter and Parker Solar Probe.