Reconstructing the Coronal Magnetic Field: The Role of Cross-Field Currents in Solution Uniqueness

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Friday, October 23, 2020

We present a new 3D magnetohydrostatic (MHS) direct elliptic solver for extrapolating the coronal magnetic field from photospheric boundary conditions in a manner consistent with an assumed plasma distribution. We use it to study the uniqueness of the reconstructed magnetic field as a function of how significant the plasma forcing is on the force balance of the magnetic field. To this end, we consider an analytic MHS model as ground truth. The model uses two free parameters to decompose the current into two parts: a magnetic-field aligned component and a cross-field component. We perform a comprehensive study of the 2D parameter space to understand under what conditions the ground truth can be reproduced uniquely. From this we conclude that a significant cross-field current and associated plasma distribution results in a nearly one-to-one relationship between the photospheric boundary and the atmospheric magnetic field in force balance with that plasma distribution, enabling the solver to converge to a unique solution.

Graphic image of analytic model magnetic field lines
Comparison of analytic model magnetic field lines to results of numerical reconstruction. Despite containing more currents, the reconstruction shown on the bottom row is closer to ground truth than the top. The implication is that cross-field currents (characterized by parameter a) enable the solver to converge to a unique solution.

The publisher version:

Publication: Astrophysical Journal
First HAO Author: Sarah Gibson