On single-point inversions of magnetic dipole lines in the corona

TL;DR

This paper revisits the problem of inferring the magnetic properties of the solar corona from polarimetric observations of magnetic dipole lines, addressing degeneracies and clarifying the inversion process.

Contribution

It clarifies the nature of degeneracies in magnetic field inversion and proposes resolving them by determining the scattering geometry from observed elongation.

Findings

Degeneracy in magnetic field inversion can be resolved by analyzing scattering geometry.

Clarification of the inversion formalism in the observer's reference frame.

Resolution of conceptual issues raised by previous studies.

Abstract

Prompted by a recent paper by Dima and Schad, we re-consider the problem of inferring magnetic properties of the corona using polarimetric observations of magnetic dipole (M1) lines. Dima and Schad point to a potential source of degeneracy in a formalism developed by Plowman, which under some circumstances can lead to the solution being under-determined. Here we clarify the nature of the problem. Its resolution lies in solving for the scattering geometry using the elongation of the observed region of the corona. We discuss some conceptual problems that arise when casting the problem for inversion in the observer's reference frame, and satisfactorily resolve difficulties identified by Plowman, Dima and Schad.