A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. II. Numeric Code and Tests

TL;DR

This paper presents a fast numerical code for fitting nonlinear force-free magnetic field models to coronal loop data, achieving high accuracy and efficiency, and validated through multiple tests including simulated and real models.

Contribution

The authors develop a rapid, reliable numerical code for forward-fitting analytical nonlinear force-free magnetic fields to coronal data, enhancing existing NLFFF modeling techniques.

Findings

Achieved typical misalignment angles of 1-10 degrees.

Computation times range from seconds to minutes.

High fidelity in retrieving force-free alpha parameters.

Abstract

Based on a second-order approximation of nonlinear force-free magnetic field solutions in terms of uniformly twisted field lines derived in Paper I, we develop here a numeric code that is capable to forward-fit such analytical solutions to arbitrary magnetogram (or vector magnetograph) data combined with (stereoscopically triangulated) coronal loop 3D coordinates. We test the code here by forward-fitting to six potential field and six nonpotential field cases simulated with our analytical model, as well as by forward-fitting to an exactly force-free solution of the Low and Lou (1990) model. The forward-fitting tests demonstrate: (i) a satisfactory convergence behavior (with typical misalignment angles of $\mu \approx 1^\circ-10^\circ$), (ii) relatively fast computation times (from seconds to a few minutes), and (iii) the high fidelity of retrieved force-free $\alpha$-parameters ($\alpha_{\rm fit}/\alpha_{\rm model} \approx 0.9-1.0$ for simulations and $\alpha_{\rm fit}/\alpha_{\rm model} \approx 0.7\pm0.3$ for the Low and Lou model). The salient feature of this numeric code is the relatively fast computation of a quasi-forcefree magnetic field, which closely matches the geometry of coronal loops in active regions, and complements the existing {\sl nonlinear force-free field (NLFFF)} codes based on photospheric magnetograms without coronal constraints.