On measuring divergence for magnetic field modeling

Abstract

A physical magnetic field has a divergence of zero. Numerical error in constructing a model field and computing the divergence, however, introduces a finite divergence into these calculations. A popular metric for measuring divergence is the average fractional flux $⟨|f_i|⟩$. We show that $⟨|f_i|⟩$ scales with the size of the computational mesh, and may be a poor measure of divergence because it becomes arbitrarily small for increasing mesh resolution, without the divergence actually decreasing. We define a modified version of this metric that does not scale with mesh size. We apply the new metric to the results of DeRosa et al. (2015), who measured $⟨|f_i|⟩$ for a series of Nonlinear Force-Free Field (NLFFF) models of the coronal magnetic field based on solar boundary data binned at different spatial resolutions. We compute a number of divergence metrics for the DeRosa et al. (2015) data and analyze the effect of spatial resolution on these metrics using a non-parametric method. We find that some of the trends reported by DeRosa et al. (2015) are due to the intrinsic scaling of $⟨|f_i|⟩$. We also find that different metrics give different results for the same data set and therefore there is value in measuring divergence via several metrics.

arXiv commentAccepted for publication in ApJ

References in corpus (11)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• The Solar Optical Telescope for the Hinode Mission: An Overview
• A Critical Assessment of Nonlinear Force-Free Field Modeling of the Solar Corona for Active Region 10953
• How to optimize nonlinear force-free coronal magnetic field extrapolations from SDO/HMI vector magnetograms?
• The Influence of Spatial Resolution on Nonlinear Force-Free Modeling
• Testing magnetofrictional extrapolation with the Titov-Démoulin model of solar active regions
• Accuracy of magnetic energy computations
• Magnetic Field Extrapolations in the Corona: Success and Future Improvements
• Validation and Benchmarking of a Practical Free Magnetic Energy and Relative Magnetic Helicity Budget Calculation in Solar Magnetic Structures
• Statistical study of free magnetic energy and flare productivity of solar active regions
• Nonlinear force-free field modeling of a solar active region using SDO/HMI and SOLIS/VSM data

Cited by in corpus (4)

• Magnetic helicity estimations in models and observations of the solar magnetic field. Part IV: Application to solar observations
• Deducing the reliability of relative helicities from nonlinear force-free coronal models
• Relative field line helicity of a large eruptive solar active region
• The effect of spatial sampling on magnetic field modeling and helicity computation