# On the reliability of magnetic energy and helicity computations based on nonlinear force-free coronal magnetic field models

## TL;DR

This study assesses how the quality of nonlinear force-free magnetic field models affects the accuracy of magnetic energy and helicity calculations in the solar corona, emphasizing the importance of solenoidal properties.

## Contribution

It demonstrates the sensitivity of magnetic energy and helicity computations to the divergence-free quality of NLFF models and provides thresholds for reliable calculations.

## Key findings

- Magnetic helicity calculations are highly sensitive to the divergence-free condition.
- Magnetic energy is less sensitive than helicity to model quality.
- Proxies for eruptivity depend strongly on the solenoidal property of the models.

## Abstract

We demonstrate the sensitivity of magnetic energy and helicity computations regarding the quality of the underlying coronal magnetic field model. We apply the method of Wiegelmann & Inhester (2010) to a series of SDO/HMI vector magnetograms, and discuss nonlinear force-free (NLFF) solutions based on two different sets of the free model parameters. The two time series differ from each other concerning their force-free and solenoidal quality. Both force- and divergence-freeness are required for a consistent NLFF solution. Full satisfaction of the solenoidal property is inherent in the definition of relative magnetic helicity in order to insure gauge-independence. We apply two different magnetic helicity computation methods (Thalmann et al. 2011; Valori et al. 2012) to both NLFF time series and find that the output is highly dependent on the level to which the NLFF magnetic fields satisfy the divergence-free condition, with the computed magnetic energy being less sensitive than the relative helicity. Proxies for the non-potentiality and eruptivity derived from both quantities are also shown to depend strongly on the solenoidal property of the NLFF fields. As a reference for future applications, we provide quantitative thresholds for the force- and divergence-freeness, for the assurance of reliable computation of magnetic energy and helicity, and of their related eruptivity proxies.