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We demonstrate the sensitivity of magnetic energy and helicity computationsregarding the quality of the underlying coronal magnetic field model. We applythe method of Wiegelmann & Inhester (2010) to a series of SDO/HMI vectormagnetograms, and discuss nonlinear force-free (NLFF) solutions based on twodifferent sets of the free model parameters. The two time series differ fromeach other concerning their force-free and solenoidal quality. Both force- anddivergence-freeness are required for a consistent NLFF solution. Fullsatisfaction of the solenoidal property is inherent in the definition ofrelative magnetic helicity in order to insure gauge-independence. We apply twodifferent magnetic helicity computation methods (Thalmann et al. 2011; Valoriet al. 2012) to both NLFF time series and find that the output is highlydependent on the level to which the NLFF magnetic fields satisfy thedivergence-free condition, with the computed magnetic energy being lesssensitive than the relative helicity. Proxies for the non-potentiality anderuptivity derived from both quantities are also shown to depend strongly onthe solenoidal property of the NLFF fields. As a reference for futureapplications, we provide quantitative thresholds for the force- anddivergence-freeness, for the assurance of reliable computation of magneticenergy and helicity, and of their related eruptivity proxies.

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