On the reliability of magnetic energy and helicity computations based on nonlinear force-free coronal magnetic field models. (arXiv:1907.01179v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Thalmann_J/0/1/0/all/0/1">Julia K. Thalmann</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Linan_L/0/1/0/all/0/1">Luis Linan</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Pariat_E/0/1/0/all/0/1">Etienne Pariat</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Valori_G/0/1/0/all/0/1">Gherardo Valori</a>
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.
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.
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