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We assess the validity of the free magnetic energy - relative magnetichelicity diagram for solar magnetic structures. We used two different methodsof calculating the free magnetic energy and the relative magnetic helicitybudgets: a classical, volume-calculation nonlinear force-free (NLFF) methodapplied to finite coronal magnetic structures and a surface-calculation NLFFderivation that relies on a single photospheric or chromospheric vectormagnetogram. Both methods were applied to two different data sets, namelysynthetic active-region cases obtained by three-dimensionalmagneto-hydrodynamic (MHD) simulations and observed active-region cases, whichinclude both eruptive and noneruptive magnetic structures. The derivedenergy--helicity diagram shows a consistent monotonic scaling between relativehelicity and free energy with a scaling index 0.84$\pm$0.05 for both data setsand calculation methods. It also confirms the segregation between noneruptiveand eruptive active regions and the existence of thresholds in both free energyand relative helicity for active regions to enter eruptive territory. Weconsider the previously reported energy-helicity diagram of solar magneticstructures as adequately validated and envision a significant role of theuncovered scaling in future studies of solar magnetism.

Validation of the magnetic energy vs. helicity scaling in solar magnetic structures