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

TL;DR

This study validates the scaling relationship between magnetic energy and helicity in solar magnetic structures using two calculation methods across synthetic and observed data, confirming thresholds for eruptions.

Contribution

It demonstrates the robustness of the energy-helicity scaling law across different datasets and methods, confirming its relevance in solar magnetic activity analysis.

Findings

Consistent scaling index of 0.84±0.05 between helicity and free energy.

Segregation between eruptive and noneruptive active regions.

Existence of thresholds in energy and helicity for eruptions.

Abstract

We assess the validity of the free magnetic energy - relative magnetic helicity diagram for solar magnetic structures. We used two different methods of calculating the free magnetic energy and the relative magnetic helicity budgets: a classical, volume-calculation nonlinear force-free (NLFF) method applied to finite coronal magnetic structures and a surface-calculation NLFF derivation that relies on a single photospheric or chromospheric vector magnetogram. Both methods were applied to two different data sets, namely synthetic active-region cases obtained by three-dimensional magneto-hydrodynamic (MHD) simulations and observed active-region cases, which include both eruptive and noneruptive magnetic structures. The derived energy--helicity diagram shows a consistent monotonic scaling between relative helicity and free energy with a scaling index 0.84$\pm$0.05 for both data sets and calculation methods. It also confirms the segregation between noneruptive and eruptive active regions and the existence of thresholds in both free energy and relative helicity for active regions to enter eruptive territory. We consider the previously reported energy-helicity diagram of solar magnetic structures as adequately validated and envision a significant role of the uncovered scaling in future studies of solar magnetism.