Magnetic Helicity and Free Magnetic Energy: Their Relation and Predictive Power in Eruptive Solar Magnetic Configurations

Solar and space weather forecasting seek metrics with predictive power that can help mitigate the adverse effects of solar eruptions and their consequences. These metrics often rely on a reduced, simplified physical background, but this does not mean that space weather itself should necessarily trade well-founded physics for operational convenience. Solar eruptions are triggered in tangled, helical, solar magnetic fields stressed well beyond their minimum energy state. We aim to precisely calculate the two physical quantities thought to be responsible for eruptions, namely, the relative magnetic helicity and the free magnetic energy of the source active regions. Using the nonlinear force-free approximation, we first relate the magnetic free energy to the relative helicity and then we proceed to distinguish eruptive from non-eruptive active regions purely from their free energy and helicity values. Results with sufficient statistics, pending the availability of high-quality solar vector magnetograms, can establish "all-clear" free-energy and helicity thresholds. Moreover, the free energy/helicity buildup in the absence of eruptions in solar active regions can be viewed as a course through a sequence of metastable states with eruptions occurring spontaneously when the system reaches local or global minimal stability. This allows the careful use of the self-organized criticality (SOC) concept to describe the dynamics of the system and leads to important conclusions about how far we can go when predicting solar eruptions.