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The Magnetic Energy - Helicity Diagram of Solar Active Regions

Using a recently proposed nonlinear force-free method designed for single vector magnetograms of solar active regions we calculate the instantaneous free magnetic energy and relative magnetic helicity budgets in 162 vector magnetograms corresponding to 42 different active regions. We find a statistically robust, monotonic correlation between the free magnetic energy and the relative magnetic helicity in the studied regions. This correlation implies that magnetic helicity, besides free magnetic energy, may be an essential ingredient for major solar eruptions. Eruptive active regions appear well segregated from non-eruptive ones in both free energy and relative helicity with major (at least M-class) flares occurring in active regions with free energy and relative helicity exceeding 4x10^{31} erg and 2x10^{42} Mx^2, respectively. The helicity threshold agrees well with estimates of helicity contents of typical coronal mass ejections.