THE MAGNETIC ENERGY-HELICITY DIAGRAM OF SOLAR ACTIVE REGIONS

Abstract

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