Magnetic helicity and free magnetic energy as tools for probing eruptions in two differently evolving solar active regions

Aims: We study the role of magnetic helicity and free magnetic energy in the initiation of eruptions in two differently evolving solar active regions (ARs).
Methods: Using vector magnetograms from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory and a magnetic connectivity-based method, we calculate the instantaneous relative magnetic helicity and free magnetic energy budgets for several days in two ARs, AR11890 and AR11618, both with complex photospheric magnetic field configurations.
Results: The ARs produced several major eruptive flares while their photospheric magnetic field exhibited different evolutionary patterns: primarily flux decay in AR11890 and primarily flux emergence in AR11618. Throughout much of their evolution, both ARs featured substantial budgets of free magnetic energy and of both positive (right-handed) and negative (left-handed) helicity. In fact, the imbalance between the signed components of their helicity was as low as in the quiet Sun and their net helicity eventually changed sign 14−19 h after their last major flare. Despite this incoherence, the eruptions occurred at times of net helicity peaks that were co-temporal with peaks in the free magnetic energy. The percentage losses, associated with the eruptive flares, in the normalized free magnetic energy were significant, in the range of ∼10−60%. For the magnetic helicity, changes ranged from ∼25% to the removal of the entire excess helicity of the prevailing sign, leading a roughly zero net helicity, but with significant equal and opposite budgets of both helicity senses. Respective values ranged from (0.3 − 2)×10³² erg and (1.3 − 20)×10⁴² Mx² for energy and helicity losses. The removal of the slowly varying background component of the free energy and helicity (either the net helicity or the prevailing signed component of helicity) time series revealed that all eruption-related peaks of both quantities exceeded the 2σ levels of their detrended time series above the removed background. There was no eruption when only one or none of these quantities exceeded its 2σ level.
Conclusions: Our results indicate that differently evolving ARs may produce major eruptive flares even when, in addition to the accumulation of significant free magnetic energy budgets, they accumulate large amounts of both left- and right-handed helicity without a strong dominance of one handedness over the other. In most cases, these excess budgets appear as localized peaks, co-temporal with the flare peaks, in the time series of free magnetic energy and helicity (and normalized values thereof). The corresponding normalized free magnetic energy and helicity losses can be very significant at certain times.

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