Magnetic helicity and energy budget around large confined and eruptive solar flares

Abstract

Context. In order to better understand the underlying processes and prerequisites for solar activity, it is essential to study the time evolution of the coronal magnetic field of solar active regions (ARs) associated with flare activity. Aims. We investigate the coronal magnetic energy and helicity budgets of ten solar ARs around the times of large flares. In particular, we are interested in a possible relation of the derived quantities to the particular type of the flares that the AR produces, namely, whether they are associated with a CME or whether they are confined (i.e., not accompanied by a CME). Methods. Using an optimization approach, we employed time series of 3D nonlinear force-free magnetic field models of ten ARs, covering a time span of several hours around the time of occurrence of large solar flares (GOES class M1.0 and larger). We subsequently computed the 3D magnetic vector potentials associated to the model 3D coronal magnetic field using a finite-volume method. This allows us to correspondingly compute the coronal magnetic energy and helicity budgets, as well as related (intensive) quantities such as the relative contribution of free magnetic energy, EF/E (energy ratio), the fraction of non-potential (current-carrying) helicity, |HJ|/|HV| (helicity ratio), and the normalized current-carrying helicity, |HJ|/ϕ′2. Results. The total energy and helicity budgets of flare-productive ARs (extensive parameters) cover a broad range of magnitudes, with no obvious relation to the eruptive potential of the individual ARs, that is, whether or not a CME is produced in association with the flare. The intensive eruptivity proxies, EF/E and |HJ|/|HV|, and |HJ|/ϕ′2, however, seem to be distinctly different for ARs that produce CME-associated large flares compared to those which produce confined flares. For the majority of ARs in our sample, we are able to identify characteristic pre-flare magnitudes of the intensive quantities that are clearly associated with subsequent CME-productivity. Conclusions. If the corona of an AR exhibits characteristic values of ⟨|HJ|/|HV|⟩ > 0.1, ⟨EF/E⟩ > 0.2, and ⟨|HJ|/ϕ′2⟩ > 0.005, then the AR is likely to produce large CME-associated flares. Conversely, confined large flares tend to originate from ARs that exhibit coronal values of ⟨|HJ|/|HV|⟩ ≲ 0.1, ⟨EF/E⟩ ≲ 0.1, and ⟨|HJ|/ϕ′2⟩ ≲ 0.002.