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

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, i.e., whether they are associated with a CME or they are confined. Using an optimization approach, we employ 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 compute 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, $E_{\mathrm{F}}/{E}$ (energy ratio), the fraction of non-potential (current-carrying) helicity, $|H_{\mathrm{J}}|/|{H_{V}}|$ (helicity ratio), and the normalized current-carrying helicity, $|H_{\mathrm{J}}|/{\phi^{\prime}}^{2}$. 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, i.e., whether or not a CME is produced in association with the flare. The intensive eruptivity proxies, $E_{\mathrm{F}}/{E}$ and $|H_{\mathrm{J}}|/|{H_{V}}|$, and $|H_{\mathrm{J}}|/{\phi^{\prime}}^{2}$, however, seem to be distinctly different for ARs that produced CME-associated large flares compared to those which produced confined flares. For the majority of ARs in our sample, we are able to identify characteristic pre-flare magnitudes of the intensive quantities, clearly associated to subsequent CME-productivity.