Helicities of the polarity-inversion line and solar eruptivity

Aims. We examine the relation between solar eruptivity and the relative helicity that is contained around the polarity-inversion line (PIL) of the magnetic field, along with its current-carrying component. Methods. To this end, we analysed the evolution of the PIL helicities in a sample of ∼40 solar active regions that exhibited more than 200 flares of class M or higher. We computed the PIL helicities with the help of the relative field line helicity, the recently developed proxy for the density of relative helicity, following the extrapolation of the 3D coronal magnetic field with a non-linear force-free method. Results. The relative helicity of the PIL decreases significantly on average by more than 10% during stronger eruptive flares (M5.0 class and above), while smaller changes are observed for confined and/or weaker flares. The PIL current-carrying helicity shows higher-magnitude decreases in strong and weak flares and reaches an average of 20% of changes during the stronger eruptive flares. Notably, the PIL current-carrying helicity differs most between eruptive and confined flares, which indicates its strong potential as a diagnostic of solar eruptivity. We discuss the implications of these findings for solar flare forecasting.