Eruptivity in Solar Flares: The Challenges of Magnetic Flux Ropes

Two new schemes for identifying field lines involved in eruptions, the r-scheme and q-scheme, are proposed to analyze the eruptive and confined nature of solar flares, as extensions to the original r ( m ) scheme proposed in Lin et al. Motivated by three solar flares originating from NOAA Active Region 12192 that are misclassified by r ( m ), we introduce refinements to the r-scheme employing the "magnetic twist flux" to approximate the force balance acting on a magnetic flux rope (MFR); in the q-scheme, the reconnected field is represented by those field lines that anchor in the flare ribbons. Based on data obtained by the Solar Dynamics Observatory/Helioseismic and Magnetic Imager, the coronal magnetic field for 51 flares larger than M5.0 class, from 29 distinct active regions, is constructed using a nonlinear force-free field extrapolation model. Statistical analysis based on linear discriminant function analysis is then performed, revealing that despite both schemes providing moderately successful classifications for the 51 flares, the coronal mass ejection-eruptivity classification for the three target events can only be improved with the q-scheme. We find that the highly twisted field lines and the flare-ribbon field lines have equal average force-free constant alpha, but all of the flare-ribbon-related field lines are shorter than 150 Mm in length. The findings lead us to conclude that it is challenging to distinguish the MFR from the ambient magnetic field using any quantity based on common magnetic nonpotentiality measures.