Critical Parameters of Photospheric Magnetic Field to Produce Eruptive Flares in Solar Active Regions

Solar flares and coronal mass ejections (CMEs) are eruptive phenomena caused by magnetic field in the solar corona. In particular, large eruptive events originate in active regions (AR) on the solar surface. However, it is still unclear what determines the capability of an AR to produce eruptive flares and CMEs, and it hinders our ability to predict CMEs. In this study, we propose a new parameter r _m to measure the possibility that a flare on an AR can be eruptive and produce a CME. The parameter r _m is defined by the ratio of the magnetic flux of twist higher than a threshold T _c to the overlying magnetic flux. The value of r _m for each AR can be estimated using the nonlinear force-free field (NLFFF) extrapolation. Based on the data obtained by the Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI), we calculated the values of r _m for 29 ARs at 51 times before to flares larger than M5.0 class. We find that the foot-point of field lines with twist larger than 0.2 can well represent the flare ribbons. Moreover, field lines that are overlying and fencing in these highly twisted regions will confine the eruption, resulting in confined flares. By using T _c =0.2 and including the overlying and fencing flux in the evaluation of r _m , the discriminant analysis shows that r _m is moderately able to discriminate ARs which have capability to produce eruptive flares. Furthermore, we in detail analyze the exceptional events, in which the eruptive flare cannot be predicted by r _m , and discuss the possible reason for failed prediction.