A statistical study of photospheric magnetic field properties of active regions associated with M- and X-class flares using SDO/HMI vector magnetic field data

With the aim of understanding the photospheric magnetic field properties of active regions (ARs) that produce M-class or greater flares, physical magnetic parameters of ARs provided by the Space-weather HMI Active Region Patches (SHARP) are examined. A total of 223 flares are collected in 83 ARs, including 31 X- and 192 M-class flares. In this study, twelve SHARP parameters are analyzed, which are the sums of various physical quantities (e.g., magnetic flux, magnetic free energy density, vertical current, current helicity, shear angle, and Lorentz force). For X- and M-class flares, good correlation coefficients (greater than or similar to 0.90) are obtained among the seven magnetic parameters, namely, total unsigned quantities of (1) magnetic flux, (2) vertical current, (3) current helicity, and (4) flux near polarity inversion line, as well as (5) total photospheric magnetic free energy density, (6) total magnitude of Lorentz force (TOTBSQ), and (7) area of AR. A threshold for low bound is estimated for each of the seven magnetic parameters based on X-class flares. Only similar to 5% of M-flares occur below the estimated thresholds. A time difference (T-SF) is calculated between the time when all the magnetic parameter thresholds but TOTBSQ are met (T-1) and the time when the flare starts. The TOTBSQ is excluded in the T-1 calculation because its value is often missing in the interval of interest. Results show that (1) similar to 77% of X-flares occur within 7 days after T-1, with an occurrence peak at T-SF = 2 (similar to 20% probability), (2) similar to 78% of M-flares also occur within 7 days after T-1, with an occurrence peak at T-SF = 4 (similar to 20% probability), and (3) no major flare occurs after T-SF = 11. It is found that the GOES soft X-ray peak flux has a very weak relationship with the magnetic free energy density. This weak relationship can be interpreted in terms of the energy partition in a flare. In conclusion, the obtained seven thresholds will be useful for monitoring an AR that has a high potential to produce an M- or X-class flare.