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Solar flares and coronal mass ejections (CMEs), especially the larger ones,emanate from active regions (ARs). With the aim to understand the magneticproperties that govern such flares and eruptions, we systematically survey allflare events with GOES levels of >=M5.0 within 45 deg from disk center betweenMay 2010 and April 2016. These criteria lead to a total of 51 flares from 29ARs, for which we analyze the observational data obtained by the Solar DynamicsObservatory. More than 80% of the 29 ARs are found to exhibit delta-sunspotsand at least three ARs violate Hale's polarity rule. The flare durations areapproximately proportional to the distance between the two flare ribbons, tothe total magnetic flux inside the ribbons, and to the ribbon area. From ourstudy, one of the parameters that clearly determine whether a given flare eventis CME-eruptive or not is the ribbon area normalized by the sunspot area, whichmay indicate that the structural relationship between the flaring region andthe entire AR controls CME productivity. AR characterization show that evenX-class events do not require delta-sunspots or strong-field, high-gradientpolarity inversion lines. An investigation of historical observational datasuggests the possibility that the largest solar ARs, with magnetic flux of2x10^23 Mx, might be able to produce "superflares" with energies of order of10^34 erg. The proportionality between the flare durations and magneticenergies is consistent with stellar flare observations, suggesting a commonphysical background for solar and stellar flares.

Magnetic Properties of Solar Active Regions that Govern Large Solar Flares and Eruptions