Quantitative Forecasting of Major Solar Flares

We define the effective connected magnetic field, B_eff, a single metric of the flaring potential in solar active regions. We calculated B_eff for 298 active regions (93 X- and M-flaring, 205 nonflaring) as recorded by SOHO/MDI during a 10 yr period covering much of solar cycle 23. We find that B_eff is a robust criterion for distinguishing flaring from nonflaring regions. A well-defined 12 hr conditional probability for major flares depends solely on B_eff. This probability exceeds 0.95 for M-class and X-class flares if B_eff>1600 G and B_eff>2100 G, respectively, while the maximum calculated B_eff-values are near 4000 G. Active regions do not give M-class and X-class flares if B_eff<200 G and B_eff<750 G, respectively. We conclude that B_eff is an efficient flare-forecasting criterion that can be computed on a timely basis from readily available data.