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.