Photospheric magnetic field properties of flaring versus flare-quiet active regions. IV. A statistically significant sample

Statistical tests based on linear discriminant analysis are applied to numerous photospheric magnetic parameters, continuing toward the goal of identifying properties important for the production of solar flares. For this study, the vector field data are University of Hawai`i Imaging Vector Magnetograph daily magnetograms obtained between 2001 and 2004. Over 1200 separate magnetograms of 496 numbered active regions comprise the data set. At the soft X-ray C1.0 level, 359 magnetograms are considered flare productive'' in the 24 hr postobservation. Considering multiple photospheric variables simultaneously indicates that combinations of only a few familiar variables encompass the majority of the predictive power available. However, the choice of which few variables is not unique, due to strong correlations among photospheric quantities such as total magnetic flux and total vertical current, two of the most powerful predictors. The best discriminant functions result from combining one of these with additional uncorrelated variables, such as measures of the magnetic shear, and successfully classify over 80% of the regions. By comparison, a success rate of approximately 70% is achieved by simply classifying all regions as flare quiet.'' Redefining flare-productive'' at the M1.0 level, parameterizations of excess photospheric magnetic energy outperform other variables. However, the uniform flare-quiet classification rate is approximately 90%, while incorporating photospheric magnetic field information results in at most a 93% success rate. Using nonparametric discriminant analysis, we demonstrate that the results are quite robust. Thus, we conclude that the state of the photospheric magnetic field at any given time has limited bearing on whether that region will be flare productive.