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Nonlinear force-free field (NLFFF) models are thought to be viable tools for investigating the structure, dynamics, and evolution of the coronae of solar active regions. In a series of NLFFF modeling studies, we have found that NLFFF models are successful in application to analytic test cases, and relatively successful when applied to numerically constructed Sun-like test cases, but they are less successful in application to real solar data. Different NLFFF models have been found to have markedly different field line configurations and to provide widely varying estimates of the magnetic free energy in the coronal volume, when applied to solar data. NLFFF models require consistent, force-free vector magnetic boundary data. However, vector magnetogram observations sampling the photosphere, which is dynamic and contains significant Lorentz and buoyancy forces, do not satisfy this requirement, thus creating several major problems for force-free coronal modeling efforts. In this paper, we discuss NLFFF modeling of NOAA Active Region 10953 using Hinode/SOT-SP, Hinode/XRT, STEREO/SECCHI-EUVI, and SOHO/MDI observations, and in the process illustrate three such issues we judge to be critical to the success of NLFFF modeling: (1) vector magnetic field data covering larger areas are needed so that more electric currents associated with the full active regions of interest are measured, (2) the modeling algorithms need a way to accommodate the various uncertainties in the boundary data, and (3) a more realistic physical model is needed to approximate the photosphere-to-corona interface in order to better transform the forced photospheric magnetograms into adequate approximations of nearly force-free fields at the base of the corona. We make recommendations for future modeling efforts to overcome these as yet unsolved problems.

A test of a new Bayesian approach to solar flare prediction is presented. The approach uses the past history of flaring together with phenomenological rules of flare statistics to make a prediction for the probability of occurrence of a large flare within an interval of time, or to refine an initial prediction (which may incorporate other information). The test of the method is based on data from the Geostationary Observational Environmental Satellites, and involves whole-Sun prediction of soft X-ray flares for 1976–2003. The results show that the method somewhat over-predicts the probability of all events above a moderate size, but performs well in predicting large events.

AbstractA test of a new Bayesian approach to solar flare prediction is presented. The approach uses the past history of flaring together with phenomenological rules of flare statistics to make a prediction for the probability of occurrence of a large flare within an interval of time, or to refine an initial prediction (which may incorporate other information). The test of the method is based on data from the Geostationary Observational Environmental Satellites, and involves whole-Sun prediction of soft X-ray flares for 1976–2003. The results show that the method somewhat over-predicts the probability of all events above a moderate size, but performs well in predicting large events.

Solar flares and coronal mass ejections (CMEs) involve the sudden release of magnetic energy that can lead to the ejection from the Sun of large masses of gas with entrained magnetic field. In dynamical systems, such sudden events are characteristic of metastable configurations that are stable against small perturbations but unstable to sufficiently large perturbations. Linear stability analysis indicates whether or not the first requirement is met, and energetic analysis can indicate whether or not the second requirement is met: if a magnetic configuration that is stable against small perturbations can make a transition to a lower energy state, then it is metastable.