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, forcefree 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 article, 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 the 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.

The physical mechanism responsible for coronal mass ejections has been uncertain for many years, in large part because of the difficulty of knowing the three-dimensional magnetic field in the low corona. Two possible models have emerged. In the first, a twisted flux rope moves out of equilibrium or becomes unstable, and the subsequent reconnection then powers the ejection. In the second, a new flux rope forms as a result of the reconnection of the magnetic lines of an arcade (a group of arches of field lines) during the eruption itself. Observational support for both mechanisms has been claimed. Here we report modelling which demonstrates that twisted flux ropes lead to the ejection, in support of the first model. After seeing a coronal mass ejection, we use the observed photospheric magnetic field in that region from four days earlier as a boundary condition to determine the magnetic field configuration. The field evolves slowly before the eruption, such that it can be treated effectively as a static solution. We find that on the fourth day a flux rope forms and grows (increasing its free energy). This solution then becomes the initial condition as we let the model evolve dynamically under conditions driven by photospheric changes (such as flux cancellation). When the magnetic energy stored in the configuration is too high, no equilibrium is possible and the flux rope is 'squeezed' upwards. The subsequent reconnection drives a mass ejection.