Comparison of a CME Flux-rope Model with LASCO data

The theoretical flux rope model (Chen 1989, 1996) of CME dynamics is investigated and compared with height-time curves of flux rope CME observations from LASCO. This model has been shown by Krall et al. (2001) to be a good match to numerous observed CME events. It is useful to study the model parametric dependences of CME initial acceleration, which is important for understanding the driving mechanisms of the ejections. STEREO will be able to provide data of the lower parts of the corona, capturing the initial acceleration of CMEs. The physics-based flux rope model is a low dimensional model comprising two second-order ordinary differential equations for the acceleration of the height Z(t) and the minor radius a(t) for the toroidal plasma loop. Given an initial parameter vector, an MHD-stable equilibrum is found that is a partial torus with two stationary footpoints separated by a distance Sf and anchored in the massive photosphere. The equilibrium flux rope is embedded in a background corona of finite pressure pc and magnetic field Bc and balances the J × B Lorentz force, gravity, and pressure gradient force. Injection of poloidal flux (toroidal current) serves as a direct drive toward destabilization and eruption. A code solves in seconds the dynamical evolution of the system in the d=4 state space for a given set of initial physical parameters (μ5 = \{Z0,Sf,a0,\bar{p}/pc,Bc\}), model coronal magnetic field, model solar wind, and the functional form of the flux injection dΦp(t)/dt. A physically acceptable range of parameters is sampled, and comparison with CME height-time data yields optimal parameters by the inverse method. Both the Very Fast Simulated Annealing Method (VFSA) and the Genetic Algorithm (GA) are used for optimization, and results are compared. The average relative variance of the model height versus time curves with the data sets are reported. The work is supported by NSF grant ATM-0638480 and the U.S. Department of Energy.