Numerical Experiments Based On The Catastrophe Model Of Solar Eruptions

On the basis of the catastrophe model developed by Isenberg et al.(1993),we used NIRVANA code to perform the MHD numerical experiments to look into various behaviors of the coronal magnetic configuration that includes a current-carrying flux rope used to model the prominence levitating in the corona.These behaviors include the evolution in equilibrium heights of the flux rope versus the change in the background magnetic field,the corresponding internal equilibrium of the flux rope,dynamic properties of the flux rope after the system loses equilibrium,as well as the impact of the referential radius on the equilibrium heights of the flux rope.In our calculations,an empirical model of the coronal density distribution given by Sittler & Guhathakurta was used,and the physical diffusion was included.Our experiments showed that the deviation of simulations in the equilibrium heights from the theoretical results exists,but is not apparent,and the evolutionary features of the two results are similar.If the flux rope was initially located at the stable branch of the theoretical equilibrium curve,the flux rope would quickly reach the equilibrium position in the simulation after several round of oscillations as a result of the self-adjustment of the system;and the flux rope does lose the equilibrium if the initial location of the flux rope was set at the critical point on the theoretical equilibrium curve.Correspondingly,the internal equilibrium of the flux rope could be reached as well,and the deviation from the theoretical results was somewhat apparent since the approximation of the small radius of the flux rope was lifted in our experiments,but such deviation did not affect the global equilibrium in the system.The impact of the referential radius on the equilibrium heights of the flux rope is consistent with the prediction of the theory.Our calculations indicated that the motion of the flux rope after the loss of equilibrium is consistent with that predicted by the Lin-Forbes model and observations.Formation of the fast mode shock ahead of the flux rope was observed in our experiments.Outward motions of the flux rope were smooth and magnetic energy was continuously converted into the other types of energy because both the diffusions were considered in calculations,and magnetic reconnection was allowed to occur successively in the current sheet behind the flux rope.