Failed ejection and oscillations of a current-carrying filament balanced by gravity

Context. Solar filaments are often associated with solar eruptions and coronal mass ejections. However, in some cases, the ejection process is halted, resulting in a failed eruption. Understanding the processes that occur after filament destabilization is therefore of great importance. Aims. In this study, we investigate the post-destabilization evolution of a filament in a gravity-balanced model. Methods. We adopted the filament model, in which a dense filament is supported against gravity by the repulsive force between the filament current and its sub-photospheric image. We first performed an analytical investigation of this model. For the numerical study, we used a two-dimensional magnetohydrodynamic (MHD) model that solved the MHD equations with the Lare2d numerical code. Results. In this filament model, analytical expressions were derived for the electric current density, plasma density, and their spatial distributions as functions of the model parameters. The total electric current and the filament weight were also calculated. For the numerical simulations, we constructed an equilibrium filament characterized by a magnetic field of B 0 = 10 −3 T, a mass density ρ 0 ∼ 1.3 × 10 −9 kg m −3 , and temperature T ∼ 13 000 K. The system was destabilized either by increasing the currents or by reducing the filament density, and its evolution was computed. In both destabilization regimes, the filament was ejected, then halted at a certain altitude, and subsequently fell back, repeating this cycle with a period of about 600 s. The maximum filament ejection velocity was approximately 80 and 40 km s −1 , respectively. Beneath the ejected filament, a current sheet forms, where magnetic reconnection occurs. The maximum ejection altitudes were determined as functions of both the destabilizing currents and the degree of filament plasma dilution. Finally, we compared results of this MHD model with those of an ideal vacuum model and discussed all of the results.