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

TL;DR

Solar filaments are stabilized by gravity and magnetic forces in a current-carrying configuration, and this paper investigates their post-destabilization evolution within the Solov'ev gravity-balanced framework. It derives analytical expressions for the current density $j_z$ and density in the filament and then validates the dynamics with 2D MHD simulations using the Lare2d code. The study finds that both increasing the filament current and reducing its density can trigger a failed ejection, with a maximum ejection velocity up to $80$ km s$^{-1}$ and a recurrent oscillation period of about $6\times 10^2$ s, accompanied by the formation of a current sheet and reconnection beneath the filament. The results differ from an ideal vacuum model due to reconnection and finite-$β$ effects, offering a mechanism to explain observed failed eruptions and highlighting the coupling between magnetic and plasma processes in filament evolution.

Abstract

In this study, we investigate the post-destabilization evolution of a filament in a gravity-balanced model. We adopt the filament model proposed by Solov'ev (2010), 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 use a two-dimensional magnetohydrodynamic (MHD) model that solves the MHD equations with the Lare2d numerical code. Results: In this filament model, analytical expressions are 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 are also calculated. For the numerical simulations, we constructed an equilibrium filament characterized by a magnetic field of $B_0$ = $10^{-3}$ T, mass density $ρ_0$ ~ 1.3 x $10^{-9}$ kg m$^{-3}$, and temperature T ~ 13000 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 results.

Figures (14)

• Figure 1: Electric current density (z-component) along the $y$-axis $(x = 0)$ for $B_0 = 10^{-3}~\mathrm{T}$, $h_0 = 5~\mathrm{Mm}$ and three values of the parameter $k$.
• Figure 2: Total electric current (upper panel) in the z-direction and maximum of the z-component of the current density (lower panel) in the filament in dependence on the parameter $k$ for $B_0 = 10^{-3}~\mathrm{T}$.
• Figure 3: Mass density along the $y$-axis $(x = 0)$ for $B_0 = 10^{-3}~\mathrm{T}$, $h_0~=~5~\mathrm{Mm}$ and three values of the parameter $k$.
• Figure 4: Weight of the filament per one meter in the perpendicular direction to the $x-y$ plane (above $h_0 = 5~\mathrm{Mm}$) (upper panel) and maximum mass density (lower panel) in the filament in dependence on the parameter $k$ for $B_0 = 10^{-3}~\mathrm{T}$.
• Figure 5: Vertical profiles of the absolute value of $B_x$ component of magnetic field (green line), mass density $\rho$ (blue line), temperature T (red line), and plasma beta parameter $\beta$ (brown line) along the axis of symmetry $(x = 0~\mathrm{Mm})$ in the initial equilibrium state for $B_0$ = 10$^{-3}$ T and $k = 5\times10^{-7}~\mathrm{m^{-1}}$. The solid black vertical line shows the location of the transition region, $h_{\mathrm{TR}} = 5~\mathrm{Mm}$, as defined in our model, while the dotted vertical line denotes the midpoint between the filaments $h_0 = 4.7~\mathrm{Mm}$. Note that the $y$-axis is on a logarithmic scale.