Finite amplitude transverse oscillations of a magnetic rope

TL;DR

This paper investigates how finite amplitude transverse oscillations in a magnetic rope prominence are coupled and influenced by nonlinear effects, revealing new metastable states and complex oscillation behaviors.

Contribution

It introduces a detailed analysis of finite amplitude effects on prominence oscillations, including coupling phenomena and metastable equilibria, extending previous linear models.

Findings

Finite amplitude oscillations are strongly coupled horizontally and vertically.

Resonant cases produce Lissajous-like oscillation patterns with hourglass limit cycles.

Metastable equilibrium states exist, stable at small amplitudes but unstable beyond a threshold.

Abstract

The effects of finite amplitudes on the transverse oscillations of a quiescent prominence represented by a magnetic rope are investigated in terms of the model proposed by Kolotkov et al. 2016. We consider a weakly nonlinear case governed by a quadratic nonlinearity, and also analyse the fully nonlinear equations of motion. We treat the prominence as a massive line current located above the photosphere and interacting with the magnetised dipped environment via the Lorentz force. In this concept the magnetic dip is produced by two external current sources located at the photosphere. Finite amplitude horizontal and vertical oscillations are found to be strongly coupled between each other. The coupling is more efficient for larger amplitudes and smaller attack angles between the direction of the driver and the horizontal axis. Spatial structure of oscillations is represented by Lissajous-like curves with the limit cycle of a hourglass shape, appearing in the resonant case, when the frequency of the vertical mode is twice the horizontal mode frequency. A metastable equilibrium of the prominence is revealed, which is stable for small amplitude displacements, and becomes horizontally unstable, when the amplitude exceeds a threshold value. The maximum oscillation amplitudes are also analytically derived and analysed. Typical oscillation periods are determined by the oscillation amplitude, prominence current, its mass and position above the photosphere, and the parameters of the magnetic dip. The main new effects of the finite amplitude are the coupling of the horizontally and vertically polarised transverse oscillations (i.e. the lack of a simple, elliptically polarised regime) and the presence of metastable equilibria of prominences.