Gravitational instability of solar prominence threads I. Curved magnetic fields without dips

TL;DR

This paper analytically investigates the gravitational stability of solar prominence threads on curved magnetic fields without dips, revealing bifurcation behaviors and stability criteria based on initial conditions and physical parameters.

Contribution

It provides the first analytical model for the gravitational stability and bifurcation analysis of prominence threads on curved magnetic fields without dips.

Findings

Stable and unstable equilibrium solutions depend on initial position, density contrast, and length.

Bifurcation points are analytically determined, including supercritical pitchfork and S-shaped bifurcations.

Results enhance understanding of thread behavior in curved magnetic fields, aiding interpretation of complex MHD simulations.

Abstract

Prominence threads are dense and cold structures lying on curved magnetic fields that can be suspended in the solar atmosphere against gravity. The gravitational stability of threads, in the absence of non-ideal effects, is comprehensively investigated in the present work by means of an elementary but effective model. Based on purely hydrodynamic equations in one spatial dimension and applying line-tying conditions at the footpoints of the magnetic field lines, we derive analytical expressions for the different feasible equilibria and the corresponding frequencies of oscillation. We find that the system allows for stable and unstable equilibrium solutions subject to the initial position of the thread, its density contrast and length, and the total length of the magnetic field lines. The transition between the two types of solutions is produced at specific bifurcation points that have been determined analytically in some particular cases. When the thread is initially at the top of the concave magnetic field, that is at the apex, we find a supercritical pitchfork bifurcation, while for a shifted initial thread position with respect to this point the symmetry is broken and the system is characterised by an S-shaped bifurcation. The plain results presented in this paper shed new light on the behaviour of threads in curved magnetic fields under the presence of gravity and help to interpret more complex numerical magnetohydrodynamics (MHD) simulations about similar structures.