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

Abstract

<p><em>[eng] Context. Prominence threads are dense and cold structures lying on curved magnetic fields that can be suspended in the solar atmosphere</em></p><p><em>against gravity.</em></p><p><em>Aims. The gravitational stability of threads, in the absence of non-ideal e ects, is comprehensively investigated in the present work</em></p><p><em>by means of an elementary but e ective model.</em></p><p><em>Methods. Based on purely hydrodynamic equations in one spatial dimension and applying line-tying conditions at the footpoints of</em></p><p><em>the magnetic field lines, we derive analytical expressions for the di erent feasible equilibria (se) and the corresponding frequencies</em></p><p><em>of oscillation (!).</em></p><p><em>Results. We find that the system allows for stable and unstable equilibrium solutions subject to the initial position of the thread (s0),</em></p><p><em>its density contrast ( t) and length (lt), and the total length of the magnetic field lines (L). The transition between the two types of</em></p><p><em>solutions is produced at specific bifurcation points that have been determined analytically in some particular cases. When the thread</em></p><p><em>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</em></p><p><em>initial thread position with respect to this point the symmetry is broken and the system is characterised by an S-shaped bifurcation.</em></p><p><em>Conclusions. The plain results presented in this paper shed new light on the behaviour of threads in curved magnetic fields under the</em></p><p><em>presence of gravity and help to interpret more complex numerical magnetohydrodynamics simulations about similar structures.</em></p>