Magnetic Rayleigh–Taylor instability at a contact discontinuity with an oblique magnetic field

¹ School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Rd., Sheffield, UK
e-mail: evickersl@sheffield.ac.uk
² Dept. of Astronomy, Eötvös L. University, Pázmány P. sétány 1/A, Budapest H1117, Hungary

Received: 9 August 2019
Accepted: 24 November 2019

Abstract

Aims. We investigate the nature of the magnetic Rayleigh–Taylor instability at a density interface that is permeated by an oblique homogeneous magnetic field in an incompressible limit.

Methods. Using the system of linearised ideal incompressible magnetohydrodynamics equations, we derive the dispersion relation for perturbations of the contact discontinuity by imposing the necessary continuity conditions at the interface. The imaginary part of the frequency describes the growth rate of waves due to instability. The growth rate of waves is studied by numerically solving the dispersion relation.

Results. The critical wavenumber at which waves become unstable, which is present for a parallel magnetic field, disappears because the magnetic field is inclined. Instead, waves are shown to be unstable for all wavenumbers. Theoretical results are applied to diagnose the structure of the magnetic field in prominence threads. When we apply our theoretical results to observed waves in prominence plumes, we obtain a wide range of field inclination angles, from 0.5° up to 30°. These results highlight the diagnostic possibilities that our study offers.