The Dynamics of Rayleigh-Taylor Stable and Unstable Contact Discontinuities with Anisotropic Thermal Conduction

Abstract

We study the effects of anisotropic thermal conduction along magnetic field lines on an accelerated contact discontinuity in a weakly collisional plasma. We first perform a linear stability analysis similar to that used to derive the Rayleigh-Taylor instability (RTI) dispersion relation. We find that anisotropic conduction is only important for compressible modes, as incompressible modes are isothermal. Modes grow faster in the presence of anisotropic conduction, but growth rates do not change by more than a factor of order unity. We next run fully non-linear numerical simulations of a contact discontinuity with anisotropic conduction. The non-linear evolution can be thought of as a superposition of three physical effects: temperature diffusion due to vertical conduction, the RTI, and the heat flux driven buoyancy instability (HBI). In simulations with RTI-stable contact discontinuities, the temperature discontinuity spreads due to vertical heat conduction. This occurs even for initially horizontal magnetic fields due to the initial vertical velocity perturbation and numerical mixing across the interface. The HBI slows this temperature diffusion by reorienting initially vertical magnetic field lines to a more horizontal geometry. In simulations with RTI-unstable contact discontinuities, the dynamics are initially governed by temperature diffusion, but the RTI becomes increasingly important at late times. We discuss the possible application of these results to supernova remnants, solar prominences, and cold fronts in galaxy clusters.

arXiv comment18 pages, 15 figures, submitted to MNRAS

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• Cold Fronts: Probes of Plasma Astrophysics in Galaxy Clusters
• The Braginskii model of the Rayleigh-Taylor instability. I. Effects of self-generated magnetic fields and thermal conduction in two dimensions
• Relaxation by thermal conduction of a magnetically confined mountain on an accreting neutron star
• Enhancement of ablative Rayleigh-Taylor instability growth by thermal conduction suppression in a magnetic field
• Scaling of Small-Scale Dynamo Properties in the Rayleigh-Taylor Instability