Buoyancy Instabilities in Degenerate, Collisional, Magnetized Plasmas

TL;DR

This paper investigates buoyancy instabilities in degenerate, collisional, magnetized plasmas, revealing that such plasmas are inherently convectively unstable regardless of temperature gradient sign, with implications for astrophysical objects like white dwarfs and neutron stars.

Contribution

It demonstrates that collisional degenerate plasmas exhibit buoyancy instabilities independent of magnetic field strength and temperature gradient, extending understanding of plasma stability in astrophysical contexts.

Findings

Instability range is independent of magnetic field strength.

Growth time increases as magnetic field decreases.

Instabilities are relevant in white dwarf and neutron star environments.

Abstract

In low-collisionality plasmas, anisotropic heat conduction due to a magnetic field leads to buoyancy instabilities for any nonzero temperature gradient. We study analogous instabilities in degenerate {\it collisional} plasmas, i.e., when the electron collision frequency is large compared to the electron cyclotron frequency. Although heat conduction is nearly isotropic in this limit, the small residual anisotropy ensures that collisional degenerate plasmas are also convectively unstable independent of the sign of the temperature gradient. We show that the range of wavelengths that are unstable is independent of the magnetic field strength, while the growth time increases with decreasing magnetic field strength. We discuss the application of these collisional buoyancy instabilities to white dwarfs and neutron stars. Magnetic tension and the low specific heat of a degenerate plasma significantly limit their effectiveness; the most promising venues for growth are in the liquid oceans of young, weakly magnetized neutron stars ($B \lesssim 10^9$ G) and in the cores of young, high magnetic field white dwarfs ($B \sim 10^9$ G).