Magnetohydrodynamic stability of magnetars in the ultrastrong field regime I: the core

Abstract

ABSTRACT We study magnetohydrodynamic stability of neutron star core matter composed of neutrons, protons, and leptons threaded by a magnetar-strength magnetic field 1014–1017 G, where quantum electrodynamical effects and Landau quantization of fermions are important. Stability is determined using the Friedman–Schutz formalism for the canonical energy of fluid perturbations, which we calculate for a magnetizable fluid with H ≠ B. Using this and the Euler–Heisenberg–Fermi–Dirac Lagrangian for a strongly magnetized fluid of Landau-quantized charged fermions, we calculate the local stability criteria for a neutron star core with a spherical axisymmetric geometry threaded by a toroidal field, accounting for magnetic and composition gradient buoyancy. We find that, for sufficiently strong fields B ≳ 1015 G, the magnetized fluid is unstable to a magnetosonic-type instability with growth times of the order of 10−3 s. The instability is triggered by sharp changes in the second-order field derivative of the Euler–Heisenberg–Fermi–Dirac Lagrangian that occur where additional Landau levels start being populated. These sharp changes are divergent at zero temperature, but are finite for non-zero temperature, so realistic neutron star core temperatures 5 × 107 K < T < 5 × 108 K are used. We conjecture that this mechanism could promote the formation of magnetic domains as predicted by Blandford and Hernquist and Suh and Mathews.