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

We study magnetohydrodynamic stability of neutron star core matter composed of neutrons, protons, and leptons threaded by a magnetar-strength magnetic field 10(14)-10(17) 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 not equal 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 greater than or similar to 10(15) 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 x 10(7) K < T < 5 x 10(8) 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.