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

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 order 10−3 s. The instability is triggered by sharp changes in the second-order field derivative of the Euler–Heisenberg–Fermi–Dirac Lagrangian which occur where additional Landau levels start being populated. These sharp changes are divergent at zero temperature, but are finite for nonzero 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 (1982) and Suh and Mathews (2010).

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

“…The next logical step is to apply this formalism to the crust (Rau & Wasserman 2021), which due to lower densities and sound speeds may support similar instabilities as in the core even with lower field strengths. However, the stability analysis in the crust is fundamentally different due to the lack of a canonical energy procedure (Lyutikov 2013), so this is left to a follow-up paper.…”

“…We extend the nonrelativistic magnetohydrodynamic perturbation theory of Glampedakis & Andersson (2007) to 𝐵 = 𝐻 to allow us to consider the effect of the medium and vacuum magnetization on MHD stability. We also consider non-barotropic EOS, and employ a Brunt-Väisälä frequency accounting for both neutron-proton fraction buoyancy (Reisenegger & Goldreich 1992) and leptonic buoyancy (Kantor & Gusakov 2014;Passamonti et al 2016;Yu & Weinberg 2017;Rau & Wasserman 2018), in contrast to e.g. Akgün et al (2013), who only included the neutron-proton fraction buoyancy in their analysis and were considering the global instability of specific axisymmetric fields.…”

Magnetohydrodynamic stability of magnetars in the ultrastrong field regime II: The crust

“…In Rau & Wasserman (2021) (henceforth Paper I), we studied MHD stability in ultrastrong magnetic fields relevant to magnetar cores using ideal MHD and a canonical energy principle (Friedman & Schutz 1978;Glampedakis & Andersson 2007). We included the magnetic field-dependence of the internal energy due to Landau quantization of fermions, showing how this can lead to a fast-growing, but spatially limited, instability.…”