Hydrodynamic Stability Analysis of the Neutron Star Core

TL;DR

This paper investigates the stability of neutron star cores, showing that magnetic fields stabilize certain instabilities but not others, with implications for neutron star spin behavior and precession.

Contribution

It provides a detailed analysis of hydrodynamic instabilities in neutron star cores, highlighting the stabilizing role of magnetic fields on two-stream instabilities.

Findings

Toroidal magnetic fields stabilize two-stream instabilities at high field strengths.

Steady spin-down of neutron stars is stable against these instabilities.

Donnelly–Glaberson instability remains unstabilized and may influence precession.

Abstract

Hydrodynamic instabilities and turbulence in neutron stars have been suggested to be related to observable spin variations in pulsars, such as spin glitches, timing noise, and precession (nutation). Accounting for the stabilizing effects of the stellar magnetic field, we revisit the issue of whether the inertial modes of a neutron star can become unstable when the neutron and proton condensates flow with respect to one another. The neutron and proton condensates are coupled through the motion of imperfectly pinned vorticity (vortex slippage) and vortex-mediated scattering (mutual friction). Two-stream instabilities that occur when the two condensates rotate with respect to one another in the outer core are stabilized by the toroidal component of the magnetic field. This stabilization occurs when the Alfv\'en speed of the toroidal component of the magnetic field becomes larger than the relative rotational velocity of the condensates, corresponding to toroidal field strengths in excess of $\simeq 10^{10}\,{\rm G}$. In contrast with previous studies, we find that spin down of a neutron star under a steady torque is stable. The Donnelly--Glaberson instability is not stabilized by the magnetic field, and could play an important role if neutron stars undergo precession.