The r-modes in accreting neutron stars with magneto-viscous boundary layers

TL;DR

This paper investigates how magneto-viscous boundary layers influence r-mode damping in accreting neutron stars, considering both normal and superfluid core models, and examines their impact on star spin evolution and gravitational wave emission.

Contribution

It introduces a detailed analysis of magneto-viscous boundary layer effects on r-modes in superfluid and normal neutron star cores, including the impact of vortex pinning and magnetic fields.

Findings

Superfluid models with both vortex species pinned lack solutions; partial pinning yields solutions.

Weak magnetic fields significantly influence the boundary layer in superfluid cores.

Magnetic fields and r-mode saturation affect neutron star spin cycles and gravitational wave emission.

Abstract

We explore the dynamics of the r-modes in accreting neutron stars in two ways. First, we explore how dissipation in the magneto-viscous boundary layer (MVBL) at the crust-core interface governs the damping of r-mode perturbations in the fluid interior. Two models are considered: one assuming an ordinary-fluid interior, the other taking the core to consist of superfluid neutrons, type II superconducting protons, and normal electrons. We show, within our approximations, that no solution to the magnetohydrodynamic equations exists in the superfluid model when both the neutron and proton vortices are pinned. However, if just one species of vortex is pinned, we can find solutions. When the neutron vortices are pinned and the proton vortices are unpinned there is much more dissipation than in the ordinary-fluid model, unless the pinning is weak. When the proton vortices are pinned and the neutron vortices are unpinned the dissipation is comparable or slightly less than that for the ordinary-fluid model, even when the pinning is strong. We also find in the superfluid model that relatively weak radial magnetic fields ~ 10^9 G (10^8 K / T)^2 greatly affect the MVBL, though the effects of mutual friction tend to counteract the magnetic effects. Second, we evolve our two models in time, accounting for accretion, and explore how the magnetic field strength, the r-mode saturation amplitude, and the accretion rate affect the cyclic evolution of these stars. If the r-modes control the spin cycles of accreting neutron stars we find that magnetic fields can affect the clustering of the spin frequencies of low mass x-ray binaries (LMXBs) and the fraction of these that are currently emitting gravitational waves.