Resistive relaxation of a magnetically confined mountain on an accreting neutron star

TL;DR

This study uses 3D MHD simulations to show that magnetically confined mountains on neutron stars relax resistively over hundreds of thousands to hundreds of millions of years, affecting gravitational wave emission.

Contribution

It provides the first detailed resistive relaxation timescale analysis of neutron star mountains using 3D MHD simulations, including nonaxisymmetric effects and oscillations.

Findings

Mountains relax gradually over 10^5 to 10^8 years.

No evidence of short-term non-ideal MHD instabilities.

Oscillations can decrease relaxation time by an order of magnitude.

Abstract

Three-dimensional numerical magnetohydrodynamic (MHD) simulations are performed to investigate how a magnetically confined mountain on an accreting neutron star relaxes resistively. No evidence is found for non-ideal MHD instabilities on a short time-scale, such as the resistive ballooning mode or the tearing mode. Instead, the mountain relaxes gradually as matter is transported across magnetic surfaces on the diffusion time-scale, which evaluates to $\tau_\mathrm{I} \sim 10^5 - 10^8$ yr (depending on the conductivity of the neutron star crust) for an accreted mass of $M_a = 1.2 \times 10^{-4} M_\odot$. The magnetic dipole moment simultaneously reemerges as the screening currents dissipate over $\tau_\mathrm{I}$. For nonaxisymmetric mountains, ohmic dissipation tends to restore axisymmetry by magnetic reconnection at a filamentary neutral sheet in the equatorial plane. Ideal-MHD oscillations on the Alfv\'{e}n time-scale, which can be excited by external influences, such as variations in the accretion torque, compress the magnetic field and hence decrease $\tau_\mathrm{I}$ by \change{one order of magnitude} relative to its standard value (as computed for the static configuration). The implications of long-lived mountains for gravitational wave emission from low-mass X-ray binaries are briefly explored.