Continuous frequency spectrum of the global hydromagnetic oscillations of a magnetically confined mountain on an accreting neutron star

TL;DR

This paper calculates the continuous frequency spectrum of magnetohydrodynamic oscillations in a magnetically confined mountain on an accreting neutron star, revealing how the spectrum depends on accreted mass and magnetic field, with implications for gravitational wave detection.

Contribution

It extends the formalism for ideal-MHD spectra to include gravity and applies it to neutron star mountains, providing detailed eigenfrequency spectra and their dependence on physical parameters.

Findings

Spectrum divides into Alfvén and cusp parts.

Eigenfrequencies cover the entire spectrum above a minimum.

Spectrum is significantly affected by the Coriolis force in fast-spinning neutron stars.

Abstract

We compute the continuous part of the ideal-magnetohydrodynamic (ideal-MHD) frequency spectrum of a polar mountain produced by magnetic burial on an accreting neutron star. Applying the formalism developed by Hellsten & Spies (1979), extended to include gravity, we solve the singular eigenvalue problem subject to line-tying boundary conditions. This spectrum divides into an Alfv\'{e}n part and a cusp part. The eigenfunctions are chirped and anharmonic with an exponential envelope, and the eigenfrequencies cover the whole spectrum above a minimum $\omega_\mathrm{low}$. For equilibria with accreted mass $1.2 \times 10^{-6} \la M_a/M_\odot \la 1.7 \times 10^{-4}$ and surface magnetic fields $10^{11} \la B_\ast/\mathrm{G} \la 10^{13}$, $\omega_\mathrm{low}$ is approximately independent of $B_\ast$, and increases with $M_a$. The results are consistent with the Alfv\'{e}n spectrum excited in numerical simulations with the \textsc{zeus-mp} solver. The spectrum is modified substantially by the Coriolis force in neutron stars spinning faster than $\sim 100$ Hz. The implications for gravitational wave searches for low-mass X-ray binaries are considered briefly.