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

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 Alfvén 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 Alfvén 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.

arXiv commentaccepted by MNRAS

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Cited by in corpus (3)

• Gravitational-wave constraints on the equatorial ellipticity of millisecond pulsars
• Gravitational radiation from magnetically funnelled supernova fallback onto a magnetar
• Relaxation by thermal conduction of a magnetically confined mountain on an accreting neutron star