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

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 ωlow. For equilibria with accreted mass 1.2 × 10 . Ma/M⊙ . 1.7 × 10 −4 and surface magnetic fields 10 . B∗/G . 10 , ωlow is approximately independent of B∗, and increases with Ma. The results are consistent with the Alfvén spectrum excited in numerical simulations with the zeus-mp solver. The spectrum is modified substantially by the Coriolis force in neutron stars spinning faster than ∼ 100 Hz. The implications for gravitational wave searches for low-mass X-ray binaries are considered briefly.