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, extended to include gravity, we solve the singular eigenvalue problem subject to line-tying boundary conditions. This spectrum divides into an Alfven 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(low). For equilibria with accreted mass 1.2 x 10(-6) less than or similar to M-a/M-circle dot less than or similar to 1.7 x 10(-4) and surface magnetic fields 10(11) less than or similar to B*/G <= 10(13), omega(low) is approximately independent of B*, and increases with M-a. The results are consistent with the Alfven spectrum excited in numerical simulations with the ZEUS-MPsolver. The spectrum is modified substantially by the Coriolis force in neutron stars spinning faster than similar to 100 Hz. The implications for gravitational-wave searches for low-mass X-ray binaries are considered briefly.