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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 &amp; Spies, 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 ω low . For equilibria with accreted mass  1.2 × 10 −6 ≲ M  a /M ⊙ ≲ 1.7 × 10 −4   and surface magnetic fields  10 11 ≲ B  * /G ≲ 10 13 , ω low   is approximately independent of   B  *  , and increases with  M  a . 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.

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