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 , 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 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 .