Core-crust interaction of toroidal modes of magnetized neutron stars

We calculate axisymmetric toroidal modes of magnetized neutron stars with a solid crust. We assume the interior of the star is threaded by a poloidal magnetic field that is continuous at the surface with the outside dipole field whose strength B_p at the magnetic pole is B_p ∼ 10 ¹⁶G. Since separation of variables is not possible for oscillations of magnetized stars, to represent the angular dependence of the oscillation modes we employ finite series expansions in terms of spherical harmonic functions. For B_p ∼ 10¹⁶G, we find isolated sequences of low radial order toroidal modes, whose oscillation frequency slowly increases as the number of radial nodes of the eigenfunction increases. The frequency spectrum of toroidal modes for B_p ∼ 10¹⁶G is largely different from that of crustal toroidal modes of the non-magnetized model.