2018MNRAS.476.3399L

We calculate axisymmetric magnetic modes of a neutron star possessing a mixed poloidal and toroidal magnetic field, where the toroidal field is assumed to be proportional to a dimensionless parameter ζ₀. Here, we assume an isentropic structure for the neutron star and consider no effects of rotation. Ignoring the equilibrium deformation due to the magnetic field, we employ a polytrope of the index n = 1 as the background model for our modal analyses. For the mixed poloidal and toroidal magnetic field with ζ_0≠0, axisymmetric spheroidal and toroidal modes are coupled. We compute axisymmetric spheroidal and toroidal magnetic modes as a function of the parameter ζ₀ from 0 to ∼1 for the surface field strengths B_S = 10¹⁴ G and 10¹⁵ G. We find that the frequency ω of the magnetic modes decreases with increasing ζ₀. We also find that the frequency of the spheroidal magnetic modes is almost exactly proportional to B_S for ζ₀ <= 1 but that this proportionality holds only when ζ₀ ≪ 1 for the toroidal magnetic modes. The wave patterns of the spheroidal magnetic modes and toroidal magnetic modes are not strongly affected by the coupling so long as ζ₀ <= 1. We find no unstable modes having ω² < 0.