Non-axisymmetric low-frequency oscillations of rotating and magnetized neutron stars

We investigate non-axisymmetric low-frequency modes of a rotating and magnetized neutron star, assuming that the star is threaded by a dipole magnetic field whose strength at the stellar surface, B₀, is less than G, and whose magnetic axis is aligned with the rotation axis. For modal analysis, we use a neutron star model composed of a fluid ocean, a solid crust and a fluid core, where we treat the core as being non-magnetic assuming that the magnetic pressure is much smaller than the gas pressure in the core. For non-axisymmetric modes, spheroidal modes and toroidal modes are coupled in the presence of a magnetic field even for a non-rotating star. Here, we are interested in low-frequency modes of a rotating and magnetized neutron star whose oscillation frequencies are similar to those of toroidal crust modes of low spherical harmonic degree and low radial order. For a magnetic field of G, we find Alfvén waves in the ocean have similar frequencies to the toroidal crust modes, and we find no r modes confined in the ocean for this strength of the field. We calculate the toroidal crustal modes, the interfacial modes peaking at the crust/core interface and the core inertial modes and r modes, and all these modes are found to be insensitive to the magnetic field of strength G. We find the displacement vector of the core r modes have large amplitudes around the rotation axis at the stellar surface even in the presence of a surface magnetic field G, where and m are the spherical harmonic degree and the azimuthal wavenumber of the r modes, respectively. We suggest that millisecond X-ray variations of accretion-powered X-ray millisecond pulsars can be used as a probe into the core r modes destabilized by gravitational wave radiation. If the r mode is excited, we will have the pulsation of the frequency with being the spin frequency of the star.