Couplings of torsional and shear oscillations in a neutron star crust

Abstract

Mature neutron stars are thought to be sufficiently cold that nuclei in the outer layers freeze, solidifying a crust. Crustal elasticity allows the star to support a set of seismic modes, such as torsional oscillations. These axial-parity modes can couple to the polar sector in a number of ways, for example via rotation or a magnetic field. Even in a static, spherically-symmetric star however these modes can couple at non-linear order. In this study, such couplings in the crust are examined for the first time: we derive the axisymmetric perturbation equations for second-order axial eigenfunctions, which are sourced by axial-polar couplings at first-order, and solve the resulting equations in the time domain. Through our studies, we find that the second-order spectrum contains additional oscillation modes, not predicted by the linear analysis with either axial or polar perturbations, which can be excited to relatively large amplitudes.