Anisotropic Neutron Star W-mode

Typically, pressure inside a neutron star is assumed to be isotropic. However, pressure anisotropy, the difference in pressure between the radial and tangential directions, may arise from strong magnetic fields, viscosity, and elasticity. Neutron-star quasi-normal modes are oscillations with significant damping over time. These modes are classified according to their restoring force. Previous studies showed that pressure modes (p-modes) can become unstable when the neutron star becomes anisotropic. This drove us to study the behaviour of another mode, the w-mode, in anisotropic neutron stars. W-modes are driven mostly by spacetime oscillations with only minor matter perturbations. In this talk, I report the first ever calculation of anisotropic w-modes. Unlike p-modes, we found w-modes to be stable for multiple equation of states in the presence of pressure anisotropy. We have also discovered an equation-of-state-independent relation for w-mode frequency that may potentially help with probing the neutron-star interior without knowing its exact equation of state. This numerical stability finding is further supported by a semi-analytic analysis that ensures stability beyond the scope of the numerical work. We have also found that an approximation scheme that is known to work well for isotropic neutron stars w-modes ceases to be valid when pressure anisotropy is introduced.