Axial Quasi-normal Modes of Admixed Neutron Stars

Abstract

We study axial quasi-normal modes of admixed neutron stars composed of ordinary nuclear matter and a self-interacting bosonic dark matter component. The equilibrium configurations are obtained by solving the coupled two-fluid Tolman-Oppenheimer-Volkoff equations, where the neutron sector is modeled with several realistic equations of state and the bosonic sector is described by a repulsively self-interacting complex scalar field in the strong-coupling regime. We analyze linear axial perturbations governed by a Regge-Wheeler type equation whose effective potential reflects the combined matter distribution. Using a continued-fraction method, we compute the complex eigenfrequencies of the fundamental and overtone $w$ modes. We obtain the quasi-normal mode spectrum and investigate its dependence on the dark matter particle mass, self-coupling, and the central densities of both fluids for several realistic neutron star equations of state. We find that increasing the dark matter fraction shifts the oscillation frequencies and damping times. It can also reorder the mode hierarchy through crossings, and it drives a continuous transition from neutron star-like to boson star-like ringdown behavior. Our results demonstrate that the ringdown gravitational-wave signal from post-merger compact objects could encode clear imprints of a dark matter component, offering a new probe of the dark sector with future gravitational-wave observatories.