Emergence of new oscillation modes in dark matter admixed neutron stars

Dark matter admixed neutron stars provide a promising avenue for observationally probing the dark matter characteristic. In this study, we examine non-radial oscillations in neutron stars containing self-interacting dark matter, which interacts with normal matter exclusively via gravity. To achieve this, we derive a new set of perturbation equations for a multi-fluid system under the Cowling approximation. Using these equations, we analyze the oscillation spectra and identify additional modes associated with dark matter, alongside those of normal matter. We find that the frequency behavior becomes more intricate with increasing self-coupling strength of dark matter, particularly as the stellar structure transitions between dark core and dark halo configurations, depending on the total stellar mass. Nevertheless, we find that in the dark core structure, the fundamental ($f$) mode frequencies associated with dark matter exceed those of normal matter, at least when the central energy densities of both fluids are equal. Furthermore, we find that the $f$-mode frequencies associated with normal matter in dark core configurations adhere to a universal relation between the mass-scaled frequency and stellar compactness.