Two-fluid $f$-mode oscillations of dark-matter-admixed neutron stars
We study quadrupolar $f$-mode oscillations of dark-matter-admixed neutron stars (DANSs) in full general relativity (GR). The ordinary component is described by microscopic Brueckner-Hartree-Fock matter matched to the Shen2020 crust, while the dark matter (DM) component is treated as a cold self-interacting fermion fluid coupled to ordinary matter only by gravity. For fixed-DM-fraction sequences we solve the polar two-fluid perturbation equations with an outgoing gravitational-wave (GW) boundary condition, obtaining complex eigenfrequencies rather than only real mode frequencies. The spectrum contains two principal $f$-like sequences. Their local character can be ordinary-matter-led, DM-led, or mixed, and is diagnosed using the component kinetic energies, the displacement overlap, and the cancellation of the matter quadrupole. A main result is that, for intermediate DM fractions, one of the two-fluid branches can become weakly radiating, with damping times enhanced by several orders of magnitude. The same calculation gives the outgoing Zerilli amplitude and the GW damping time, which we use to estimate the GW energy required to reach a prescribed detector threshold. Thus the analysis extends previous two-fluid Cowling studies by retaining metric perturbations and the radiative boundary condition.