Time Evolution and Stellar Impacts of a Fermionic Asymmetric Dark Matter Admixture in Non-rotating Neutron Stars

In this work, we study the accumulation of asymmetric fermionic dark matter inside a cold, non-rotating neutron star. Using a three-layer neutron-star model with the polytropic equation of state p = K_iρ_i(r)^Γ_i, together with the two-fluid Tolman–Oppenheimer–Volkoff equations, we derive the coupled structure and state functions of dark-matter-admixed neutron stars. For the capture scenario, we discuss the inter-relations among parameters that determine the capture rate and explore the most aggressive parameter combinations that maximize dark-matter accumulation. By matching the capture rate with the total number of accumulated particles, we track the evolution of the dark-matter mass and its distribution radius. Even under such extreme conditions, the resulting accumulation produces negligible effects on stellar properties over a Hubble time, implying that the admixture is unlikely to leave observable imprints. In contrast, if neutron decay into dark matter is allowed, a dark core may grow to ~15% of the total stellar mass, leading to observable modifications of the stellar structure. For both capture and decay scenarios, we find that the presence of a dark-matter component increases the compactness and reduces the tidal deformability of neutron stars, driving binary systems to evolve toward more asymmetric mass ratios over time. We also examine how these effects influence the inspiral and post-merger dynamics, including the reduction of ejecta mass and potential changes in kilonova emission. We are further exploring the temporal evolution of this decay-induced component and the dynamical distinctions between dark-matter-admixed and purely baryonic neutron stars.