Dark Matter Admixed Quark Stars: A Relativistic Two-Fluid Approach

Abstract

In this paper, we examine the stellar properties of quark stars containing dark matter, focusing on both non-rotating and slowly rotating configurations. By employing a two-fluid framework, we formulate the generalized Tolman--Oppenheimer--Volkoff equations, treating dark matter and ordinary matter as independent perfect fluids that interact solely through gravitational forces. We model ordinary matter using the color-flavor-locked and the MIT bag model equation of state, while for dark matter, we apply a self-interacting bosonic condensate along with fermionic equation of state. By considering a dark matter fraction of $f_\x=5\%$ and varying the bag constant for ordinary matter, we investigate how dark matter accumulation affects global stellar features such as maximum gravitational mass, radius, and dimensionless tidal deformability. Further, we extend our analysis to first-order rotational effects, calculating the frame-dragging equation and the influence of moments of inertia on the two-fluid system. We also explore universal relations, particularly the connection between rotation and tidal effects, to understand how the inclusion of dark matter affects the relationship between rotational and the tidal deformability. Our findings indicate that a dark matter fraction of $f_\x=5\%$ can lead to notable deviations from the traditional single-fluid quark star characteristics in stellar radius, gravitational mass and tidal deformability. Moreover, the response to rotational and tidal forces remains consistent even in the inclusion of the dark matter component. Finally, we compare our theoretical results with current observational data from GW events and the NICER mission, thereby demonstrating that our developed two-fluid models are consistent with these observations.