Two fluid CFL strange quark stars with scalar dark matter: critical mass and mass gap implications

Abstract

We investigate the structure of strange quark stars (SQSs) in the color--flavor--locked (CFL) phase in the presence of scalar bosonic dark matter within a two--fluid formalism employing perturbative QCD. By considering different dark matter masses and varying the pairing gap $\Delta$ and {the central dark matter pressure fraction} $f_r$, we analyze the impact of dark matter on the structural properties of SQSs, including the maximum gravitational mass $M_{\mathrm{TOV}}$, the ratio of dark matter to strange-quark-matter radii $R_{\mathrm{DM}}/R_{\mathrm{SQM}}$, and the dimensionless tidal deformability $\Lambda$. We further examine the compatibility of the resulting mass--radius relations with the recent NICER measurements of compact stars. Within the parameter space considered in this study, we find that $M_{\mathrm{TOV}}$ exhibits a non-monotonic dependence on the dark matter mass, with a critical value beyond which $M_{\mathrm{TOV}}$ decreases. We also show that some pure CFL strange quark star configurations, particularly those associated with very stiff EOSs and larger maximum masses, may not simultaneously remain compatible with the $\Lambda$ range inferred from GW170817 while occupying the lower mass--gap region. In contrast, the inclusion of dark matter allows two-fluid CFL strange quark star configurations to reproduce the observed properties of massive compact objects in the lower mass--gap region, such as the secondary component of GW190814, while remaining qualitatively compatible with the $\Lambda$ range inferred from GW170817. We note, however, that the GW170817 constraints were originally inferred within single-fluid compact-star frameworks and therefore provide only {qualitative guidance} for the present two-fluid halo configurations. Our results suggest that exotic compact-star configurations may populate part of the conventionally defined lower mass--gap region.