SIMBAD references

We propose a model of asymmetric bosonic dark matter (DM) with self-repulsion. By adopting the two-fluid formalism, we study different DM distribution regimes, either, fully condensed inside the core of a star, or, otherwise, distributed in a dilute halo around a neutron star (NS). We show that for a given total gravitational mass, DM condensed in a core leads to a smaller radius and tidal deformability compared to a pure baryonic star. This effect may be interpreted as an effective softening of the equation of state. On the other hand, the presence of a DM halo increases the tidal deformability and total gravitational mass. As a result, an accumulated DM inside compact stars could mimic an apparent softening/stiffening of strongly interacting matter EoS and constraints we impose on it at high densities. We limit the model parameter space by confronting the cross section of the DM self-interaction to the constraint extracted from the analysis of the Bullet Cluster. Furthermore, from the analysis of the effect of DM particles, interaction strength, and relative DM fractions inside NSs we obtained a rigorous constraint on model parameters. To identify its impact on NSs we consider the DM fraction may reach up to 5%, which could be considered too high in several scenarios. Finally, we discuss several pieces of smoking gun evidence of the presence of DM that is free from the abovementioned degeneracy between the effect of DM and properties of strongly interacting matter. These signals could be probed with future and ongoing astrophysical and gravitational wave surveys.