  We study the impact of asymmetric bosonic dark matter on neutron star
properties, including possible changes of tidal deformability, maximum mass,
radius, and matter distribution inside the star. The conditions at which dark
matter particles tend to condensate in the star's core or create an extended
halo are presented. We show that dark matter condensed in a core leads to a
decrease of the total gravitational mass and tidal deformability compared to a
pure baryonic star, which we will perceive as an effective softening of the
equation of state. On the other hand, the presence of a dark matter halo
increases those observable quantities. Thus, observational data on compact
stars could be affected by accumulated dark matter and, consequently,
constraints we put on strongly interacting matter at high densities. To confirm
the presence of dark matter in the compact star's interior, and to break the
degeneracy between the effect of accumulated dark matter and strongly
interacting matter properties at high densities, several astrophysical and GW
tests are proposed.
