The Second Love Number of Dark Compact Planets and Neutron Stars with Dark Matter

We study the mass-radius relation and the second Love number of compact objects made of ordinary matter and non-selfannihilating fermionic dark matter for a wide range of dark matter particle masses, and for the cases of weakly and strongly interacting dark matter. We obtain stable configurations of compact objects with radii smaller than 10 km and masses similar to Earth- or Jupiter-like stellar objects. In certain parameter ranges we find second Love numbers which are markedly different compared to those expected for neutron stars without dark matter. Thus, by obtaining the compactness of these compact objects and measuring their tidal deformability from gravitational wave detections from binary neutron star mergers, the extracted value of second Love number would allow to determine the existence of dark matter inside neutron stars irrespective of the equation of state of ordinary matter.