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

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