We propose three scenarios for compact hybrid stars consisting of nuclear and dark matters which could possibly serve as alternative interpretations to the LIGO/Virgo events GW170817 and GW190425. To demonstrate our proposal, we adopt the SLy4 equation of state (EoS) for nuclear matter, and an EoS for a bosonic self-interacting dark matter (SIDM), which is simple and capable of yielding both reasonable halo density and compact stars. We study the mass-radius and tidal Love number (TLN)-mass relations for these compact hybrid stars, and also generalize the Bardeen-Thorne-Meltzer (BTM) criteria to discuss in details the possible saddle instability due to the nature of two-fluid model. Our results show that it is possible for our hybrid star scenarios to explain GW170817 and GW190425. Some of the hybrid stars can have compact neutron or mixed cores around 10km while possessing thick dark matter shells, which can then explain the astrophysical observations of neutron stars with compact photon radius and mass higher than 2 solar masses. Reversely, we also infer the dark matter model from the parameter estimation of GW190425. Our scenarios of compact hybrid stars can be further tested by the coming LIGO/Virgo O3 events.
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