Neutron-quark stars: Discerning viable alternatives for the higher-density part of the equation of state of compact stars

By taking into account the latest observations and theoretical constraints, we investigate the merger and post-merger of binary neutron stars (NSs) with numerical simulations employing hadronic and hybrid equations of state (EOSs). We name our hybrid stars Neutron-quark stars (NQS), because the transition from hadrons to quarks starts at a density lower than the central density of ~ 1 M_ stars. The two scenarios of transition to quark matter, a strong first-order phase transition (1PT) or a crossover, feature either a drop to almost zero or a rapid increase (peak) in the square of the sound speed cₛ², implying a softening or stiffening during the transition, respectively. Although the properties of NQSs in equilibrium may not be distinguishable from those of NSs, we find that the post-merger gravitational-wave (GW) main frequency f₂ for the crossover scenario is generally lower than that of hadronic models with the same tidal deformability, indicating that a crossover transition is in principle observable when both the inspiral and post-merger signals are detected. Since it is viable according to current multi-messenger constraints, we also consider an EOS with a 1PT taking place at 1.8 times the nuclear saturation density (n₀), with a stiff quark EOS (cₛ² = 2/3~c²) after the transition. It is the first time that such a binary merger is studied numerically in full general relativity. Although its f₂ is ~ 300 Hz higher than that of its baseline, the relation between f₂ and the tidal deformability of inspiralling stars is close to that for hadronic EOSs.