Neutron-quark Stars: Discerning Viable Alternatives for the Higher-density Part of the Equation of State of Compact Stars

Abstract We investigate binary neutron star (BNS) mergers using general-relativistic numerical simulations with hadronic and hybrid equations of state (EOSs), incorporating the latest observations and theoretical constraints. We address two viable scenarios for the transition to quark matter: a quark-hadron crossover (QHC) or a strong first-order phase transition (1PT). To distinguish between different models, we define neutron-quark stars (NQSs) as configurations where quark effects emerge at masses below the lowest observed neutron-star mass. While traditional “hybrid stars” may be distinguished by purely hadronic configurations through mass–radius measurements, the mass–radius relations of NQSs resemble those of purely hadronic models, with no sharp boundary between hadrons and quarks. The name NQS effectively captures the absence of a phase boundary between hadrons and quarks in QHC scenarios. Our results indicate that QHC models can be distinguished from hadronic ones if both the inspiral and postmerger gravitational waves (GWs) are observed. In particular, the dominant postmerger frequency ( f 2 ) tends to be lower than in hadronic models with the same tidal deformability (Λ). We also present the first general-relativistic simulations of BNS mergers where the stars already contain quark matter before merging. These involve a strong 1PT at 1.8 times nuclear saturation density, followed by a stiff quark EOS. Finally, we identify a robust linear correlation between the total GW energy emitted after the merger and the f 2 frequency. Remarkably, this relation holds regardless of the quark presence.