Constraining the onset density of the hadron-quark phase transition with gravitational-wave observations

We study the possible occurrence of the hadron-quark phase transition (PT) during the merging of neutron star binaries by hydrodynamical simulations employing a set of temperature-dependent hybrid equations of state (EOSs). Following previous work, we describe an unambiguous and measurable signature of deconfined quark matter in the gravitational-wave (GW) signal of neutron star binary mergers including equal-mass and unequal-mass systems of different total binary mass. The softening of the EOS by the PT at higher densities, i.e., after merging, leads to a characteristic increase of the dominant postmerger GW frequency f(peak) relative to the tidal deformability A inferred during the premerger inspiral phase. Hence, measuring such an increase of the postmerger frequency provides evidence for the presence of a strong PT. If the postmerger frequency and the tidal deformability are compatible with results from purely baryonic EOS models yielding very tight relations between f(peak) and A, a strong PT can be excluded up to a certain density. We find tight correlations of f(peak) and A with the maximum density during the early postmerger remnant evolution. These GW observables thus inform about the density regime which is probed by the remnant and its GW emission. Exploiting such relations, we devise a directly applicable, concrete procedure to constrain the onset density of the QCD PT from future GW measurements. We point out two interesting scenarios: if no indications for a PT are inferred from a GW detection, our procedure yields a lower limit on the onset density of the hadron-quark PT. On the contrary, if a merger event reveals evidence for the occurrence of deconfined quark matter, the inferred GW parameters set an upper limit on the PT onset density. Both scenarios would thus have strong implications for high-density matter physics, e.g., determining the range of validity of nuclear physics and constraining the properties for quark deconfinement. These prospects demonstrate the importance of simultaneously measuring pre- and postmerger GW signals to exploit the complementarity of the information encoded in both phases. Hence, our work stresses the value added by dedicated high-frequency GW instruments.