We identify an observable imprint of a first-order hadron-quark phase transition at supranuclear densities on the gravitational-wave (GW) emission of neutron-star mergers. Specifically, we show that the dominant postmerger GW frequency $f_{\mathrm{peak}}$ may exhibit a significant deviation from an empirical relation between $f_{\mathrm{peak}}$ and the tidal deformability if a strong first-order phase transition leads to the formation of a gravitationally stable extended quark matter core in the postmerger remnant. A comparison of the GW signatures from a large, representative sample of microphysical, purely hadronic equations of state indicates that this imprint is only observed in those systems which undergo a strong first-order phase transition. Such a shift of the dominant postmerger GW frequency can be revealed by future GW observations, which would provide evidence for the existence of a strong first-order phase transition in the interior of neutron-stars.

Using hydrodynamical simulations for a large set of high-density matter equations of state (EOSs), we systematically determine the threshold mass $M_{\text{thres}}$ for prompt black-hole formation in equal-mass and asymmetric neutron star (NS) mergers. We devise the so far most direct, general, and accurate method to determine the unknown maximum mass of nonrotating NSs from merger observations revealing $M_{\text{thres}}$. Considering hybrid EOSs with hadron-quark phase transition, we identify a new, observable signature of quark matter in NS mergers. Furthermore, our findings have direct applications in gravitational wave searches, kilonova interpretations, and multimessenger constraints on NS properties.

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 $f_{\mathrm{peak}}$ relative to the tidal deformability $\mathrm{\Lambda }$ 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 $f_{\mathrm{peak}}$ and $\mathrm{\Lambda }$, a strong PT can be excluded up to a certain density. We find tight correlations of $f_{\mathrm{peak}}$ and $\mathrm{\Lambda }$ 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.

A two-phase description of the quark–nuclear matter hybrid equation of state that takes into account the effect of excluded volume in both the hadronic and the quark-matter phases is introduced. The nuclear phase manifests a reduction of the available volume as density increases, leading to a stiffening of the matter. The quark-matter phase displays a reduction of the effective string tension in the confining density functional from available volume contributions. The nuclear equation of state is based upon the relativistic density-functional model DD2 with excluded volume. The quark-matter equation of state is based upon a quasiparticle model derived from a relativistic density-functional approach and will be discussed in greater detail. The interactions are decomposed into mean scalar and vector components. The scalar interaction is motivated by a string potential between quarks, whereas the vector interaction potential is motivated by higher-order interactions of quarks leading to an increased stiffening at high densities. As an application, we consider matter under compact star constraints of electric neutrality and $\beta$ equilibrium. We obtain mass-radius relations for hybrid stars that form a third family, disconnected from the purely hadronic star branch, and fulfill the $2M_{\odot }$ constraint.

We investigate the robustness of third family solutions for hybrid compact stars with a quark matter core that correspond to the occurrence of high-mass twin stars against a softening of the phase transition by means of a construction that mimics the effects of pasta structures in the mixed phase. We consider a class of hybrid equations of state that exploits a relativistic mean-field model for the hadronic as well as for the quark matter phase. We present parametrizations that correspond to branches of high-mass twin star pairs with maximum masses between $2.05M_{\odot }$ and $1.48M_{\odot }$ having radius differences between 3.2 and 1.5 km, respectively. When compared to a Maxwell construction with a fixed value of critical pressure $P_c$, the effect of the mixed phase construction consists in the occurrence of a region of pressures around $P_c$ belonging to the coexistence of hadronic and quark matter phases between the onset pressure at $P_H$ and the end of the transition at $P_Q$. The maximum broadening which would still allow mass-twin compact stars is found to be ${(P_Q-P_H)}_{\max }\approx P_c$ for all parametrizations within the present class of models. At least the heavier of the neutron stars of the binary merger GW170817 could have been a member of the third family of hybrid stars. We present the example of another class of hybrid star equations of state for which the appearance of the third family branch is not as robust against mixed phase effects as that of the present work.