We investigate nuclear matter at a finite temperature and density, including the formation of light clusters up to the $\alpha${} particle (1$\leqslant${}A$\leqslant${}4). The novel feature of this work is to include the formation of clusters as well as their dissolution due to medium effects in a systematic way using two many-body theories: a microscopic quantum statistical (QS) approach and a generalized relativistic mean-field (RMF) model. Nucleons and clusters are modified by medium effects. While the nucleon quasiparticle properties are determined within the RMF model from the scalar and vector self-energies, the cluster binding energies are reduced because of Pauli blocking shifts calculated in the QS approach. Both approaches reproduce the limiting cases of nuclear statistical equilibrium (NSE) at low densities and cluster-free nuclear matter at high densities. The treatment of the cluster dissociation is based on the Mott effect due to Pauli blocking, implemented in slightly different ways in the QS and the generalized RMF approaches. This leads to somewhat different results in the intermediate density range of about 10-3 to 10-1$\hskip0.3em${}fm-3, which gives an estimate of the present accuracy of the theoretical predictions. We compare the numerical results of these models for cluster abundances and thermodynamics in the region of medium excitation energies with temperatures T$\leqslant${}20\,MeV and baryon number densities from zero to a few times saturation density. The effects of cluster formation on the liquid-gas phase transition and on the density dependence of the symmetry energy are studied. It is demonstrated that the parabolic approximation for the asymmetry dependence of the nuclear equation of state breaks down at low temperatures and at subsaturation densities because of cluster formation. Comparison is made with other theoretical approaches, in particular, those that are commonly used in astrophysical calculations. The results are relevant for heavy-ion collisions and astrophysical applications.

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.

A new scheme for testing nuclear matter equations of state (EoSs) at high densities using constraints from neutron star (NS) phenomenology and a flow data analysis of heavy-ion collisions is suggested. An acceptable EoS shall not allow the direct Urca process to occur in NSs with masses below $1.5M_{\odot }$, and also shall not contradict flow and kaon production data of heavy-ion collisions. Compact star constraints include the mass measurements of $2.1\pm 0.2M_{\odot }$ ($1\sigma$ level) for PSR J0751+1807 and of $2.0\pm 0.1M_{\odot }$ from the innermost stable circular orbit for 4U 1636–536, the baryon mass—gravitational mass relationships from Pulsar B in J0737–3039 and the mass-radius relationships from quasiperiodic brightness oscillations in 4U 0614+09 and from the thermal emission of RX J1856–3754. This scheme is applied to a set of relativistic EoSs which are constrained otherwise from nuclear matter saturation properties. We demonstrate on the given examples that the test scheme due to the quality of the newly emerging astrophysical data leads to useful selection criteria for the high-density behavior of nuclear EoSs.

Gravitational wave observations of GW170817 placed bounds on the tidal deformabilities of compact stars, allowing one to probe equations of state for matter at supranuclear densities. Here we design new parametrizations for hybrid hadron-quark equations of state, which give rise to low-mass twin stars, and test them against GW170817. We find that GW170817 is consistent with the coalescence of a binary hybrid star-neutron star. We also test and find that the I-Love-Q relations for hybrid stars in the third family agree with those for purely hadronic and quark stars within $\sim 3\%$ for both slowly and rapidly rotating configurations, implying that these relations can be used to perform equation-of-state independent tests of general relativity and to break degeneracies in gravitational waveforms for hybrid stars in the third family as well.

Aims. We present a new microscopic hadron-quark hybrid equation of state model for astrophysical applications, from which compact hybrid star configurations are constructed. These are composed of a quark core and a hadronic shell with a first-order phase transition at their interface. The resulting mass-radius relations are in accordance with the latest astrophysical constraints.Methods. The quark matter description is based on a quantum chromodynamics (QCD) motivated chiral approach with higher-order quark interactions in the Dirac scalar and vector coupling channels. For hadronic matter we select a relativistic mean-field equation of state with density-dependent couplings. Since the nucleons are treated in the quasi-particle framework, an excluded volume correction has been included for the nuclear equation of state at suprasaturation density which takes into account the finite size of the nucleons.Results. These novel aspects, excluded volume in the hadronic phase and the higher-order repulsive interactions in the quark phase, lead to a strong first-order phase transition with large latent heat, i.e. the energy-density jump at the phase transition, which fulfils a criterion for a disconnected third-family branch of compact stars in the mass-radius relationship. These twin stars appear at high masses (~2 M ⊙) that are relevant for current observations of high-mass pulsars.Conclusions. This analysis offers a unique possibility by radius observations of compact stars to probe the QCD phase diagram at zero temperature and large chemical potential and even to support the existence of a critical point in the QCD phase diagram.