The thermodynamic properties of high temperature and high density QCD matter are explored within the chiral SU(3)-flavor parity-doublet Polyakov-loop quark-hadron mean-field model, CMF. The quark sector of the CMF model is tuned to describe the ${\mu }_B=0$ thermodynamics data of lattice QCD. The resulting lines of constant physical variables as well as the baryon number susceptibilities are studied in some detail in the temperature–chemical-potential plane. The CMF model predicts three consecutive transitions: the nuclear first-order liquid-vapor phase transition, chiral symmetry restoration, and the crossover transition to a quark matter phase. All three phenomena are crossovers, for most of the $T\text{−}{\mu }_B$ plane. The deviations from the free ideal hadron gas baseline at ${\mu }_B=0$ and $T\approx 100\text{–}200$ MeV can be attributed to remnants of the liquid-vapor first-order phase transition in nuclear matter. The chiral crossing transition determines the baryon fluctuations at much higher ${\mu }_B\approx 1.5$ GeV. At high baryon densities, ${\mu }_B\approx 2.4$ GeV, the behavior of fluctuations is controlled by crossover to quark matter. The CMF model also describe well the static properties of high ${\mu }_B$ neutron stars as well as recent neutron star merger observations. The effective equation of state presented here describes simultaneously lattice QCD results at ${\mu }_B=0$ as well as observed physical phenomena (nuclear matter and neutron star matter) at $T\cong 0$ and high densities, ${\mu }_B>1$ GeV.

Gravitational waves, electromagnetic radiation, and the emission of high energy particles probe the phase structure of the equation of state of dense matter produced at the crossroad of the closely related relativistic collisions of heavy ions and of binary neutron stars mergers. 3 + 1 dimensional special- and general relativistic hydrodynamic simulation studies reveal a unique window of opportunity to observe phase transitions in compressed baryon matter by laboratory based experiments and by astrophysical multimessenger observations. The astrophysical consequences of a hadron-quark phase transition in the interior of a compact star will be focused within this article. Especially with a future detection of the post-merger gravitational wave emission emanated from a binary neutron star merger event, it would be possible to explore the phase structure of quantum chromodynamics. The astrophysical observables of a hadron-quark phase transition in a single compact star system and binary hybrid star merger scenario will be summarized within this article. The FAIR facility at GSI Helmholtzzentrum allows one to study the universe in the laboratory, and several astrophysical signatures of the quark-gluon plasma have been found in relativistic collisions of heavy ions and will be explored in future experiments.

Binary neutron-star mergers and heavy-ion collisions are related through the properties of the hot and dense nuclear matter formed during these extreme events. In particular, low-energy heavy-ion collisions offer exciting prospects to recreate such extreme conditions in the laboratory. However, it remains unexplored to what degree those collisions can actually reproduce hot and dense matter formed in binary neutron star mergers. As a way to understand similarities and differences between these systems, we discuss their geometry and perform a direct numerical comparison of the thermodynamic conditions probed in both collisions. To enable a direct comparison, we employ a finite-temperature equation of state able to describe the entire high-energy phase diagram of quantum chromodynamics. Putting side by side the evolution of both systems, we find that laboratory heavy-ion collisions at the energy range of $E_{\mathrm{lab}}=0.4–0.6A\mathrm{MeV}$ probe (thermodynamic) states of matter that are very similar to those created in binary neutron-star mergers. These results can inform future low-energy heavy-ion collisions probing this regime.

It is demonstrated that the presence of a phase transition in heavy-ion collisions, at beam energies that probe dense quantum chromodynamics (QCD) matter, leads to a significant enhancement of the dilepton yield at low invariant mass and requires the embedding of low beam energies per produced pion due to the extended emission time. In addition, the temperature of low-mass dileptons shows a modest decrease due to the mixed phase. The emission of dileptons in the SIS18–SIS100 beam energy range is studied by augmenting the ultra-relativistic quantum molecular dynamics (UrQMD) transport model with a realistic density-dependent equation of state, as well as two different phase transitions. This is achieved by extending the molecular dynamics interaction part of the UrQMD model to a density-dependent interaction potential with a high-density minimum, leading to a phase transition and metastable coexisting high-density states. Together with a high-precision measurement, these simulations will be able to constrain the existence of a phase transition in QCD up to densities of several times nuclear saturation density.

The long-awaited detection of a gravitational wave from the merger of a binary neutron star in August 2017 (GW170817) marks the beginning of the new field of multi-messenger gravitational wave astronomy. By exploiting the extracted tidal deformations of the two neutron stars from the late inspiral phase of GW170817, it is now possible to constrain several global properties of the equation of state of neutron star matter. However, the most interesting part of the high density and temperature regime of the equation of state is solely imprinted in the post-merger gravitational wave emission from the remnant hypermassive/supramassive neutron star. This regime was not observed in GW170817, but will possibly be detected in forthcoming events within the current observing run of the LIGO/VIRGO collaboration. Numerous numerical-relativity simulations of merging neutron star binaries have been performed during the last decades, and the emitted gravitational wave profiles and the interior structure of the generated remnants have been analysed in detail. The consequences of a potential appearance of a hadron-quark phase transition in the interior region of the produced hypermassive neutron star and the evolution of its underlying matter in the phase diagram of quantum cromo dynamics will be in the focus of this article. It will be shown that the different density/temperature regions of the equation of state can be severely constrained by a measurement of the spectral properties of the emitted post-merger gravitational wave signal from a future binary compact star merger event.