First-order phase transitions, such as the liquid-gas transition, proceed via formation of structures, such as bubbles and droplets. In strongly interacting compact star matter, at the crust-core transition but also the hadron-quark transition in the core, these structures form different shapes dubbed “pasta phases”. We describe two methods to obtain one-parameter families of hybrid equations of state (EoS) substituting the Maxwell construction that mimic the thermodynamic behaviour of pasta phase in between a low-density hadron and a high-density quark matter phase without explicitly computing geometrical structures. Both methods reproduce the Maxwell construction as a limiting case. The first method replaces the behaviour of pressure against chemical potential in a finite region around the critical pressure of the Maxwell construction by a polynomial interpolation. The second method uses extrapolations of the hadronic and quark matter EoS beyond the Maxwell point to define a mixing of both with weight functions bounded by finite limits around the Maxwell point. We apply both methods to the case of a hybrid EoS with a strong first order transition that entails the formation of a third family of compact stars and the corresponding mass twin phenomenon. For both models, we investigate the robustness of this phenomenon against variation of the single parameter: the pressure increment at the critical chemical potential that quantifies the deviation from the Maxwell construction. We also show sets of results for compact star observables other than mass and radius, namely the moment of inertia and the baryon mass. Full article

We outline an approach to a unified equation of state for quark-hadron matter on the basis of a $\mathsf{\Phi }-$ derivable approach to the generalized Beth-Uhlenbeck equation of state for a cluster decomposition of thermodynamic quantities like the density. To this end we summarize the cluster virial expansion for nuclear matter and demonstrate the equivalence of the Green’s function approach and the $\mathsf{\Phi }-$ derivable formulation. As an example, the formation and dissociation of deuterons in nuclear matter is discussed. We formulate the cluster $\mathsf{\Phi }-$ derivable approach to quark-hadron matter which allows to take into account the specifics of chiral symmetry restoration and deconfinement in triggering the Mott-dissociation of hadrons. This approach unifies the description of a strongly coupled quark-gluon plasma with that of a medium-modified hadron resonance gas description which are contained as limiting cases. The developed formalism shall replace the common two-phase approach to the description of the deconfinement and chiral phase transition that requires a phase transition construction between separately developed equations of state for hadronic and quark matter phases. Applications to the phenomenology of heavy-ion collisions and astrophysics are outlined. Full article

In this work we investigate the effect a crystalline quark–hadron mixed phase can have on the neutrino emissivity from the cores of neutron stars. To this end we use relativistic mean-field equations of state to model hadronic matter and a nonlocal extension of the three-flavor Nambu–Jona–Lasinio model for quark matter. Next we determine the extent of the quark–hadron mixed phase and its crystalline structure using the Glendenning construction, allowing for the formation of spherical blob, rod, and slab rare phase geometries. Finally, we calculate the neutrino emissivity due to electron–lattice interactions utilizing the formalism developed for the analogous process in neutron star crusts. We find that the contribution to the neutrino emissivity due to the presence of a crystalline quark–hadron mixed phase is substantial compared to other mechanisms at fairly low temperatures (≲10 ${}^9$ K) and quark fractions (≲30%), and that contributions due to lattice vibrations are insignificant compared to static-lattice contributions. There are a number of open issues that need to be addressed in a future study on the neutrino emission rates caused by electron–quark blob bremsstrahlung. Chiefly among them are the role of collective oscillations of matter, electron band structures, and of gaps at the boundaries of the Brillouin zones on bremsstrahlung, as discussed in the summary section of this paper. We hope this paper will stimulate studies addressing these issues. Full article

We study the anomalous electromagnetic transport properties of a quark-matter phase that can be realized in the presence of a magnetic field in the low-temperature/moderate-high-density region of the Quantum Chromodynamics (QCD) phase map. In this so-called Magnetic Dual Chiral Density Wave phase, an inhomogeneous condensate is dynamically induced producing a nontrivial topology, a consequence of the asymmetry of the lowest Landau level modes of the quasiparticles in this phase. The nontrivial topology manifests in the electromagnetic effective action via a chiral anomaly term $\theta F^{\mu \nu }{\tilde{F}}_{\mu \nu }$ , with an axion field $\theta$ given by the phase of the Dual Chiral Density Wave condensate. The coupling of the axion with the electromagnetic field leads to several macroscopic effects that include, among others, an anomalous, nondissipative Hall current, an anomalous electric charge, magnetoelectricity, and the formation of a hybridized propagating mode known as an axion polariton. The possible existence of this phase in the inner core of neutron stars opens a window to search for signals of its anomalous transport properties. Full article

We compute the principal non-radial oscillation mode frequencies of Neutron Stars described with a Skyrme-like Equation of State (EoS), taking into account the possibility of neutron and proton superfluidity. Using the CompOSE database and interpolation routines to obtain the needed thermodynamic quantities, we solve the fluid oscillation equations numerically in the background of a fully relativistic star, and identify imprints of the superfluid state. Though these modes cannot be observed with current technology, increased sensitivity of future Gravitational-Wave Observatories could allow us to observe these oscillations and potentially constrain or refine models of dense matter relevant to the interior of neutron stars. Full article

The fixed-target NA61/SHINE experiment at the CERN Super Proton Synchrotron (SPS) seeks to find the critical point (CR) of strongly interacting matter as well as the properties of the onset of deconfinement. The experiment provides a scan of measurements of particle spectra and fluctuations in proton–proton, proton–nucleus, and nucleus–nucleus interactions as functions of collision energy and system size, corresponding to a two-dimensional phase diagram (T- ${\mu }_B$ ). New NA61/SHINE results are shown here, including transverse momentum and multiplicity fluctuations in Ar+Sc collisions as compared to NA61 p+p and Be+Be data, as well earlier NA49 A+A results. Recently, a preliminary effect of change in the system size dependence, labelled as the “percolation threshold” or the “onset of fireball”, was observed in NA61/SHINE data. This effect is closely related to the vicinity of the hadronic phase space transition region and will be discussed in the text. Full article

The hadron–quark combustion front is a system that couples various processes, such as chemical reactions, hydrodynamics, diffusion, and neutrino transport. Previous numerical work has shown that this system is very nonlinear, and can be very sensitive to some of these processes. In these proceedings, we contextualize the hadron–quark combustion as a nonlinear system, subject to dramatic feedback triggered by leptonic weak decays and neutrino transport. Full article

We have built quasi-equilibrium models for uniformly rotating quark stars in general relativity. The conformal flatness approximation is employed and the Compact Object CALculator (cocal) code is extended to treat rotating stars with surface density discontinuity. In addition to the widely used MIT bag model, we have considered a strangeon star equation of state (EoS), suggested by Lai and Xu, that is based on quark clustering and results in a stiff EoS. We have investigated the maximum mass of uniformly rotating axisymmetric quark stars. We have also built triaxially deformed solutions for extremely fast rotating quark stars and studied the possible gravitational wave emission from such configurations. Full article

In this work, we explore different aspects in which strong magnetic fields play a role in the composition, structure and evolution of neutron stars. More specifically, we discuss (i) how strong magnetic fields change the equation of state of dense matter, alter its composition, and create anisotropies, (ii) how they change the structure of neutron stars (such mass and radius) and the formalism necessary to calculate those changes, and (iii) how they can affect neutron stars’ evolution. In particular, we focus on how a time-dependent magnetic field modifies the cooling of a special group known as X-ray dim neutron stars. Full article

The properties of dense matter in quantum chromodynamics (QCD) are delineated through equations of state constrained by the neutron star observations. The two solar mass constraint, the radius constraint of ≃11–13 km, and the causality constraint on the speed of sound, are used to develop the picture of hadron–quark continuity in which hadronic matter continuously transforms into quark matter. A unified equation of state at zero temperature and β-equilibrium is constructed by a phenomenological interpolation between nuclear and quark matter equations of state. Full article

The Lense-Thirring effect from spinning neutron stars in double neutron star binaries contributes to the periastron advance of the orbit. This extra term involves the moment of inertia of the neutron stars. The moment of inertia, on the other hand, depends on the mass and spin of the neutron star, as well as the equation of state of the matter. If at least one member of the double neutron star binary (better the faster one) is a radio pulsar, then accurate timing analysis might lead to the estimation of the contribution of the Lense-Thirring effect to the periastron advance, which will lead to the measurement of the moment of inertia of the pulsar. The combination of the knowledge on the values of the moment of inertia, the mass and the spin of the pulsar will give a new constraint on the equation of state. Pulsars in double neutron star binaries are the best for this purpose as short orbits and moderately high eccentricities make the Lense-Thirring effect substantial, whereas tidal effects are negligible (unlike pulsars with main sequence or white-dwarf binaries). The most promising pulsars are PSR J0737 − 3039A and PSR J1757 − 1854. The spin-precession of pulsars due to the misalignment between the spin and the orbital angular momentum vectors affect the contribution of the Lense-Thirring effect to the periastron advance. This effect has been explored for both PSR J0737 − 3039A and PSR J1757 − 1854, and as the misalignment angles for both of these pulsars are small, the variation in the Lense-Thirring term is not much. However, to extract the Lense-Thirring effect from the observed rate of the periastron advance, more accurate timing solutions including precise proper motion and distance measurements are essential. Full article

An extension of the relativistic density functional approach to the equation of state for strongly interacting matter is suggested that generalizes a recently developed modified excluded-volume mechanism to the case of temperature- and density-dependent available-volume fractions. A parametrization of this dependence is presented for which, at low temperatures and suprasaturation densities, a first-order phase transition is obtained. It changes for increasing temperatures to a crossover transition via a critical endpoint. This provides a benchmark case for studies of the role of such a point in hydrodynamic simulations of ultrarelativistic heavy-ion collisions. The approach is thermodynamically consistent and extendable to finite isospin asymmetries that are relevant for simulations of neutron stars, their mergers, and core-collapse supernova explosions. Full article

A commonly applied quark matter model in astrophysics is the thermodynamic bag model (tdBAG). The original MIT bag model approximates the effect of quark confinement, but does not explicitly account for the breaking of chiral symmetry, an important property of Quantum Chromodynamics (QCD). It further ignores vector repulsion. The vector-interaction-enhanced bag model (vBag) improves the tdBAG approach by accounting for both dynamical chiral symmetry breaking and repulsive vector interactions. The latter is of particular importance to studies of dense matter in beta-equilibriumto explain the two solar mass maximum mass constraint for neutron stars. The model is motivated by analyses of QCD based Dyson-Schwinger equations (DSE), assuming a simple quark-quark contact interaction. Here, we focus on the study of hybrid neutron star properties resulting from the application of vBag and will discuss possible extensions. Full article

Exploiting a stiff equation of state of the relativistic mean-field model MKVORH $\varphi$ with $\sigma$ -scaled hadron effective masses and couplings, including hyperons, we demonstrate that the existing neutron-star cooling data can be appropriately described within “the nuclear medium cooling scenario” under the assumption that different sources have different masses. Full article

In this article, we start by presenting state-of-the-art methods allowing us to compute moments related to the globally conserved baryon number, by means of first principle resummed perturbative frameworks. We focus on such quantities for they convey important properties of the finite temperature and density equation of state, being particularly sensitive to changes in the degrees of freedom across the quark-hadron phase transition. We thus present various number susceptibilities along with the corresponding results as obtained by lattice quantum chromodynamics collaborations, and comment on their comparison. Next, omitting the importance of coupling corrections and considering a zero-density toy model for the sake of argument, we focus on corrections due to the small size of heavy-ion collision systems, by means of spatial compactifications. Briefly motivating the relevance of finite size effects in heavy-ion physics, in opposition to the compact star physics, we present a few preliminary thermodynamic results together with the speed of sound for certain finite size relativistic quantum systems at very high temperature. Full article

We discuss the different signals, in gravitational and electromagnetic waves, emitted during the merger of two compact stars. We will focus in particular on the possible contraints that those signals can provide on the equation of state of dense matter. Indeed, the stiffness of the equation of state and the particle composition of the merging compact stars strongly affect, e.g., the life time of the post-merger remnant and its gravitational wave signal, the emission of the short gamma-ray-burst, the amount of ejected mass and the related kilonova. The first detection of gravitational waves from the merger of two compact stars in August 2017, GW170817, and the subsequent detections of its electromagnetic counterparts, GRB170817A and AT2017gfo, is the first example of the era of “multi-messenger astronomy”: we discuss what we have learned from this detection on the equation of state of compact stars and we provide a tentative interpretation of this event, within the two families scenario, as being due to the merger of a hadronic star with a quark star. Full article

High-density nuclear symmetry energy is of crucial importance in astrophysics. Information on such energy has been obtained from mass–radius determinations of neutron stars (NSs), and in the future NS mergers will increasingly contribute. In the laboratory, the symmetry energy can be studied in heavy-ion collisions (HICs) at different incident energies over a large range, from very low to several times higher saturation density. Transport theory is necessary to extract the symmetry energy from the typically non-equilibrated nuclear collisions. In this contribution, we first review the transport approaches, their differences, and recent studies of their reliability. We then discuss several prominent observables, which have been used to determine the symmetry energy at high density: collective flow, light cluster emission, and particle production. It is finally argued that the results of the symmetry energy from microscopic many-body calculations, nuclear structure, nuclear reactions, and astrophysics begin to converge but still need considerable improvements in terms of accuracy. Full article

We construct a dense matter equation of state (EoS) starting from a hadronic density dependent relativistic mean-field model with a DD2 parametrization including the excluded volume corrections at low densities. The high density part is given by a Nambu–Jona–Lasinio (NJL) model with multi-quark interactions. This EoS is characterized by increasing speed of sound below and above the phase transition region. The first order transition region has a large latent heat leaving a distinctive signature in the mass-radii relations in terms of twin stars. Full article

Strange stars are one of the possible compact stellar objects formed in the core collapse of supernovae. These hypothetical stars are made by deconfined quark matter and are selfbound. In our study, we focus on the torsional oscillations of a non bare strange star, i.e., a strange star with a thin crust made of standard nuclear matter. We construct a theoretical model assuming that the inner parts of the star are in two different phases, namely the color flavour locked phase and the crystalline colour superconducting phase. Since the latter phase is rigid, with a large shear modulus, it corresponds to a first stellar crust. Above this crust a second small crust made by standard nuclear matter is suspended thanks to a strong electromagnetic dipolar moment. We focus on the electromagnetically coupled oscillations of the two stellar crusts. Notably, we find that if a small fraction of the energy of a glitch event like a typical Vela glitch is conveyed in torsional oscillations, the small nuclear crust will likely break. This is due to the fact that in this model the maximum stress, due to torsional oscillations, is likely located near the star surface. Full article

Simulating Many Accelerated Strongly-interacting Hadrons (SMASH) is a new hadronic transport approach designed to describe the non-equilibrium evolution of heavy-ion collisions. The production of strange particles in such systems is enhanced compared to elementary reactions (Blume and Markert 2011), providing an interesting signal to study. Two different strangeness production mechanisms are discussed: one based on resonances and another using forced canonical thermalization. Comparisons to experimental data from elementary collisions are shown. Full article

Knowledge of the equation of state (EoS) of cold and dense baryonic matter is essential for the description of properties of neutron stars (NSs). With an increase of the density, new baryon species can appear in NS matter, as well as various meson condensates. In previous works, we developed relativistic mean-field (RMF) models with hyperons and $\Delta$ -isobars, which passed the majority of known experimental constraints, including the existence of a $2M_{\odot }$ neutron star. In this contribution, we present results of the inclusion of ${\rho }^{-}$ -meson condensation into these models. We have shown that, in one class of the models (so-called KVOR-based models, in which the additional stiffening procedure is introduced in the isoscalar sector), the condensation gives only a small contribution to the EoS. In another class of the models (MKVOR-based models with additional stiffening in isovector sector), the condensation can lead to a first-order phase transition and a substantial decrease of the NS mass. Nevertheless, in all resulting models, the condensation does not spoil the description of the experimental constraints. Full article

Analysis of directed flow ( $v_1$ ) of protons, antiprotons and pions in heavy-ion collisions is performed in the range of collision energies $\sqrt{s_{NN}}$ = 2.7–39 GeV. Simulations have been done within a three-fluid model employing a purely hadronic equation of state (EoS) and two versions of the EoS with deconfinement transitions: a first-order phase transition and a smooth crossover transition. The crossover EoS is unambiguously preferable for the description of experimental data at lower collision energies $\sqrt{s_{NN}}\lesssim$ 20 Gev. However, at higher collision energies $\sqrt{s_{NN}}\gtrsim$ 20 Gev. the purely hadronic EoS again becomes advantageous. This indicates that the deconfinement EoS in the quark-gluon sector should be stiffer at high baryon densities than those used in the calculation. The latter finding is in agreement with that discussed in astrophysics in connection with existence of hybrid stars with masses up to about two solar masses. Full article