Hadron-quark Mixed Phase Research Articles

Properties of quark-matter cores in massive hybrid stars

Using the constraints from astrophysical observations and heavy-ion experiments, we investigate the equation of state (EOS) of hybrid star matter and the properties of quark-matter cores in hybrid stars. The quark matter interactions in hybrid stars are described based on 3-flavor Nambu-Jona-Lasinio model with various vector and vector-isovector coupling constants. In this work, we find that the hybrid star matter EOS is more sensitive to the strength of the vector interaction, and the EOS becomes stiffer with increasing vector strength $R_V$. The vector-isovector interaction characterized by the coupling constant $R_{IV}$ make main contribution to the hadron-quark mixed phase. Meanwhile, we note that a step change of both the sound velocity and the polytropic index $\gamma$ occurs in the hadron-quark phase transition, and it is restored with the decrease of nucleon and lepton degrees of freedom in the high density quark phase. Although the coupling constants increase the hybrid star maximum mass up to $2.08M_{\odot}$, they also decrease the mass and radius of the quark core and the mixed core. With different quark coupling constants, we also find that the maximum mass and radius of the quark matter core in a stable hybrid star can reach $0.80M_{\odot}$ and 6.95 km, which are close to half of the maximum mass and radius of the complete star. However, properties of quark matter have no effect on the $M = 1.4M_{\odot}$ hybrid star as a result of no quark matter inner core, which can also be confirmed by the criterion of the polytropic index, and thus our results also indicate that the quark interactions have no effect on the tidal deformability $\Lambda_{1.4}$ of hybrid stars.

Hybrid stars in a relativistic quark model

The phase transition of hadronic matter to deconfined quark matter in the interior of the neutron star is studied. A relativistic quark model is used to describe the hadronic matter whereas the MIT bag model is used to represent the quark matter. The coexistence of hadron-quark mixed phase in equilibrium is also investigated. The equation of state with nucleon $+$ quark (NP-hybrid) and nucleon $+$ hyperon $+$ quark (NP $+$ hyp-hybrid) matter is developed and stellar properties, such as the maximum mass, radii, tidal deformability, and gravitational redshift are determined. The behavior of the speed of sound and the adiabatic index in the hybrid matter are also studied. It is found that within the conformal limits of the speed of sound, stars below the $2\text{\ensuremath{-}}{M}_{\ensuremath{\bigodot}}$ limit lack a sizable quark core but exhibit mixed phase of hadrons and quarks.

Symmetry energy effects on the properties of hybrid stars

Symmetry energy is an important part of the equation of state of isospin asymmetry matter. However, the huge uncertainties of symmetry energy remain at suprasaturation densities, where the phase transitions of strongly interacting matter and the quark matter symmetry energy are likely to be taken into account. In this work, we investigate the properties of symmetry energy by using a hybrid star with the hadron-quark phase transition. The interaction among strange quark matter (SQM) in hybrid stars is based on a 3-flavor NJL model with different vector and isovector channels, while the equation of state (EOS) of the nuclear matter is obtained by considering the ImMDI-ST interaction by varying the parameters x, y, and z. Our results indicate that the various parameters and coupling constants of the interactions from the ImMDI-ST and NJL model can lead to widely different trends for the symmetry energy in the hadron-quark mixed phase and the different onsets of the hadron-quark phase transition. In addition, it has been found that the radii and tidal deformabilities of hybrid stars constrain mostly the density dependence of symmetry energy while the observed maximum masses of hybrid stars constrain mostly the EOS of symmetric nuclear and quark matter.

Hadron-quark Pasta Phase in Massive Neutron Stars

Abstract The structured hadron-quark mixed phase, known as the pasta phase, is expected to appear in the core of massive neutron stars. Motivated by the recent advances in astrophysical observations, we explore the possibility of the appearance of quarks inside neutron stars and check its compatibility with current constraints. We investigate the properties of the hadron-quark pasta phases and their influences on the equation of state (EOS) for neutron stars. In this work, we extend the energy minimization (EM) method to describe the hadron-quark pasta phase, where the surface and Coulomb contributions are included in the minimization procedure. By allowing different electron densities in the hadronic and quark matter phases, the total electron chemical potential with the electric potential remains constant, and local β equilibrium is achieved inside the Wigner–Seitz cell. The mixed phase described in the EM method shows the features lying between the Gibbs and Maxwell constructions, which is helpful for understanding the transition from the Gibbs construction to the Maxwell construction with increasing surface tension. We employ the relativistic mean-field model to describe the hadronic matter, while the quark matter is described by the MIT bag model with vector interactions. It is found that the vector interactions among quarks can significantly stiffen the EOS at high densities and help enhance the maximum mass of neutron stars. Other parameters like the bag constant can also affect the deconfinement phase transition in neutron stars. Our results show that hadron-quark pasta phases may appear in the core of massive neutron stars that can be compatible with current observational constraints.

Vector interactions inhibit quark-hadron mixed phases in neutron stars

We investigate the surface tension $\sigma$ and the curvature energy $\gamma$ of quark matter drops in the MIT bag model with vector interactions. Finite size corrections to the density of states are implemented by using the multiple reflection expansion (MRE) formalism. We find that $\sigma$ and $\gamma$ are strongly enhanced by new terms arising from vector interactions. With respect to the noninteracting case they are increased by a large factor, which can be as high as $\sim 10$ when the vector coupling constant $g$ varies within the range used in the literature. This behavior may have major consequences for the hadron-quark mixed phase speculated to exist at neutron star (NS) interiors, which may be totally suppressed or have its extension substantially reduced.

Hadron–quark phase transition in the context of GW190814

The properties of neutron stars are calculated for hadronic matter within the density-dependent relativistic mean-field model (DD-RMF). The phase transition to quark matter is studied and the hybrid star matter properties are systematically calculated using the vector-enhanced bag model. The maximum mass of a neutron star with DD-LZ1 and DD-RMF parameter sets is found to be around 2.55M ⊙ for the pure hadronic phase and around 2M ⊙ for the hadron–quark mixed phase using both Gibbs and Maxwell construction (MC). The variation in tidal deformability for the hybrid equation of state (EoS) at 1.4M ⊙ depends upon the construction of the phase transition. While it remains unchanged with MC, but decreases with the increasing neutron star mass for Gibbs construction. The pure hadron matter EoS satisfies the maximum mass constraint from recently observed GW190814 data, implying a stiff neutron star EoS. The phase transition to quark matter satisfies the maximum mass and radius constraints from the GW170817 event. Therefore, we cannot exclude the possibility of the secondary object in GW190814 as a neutron star with a phase transition to quark matter that satisfies the 2M ⊙ maximum mass limit.

Metastable hypermassive hybrid stars as neutron-star merger remnants

Hypermassive hybrid stars (HMHS) are extreme astrophysical objects that could be produced in the merger of a binary system of compact stars. In contrast to their purely hadronic counterparts, hypermassive neutron stars (HMNS), these highly differentially rotating objects contain deconfined strange quark matter in their slowly rotating inner region. HMHS and HMNS are both mestastable configurations and can survive only shortly after the merger before collapsing to rotating black holes. The appearance of the phase transition from hadronic to quark matter in the interior region of the HMHS and its conjunction with the emitted GW will be addressed in this article by focussing on a specific case study of the delayed phase-transition scenario that takes place during the post-merger evolution of the remnant. The complicated dynamics of the collapse from the HMNS to the more compact HMHS will be analysed in detail. In particular, we will show that the interplay between the spatial density/temperature distributions and the rotational profiles in the interior of the wobbling HMHS after the collapse generates a high-temperature shell within the hadron-quark mixed phase region of the remnant.

Hadron-quark mixed phase in the quark-meson coupling model

We explore the possibility of a structured hadron-quark mixed phase forming in the interior of neutron stars. The quark-meson coupling (QMC) model, which explicitly incorporates the internal quark structure of the nucleon, is employed to describe the hadronic phase, while the quark phase is described by the same bag model as the one used in the QMC framework, so as to keep consistency between the two coexisting phases. We analyze the effect of the appearance of hadron-quark pasta phases on the neutron-star properties. We also discuss the influence of nuclear symmetry energy and the bag constant $B$ in quark matter on the deconfinement phase transition. For the treatment of the hadron-quark mixed phase, we use the energy minimization method and compare it with the Gibbs construction. The finite-size effects like surface and Coulomb energies are taken into account in the energy minimization method; they play crucial roles in determining the pasta configuration during the hadron-quark phase transition. It is found that the finite-size effects can significantly reduce the region of the mixed phase relative to that of the Gibbs construction. Using a consistent value of $B$ in the QMC model and quark matter, we find that hadron-quark pasta phases are formed in the interior of massive stars, but no pure quark matter can exist.

Systematic study on the quark-hadron mixed phase in compact stars

We investigate systematically the quark-hadron mixed phase in dense stellar matter, and its influence on compact star structures. The properties of quark matter and hadronic matter are fixed based on various model predictions. Beside adopting constant values, the surface tension $\Sigma$ for the quark-hadron interface is estimated with the multiple reflection expansion method and equivparticle model. To fix the structures of quark-hadron pasta phases, a continuous dimensionality of the structure is adopted as proposed by Ravenhall, Pethick, and Wilson. The corresponding properties of hybrid stars are then obtained and confronted with pulsar observations. It is found that the correlation between radius and tidal deformability in traditional neutron stars preserves in hybrid stars. For those permitted by pulsar observations, in almost all cases the quark phase persists inside the most massive compact stars. The quark-hadron interface plays an important role on hybrid star structures once quark matter emerges. The surface tension $\Sigma$ estimated with various methods increases with density, which predicts stiffer EOSs for the quark-hadron mixed phase and increases the maximum mass of hybrid stars. The EOSs of hybrid star matter are well constrained at densities $n\lesssim 0.8$ fm${}^{-3}$, while larger uncertainty is expected at higher densities.

Hadron-quark deconfinement phase transition in hybrid stars

Astronomical statistics shows that the mass of neutron star is of the order of the solar mass, but the radius is only about ten kilometers. Therefore, the neutron star is highly condensed and there may be a variety of competing material phases inside the compact star. Hadron-quark deconfinement phase transition that is poorly understood at high density can be studied by the matter properties of hybrid star. The hybrid star contains many kinds of material phases, which cannot be described uniformly by one theory. So, different material phases are described by different theories. The hadronic phase is described by the relativistic mean-field theory with parameter set FSUGold including <i>ω</i><sup>2</sup><i>ρ</i><sup>2</sup> interaction term, and the quark phase is described by an effective mass bag model in which the quark mass is density-dependent. The hadron-quark mixed phase is constructed by the Gibbs phase transition, and the properties of hybrid star in <i>β</i> equilibrium is studied in this model. It is found that the bag constant <i>B</i> has a great influence on the starting point and ending point of the hadron-quark deconfinement phase transition and the particle composition in the hybrid star. Comparing with the starting point of phase transition, the influence of <i>B</i> on the ending point of phase transition is very obvious. For the hybrid star, the equation of state of matter becomes stiffer at low density and softer at high density as <i>B</i> increases. The overall effect is that the slope of the mass-radius curve increases with <i>B</i> increasing. The calculated results show that the maximum mass of hybrid star is between 1.3 solar mass and 1.4 solar mass (<i>M</i><sub>☉</sub>), and the radius is between 9 km and 12 km. In addition, the influence of attractive and repulsive <i>Σ</i> potential on the properties of hybrid stars are studied. The results show that the <i>Σ</i> potential has a great influence on the particle composition in the hybrid star. We also find that the repulsive <i>Σ</i> potential makes the hybrid star have a greater maximum mass then an attractive <i>Σ</i> potential. For the attractive <i>Σ</i> potential, the maximum mass of hybrid star is 1.38<i>M</i><sub>☉</sub>, while for the repulsive <i>Σ</i> potential, the maximum mass of hybrid stars is 1.41<i>M</i><sub>☉</sub>.

Phases of Hadron-Quark Matter in (Proto) Neutron Stars

In the first part of this paper, we investigate the possible existence of a structured hadron-quark mixed phase in the cores of neutron stars. This phase, referred to as the hadron-quark pasta phase, consists of spherical blob, rod, and slab rare phase geometries. Particular emphasis is given to modeling the size of this phase in rotating neutron stars. We use the relativistic mean-field theory to model hadronic matter and the non-local three-flavor Nambu–Jona-Lasinio model to describe quark matter. Based on these models, the hadron-quark pasta phase exists only in very massive neutron stars, whose rotational frequencies are less than around 300 Hz. All other stars are not dense enough to trigger quark deconfinement in their cores. Part two of the paper deals with the quark-hadron composition of hot (proto) neutron star matter. To this end we use a local three-flavor Polyakov–Nambu–Jona-Lasinio model which includes the ’t Hooft (quark flavor mixing) term. It is found that this term leads to non-negligible changes in the particle composition of (proto) neutron stars made of hadron-quark matter.

Nuclear symmetry energy and hadron-quark mixed phase in neutron stars

We study the hadron-quark mixed phase, which may occur in the interior of neutron stars. The relativistic mean-field model is employed to describe the hadronic phase, while the Nambu-Jona-Lasinio model is used for the quark phase. We examine the effects of nuclear symmetry energy in the hadronic phase and repulsive vector interaction in the quark phase. For the treatment of hadron-quark mixed phase, we describe and compare four methods: (1) energy minimization method, (2) coexisting phases method, (3) Gibbs construction, and (4) Maxwell construction. The finite-size effects like surface and Coulomb energies are taken into account in the energy minimization and coexisting phases methods, which play a key role in determining the pasta configuration during the hadron-quark phase transition. It is found that massive neutron stars may contain hadron-quark pasta phases, but pure quark matter is unlikely to occur in the interior of neutron stars.

Development of shashlik electromagnetic calorimeter for the NICA/MPD

The main goal of the NICA heavy-ion program at JINR is an experimental investigation into the properties of nuclear matter within the energy region of the maximum baryonic density. The Multi Purpose Detector (MPD) is one of the detectors at NICA collider, which is optimized for the study on properties of hot and dense matter in heavy-ion collisions and, in particular, the search for a manifestation of possible deconfinement and/or chiral symmetry restoration phase transitions, critical end-point and mixed quark-hadron phase. Electromagnetic calorimeter (ECal) is an important part of MPD . The particular goal of MPD-ECal is to measure position and energy of photons and electrons. Taking all factors (high energy resolution, high segmentation, large enough distance to the vertex, small Moliere radius, high magnetic field and high time resolution) into consideration, a shashlik-type electromagnetic calorimeter is selected. Therefore the tower consists of 220 layers of lead plates and scintillator plates whose thicknesses are namely 0.3mm/1.5mm. The tower cell is 4×4 cm2 in size. To reduce the dead zones effect, all towers should be cut from four sides at small angles, which will significantly improve the position resolution and the performance homogeneity of the ECal. Currently, energy deposition, energy resolution and position reconstruction are studied through Monte Carlo simulations. A prototype of shashlik Ecal has been built and the cosmic test results show that the number of photoelectrons (Npe) is around 522. By comparing with the previous ECal experimental results and simulation results, it is indirectly considered that the energy resolution of the prototype has reached 5%/√E (GeV) . Key technologies to increase light yield are being studied and will be used in the development of new prototypes.

Constraining quark-hadron interface tension in the multimessenger era

We study the interface effects of quark-hadron mixed phase in compact stars. The properties of nuclear matter are obtained based on the relativistic-mean-field model. For the quark phase, we adopt perturbation model with running quark masses and coupling constant. At certain choices of parameter sets, it is found that varying the quark-hadron interface tension will have sizable effects on the radii ($\Delta R \approx 600$ m) and tidal deformabilities ($\Delta \Lambda/\Lambda \approx 50\%$) of hybrid stars. These provide possibilities for us to constrain the quark-hadron interface tension with future gravitational wave observations as well as the ongoing NICER mission.

Effects of quark-matter symmetry energy on hadron-quark coexistence in neutron-star matter

We examine the effects of the isovector-vector coupling and hypercharge-vector coupling in quark matter on hadron-quark coexistence in neutron-star matter. The relativistic mean field theory with the TM1 parameter set and an extended TM1 parameter set are used to describe hadronic matter, and the Nambu-Jona-Lasinio model with scalar, isoscalar-vector, isovector-vector and hypercharge-vector couplings is used to describe deconfined quark matter. The hadron-quark phase transition is constructed via the Gibbs conditions for phase equilibrium. The isovector-vector and hypercharge-vector couplings in quark matter enhance the symmetry energy and hypercharge symmetry energy in neutron-star matter, while their effects are found to be suppressed at high densities by the strange quarks. As a result, the hadron-quark mixed phase shrinks with only isovector-vector coupling and moves to higher density with isovector-vector and hypercharge-vector couplings. The maximum mass of neutron-star increases slightly with isovector-vector and hypercharge-vector couplings.

Neutrino Emissivity in the Quark-Hadron Mixed Phase

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.

Finite-size effects on the hadron-quark phase transition in neutron stars

We study the finite-size effects, like the surface and Coulomb energies, on the hadron-quark mixed phase in neutron stars. The equilibrium conditions for coexisting hadronic and quark phases are derived by minimizing the total energy including the surface and Coulomb contributions, which are different from the Gibbs conditions without finite-size effects. We employ the relativistic mean-field model to describe the hadronic phase, while the Nambu-Jona-Lasinio model with vector interactions is used for the quark phase. It is found that finite-size effects can significantly reduce the region of the mixed phase, and the results lie between those of the Gibbs and Maxwell constructions. We show that a massive star may contain a mixed-phase core and its size depends on the surface tension of the hadron-quark interface and the vector coupling between quarks. The repulsive vector interaction in the Nambu-Jona-Lasinio model can stiffen the equation of state of quark matter, and therefore, delay the phase transition and increase the maximum mass of neutron stars.

Rotating NSs/QSs and recent astrophysical observations

Both fast and slow configurations of rotating neutron stars (NSs) are studied with the recently-constructed unified NS EoSs. The calculations for pure quark stars (QSs) and hybrid stars (HSs) are also done, using several updated quark matter EoSs and Gibbs construction for obtaining hadron-quark mixed phase. All three types of EoSs fulfill the recent 2-solar-mass constraint. By confronting the glitch observations with the theoretical calculations for the crustal moment of inertia (MoI), we find that the glitch crisis is still present in Vela-like pulsars. An upcoming accurate MoI measurement (eg., a possible 10% accuracy for pulsar PSR J0737–3039A) allows one to distinguish QSs from NSs, since the MoIs of QSs are generally ≳ 1.5 times larger than NSs and HSs, no matter the compactness and the mass of the stars. Using tabulated EoSs, we compute stationary and equilibrium sequences of rapidly rotating, relativistic stars in general relativity from the well-tested rns code, assuming the matter comprising the star to be a perfect fluid. All three observed properties of the short gamma-ray bursts (SGRBs) internal plateaus sample are simulated using the rotating configurations of NSs/QSs as basic inputs. We finally argue that for some characteristic SGRBs, the post-merger products of NS-NS mergers are probably supramassive QSs rather than NSs, and NS-NS mergers are a plausible location for quark deconfinement and the formation of QSs.

Quark Deconfinement in Rotating Neutron Stars

In this paper, we use a three flavor non-local Nambu–Jona-Lasinio (NJL) model, an improved effective model of Quantum Chromodynamics (QCD) at low energies, to investigate the existence of deconfined quarks in the cores of neutron stars. Particular emphasis is put on the possible existence of quark matter in the cores of rotating neutron stars (pulsars). In contrast to non-rotating neutron stars, whose particle compositions do not change with time (are frozen in), the type and structure of the matter in the cores of rotating neutron stars depends on the spin frequencies of these stars, which opens up a possible new window on the nature of matter deep in the cores of neutron stars. Our study shows that, depending on mass and rotational frequency, up to around 8% of the mass of a massive neutron star may be in the mixed quark-hadron phase, if the phase transition is treated as a Gibbs transition. We also find that the gravitational mass at which quark deconfinement occurs in rotating neutron stars varies quadratically with spin frequency, which can be fitted by a simple formula.

Probing the hadron-quark mixed phase at high isospin and baryon density

We discuss the isospin effect on the possible phase transition from hadronic to quark matter at high baryon density and finite temperatures. The two-Equation of State (Two-EoS) model is adopted to describe the hadron-quark phase transition in dense matter formed in heavy-ion collisions. For the hadron sector we use Relativistic Mean Field (RMF) effective models, already tested on heavy ion collision (HIC). For the quark phase we consider various effective models, the MIT-Bag static picture, the Nambu--Jona-Lasinio (NJL) approach with chiral dynamics and finally the NJL coupled to the Polyakov-loop field (PNJL), which includes both chiral and (de)confinement dynamics. The idea is to extract mixed phase properties which appear robust with respect to the model differences. In particular we focus on the phase transitions of isospin asymmetric matter, with two main results: i) an earlier transition to a mixed hadron-quark phase, at lower baryon density/chemical potential with respect to symmetric matter; ii) an "Isospin Distillation" to the quark component of the mixed phase, with predicted effects on the final hadron production. Possible observation signals are suggested to probe in heavy-ion collision experiments at intermediate energies, in the range of the NICA program.