Pure Quark Matter Research Articles

Hadron-quark transition and chiral symmetry restoration at high density

A simple phenomenological hybrid hadron-quark model with excluded volume effects of baryons and chiral dynamics is investigated. The hybrid equation of state naturally connects the low-density baryonic matter with the high-density quark matter. In the intermediate region, a phase, which cannot be regarded as pure hadron matter or pure quark matter, appears. In this model, there is a possibility that the abrupt first-order-like transition to pure quark matter induces the strong chiral symmetry restoration and the speed of sound has a large peak at considerable large density. Published by the American Physical Society 2024

Non-radial oscillation modes in hybrid stars: consequences of a mixed phase

We study the possibility of the existence of a deconfined quark matter in the core of neutron star (NS)s and its relation to non-radial oscillation modes in NSs and hybrid star (HS)s. We use relativistic mean field (RMF) models to describe the nuclear matter at low densities and zero temperature. The Nambu-Jona-Lasinio (NJL) model is used to describe the quark matter at high densities and zero temperature. A Gibbs construct is used to describe the hadron-quark phase transition (HQPT) at large densities. Within the model, as the density increases, a mixed phase (MP) appears at density about 2.5 times the nuclear matter saturation density (ρ 0) and ends at density about 5ρ 0 beyond which the pure quark matter phase appears. It turns out that a stable HS of maximum mass, M = 2.27 M ⊙ with radius R = 14 km (for NL3 parameterisation of nuclear RMF model), can exist with the quark matter in the core in a MP only. HQPT in the core of maximum mass HS occurs at radial distance, rc = 0.27R where the equilibrium speed of sound shows a discontinuity. Existence of quark matter in the core enhances the non-radial oscillation frequencies in HSs compared to NSs of the same mass. This enhancement is significantly large for the g modes. Such an enhancement of the g modes is also seen for a density dependent Bayesian (DDB) parmeterisation of the nucleonic EOS. The non-radial oscillation frequencies depend on the vector coupling in the NJL model. The values of g and f mode frequencies decrease with increase the vector coupling in quark matter.

Constraining the Equation of State of Hybrid Stars Using Recent Information from Multidisciplinary Physics

At the ultrahigh densities existing in the core of neutron stars (NSs), it is expected that a phase transition from baryonic to deconfined quark matter may occur. Such a phase transition would affect the underlying equation of state (EoS) as well as the observable astrophysical properties of NSs. Comparison of EoS model predictions with astronomical data from multimessenger signals then provides us an opportunity to probe the behavior of dense matter. In this work, we restrict the allowed parameter space of EoS models in NSs for both nucleonic (relativistic mean field model) and quark matter (MIT bag model) sectors by imposing state-of-the-art constraints from nuclear calculations, multimessenger astrophysical data, and perturbative quantum chromodynamics (pQCD). We systematically investigate the effect of each constraint on the parameter space of uncertainties using a cutoff filter scheme, as well as the correlations among the parameters and with NS astrophysical observables. Using the constraints, we obtain limits for maximum NS mass, maximum central density, as well as for NS radii and tidal deformability. Although pQCD constraints are only effective at very high densities, they significantly reduce the parameter space of the quark model. We also conclude that astrophysical data supports high values of the bag parameter B and disfavors the existence of a pure quark matter core in hybrid stars.

Quark formation and phenomenology in binary neutron-star mergers using V-QCD

Using full 3+1 dimensional general-relativistic hydrodynamic simulations of equal- and unequal-mass neutron-star binaries with properties that are consistent with those inferred from the inspiral of GW170817, we perform a detailed study of the quark-formation processes that could take place after merger. We use three equations of state consistent with current pulsar observations derived from a novel finite-temperature framework based on V-QCD, a non-perturbative gauge/gravity model for Quantum Chromodynamics. In this way, we identify three different post-merger stages at which mixed baryonic and quark matter, as well as pure quark matter, are generated. A phase transition triggered collapse already \lesssim 10 ms≲10ms after the merger reveals that the softest version of our equations of state is actually inconsistent with the expected second-long post-merger lifetime of GW170817. Our results underline the impact that gravitational wave observations of binary neutron-star mergers can have in constraining the equation of state of nuclear matter, especially in its most extreme regimes.

Core-collapse Supernova Simulations and the Formation of Neutron Stars, Hybrid Stars, and Black Holes

Abstract We investigate observable signatures of a first-order quantum chromodynamics (QCD) phase transition in the context of core-collapse supernovae. To this end, we conduct axially symmetric numerical relativity simulations with multi-energy neutrino transport, using a hadron–quark hybrid equation of state (EOS). We consider four nonrotating progenitor models, whose masses range from 9.6 to 70 M ⊙. We find that the two less-massive progenitor stars (9.6 and 11.2 M ⊙) show a successful explosion, which is driven by the neutrino heating. They do not undergo the QCD phase transition and leave behind a neutron star. As for the more massive progenitor stars (50 and 70 M ⊙), the proto-neutron star (PNS) core enters the phase transition region and experiences the second collapse. Because of a sudden stiffening of the EOS entering to the pure quark matter regime, a strong shock wave is formed and blows off the PNS envelope in the 50 M ⊙ model. Consequently the remnant becomes a quark core surrounded by hadronic matter, leading to the formation of the hybrid star. However, for the 70 M ⊙ model, the shock wave cannot overcome the continuous mass accretion and it readily becomes a black hole. We find that the neutrino and gravitational wave (GW) signals from supernova explosions driven by the hadron–quark phase transition are detectable for the present generation of neutrino and GW detectors. Furthermore, the analysis of the GW detector response reveals unique kHz signatures, which will allow us to distinguish this class of supernova explosions from failed and neutrino-driven explosions.

Density-dependent quark mass model revisited: thermodynamic consistency, stability windows and stellar properties

In this work a density-dependent quark model is revisited, its thermodynamic consistency checked and the stability window for absolutely stable quark matter obtained. The hypotheses of both pure quark matter with equal quark chemical potentials and stellar matter subject to chemical stability and charge neutrality are investigated. The parameters that appear in the density-dependent mass and satisfy the Bodmer–Witten conjecture are then used to compute the masses and radii of strange stars. We show that the obtained values are compatible with the recently observed massive stars.

Finding quark content of neutron stars in light of GW170817

The detection of gravitational waves from GW170817 has provided a new opportunity to constrain the equation of state (EOS) of neutron stars. In this article, we investigate the possible existence of quarks inside the neutron star core in the context of GW170817. The nucleon phase is treated within the relativistic nuclear mean-field approach where we have employed a fully comprehensive set of available models, and the quark phase is described in the Bag model. We show that the nucleonic EOSs which are inconsistent with the tidal deformability bound become consistent when phase transition to quark matter via Gibbs construction is allowed. We find that several nucleonic EOSs support the presence of pure quark matter core with a small mass not more than \(0.17M_\odot \) confined within a radius of 0.9 km. We also find that the strong correlation between tidal deformability and neutron star radii observed for pure nucleonic stars does persist even with a nucleon-quark phase transition and provides an upper limit on the radius of \(R_{1.4} \lesssim 12.9\) km for a \(1.4M_\odot \) neutron star.

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.

Toward a unified equation of state for multi-messenger astronomy

Aims. We aim to present a first step in developing a benchmark equation-of-state (EoS) model for multi-messenger astronomy that unifies the thermodynamics of quark and hadronic degrees of freedom. Methods. A Lagrangian approach to the thermodynamic potential of quark-meson-nucleon matter was used. In this approach, dynamical chiral-symmetry breaking is described by the scalar mean-field dynamics coupled to quarks and nucleons and their chiral partners, whereby its restoration occurs in the hadronic phase by parity doubling, as well as in the quark phase. Quark confinement was achieved by an auxiliary scalar field that parametrizes a dynamical infrared cut-off in the quark sector, serving as an ultraviolet cut-off for the nucleonic phase space. The gap equations were solved for the isospin-symmetric case, as well as for neutron star (NS) conditions. We also calculated the mass-radius (MR) relation of NSs and their tidal deformability (TD) parameter. Results. The obtained EoS is in accordance with nuclear matter properties at saturation density and with the flow constraint from heavy ion collision experiments. For isospin-asymmetric matter, a sequential occurrence of light quark flavors is obtained, allowing for a mixed phase of chirally-symmetric nucleonic matter with deconfined down quarks. The MR relations and TDs for compact stars fulfill the constraints from the latest astrophysical observations for PSR J0740+6620, PSR J0030+0451, and the NS merger GW170817, whereby the tension between the maximum mass and compactness constraints rather uniquely fixes the model parameters. The model predicts the existence of stars with a core of chirally restored but purely hadronic (confined) matter for masses beyond 1.8 M⊙. Stars with pure-quark matter cores are found to be unstable against the gravitational collapse. This instability is shifted to even higher densities if repulsive interactions between quarks are included.

Holographic quarkyonic matter

We point out a new configuration in the Witten-Sakai-Sugimoto model, allowing baryons in the pointlike approximation to coexist with fundamental quarks. The resulting phase is a holographic realization of quarkyonic matter, which is predicted to occur in QCD at a large number of colors, and possibly plays a role in real-world QCD as well. We find that holographic quarkyonic matter is chirally symmetric and that, for large baryon chemical potentials, it is energetically preferred over pure nuclear matter and over pure quark matter. The zero-temperature transition from nuclear matter to the quarkyonic phase is of first order in the chiral limit and for a realistic pion mass. For pion masses far beyond the physical point we observe a quark-hadron continuity due to the presence of quarkyonic matter.

Magnetized hybrid stars: effects of slow and rapid phase transitions at the quark–hadron interface

ABSTRACT We study the influence of strong magnetic fields in hybrid stars, composed by hadrons and a pure quark matter core, and analyse their structure and stability as well as some possible evolution channels due to the magnetic field decay. Using an ad hoc parametrization of the magnetic field strength and taking into account Landau-quantization effects in matter, we calculate hybrid magnetized equations of state and some associated quantities, such as particle abundances and matter magnetization, for different sets of parameters and different magnetic field strengths. Moreover, we compute the magnetized stable stellar configurations, the mass versus radius and the gravitational mass versus central energy density relationships, the gravitational mass versus baryon mass diagram, and the tidal deformability. Our results are in agreement with both, the $\sim 2\, \mathrm{M}_\odot$ pulsars and the data obtained from GW170817. In addition, we study the stability of stellar configurations assuming that slow and rapid phase transitions occur at the sharp hadron–quark interface. We find that, unlike in the rapid transition scenario, where ∂M/∂ϵc < 0 is a sufficient condition for instability, in the slow transition scenario there exists a connected extended stable branch beyond the maximum mass star, for which ∂M/∂ϵc < 0. Finally, analysing the gravitational mass versus baryon mass relationship, we have calculated the energy released in transitions between stable stellar configurations. We find that the inclusion of the magnetic field and the existence of new stable branches allows the possibility of new channels of transitions that fulfil the energy requirements to explain gamma-ray bursts.

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.

Effects of hadron–quark phase transition on properties of neutron stars

We investigate the possible scenario of deconfinement of hyperon rich hadronic matter to quark matter at high densities and the resulting hybrid star (HS) properties are analyzed. In the relativistic mean-field framework, we construct the equation of state (EoS) of hadronic matter using the effective chiral model while the pure quark matter is described using the MIT bag model. We revisit the hyperon puzzle and analyze the possibility of hadron–quark phase transition with proper choice of the bag constant. In static condition the maximum mass of the resultant HSs are in good agreement with the recent observational bounds on the same from high mass pulsars such as PSR J1614−2230 and PSR J0348+0432. On invoking the phenomenon of phase transition, the radius of canonical mass (R1.4) and value of R1.6 predicted by the model lie within the range prescribed from binary neutron star merger detected by the LIGO-Virgo collaboration in 2017. The surface redshift obtained for the HSs also satisfy the constraints from pulsars RX J0 720.4-3125 and 1E 1 207.4-5209. It is worth noting that unlike several other works, we add no modifications to the original form of the Bag model to satisfy these recent observational and empirical constraints on NS properties. We also discuss the rotational aspects of the HSs by calculating the properties like rotational mass, radius, energy density, moment of inertia at different angular velocities. The maximum bound on rotational frequency from the rapidly rotating pulsars like PSR B1937+21 and PSR J1748−2446ad are satisfied with the HS configuration. We also test the universality of our hybrid EoS in terms of normalized moment of inertia.

Oscillation modes of hybrid stars within the relativistic Cowling approximation

The first direct detection of gravitational waves has opened a new window to study the Universe and would probably start a new era: the gravitational wave Astronomy. Gravitational waves emitted by compact objects like neutron stars could provide significant information about their structure, composition and evolution. In this paper we calculate, using the relativistic Cowling approximation, the oscillations of compact stars focusing on hybrid stars, with and without a mixed phase in their cores. We study the existence of a possible hadron-quark phase transition in the central regions of neutron stars and the changes it produces on the gravitational modes frequencies emitted by these stars. We pay particular attention to the g-modes, which are extremely important as they could signal the existence of pure quark matter inside neutron stars. Our results show a relationship between the frequency of the g-modes and the constant speed of sound parametrization for the quark matter phase. We also show that the inclusion of color superconductivity produces an increase on the oscillation frequencies. We propose that observations of g-modes with frequencies fg between 1 kHz and 1.5 kHz should be interpreted as an evidence of a sharp hadron-quark phase transition in the core of a compact object.

Scalarization of neutron stars with realistic equations of state

We consider the effect of scalarization on static and slowly rotating neutron stars for a wide variety of realistic equations of state, including pure nuclear matter, nuclear matter with hyperons, hybrid nuclear and quark matter, and pure quark matter. We analyze the onset of scalarization, presenting a universal relation for the critical coupling parameter versus compactness. We find that the onset and the magnitude of the scalarization are strongly correlated with the value of the gravitational potential (the metric component $g_{tt}$) at the center of the star. We also consider the moment-of-inertia--compactness relations and confirm universality for the nuclear matter, hyperon and hybrid equations of state.

Hybrid Stars in the Framework of NJL Models

We compute models for the equation of state (EoS) of the matter in the cores of hybrid stars. Hadronic matter is treated in the non-linear relativistic mean-field approximation, and quark matter is modeled by three-flavor local and non-local Nambu−Jona-Lasinio (NJL) models with repulsive vector interactions. The transition from hadronic to quark matter is constructed by considering either a soft phase transition (Gibbs construction) or a sharp phase transition (Maxwell construction). We find that high-mass neutron stars with masses up to [Formula: see text] may contain a mixed phase with hadrons and quarks in their cores, if global charge conservation is imposed via the Gibbs conditions. However, if the Maxwell conditions is considered, the appearance of a pure quark matter core either destabilizes the star immediately (commonly for non-local NJL models) or leads to a very short hybrid star branch in the mass-radius relation (generally for local NJL models).

Two-solar-mass hybrid stars: A two model description using the Nambu–Jona-Lasinio quark model

Hybrid stars with a quark phase described by the Nambu$-$Jona-Lasinio model are studied. The hadron-quark model used to determine the stellar matter equation of state favors the appearance of quark matter: the coincidence of the deconfinement and chiral transitions and a low vacuum constituent quark mass. These two properties are essential to build equations of state that predict pure quark matter in the center of neutron stars. The effect of vector-isoscalar and vector-isovector terms is discussed, and it is shown that the vector-isoscalar terms are necessary to describe 2$M_\odot$ hybrid stars, and the vector-isovector terms result in larger quark cores and a smaller deconfinement density.

Constraints on the braneworld from compact stars

According to the braneworld idea, ordinary matter is confined on a three-dimensional space (brane) that is embedded in a higher-dimensional space-time where gravity propagates. In this work, after reviewing the limits coming from general relativity, finiteness of pressure and causality on the brane, we derive observational constraints on the braneworld parameters from the existence of stable compact stars. The analysis is carried out by solving numerically the brane-modified Tolman–Oppenheimer–Volkoff equations, using different representative equations of state to describe matter in the star interior. The cases of normal dense matter, pure quark matter and hybrid matter are considered.

EQUATION OF STATE FOR NEUTRON STARS WITH HYPERONS AND QUARKS IN THE RELATIVISTIC HARTREE–FOCK APPROXIMATION

We construct the equation of state (EoS) for neutron stars explicitly including hyperons and quarks. Using the quark-meson coupling model with relativistic Hartree-Fock approximation, the EoS for hadronic matter is derived by taking into account the strange ($\sigma^{\ast}$ and $\phi$) mesons as well as the light non-strange ($\sigma$, $\omega$, $\vec{\pi}$ and $\vec{\rho}$) mesons. Relevant coupling constants are determined to reproduce the experimental data of nuclear matter and hypernuclei in SU(3) flavor symmetry. For quark matter, we employ the MIT bag model with one-gluon-exchange interaction, and Gibbs criteria for chemical equilibrium in the phase transition from hadrons to quarks. We find that the strange vector ($\phi$) meson and the Fock contribution make the hadronic EoS stiff, and that the maximum mass of a neutron star can be consistent with the observed mass of heavy neutron stars even if the coexistence of hadrons and quarks takes place in the core. However, in the present calculation the transition to pure quark matter does not occur in stable neutron stars. Furthermore, the lower bound of the critical chemical potential of the quark-hadron transition at zero temperature turns out to be around 1.5 GeV in order to be consistent with the recent observed neutron star data.

Finite-size effects at the hadron-quark transition and heavy hybrid stars

We study the role of finite-size effects at the hadron-quark phase transition in a new hybrid equation of state constructed from an ab-initio Br\"uckner-Hartree-Fock equation of state with the realistic Bonn-B potential for the hadronic phase and a covariant non-local Nambu--Jona-Lasinio model for the quark phase. We construct static hybrid star sequences and find that our model can support stable hybrid stars with an onset of quark matter below $2 M_\odot$ and a maximum mass above $2.17 M_\odot$ in agreement with recent observations. If the finite-size effects are taken into account the core is composed of pure quark matter. Provided that the quark vector channel interaction is small, and the finite size effects are taken into account, quark matter appears at densities 2-3 times the nuclear saturation density. In that case the proton fraction in the hadronic phase remains below the value required by the onset of the direct URCA process, so that the early onset of quark matter shall affect on the rapid cooling of the star.