Quark Matter Equation Of State Research Articles

Properties of strange quark stars with isovector interactions

We study the properties of strange quark stars by employing a 3-flavor Nambu-Jona-Lasinio model with both scalar-isovector and vector-isovector interactions. Using the constraint on the vector-isoscalar interaction strength obtained from the elliptic flow splitting between particles and their antiparticles in relativistic heavy-ion collisions, we investigate the dependence of the properties of strange quark stars on the vector-isovector and the scalar-isovector interactions, and compare the results with the state-of-art astrophysical constraints on the compact star radius and mass as well as its tidal deformability from the GW170817 event. Results from our study reinforce the prospect of using both heavy-ion collisions and astrophysical observations to provide constraints on the isovector coupling strength in quark matter and thus the quark matter equation of state as well as the QCD phase structure at finite isospin chemical potentials.

First-order phase transition from hypernuclear matter to deconfined quark matter obeying new constraints from compact star observations

We reconsider the problem of the hyperon puzzle and its suggested solution by quark deconfinement within the two-phase approach to hybrid compact stars with recently obtained hadronic and quark matter equations of state. For the hadronic phase we employ the hypernuclear equation of state from the lowest order constrained variational method and the quark matter phase is described by a sufficiently stiff equation of state based on a color superconducting nonlocal Nambu-Jona-Lasinio model with constant (model nlNJLA) and with density-dependent (model nlNJLB) parameters. We study the model dependence of the phase transition obtained by a Maxwell construction. Our study confirms that also with the present set of equations of state quark deconfinement presents a viable solution of the hyperon puzzle even for the new constraint on the lower limit of the maximum mass from PSR J0740+6620. In this work we provide with model nlNJLB for the first time a hybrid star EoS with an intermediate hypernuclear matter phase between the nuclear and color superconducting quark matter phases, for which the maximum mass of the compact star reaches $2.2~M_\odot$, in accordance with most recent constraints. In model nlNJLA such a phase cannot be realised because the phase transition onset is at low densities, before the hyperon threshold density is passed. We discuss possible consequences of the hybrid equation of state for the deconfinement phase transition in symmetric matter as it will be probed in future heavy-ion collisions at FAIR, NICA and corresponding energy scan programs at the CERN and RHIC facilities.

Elliptic flow splittings between particles and their antiparticles in relativistic heavy-ion collisions

Relativistic heavy-ion collisions are an important experimental way of studying the new state of matter as well as the phase diagram of the quantum chromodynamics (QCD) under extremely high temperatures and high densities. The elliptic flow is an important experimental observable in relativistic heavy-ion collisions. In recent years, the beam-energy scan program has been carried out on the relativistic heavy-ion collider at Brookhaven National Laboratory in USA, where phenomena different from those in heavy-ion collisions at extremely high energies, such as the elliptic flow splittings between particles and their antiparticles, are observed. Based on an extended multiphase transport model, this phenomenon can be explained through different mean-field potentials for particles and their antiparticles. In the almond-shaped medium produced in these collisions, particles affected by the repulsive potential are more likely to leave the system, while those affected by the attractive potential are more likely to be trapped in the system, enhancing and reducing their respective elliptic flow. The partonic mean-field potentials are extracted from an extended 3-flavor Nambu-Jona-Lasinio (NJL) model. Quarks are affected by more repulsive potentials compared with their antiquarks as a result of the vector-isoscalar coupling, while d quarks are affected by a more repulsive potential compared with u quarks as a result of the vector-isovector coupling, in the baryon-rich and d -quark-rich medium. The hadronic mean-field potentials are also incorporated through the relativistc mean-field model for baryons and antibaryons, and through the chiral effective field theory for kaons and antikaons as well as for π + and π − . In the baryon-rich and neutron-rich medium, antinucleons, antikaons, and π + are affected by more attractive potentials than nucleons, kaons, and π − , respectively. It is found that a strong vector-isoscalar and vector-isovector coupling are needed to reproduce the elliptic flow splittings between nucleons and antinucleons, kaons and antikaons, as well as π + and π − , as observed experimentally by the STAR Collaboration. On the other hand, the NJL model can be used to study the spontaneous chiral symmetry breaking and the phase diagram of the chiral phase transition. In order to describe both the chiral and deconfinement phase transition, one needs to extend the NJL model by incorporating the Polyakov-loop contribution (pNJL). Although the temperature of the crtical point for the chiral phase transition is higher in the pNJL model, it is found that the position or the behavior of the critical point is sensitive to the strength of the vector-isoscalar and the vector-isovector couplings in both the NJL and the pNJL model. In addition, the equation of state of baryon-rich and d -quark-rich quark matter is sensitive to these couplings as well. With these couplings constrainted by the elliptic flow splittings between particles and their antiparticles, information of the quark matter equation of state as well as the QCD phase diagram at finite baryon and isospin chemical potentials can be thus extracted. The study shows that the QCD critical point may be at very low temperatures or does not even exist, while the strong vector-isoscalar and vector-isovector couplings favor a stiff equation of state of quark matter at high net-baryon and isovector densities. In future studies, the transport framework can be further extended to incorporate the Polyakov-loop contribution.

Thomas–Fermi approximation in the phase transition of neutron star matter from [formula omitted]-stable nuclear matter to quark matter

The equation of state (EOS) of hybrid neutron star (HNS) matter is investigated within a model where the phase transition from non-strange baryonic matter to quark matter is described with the help of the Gibbs construction. We use the Myers and Swiatecki (MS) interactions of TF(96) and TF(90) to extract the EOS of β-stable nuclear matter from the Thomas–Fermi (TF) approximation in a semi-classical mean-field (MF) model. The EOS of the deconfined quark phase is obtained from the Nambu–Jona–Lasinio (NJL) model. In studying the EOS of HNS matter, we take into account the two-solar-mass constraint placed by the measurement of the masses of pulsars PSR J1614−2230, PSR J0348＋ 0432 and PSR J0740+6620. We find that the vector coupling of the NJL model has a strong influence on the formation of the stable HNSs. Our results show that the pure quark phase does not exist in the inner core of HNSs. As the repulsion in the quark matter EOS becomes stronger, the stable configurations of an HNS are formed at lower values of the stellar radius. The quark phase with larger repulsive vector interaction indicates smaller mixed phase region in the inner core of the same-mass HNSs. In addition, the stable HNSs occur at larger radii for the configurations constructed using the stiffer one of the two baryonic EOSs we considered [TF(90)].

Isospin splitting of pion elliptic flow in relativistic heavy-ion collisions

Based on the framework of an extended multiphase transport model with mean-field potentials in both the partonic phase and the hadronic phase, we explain the elliptic flow difference between π+ and π− in the beam-energy scan program at the relativistic heavy-ion collider by incorporating the vector-isovector potential for quarks and antiquarks with different flavors or isospins. It is found that the isospin splitting of pion elliptic flow favors a strong vector-isovector interaction, and thus serves as a probe of the quark matter equation of state as well as the QCD phase structure at finite baryon and isospin chemical potentials.

Constraints on hybrid neutron stars equation of state from neutron stars merging

Using recent gravitational and electromagnetic constraints on the neutron star matter equation of state (EOS) coming from the merge of two neutron stars, we study the physical conditions for which a quark deconfinement phase transition in cold neutron star matter is consistent with these new measurements. To this end, we consider several microscopic EOSs based on various ab initio approaches to describe the confined hadronic phase, and combine them with two phenomenological quark matter EOSs for the deconfined phase. The low and high density phases are then joined up through a mixed phase determined by a Gibbs construction. For each EOS we calculate the dimensionless binary deformability parameter \(\tilde{\Lambda}\) which can be directly related to the constraints derived from the gravitational waves detection. We find that in order to see any difference between the pure hadronic and the hadron-quark EOS for neutron stars with mass in the range (1.4-1.6) \(M_{\odot}\) through the calculation of \(\tilde{\Lambda}\), the EOSs of both hadronic and quark matter should be quite stiff, otherwise the variation on \( \tilde{\Lambda}\) can be valued just on neutron star masses above 1.8 \( M_{\odot}\) which currently are not constrained by present gravitational waves data. We find in addition that the softening of the hadronic EOS induced by the quark deconfinement phase transition can change the compatibility of a given hadronic EOS with the constraints obtained from neutron stars merging.

The equation of state of dense matter: Stiff, soft, or both?

We review the constraints on the equation of state (EoS) of dense matter that have been obtained with the detection of GW170817 and its electromagnetic counterparts. While extremely stiff EoSs are ruled out by the gravitational wave signal, also extremely soft EoSs seem disfavored because they are unable to provide massive enough accretion disks. In this respect, the two‐families scenario, in which hadronic stars (HSs) and quark stars (QSs) coexist, could offer a viable solution: the hadronic matter EoS is very soft and leads to very small radii, whereas the quark matter EoS is stiff and leads to large masses. In this scenario, GW170817 could be interpreted as due to the merger of an HS and a QS. We present a parametric study of the two‐families scenario in which the quark matter EoS is computed by a constant‐speed‐of‐sound (cs) model and study the astrophysical constraints on the free parameters of the model. For this study, we fix , which holds true at asymptotically high densities (the conformal limit). If quark matter is absolutely stable, its baryon density at zero pressure must be smaller than twice the nuclear saturation density and its energy per baryon is a few tens of MeV smaller than that of iron.

Two Novel Approaches to the Hadron-Quark Mixed Phase in Compact Stars

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.

Dynamical Phase Transition in Neutron Stars

Abstract We have studied the dynamical evolution of the shock in a neutron star (NS). The conversion of nuclear to quark matter (QM) is assumed to take place at the shock discontinuity. The density and pressure discontinuity is studied both spatially and temporally as it starts near the center of the star and moves toward the surface. Polytropic equations of state (EoS), which mimic original nuclear and QM EoS, are used to study such dynamical phase transition (PT). Solving relativistic hydrodynamic equations for a spherically symmetric star, we study the PT, assuming a considerable density discontinuity near the center. We find that as the shock wave propagates outward, its intensity decreases with time; however, the shock velocity peaks up and reaches a value close to that of light. Such fast shock velocity indicates rapid PT in NS taking place on a timescale of some 10s of microseconds. Such a result is quite interesting, and it differs from previous calculations that the PT in NSs takes at least some 10s of milliseconds. Rapid PT can have significant observational significance, because such fast PT would imply rather strong gravitational wave (GW) signals that are rather short lived. Such short-lived GW signals would be accompanied with short-lived gamma-ray bursts and neutrino signals originating from the neutrino and gamma-ray generation from the PT of nuclear matter to QM.

Hybrid Stars in the Light of GW170817

Abstract We have studied the effect of the tidal deformability constraint given by the binary neutron star merger event GW170817 on the equations of state (EOS) of hybrid stars. The EOS are constructed by matching the hadronic EOS described by the relativistic mean-field model and parameter sets NL3, TM1, and NL3ωρ with the quark matter EOS described by the modified MIT bag model, via a Gibbs construction. It is found that the tidal deformability constraints along with the lower bound on the maximum mass (M max = 2.01 ± 0.04 M ⊙) significantly limits the bag model parameter space ( , a 4). We also obtain upper limits on the radius of 1.4 M ⊙ and 1.6 M ⊙ stars as R 1.4 ≤ 13.2–13.5 km and R 1.6 ≤ 13.2–13.4 km, respectively, for the different hadronic EOS considered here.

QCD Equations of State in Hadron–Quark Continuity

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.

Twin stars within the SU(3) chiral quark-meson model

We present new stable solutions of the Tolman Oppenheimer Volkoff equations for quark stars using a quark matter equation of state based on the SU(3) Quark-Meson model that exhibits the onset of the chiral phase transition. These new solutions appear as two stable branches in the mass-radius relation allowing for so called twin stars, i.e. two stable quark star solutions with the same mass, but distinctly different radii. We find solutions which are compatible with causality, the stability conditions of dense matter, the astrophysical constraints of the rotation of the millisecond pulsar PSR J1748-2446ad and the 2$M_{\odot}$ pulsar mass constraint.

Constant entropy hybrid stars: a first approximation of cooling evolution

We aim to study the possibility of a hadron-quark phase transition in the interior of neutron stars, taking into account different schematic evolutionary stages at finite temperature. We also discuss the strange quark matter stability in the quark matter phase. Furthermore, we aim to analyze the astrophysical properties of hot and cold hybrid stars, considering the constraint on maximum mass given by the pulsars J1614-2230 and J0348+0432. We have developed a computational code to construct semi-analytical hybrid equations of state at fixed entropy per baryon and to obtain different families of hybrid stars. An analytical approximation of the Field Correlator Method is developed for the quark matter equation of state. For the hadronic equation of state we use a table based on the relativistic mean field theory, without hyperons. We solved the relativistic structure equations of hydrostatic equilibrium and mass conservation for hybrid star configurations. For the different equations of state obtained, we calculated the stability window for the strange quark matter, lepton abundances, temperature profiles and contours profiles for the maximum mass star depending on the parameters of the Field Correlator Method. We also computed the mass-radius and gravitational mass-baryonic mass relationships for different hybrid star families. We have analyzed different stages of hot hybrid stars as a first approximation of the cooling evolution of neutron stars with quark matter cores. We obtain cold hybrid stars with maximum masses $\geq 2 M_\odot$ for different combinations of the Field Correlator Method parameters. In addition, our study based on the gravitational mass - baryonic mass plane shows a late phase transition between hadronic and quark matter during the proto-hybrid star evolution, in contrast with previous studies of proto-neutron stars.

Quark Matter Equation of State from Perturbative QCD

In this proceedings contribution, we discuss recent developments in the perturbative determination of the Equation of State of dense quark matter, relevant for the microscopic description of neutron star cores. First, we introduce the current state of the art in the problem, both at zero and small temperatures, and then present results from two recent perturbative studies that pave the way towards extending the EoS to higher orders in perturbation theory.

Phenomenological neutron star equations of state

We discuss the 3-window modeling of cold, dense QCD matter equations of state at density relevant to neutron star properties. At low baryon density, n_B < ~ 2n_s (n_s: nuclear saturation density), we utilize purely hadronic equations of state that are constrained by empirical observations at density n_B ~ n_s and neutron star radii. At high density, n_B > ~ 5n_s, we use the percolated quark matter equations of state which must be very stiff to pass the two-solar mass constraints. The intermediate domain at 2 < n_B/n_s < 5 is described as neither purely hadronic nor percolated quark matter, and the equations of state are inferred by interpolating hadronic and percolated quark matter equations of state. Possible forms of the interpolation are severely restricted by the condition on the (square of) speed of sound, 0 < c_s^2 < 1. The characteristics of the 3-window equation of state are compared with those of conventional hybrid and self-bound quark matters. Using a schematic quark model for the percolated domain, it is argued that the two-solar mass constraint requires the model parameters to be as large as their vacuum values, indicating that the gluon dynamics remains strongly non-perturbative to n_B ~ 10n_s. The hyperon puzzle is also briefly discussed in light of quark descriptions.

Characteristics of hybrid compact stars with a sharp hadron-quark interface

We describe two aspects of the physics of hybrid stars that have a sharp interface between a core of quark matter and a mantle of nuclear matter. Firstly, we analyze the mass-radius relation. We describe a generic “Constant-Speed-of-Sound” (CSS) parameterization of the quark matter equation of state (EoS), in which the speed of sound is independent of density. In terms of the three parameters of the CSS EoS we obtain the phase diagram of possible forms of the hybrid star mass-radius relation, and we show how observational constraints on the maximum mass and typical radius of neutron stars can be expressed as constraints on the CSS parameters. Secondly, we propose a mechanism for the damping of density oscillations, including r-modes, in hybrid stars with a sharp interface. The dissipation arises from the periodic conversion between quark matter and nuclear matter induced by the pressure oscillations in the star. We find the damping grows nonlinearly with the amplitude of the oscillation and is powerful enough to saturate an r-mode at very low saturation amplitude, of order $ 10^{-10}$ , which is compatible with currently available observations of neutron star spin frequencies and temperatures.

Hydrodynamical study on the conversion of hadronic matter to quark matter. II. Diffusion-induced conversion

We study transitions of hadronic matter (HM) to three-flavor quark matter (3QM), regarding the conversion processes as combustion and describing them hydrodynamically. Under the assumption that HM is metastable with their free energies being larger than those of 3QM but smaller than those of two-flavor quark matter, we consider in this paper the conversion induced by diffusions of the seed 3QM. This is a sequel to our previous paper, in which the shock-induced conversion was studied in the same framework. We not only pay attention to the jump condition on both sides of the conversion front, but the structures inside the front are also considered by taking into account what happens during the conversion processes on the time scale of weak interactions. We employ for HM Shen's equation of state (EOS), which is based on the relativistic mean field theory, and the bag model-based EOS for quark matter just as in the previous paper. We demonstrated in that paper that in this combination of EOSs, the combustion will occur for a wide range of the bag constant and strong coupling constant in the so-called endothermic regime, in which the Hugoniot curve for combustion runs below the initial state. Elucidating the essential features of the diffusion-induced conversion both in the exothermic and endothermic regimes first by a toy model, we then analyze more realistic models. We find that weak deflagration nearly always occurs and that weak detonation is possible only when the diffusion constant is (unrealistically) large and the critical strange fraction is small. The velocities of the conversion front are $\ensuremath{\sim}{10}^{3}--{10}^{7}\text{ }\text{ }\mathrm{cm}/\mathrm{s}$ depending on the initial temperature and density as well as the parameters in the quark matter EOS and become particularly small when the final state is in the mixed phase. Finally we study linear stability of the laminar weak-deflagration front and find that it is unstable in the exothermic regime (Darrius-Landau instability) but stable in the endothermic regime, which is quite contrary to the ordinary combustions.

Consistent neutron star models with magnetic-field-dependent equations of state

We present a self-consistent model for the study of the structure of a neutron star in strong magnetic fields. Starting from a microscopic Lagrangian, this model includes the effect of the magnetic field on the equation of state, the interaction of the electromagnetic field with matter (magnetisation), and anisotropies in the energy-momentum tensor, as well as general relativistic aspects. We build numerical axisymmetric stationary models and show the applicability of the approach with one example quark matter equation of state (EoS) often employed in the recent literature for studies of strongly magnetised neutron stars. For this EoS, the effect of inclusion of magnetic field dependence or the magnetisation do not increase the maximum mass significantly in contrast to what has been claimed by previous studies.

Generic Conditions for Stable Hybrid Stars

We study the mass-radius curve of hybrid stars, assuming a single first-order phase transition between nuclear and quark matter, with a sharp interface between the quark matter core and nuclear matter mantle. We use a generic parameterization of the quark matter equation of state, which has a constant, i.e. density-independent, speed of sound (CSS). We argue that this parameterization provides a framework for compar- ison and empirical testing of models of quark matter. We obtain the phase diagram of possible forms of the hybrid star mass-radius relation, where the control parameters are the transition pressure, energy density discontinuity, and the quark matter speed of sound. We find that this diagram is sensitive to the quark matter parameters but fairly insensitive to details of the nuclear matter equation of state. We calculate the maximum hybrid star mass as a function of the parameters of the quark matter EoS, and find that there are reasonable values of those parameters that give rise to hybrid stars with mass above 2 M� .

Neutron Star masses from the Field Correlator Method Equation of State

We analyse the hadron-quark phase transition in neutron stars by confronting the hadronic Equation of State (EoS) obtained according to the microscopic Brueckner-Hartree-Fock many body theory, with the quark matter EoS derived within the Field Correlator Method. In particular, the latter EoS is only parametrized in terms of the gluon condensate and the large distance quark-antiquark potential, so that the comparison of the results of this analysis with the most recent measurements of heavy neutron star masses provides some physical constraints on these two parameters.