Quark Matter Equation Of State Research Articles

Structure, maximum mass, and stability of compact stars in f(Q,T) gravity

We investigate the properties of compact objects in the f(Q, T) theory, where Q is the non-metricity scalar and T is the trace of the energy–momentum tensor. We derive an interior analytical solution for anisotropic perfect-fluid spheres in hydrostatic equilibrium using the linear form of f(Q,T)=Q+ψT, where ψ represents a dimensional parameter. Based on the observational constraints related to the mass and radius of the pulsar SAX J1748.9-2021, ψ is set to a maximum negative value of ψ1=ψ/κ2=-0.04, where κ2 is the gravitational coupling constant. The solution results in a stable compact object, which does not violate the speed of sound condition cs2≤c23. The effective equation of state is similar to the quark matter equation of state, and involves the presence of an effective bag constant. When ψ is negative, the star has a slightly larger size as compared to GR stars with the same mass. The difference in the predicted star size between the theory with a negative ψ and GR for the same mass is attributed to an additional force appearing in the hydrodynamic equilibrium equation. The maximum compactness allowed by the strong energy condition for f(Q,T) theory and for GR is C=0.514 and 0.419, respectively, with the f(Q,T) prediction about 10% higher than the GR one. Assuming a surface density at saturation nuclear density of ρnuc=4×1014g/cm3, the maximum mass of the star is 4.66M⊙, with a radius of 14.9 km.

The role of pressure anisotropy on quark stars in gravity’s rainbow

This work is seeking for the existence of stable quark stars (QSs) in the framework of a modified theory of gravity known as gravity’s rainbow. This modification comes from the fact that the geometry of spacetime depends on the energy of the test particle. We solve numerically the modified TOV equations and present the mass–radius (M–R) diagram for quark matter equations of state. To constrain the allowed values of the model parameters, we use current astrophysical measurements of the masses and radii of neutron stars. Finally, we investigate the dynamical stability of the hydrostatic equilibrium equations in gravity’s rainbow by analyzing the static stability, adiabatic index, and sound velocity profiles.

Hybrid Star Models in the Light of New Multimessenger Data

Recent astrophysical mass inferences of compact stars HESS J1731-347 and PSR J0952-0607, with extremely small and large masses respectively, as well as the measurement of the neutron skin of Ca in the CREX experiment challenge and constrain the models of dense matter. We examine the concept of hybrid stars—objects containing quark cores surrounded by nucleonic envelopes—as models that account for these new data along with other inferences. We employ a family of 81 nucleonic equations of state (EOSs) with variable skewness and slope of symmetry energy at saturation density and a constant speed-of-sound EOS for quark matter. For each nucleonic EOS, a family of hybrid EOSs is generated by varying the transition density, the energy jump, and the speed of sound. These models are tested against the data from GW170817 and J1731-347, which favor low-density soft EOS and J0592-0607 and J0740+6620, which require high-density stiff EOS. The addition of J0592-0607's mass measurement to the constraints has no significant impact on the parameter space of the admissible EOS, but allows us to explore the potential effect of pulsars more massive than J0740+6620, if such exists. We then examine the occurrence of twin configurations and quantify the ranges of masses and radii that they can possess. It is shown that including J1731-347 data favors EOSs that predict low-mass twins with M ≲ 1.3 M ⊙ that can be realized if the deconfinement transition density is low. If combined with large speed of sound in quark matter such models allow for maximum masses of hybrid stars in 2.0–2.6 M ⊙.

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Color-flavor locked quark stars in Rastall–Rainbow gravity

We investigate the hydrostatic equilibrium configurations of strange stars within the framework of Rastall–Rainbow theory of gravity. These stars are primarily composed of strange quark matter, with its distribution governed by the color-flavor-locked phase of quark matter equation of state (EoS). Using this EoS, we numerically solve the modified Tolman–Oppenheimer–Volkoff equation to obtain different quark star models. We find that the parameters from this modified gravity have specific contributions to the structure of quark stars and introduce new descriptions for massive celestial bodies. Also, the mass–radius relation strongly depends on the parameters from the considered EoS. Furthermore, we analyze the impact of these parameters on the gravitational redshift and compactness of quark stars.

Investigating stable quark stars in Rastall-Rainbow gravity and their compatibility with gravitational wave observations

We present a stable model for quark stars in Rastall-Rainbow (R-R) gravity. The structure of this configuration is obtained by utilizing an interacting quark matter equation of state. The R-R gravity theory is developed as a combination of two distinct theories, namely, the Rastall theory and the gravity's rainbow formalism. Depending on the model parameters (λ¯,η,Σ,Beff), the mass-radius relations are numerically computed for modified Tolman-Oppenheimer-Volkoff (TOV) equations with proper boundary conditions. The stability of equilibrium configuration has been checked through the static stability criterion, adiabatic index and the sound velocity. Our calculations predict larger maximum masses for quark stars, and the obtained results are compatible with accepted masses and radii values, including constraints from GW190814 and GW170817 events in all the studied cases.

Anisotropic quark stars within 4D Einstein–Gauss–Bonnet gravity

By constructing models of quark stars (QSs), we use the MIT bag model as a strange quark matter equation of state (EoS). According to the strange matter hypothesis, the MIT bag model is the most successful phenomenological models of quarks confined to hadrons. This paper aims to explore the internal structure and the physical properties of QSs in the context of four-dimensional (4D) Einstein–Gauss–Bonnet (EGB) theory of gravity. The main feature of 4D EGB theory is that there is a nontrivial contribution to the gravitational dynamics in 4D spacetime. We present the essential features of QSs concerning the mass-radius relation depending on the interplay of matter parameters and the GB coupling constant. Our results show that all studied cases are found to be consistent with observations and physically relevant.

Testing the phase transition parameters inside neutron stars with the production of protons and lambdas in relativistic heavy-ion collisions

We demonstrate the consistency of the quark deconfinement phase transition parameters in the beta-stable neutron star matter and in the nearly symmetric nuclear matter formed in heavy-ion collisions (HICs). We investigate the proton and $\mathrm{\ensuremath{\Lambda}}$ flow in $\mathrm{Au}+\mathrm{Au}$ collisions at 3 and $4.5\text{ }\text{ }\mathrm{GeV}/\mathrm{nucleon}$ incident beam energies with the pure hadron cascade version of a multiphase transport model. The phase transition in HICs and neutron stars is described based on a class of hybrid equations of state from the quark mean-field model for the hadronic phase and a constant-speed-of-sound parametrization for the high-density quark phase. The measurements of the anisotropic proton flow at $3\text{ }\text{ }\mathrm{GeV}/\mathrm{nucleon}$ by the STAR Collaboration favor a relatively low phase transition density lower than $\ensuremath{\sim}2.5$ times saturation density indicated by the gravitational wave and electromagnetic observations of neutron stars. And the proton flow data at the higher energy of $4.5\text{ }\text{ }\mathrm{GeV}/\mathrm{nucleon}$ can be used to effectively constrain the softness of high-density quark matter equations of state. Finally, compared to the proton flow, the $\mathrm{\ensuremath{\Lambda}}$ flow is found to be less sensitive and not constraining to the equations of state.

Binary neutron star mergers as a probe of quark-hadron crossover equations of state

It is anticipated that the gravitational radiation detected in future gravitational wave (GW) detectors from binary neutron star (NS) mergers can probe the high-density equation of state (EOS). We perform the first simulations of binary NS mergers which adopt various parametrizations of the quark-hadron crossover (QHC) EOS. These are constructed from combinations of a hadronic EOS ($n_{b} ~5~n_0$), where $n_{b}$ and $n_0$ are the baryon number density and the nuclear saturation density, respectively. At the crossover densities ($2~ n_0 < n_{b} < 5~ n_0$) the QHC EOSs continuously soften, while remaining stiffer than hadronic and first-order phase transition EOSs, achieving the stiffness of strongly correlated quark matter. This enhanced stiffness leads to significantly longer lifetimes of the postmerger NS than that for a pure hadronic EOS. We find a dual nature of these EOSs such that their maximum chirp GW frequencies $f_{max}$ fall into the category of a soft EOS while the dominant peak frequencies ($f_{peak}$) of the postmerger stage fall in between that of a soft and stiff hadronic EOS. An observation of this kind of dual nature in the characteristic GW frequencies will provide crucial evidence for the existence of strongly interacting quark matter at the crossover densities for QCD.

Study of a realistic model for electrically charged anisotropic stars with a simplest non-interacting quark matter equation of state

In this article a self bound quark star model that possesses some net electric charge is introduced. The quarks considered here are deconfined non-interacting Fermi gas. The solution has been found by solving Einstein-Maxwell field equations through MIT-bag equation of state and a metric potential. The obtained solution is further use to present a comparative studies of four compact stars 4U 1820-30, PSR J1903 + 327, Vela X-1 and PSR J1614-2230. The models are free from singularity, fulfil energy conditions, stability criteria and far within Buchdahl-Andreasson limit. Finally, we have predicted radii of these four compact objects.

Merger of a Neutron Star with a Black Hole: One-family versus Two-families Scenario

Abstract A kilonova (KN) signal is generally expected after a black hole–neutron star merger. The strength of the signal is related to the equation of state of neutron star matter, and it increases with the stiffness of the latter. The recent results obtained by NICER from the analyses of PSR J0740+6620 suggest a rather stiff equation of state, and the expected KN signal is therefore strong, at least if the mass of the black hole does not exceed ∼10 M ⊙, the adimensional spin parameter is not too small, and the orbit is prograde. We compare the predictions obtained by considering equations of state of neutron star matter satisfying the most recent observations and assuming that only one family of compact stars exists with the results predicted in the two-families scenario. In the latter a soft hadronic equation of state produces very compact stellar objects, while a rather stiff quark matter equation of state produces massive strange quark stars, satisfying NICER results. The expected KN signal in the two-families scenario is very weak: in particular, the hadronic star–black hole merger produces a much weaker signal than in the one-family scenario because the hadronic equation of state is very soft. Moreover, according to the only existing simulation, the strange quark star–black hole merger does not produce a KN signal because the amount of mass ejected is negligible. These predictions will be easily tested with the new generation of detectors if black holes with an adimensional spin parameter χ BH ≳ 0.2 or a mass M BH ≲ 4 M ⊙ can be present in the merger.

Electrically charged supermassive twin stars

By assuming that ultra dense hybrid neutron stars are endowed with a distribution of electric charge, we study the corresponding twin star solutions and their properties resulting from a sharp first order transition from confined hadronic to a deconfined quark phase. Two distinct quark matter equations of state with increasing stiffness are considered and the values for the maximum gravitational masses of the hadronic and hybrid twin configurations are obtained for different values of the total electric charge. Interestingly, our calculations indicate that sharp transitions make charged twin hybrid stars more massive than their neutral counterparts, and that the {2},{hbox {M}_{odot }} constraint from PSR J0740+6620 is surpassed for standard values of electric charge and can be considered stable only satisfying partial M/partial epsilon _0 > 0. In particular, our charged stellar models reach masses even higher than the unknown compact object measured in the GW190814 event.

Neutron Star Mergers and the Quark Matter Equation of State

As neutron stars merge they can approach very high nuclear density. Here, we summarized recent results for the evolution and gravitational wave emission from binary-neutron star mergers using a a variety of nuclear equations of state with and without a crossover transition to quark matter. We discuss how the late time gravitational wave emission from binary neutron star mergers may possibly reveal the existence of a crossover transition to quark matter.

Binary neutron star mergers of quark matter based nuclear equations of state

With observations of gravitational wave signals from binary neutron star mergers (BNSM) by LIGO-Virgo-KAGRA (LVK) Collaboration and NICER, the nuclear equation of state (EOS) is becoming increasingly testable by complementary numerical simulations. Numerous simulations currently explore the EOS at different density regimes for the constituent neutron stars specifically narrowing the uncertainty in the sub-nuclear densities. In this paper we summarize the three-dimensional general relativistic-hydrodynamics based simulations of BNSMs for EOSs with a specific emphasis on the quark matter EOS at the highest densities.

Relativistic hybrid stars in light of the NICER PSR J0740+6620 radius measurement

We explore the implications of the recent radius determination of PSR J0740+6620 by the NICER experiment combined with the neutron skin measurement by the PREX-II experiment and the associated inference of the slope of symmetry energy, for the structure of hybrid stars with a strong first-order phase transition from nucleonic to quark matter. We combine a covariant density-functional nucleonic equation of state (EOS) with a constant-speed-of-sound EOS for quark matter. We show that the radius and tidal deformability ranges obtained from GW170817 can be reconciled with the implication of the PREX-II experiment if there is a phase transition to quark matter in the low-mass compact star. In the high-mass segment, the EoS needs to be stiff to comply with the large-radius inference for PSR J0740+6620 and J0030+0451 with masses $M\simeq 2M_{\odot}$ and $M\simeq 1.4M_{\odot}$. We show that twin stars are not excluded, but the mass and radius ranges (with $M \geq M_\odot$) are restricted to narrow domains $\Delta M_{\rm twin} \lesssim 0.05 M_\odot$ and $\Delta R_{\rm twin} \sim 1.0$~km. We also show that the existence of twin configurations is compatible with the light companion in the GW190814 event being a hybrid star in the case of values of the sound-speed square $s=0.6$ and $s=1/3$.

Chiral condensates for neutron stars in hadron-quark crossover: From a parity doublet nucleon model to a Nambu–Jona-Lasinio quark model

We study the chiral condensates in neutron star matter from nuclear to quark matter domain. We describe nuclear matter with a parity doublet model (PDM), quark matter with the Nambu--Jona-Lasino (NJL) model, and a matter at the intermediate density by interpolating nuclear and quark matter equations of state. The model parameters are constrained by nuclear physics and neutron star observations. Various condensates in the interpolated domain are estimated from the chemical potential dependence of the condensates at the boundaries of the interpolation. The use of the PDM with substantial chiral invariant mass ($m_0 \gtrsim 500$ MeV, which is favored by the neutron star observations) predicts the mild chiral restoration, and the significant chiral condensate remains to baryon density $n_B \sim 2-3n_0$ ($n_0\simeq 0.16\,{\rm fm}^{-3}$: nuclear saturation density), smoothly approaching the NJL predictions for the color-flavor-locked phase at $n_B \gtrsim 5n_0$. The same method is applied to estimate diquark condensates, number densities of up-, down- and strange-quarks, and the lepton fraction. In our descriptions the chiral restoration in the interpolated domain proceeds with two conceptually distinct chiral restoration effects; the first is associated with the positive scalar density in a nucleon, relevant in dilute regime, and the other primarily arises from the modification of the quark Dirac sea, which is triggered by the growth of the quark Fermi sea. We discuss several qualitative conjectures to interpolate the microphysics in nuclear and quark matter.

Nonperturbative quark matter equations of state with vector interactions

Nonperturbative equations of state (EoSs) for two and three quark flavors are constructed with the functional renormalization group (FRG) within a quark-meson model truncation augmented by vector mesons for low temperature and high density. Based on previous FRG studies without repulsive vector meson interactions the influence of isoscalar vector ω- and ϕ-mesons on the dynamical fluctuations of quarks and (pseudo)scalar mesons is investigated. The grand potential as well as vector meson condensates are evaluated as a function of quark chemical potential and the quark matter EoS in β-equilibrium is applied to neutron star (NS) physics. The tidal deformability and mass-radius relations for hybrid stars from combined hadronic and quark matter EoSs are compared for different vector couplings. We observe a significant impact of the vector mesons on the quark matter EoS such that the resulting EoS is sufficiently stiff to support two-solar-mass neutron stars.

Structure of Quark Star: A Comparative Analysis of Bayesian Inference and Neural Network Based Modeling

Abstract In this work, we compare two powerful parameter estimation methods, namely Bayesian inference and neural network based learning, to study the quark matter equation of state with constant speed of sound parameterization and the structure of the quark stars within the two-family scenario. We use the mass and radius estimations from several X-ray sources and also the mass and tidal deformability measurements from gravitational wave events to constrain the parameters of our model. The results found from the two methods are consistent. The predicted speed of sound is compatible with the conformal limit.

Quark matter in light neutron stars

Higher-order repulsive interactions are included in the three-flavor NJL model in order to describe the quark phase of an hybrid star. The effect of 4-quark and 8-quark vector-isoscalar interactions in the stability of hybrid star configurations is analyzed. The presence of a 8-quark vector-isoscalar channel is seen to be crucial in generating large quark branches in the $M(R)$ diagram. This is due to its stiffening effect on the quark matter equation of state which arises from the non-linear density dependence of the speed of sound. This additional interaction channel allows for the appearance of a quark core at moderately low NS masses, $\sim 1M_{\odot}$, and provides the required repulsion to preserve the star stability up to $\sim2.1M_{\odot}$. Furthermore, we show that both the heaviest NS mass generated, $M_{\text{max}}$, and its radii, $R_{\text{max}}$, are quite sensitive to the strength of 8-quark vector-isoscalar channel, leading to a considerable decrease of $R_{\text{max}}$ as the coupling increases. This behavior imprints a considerable deviation from the purely hadronic matter equation of state in the $\Lambda(M)$ diagram, which might be a possible signature of the quark matter existence, even for moderately low NS masses, $\sim 1.4\, M_\odot$. The resulting $M(R)$ and $\Lambda(R)$ relations are in accordance with the latest astrophysical constraints from NICER and Ligo/VIRGO observations, respectively.

Electrically charged strange stars with an interacting quark matter equation of state

The properties of electrically charged strange quark stars predicted by an interacting quark matter equation of state (EoS) based on cold and dense perturbative quantum chromodynamics (pQCD) are investigated. The stability of strange stars is analyzed considering different models for the electric charge distribution inside the star as well as for distinct values for the total electric charge. A comparison with the predictions derived using the MIT bag model is also presented. We show that the presence of a net electric charge inside strange stars implies in a larger maximum mass in comparison to their neutral counterparts. Moreover, we demonstrate that the pQCD EoS implies larger values for the maximum mass of charged strange stars, with very heavy charged stars being stable systems against radial oscillations. For an electric charge distribution given by $q(r) = \beta r^3$, the pQCD EoS implies unstable configurations for large values of the renormalization scale as well as for large values of $\beta$, in contrast to the MIT bag model predictions.