Density Dependent Quark Mass Research Articles

Proto-strange quark stars from density-dependent quark mass model

In this paper, we investigate the evolution of strange quark stars (SQS) from birth as proto-strange quark stars to maturity as stable SQSs at a zero temperature. We assume that self-bound free quarks form entirely the compact star and study its evolution through a series of snapshots using a density-dependent quark mass model. We consider β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-equilibrated stellar matter at two major stages of the star’s evolution: neutrino trapped regime and neutrino transparent regime during the deleptonization and cooling processes of the star. We fix the entropy density per baryon and the lepton fraction to investigate the nuclear equation of state (EoS), particle distribution, temperature profile inside the star, sound velocity, polytropic index, and the structure of the star. Our results show that stars with higher neutrino concentrations are slightly more massive than the neutrino-poor ones along the evolution lines of the SQS. We obtain EoSs in agreement with the conformal boundary set through sound velocity, and also the 2 M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_\\odot $$\\end{document} mass constraint for NSs was satisfied at all stages of the star’s evolution.

Quark star matter in the color-flavor-locked state with a density-dependent quark mass model

The properties of strange quark matter (SQM) and color-flavor-locked (CFL) quark matter are investigated in quark stars (QSs) at zero temperature case within confined-isospin-density-dependent-mass (CIDDM) model. The mass–radius relation of QSs are also studied by considering newly proposed mass–radius constraints in CFL phase. Our results indicate that we can obtain more stable and stiffer equation of state (EOS) by considering CFL phase within CIDDM model at zero temperature. While the GW190814's secondary component with a mass around 2.6 M ⊙ cannot be QSs within CIDDM model in SQM case, it can be well described as QSs by considering CFL phase within CIDDM model in this work. In particular, we further construct a density-dependent pairing energy gap to connect the EOS of SQM and CFL quark matter with constant pairing energy gap Δ, and the results indicate that by extending the paring energy gap to include density dependence, the mass–radius lines within CIDDM model can satisfy most of the mass–radius region constraints in recent pulsar observations.

Gravitational wave echoes from strange quark stars in the equation of state with density-dependent quark masses

Gravitational wave echoes from strange quark stars in the equation of state with density-dependent quark masses

Confronting Strange Stars with Compact-Star Observations and New Physics

Strange stars ought to exist in the universe according to the strange quark matter hypothesis, which states that matter made of roughly equal numbers of up, down, and strange quarks could be the true ground state of baryonic matter rather than ordinary atomic nuclei. Theoretical models of strange quark matter, such as the standard MIT bag model, the density-dependent quark mass model, or the quasi-particle model, however, appear to be unable to reproduce some of the properties (masses, radii, and tidal deformabilities) of recently observed compact stars. This is different if alternative gravity theory (e.g., non-Newtonian gravity) or dark matter (e.g., mirror dark matter) are considered, which resolve these issues. The possible existence of strange stars could thus provide a clue to new physics, as discussed in this review.

Strange quark matter and proto-strange stars in a baryon density-dependent quark mass model * *Supported by the National Natural Science Foundation of China (11875052, 11575190, 11135011)

The properties of strange quark matter and the structures of (proto-)strange stars are studied within the framework of a baryon density-dependent quark mass model, where a novel quark mass scaling and self-consistent thermodynamic treatment are adopted. Our results indicate that the perturbative interaction has a significant impact on the properties of strange quark matter. It is determined that the energy per baryon increases with temperature, while the free energy decreases and eventually becomes negative. At fixed temperatures, the pressure at the minimum free energy per baryon is zero, suggesting that the thermodynamic self-consistency is preserved. Furthermore, the sound velocity v in quark matter approaches the extreme relativistic limit ( ) as the density increases. By increasing the strengths of the confinement parameter D and perturbation parameter C, the tendency for v to approach the extreme relativistic limit at high density is slightly weakened. For (proto-)strange stars, the novel quark mass scaling can accommodate massive proto-strange stars with their maximum mass surpassing twice the solar mass by considering the isentropic stages along the star evolution line, where the entropy per baryon of the star matter is set to be 0.5 and 1 with the lepton fraction = 0.4.

Strangelets at finite temperature in a baryon density-dependent quark mass model

The properties of strangelets at finite temperature are studied within the framework of a baryon densitydependent quark mass model, where a new quark mass scaling and self-consistent thermodynamic treatment are adopted. The effects of finite volume and Coulomb energy are taken into account. Our results show that the temperature $T$, baryon number $A$, and perturbation interactions have strong influences on the properties of strangelets. It is found that the energy per baryon $M/A$ and charge-to-mass ratio ${f}_{z}$ decrease with baryon number $A$, while the mechanically stable radius $R$ and strangeness per baryon ${f}_{S}$ are increasing. For a strangelet with a fixed baryon number, we note that as temperature $T$ increases the quantities $M/A$, $R$, and ${f}_{S}$ are increasing while ${f}_{z}$ is decreasing. The effects of confinement and perturbative interactions are investigated as well by readjusting the corresponding parameters.

Effects of strong magnetic fields on the hadron-quark deconfinement transition

The aim of the present work is to investigate the effects of strong magnetic fields on the hadron-quark phase transition point at zero temperature. To describe the hadronic phase, a relativistic mean field (RMF) model is used and to describe the quark phase a density dependent quark mass model (DDQM) is employed. As compared with the results obtained with non-magnetised matter, we observe a shift of the transition point towards higher pressures and, generally also towards higher chemical potentials. An investigation of the phase transitions that could sustain hybrid stars is also performed.

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.

Constraints from compact star observations on non-Newtonian gravity in strange stars based on a density dependent quark mass model

Using a density dependent quark mass (QMDD) model for strange quark matter, we investigate the effects of non-Newtonian gravity on the properties of strange stars and constrain the parameters of the QMDD model by employing the mass of PSR J0740+6620 and the tidal deformability of GW170817. We find that for QMDD model these mass and tidal deformability observations would rule out the existenceof str ange stars if non-Newtonian gravity effects are ignored. For the current quark masses of $m_{u0}=2.16$ MeV, $m_{d0}=4.67$ MeV, and $m_{s0}=93$ MeV, we find that a strange star can exist for values of the non-Newtonian gravity parameter $g^{2}/\mu^{2}$ in the range of 4.58 GeV$^{-2}\leq g^{2}/\mu^{2}\leq$ 9.32 GeV$^{-2}$, and that the parameters $D$ and $C$ of the QMDD modelare restricted to 158.3 MeV$\leq D^{1/2}\leq$ 181.2 MeV and $-0.65\leq C \leq -0.12$. It is found that the largest possible maximum mass of a strange star obtained with the QMDD model is $2.42 \, M_{\odot}$, and that the secondary componentof GW190814 with a mass of 2.59_{-0.09}^{+0.08}\, M_{\dot} could not be a static strange star. We also find that forthe mass and radius of PSR J0030+0451 given by Riley et al. through the analysis of observational data of NICER, there exists a very tiny allowed parameter space for which strange stars computed for the QMDD model agree with the observations of PSR J0740+6620, GW17 0817 and PSR J0030+0451 simultaneously. However, for the mass and radius given by Miller et al., no such parameter space exist.

Interface effects of strange quark matter with density dependent quark masses

We study the interface effects in strangelets adopting mean-field approximation (MFA). Based on an equivparticle model, the linear confinement and leading-order perturbative interactions are included with density-dependent quark masses. By increasing the confinement strength, the surface tension and curvature term of strange quark matter (SQM) become larger, while the perturbative interaction does the opposite. For those parameters constrained according to the 2$M_\odot$ strange star, the surface tension is $\sim$2.4 MeV/fm${}^2$, while unstable SQM indicates a slightly larger surface tension. The obtained results are then compared with those predicted by the multiple reflection expansion (MRE) method. In contrast to the bag model case, it is found that MRE method overestimates the surface tension and underestimates the curvature term. To reproduce our results, the density of states in the MRE approach should be modified by proper damping factors.

Isovector properties of quark matter and quark stars in an isospin-dependent confining model

The confining quark matter (CQM) model, in which the confinement and asymptotic freedom are modeled via the Richardson potential for quark-quark vector interaction and the chiral symmetry restoration at high density is described by the density dependent quark mass, is extended to include isospin dependence of the quark mass. Within this extended isospin-dependent confining quark matter (ICQM) model, we study the properties of strange quark matter and quark stars. We find that including isospin dependence of the quark mass can significantly influence the quark matter symmetry energy, the stability of strange quark matter and the mass-radius relation of quark stars. In particular, we demonstrate although the recently discovered large mass pulsars PSR J1614.2230 and PSR J0348+0432 with masses around two times solar mass ($2M_{\odot}$) cannot be quark stars within the original CQM model, they can be well described by quark stars in the ICQM model if the isospin dependence of quark mass is strong enough so that the quark matter symmetry energy is about four times that of a free quark gas. We also discuss the effects of the density dependence of quark mass on the properties of quark stars. Our results indicate that the heavy quark stars with mass around $2M_{\odot}$ (if exist) can put strong constraints on isospin and density dependence of the quark mass as well as the quark matter symmetry energy.

Quark stars with strong magnetic fields: considering different magnetic field geometries

We calculate the mass-radius relationship of quark stars with the magnetized density-dependent quark mass model in this work, considering two magnetic field geometries: a statistically isotropic, tangled field and a force-free configuration. In both cases, magnetic field production decreases in the case of maximum quark star mass. Furthermore, a tangled, isotropic magnetic field has a relatively smaller impact on the mass and radius, compared to the force-free configuration, which implies that the geometry of the interior magnetic field is at least as important as the field strength itself when the influence of the strong magnetic field on the mass and radius is assessed.

Thermodynamic consistency, quark mass scaling, and properties of strange matter

The previous thermodynamic treatment for models with density and/or temperature dependent quark masses is shown to be inconsistent with the requirement of fundamental thermodynamics. We therefore study a fully self-consistent one according to the fundamental differential equation of thermodynamics. After obtaining a new quark mass scaling with the inclusion of both confinement and leading-order perturbative interactions, we investigate properties of strange quark matter in the fully consistent thermodynamic treatment. It is found that the equation of state become stiffer, and accordingly, the maximum mass of strange stars is as large as about 2 times the solar mass, if strange quark matter is absolutely or metastable.

Strange star equation of state fits the refined mass measurement of 12 pulsars and predicts their radii

There are three categories of stars whose masses have been found accurately in recent times: (1) two for which Shapiro delay is used which is possible due to GR light bending as the partner is heavy : PSR J1614-2230 and PSR J1903+0327 (2) six eclipsing stars for which numerical Roche Lobe geometry is used and (3) 3 stars for which spectroscopic methods are used and in fact for these three the mass and radii both are estimated. Motivated by large color (N_c) expansion using a modified Richardson potential, along with density dependent quark masses thereby allowing chiral symmetry restoration, we get compact strange stars fitting all the observed masses.

Magnetized strange quark matter in a quasiparticle description

The quasiparticle model is extended to investigate the properties of strange quark matter in a strong magnetic field at finite densities. For the density-dependent quark mass, self-consistent thermodynamic treatment is obtained with an additional effective bag parameter, which depends not only on the density but also on the magnetic field strength. The magnetic field makes strange quark matter more stable energetically when the magnetic field strength is less than a critical value of the order $10^7$ Gauss depending on the QCD scale $\Lambda$. Instead of being a monotonic function of the density for the QCD scale parameter $\Lambda>126$ MeV, the effective bag function has a maximum near $0.3\sim 0.4$ fm$^{-3}$. The influence of the magnetic field and the QCD scale parameter on the stiffness of the equation of state of the magnetized strange quark matter and the possible maximum mass of strange stars are discussed

Quark stars with the density-dependent quark mass model

The recent observation of the pulsar PSR J1614-2230 with a mass of 1.97±0.04M⊙ gives a strong constraint on the equation of state (EoS) of the dense matter in compact stars. In this work, we calculate the maximum mass of quark stars with the density-dependent quark mass model, and explore the parameter ranges for this model fully, by considering the constraints of absolute stability of strange quark matter and the mass of PSR J1614-2230. Without the color-superconductivity, the maximum mass of unpaired quark stars is more sensitive to the parameter C, and complies with the constraints within the range of 96MeVfm-3≲C≲130MeVfm-3. The largest mass can reach 2.25M⊙ at C≃96.54MeVfm-3 and ms0≃145MeV. For the quark stars composed of the quark matter in color-flavor locked (CFL) phase, we can obtain quite large maximum masses at a sufficiently high gap value, but the value of ms0 is very important in deciding the maximum mass of the CFL quark stars.

The effect of dynamical quark mass on the calculation of a strange quark star's structure

We discuss the dynamical behavior of strange quark matter components, in particular the effects of density dependent quark mass on the equation of state of strange quark matter. The dynamical masses of quarks are computed within the Nambu-Jona-Lasinio model, then we perform strange quark matter calculations employing the MIT bag model with these dynamical masses. For the sake of comparing dynamical mass interaction with QCD quark-quark interaction, we consider the one-gluon-exchange term as the effective interaction between quarks for the MIT bag model. Our dynamical approach illustrates an improvement in the obtained equation of state values. We also investigate the structure of the strange quark star using Tolman-Oppenheimer-Volkoff equations for all applied models. Our results show that dynamical mass interaction leads to lower values for gravitational mass.

QUARK CONFINEMENT AND THE PROPERTIES OF QUARK MATTER

The properties of two-flavor quark matter are investigated with a model which incorporates the confinement by density-dependent quark masses (CDDM). The results are compared with those in the conventional MIT bag model. It is found that the density behavior of quark matter in the two models are significantly different. Specially, the second derivative of the energy density can be negative in the CDDM while that in the bag model is always positive. This makes the velocity of sound very different in both models.

Quark matter in compact stars

Recently reported massive compact stars ( M ∼ 2 M ⊙ ) have provided strong constraints on the properties of the ultradense matter beyond the saturation nuclear density. Therefore, realistic quark or hybrid star models must be compatible with these observational data. Some used equations of state (EoS) describing quark matter are in general too soft and hence are not suitable to explain the stability of high compact star masses. In this work, we present the calculations of static spherically symmetric quark star structure by using an equation of state which takes into account the superconducting colour-flavour locked phase of the strange quark matter. In addition, some fundamental aspects of QCD (asymptotic freedom and confinement) are considered by means of a phenomenological description of the deconfined quark phase, the density-dependent quark mass model. We discuss the influence of the obtained quark matter equation of state on the mass-radius relationship of quark stars. Massive quark stars are found due to the stiffness of the equation of state, when reasonable values of the superconducting gap, taken as a free parameter, are used.

Deconfinement phase transition in neutron star matter

The transition from hadron phase to strange quark phase in dense matter is investigated. Instead of using the conventional bag model in quark sect, we achieve the confinement by a density-dependent quark mass derived from in-medium chiral condensates, with a thermodynamic problem improved. In nuclear slot, we adopt the equation of state from Brueckner–Bethe–Goldstone approach with three-body force. It is found that the mixed phase can occur, for reasonable confinement parameter, near the normal saturation density, and transit to pure quark matter at 4–5 times the saturation, which is quite different from the previous results from other quark models that pure quark phase can not appear at neutron-star densities.