Bulk viscosity of interacting magnetized strange quark matter

The bulk viscosity of interacting strange quark matter in a strong external magnetic field B m with a real equation of state is investigated.It is found that interquark interactions can significantly increase the bulk viscosity,and the magnetic field B_(m) can cause irregular oscillations in both components of the bulk viscosity,ξ||(parallel to B_(m))and ξ⊥(perpendicular to B_(m)).A comparison with non-interacting strange quark matter reveals that when B_(m) is sufficiently large,ξ⊥is more affected by interactions than ξ||.Additionally,the quasi-oscillation of the bulk viscosity with changes in density may facilitate the for-mation of magnetic domains.Moreover,the resulting r-mode instability windows are in good agreement with observational data for compact stars in low-mass X-ray binaries.Specifically,the r-mode instability window for interacting strange quark matter in high magnetic fields has a minimum rotation frequency exceeding 1050 Hz,which may explain the observed very high spin frequency of a pulsar with V=1122 Hz.

Symmetry energy of strange quark matter and tidal deformability of strange quark stars

Research performed during the past decade revealed an important role of symmetry energy in the equation of state(EOS)of strange quark matter(SQM).By introducing an isospin-dependent term into the quark mass scaling,the SQM stability window in the equivparticle model was studied.The results show that a sufficiently strong isospin dependence C_(I)can significantly widen the SQM region of absolute stability,yielding results that simultaneously satisfy the constraints of the astrophysical observations of PSR J1614-2230 with 1.928±0.017 Mand tidal deformability 70≤Λ_(1:4)≤580 measured in the event GW170817.With increasing C_(I),the difference between the u,d,and s quark fractions for the SQM inβ-equilibrium becomes inconspicuous for C>0,leading to small isospin asymmetryδ,and further resulting in similar EOS and structures of strange quark stars(SQSs).Moreover,unlike the behavior of the maximum mass of ud QSs,which varies with C_(I)depending on the sign of the parameter C,the maximum mass of the SQSs decreases monotonously with increasing CI.

Phenomenological study of the anisotropic quark matter in the two-flavor Nambu–Jona–Lasinio model

With the two-flavor Nambu–Jona–Lasinio (NJL) model, we carried out a phenomenological study on the chiral phase structure, mesonic properties, and transport properties of momentum-space anisotropic quark matter. To calculate the transport coefficients we utilized the kinetic theory in the relaxation time approximation, where the momentum anisotropy is embedded in the estimation of both the distribution function and relaxation time. It was shown that an increase in the anisotropy parameterξmay result in a catalysis of chiral symmetry breaking. The critical endpoint(CEP) is shifted to lower temperatures and larger quark chemical potentials asξincreases, and the impact of momentum anisotropy on the CEP temperature is almost the same as that on the quark chemical potential of the CEP. The meson masses and the associated decay widths also exhibit a significant ξ dependence. It was observed that the temperature behavior of the scaled shear viscosity η/T~3 and scaled electrical conductivity σ/T exhibited a similar dip structure, with the minima of both η/T~3 and σ/T shifting toward higher temperatures with increasing ξ. Furthermore,we demonstrated that the Seebeck coefficient S decreases when the temperature rises and its sign is positive, indicating that the dominant carriers for converting the temperature gradient to the electric field are up-quarks. The Seebeck coefficient S is significantly enhanced with a largeξfor a temperature below the critical temperature.

Quark mass scaling and properties of light-quark matter

We study the properties of two-flavor quark matter in the equivparticle model.A new quark mass scaling at finite temperature is proposed and applied to the thermodynamics of two-flavor quark matter.It is found that the perturbative interaction has strong effect on quark matter properties at finite temperature and high density.The pressure at the minimum free energy per baryon is exactly zero.With increasing temperature,the energy per baryon increases,while the free energy per baryon decreases.

Effects of Density-Dependent Quark Mass on Phase Diagram of Color-Flavor-Locked Quark Matter

<正> Considering the density dependence of quark mass,we investigate the phase transition between the(un-paired)strange quark matter and the color-flavor-locked matter,which are supposed to be two candidates for the groundstate of strongly interacting matter.We find that if the current mass of strange quark m_s is small,the strange quarkmatter remains stable unless the baryon density is very high.If m_s is large,the phase transition from the strangequark matter to the color-flavor-locked matter in particular to its gapless phase is found to be different from the resultspredicted by previous works.A complicated phase diagram of three-flavor quark matter is presented,in which thecolor-flavor-locked phase region is suppressed for moderate densities.

Properties of color-flavor locked strange quark matter in an external strong magnetic field

The properties of color-flavor locked strange quark matter in an external strong magnetic field are investigated in a quark model with density-dependent quark masses.Parameters are determined by stability arguments.It is found that the minimum energy per baryon of the color-flavor locked(MCFL)matter decreases with increasing magnetic-field strength in a certain range,which makes MCFL matter more stable than other phases within a proper magnitude of the external magnetic field.However,if the energy of the field itself is added,the total energy per baryon will increase.

Critical Exponents of Quark Matter

I investigate the ferromagnetic phase transition inside strong quark matter (SQM) with one gluon exchange interaction between strong quarks. I use a variational method and the Landau-Fermi liquid theory and obtain the thermodynamics quantities of SQM. In the low temperature limit, the equation of state (EOS) and critical exponents for the second-order phase transition (ferromagnetic phase transition) in SQM are analytically calculated. The results are in agreement with the Ginzberg-Landau theory.

String Cloud and Domain Walls with Quark Matter in Lyra Geometry

We have constructed cosmological models for string cloud and domain walls coupled with quark matter in Lyra geometry. For this purpose we have solved the field equations using anisotropy feature of the universe, special law of variation for Hubble’s parameter proposed by Berman [78] which yields constant deceleration parameter;and time varying displacement field . Further some properties of the obtained solutions are discussed.

Thermodynamic properties and phase diagram of quark matter within non-extensive Polyakov chiral SU(3)quark mean field model

In the present study,we applied Tsallis non-extensive statistics to investigate the thermodynamic properties and phase diagram of quark matter in the Polyakov chiral SU(3)quark mean field model.Within this model,the properties of the quark matter were modified through the scalar fieldsσ,ζ,δ,χ,vector fieldsω,ρ,ϕ,and Polyakov fieldsΦandΦ¯at finite temperature and chemical potential.Non-extensive effects were introduced through a dimensionless parameter q,and the results were compared to those of the extensive case(q→1).In the non-extensive case,the exponential in the Fermi-Dirac(FD)function was modified to a q-exponential form.The influence of the q parameter on the thermodynamic properties,pressure,energy,and entropy density,as well as trace anomaly,was investigated.The speed of sound and specific heat with non-extensive effects were also studied.Furthermore,the effect of non-extensivity on the deconfinement phase transition as well as the chiral phase transition of u,d,and s quarks was explored.We found that the critical end point(CEP),which defines the point in the(T−μ)phase diagram where the order of the phase transition changes,shifts to a lower value of temperature,TCEP,and a higher value of chemical potential,μCEP,as the non-extensivity is increased,that is,q>1.

One-gluon-exchange effect on the properties of quark matter and strange stars

We present a modified version of quark mass scaling via considering the important one-gluonexchange interaction between quarks in the quark mass density-dependent model. The properties of strange quark matter and the structure of strange stars are then studied with the new scaling and a self-consistent thermodynamic treatment. It is found that the one-gluon-exchange effect lowers the system energy considerably, makes the equation of state stiffer, and the sound velocity tends to the ultra-relativistic value faster, which make the biggest value of the maximum mass of strange stars become as big as approximately 2 times the solar mass, in accordance with the latest astronomical observations.

Quark matter properties and fluctuations of conserved charges in(2+1)-flavored quark model

In this study,the susceptibilities of conserved charges,baryon number,charge number,and strangeness number at zero and low values of chemical potential are presented.Taylor series expansion was used to obtain results for the three-flavor Polyakov quark meson(PQM)model and the Polyakov loop extended chiral quark meanfield(PCQMF)model.Mean-field approximation was used to study quark matter with the inclusion of the isospin chemical potential,as well as the vector interactions.The effects of isospin chemical potential and vector-interactions on phase diagrams were analyzed.A comparative analysis of the two models was completed.Fluctuations of the conserved charges were enhanced in the transition temperature regime and hence provided information about the critical end point(CEP).Susceptibilities of conserved quantities were calculated by using the Taylor series method.Enhancement of fluctuations in the transition temperature neighborhood provided a clear signature of a quantum chromodynamics(QCD)critical-point.

Bulk viscosity for interacting strange quark matter and r-mode instability windows for strange stars

We investigate the bulk viscosity of strange quark matter in the framework of the equivparticle model,where analytical formulae are obtained for certain temperature ranges,which can be readily applied to those with various quark mass scalings.In the case of adopting a quark mass scaling with both linear confinement and perturbative interactions,the obtained bulk viscosity increases by 1-2 orders of magnitude compared with those in bag model scenarios.Such an enhancement is mainly due to the large quark equivalent masses adopted in the equivparticle model,which are essentially attributed to the strong interquark interactions and are related to the dynamical chiral symmetry breaki ng.Due to the high bulk viscosity,the predicted damping time of oscillatio ns for a can on ical 1.4 M⊙ strange star is less than one millisecond,which is shorter than previous findings.Consequently,the obtained r-mode instability window for the canonical strange stars well accommodates the observational frequencies and temperatures for pulsars in low-mass X-ray binaries(LMXBs).

Phase structures of neutral dense quark matter and applicationto strange stars

In the contact interaction model,the quark propagator has only one solution,namely,the chiral symmetry breaking solution,at vanishing temperature and density in the case of physical quark mass.We generalize the condensate feedback onto the coupling strength from the 2 flavor case to the 2+1 flavor case,and find the Wigner solution appears in some regions,which enables us to tackle chiral phase transition as two-phase coexistences.At finite chemical potential,we analyze the chiral phase transition in the conditions of electric charge neutrality andβequilibrium.The four chemical potentials,μ_(u),μ_(d),μ_(s) and He,are constrained by three conditions,so that one inde-pendent variable remains:we choose the average quark chemical potential as the free variable.All quark masses and number densities suffer discontinuities at the phase transition point.The strange quarks appear after the phase trans-ition since the system needg more energy to produce a d.-quark than an s-quark.Taking the EOS as an input,the TOV equations are solved numerically,and we show that the mass--radius relation is sensitive to the EOS.The max-imum mass of strange quark stars is not susceptible to the parameter Aq we introduced.

Quark-clustering in cold quark matter

Quarks are proposed to be grouped together to make quark-clusters due to the strong interaction in cold quark matter at a few nuclear densities,because a weakly coupling treatment of the interaction between quarks there would be inadequate.Cold quark matter is then conjectured to be in solid state （i.e.,forming a crystal structure） if the inter-cluster potential is deep enough to localize clusters in lattice.Such a solid state of cold quark matter would be very necessary for us to understand different manifestations of pulsar-like compact stars,and could not be ruled by first principles.

Magnetized strange quark matter in a mass-density-dependent model

We investigate the properties of strange quark matter （SQM） in a strong magnetic field with quark confinement by the density dependence of quark masses considering the total baryon number conservation, charge neutrality and chemical equilibrium. It is found that an additional term should appear in the pressure expression to maintain thermodynamic consistency. At fixed density, the energy density of magnetized SQM varies with the magnetic field strength. By increasing the field strength an energy minimum exists located at about 6×10^19 Gauss when the density is fixed at two times the normal nuclear saturation density.

Magnetic Effect Versus Thermal Effect on Quark Matter with a Running Coupling at Finite Densities

We investigate the quark matter in a strong magnetic field in the framework of SU(2) NJL model with a magnetic-field-dependent coupling. The spin polarization, the entropy per baryon, and the energy are studied by analyzing the competition of the magnetic effect and the thermal effect. The stronger magnetic field can enhance the spin polarization, arrange quarks in a uniform spin orientation, and change the energy per baryon drastically. However,it can hardly affect the entropy per baryon, which is dominated by the temperature. As the temperature increases, more quarks will be excited from the lowest Landau level up to higher Landau levels.

Landau quantization and spin polarization of cold magnetized quark matter

The magnetic field and density behaviors of various thermodynamic quantities of strange quark matter under compact star conditions are investigated in the framework of the thermodynamically self-consistent quasiparticle model.For individual species,a larger number density n_(i) leads to a larger magnetic field strength threshold that aligns all particles parallel or antiparallel to the magnetic field.Accordingly,in contrast to the finite baryon density effect which reduces the spin polarization of magnetized strange quark matter,the magnetic field effect leads to an enhancement of it.We also compute the sound velocity as a function of the baryon density and find the sound velocity shows an obvious oscillation with increasing density.Except for the oscillation,the sound velocity grows with increasing density,similar to the zero-magnetic field case,and approaches the conformal limit V_(s)^(2)=1/3 at high densities from below.

Multiple configurations of neutron stars containing quark matter

The main purpose of this study is to interpret the possibilities of hybrid star configurations under different phase transition paths and provide a general description of the conditions and features of the different configurations.We assume that there are two possible phase transition paths,i.e.,from a nuclear phase to a 2flavor(2f)/3flavor(3f)quark phase directly,or first from a nuclear phase to a 2f quark phase,and then from that phase to a 3f quark phase sequentially.In addition,we consider Maxwell and Gibbs constructions based on the assumption of a first-order transition,which yields multiple configurations of hybrid stars:N-2f,N-3f,and N-2f-3f for a Maxwell construction,and N-2fmix-2f,N-3fmix-3f,N-2f3fmix,and N-2fmix-3f for a Gibbs construction.From the radii analysis of different hybrid star configurations with the same mass of 1.95M⊙,the appearance of the quark matter(from nuclear to 2f or 3f quark matter)causes a radius difference of 0.5km^2km and provides the possibility of detection by NICER in the future.However,the sequential transition from 2f to 3f quark matter is difficult to detect because the transition does not lead to too high of a change in radius(far smaller than 0.5km).The dependence solely on the measurements of the stellar radii to probe the equation of state of dense matter in neutron stars causes difficulties.Multi-messenger observations can help us to infer the interior of a neutron star in the future.

Strange quark matter and proto-strange stars in a baryon density-dependent quark mass model

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(c/√3)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 Y_(l)=0.4.

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

According to the recent studies,the gravitational wave(GW)echoes are expected to be generated by quark stars composed of ultrastiff quark matter.The ultrastiff equations of state(EOS)for quark matter were usually obtained either by a simple bag model with artificially assigned sound velocity or by employing interacting strange quark matter(SQM)depicted by simple reparameterization and rescaling.In this study,we investigate GW echoes with EOSs for SQM in the framework of the equivparticle model with density-dependent quark masses and pairing effects.We conclude that strange quark stars(SQSs)can be sufficiently compact to possess a photon sphere capable of generating GW echoes with frequencies in the range of approximately 20 kHz.However,SQSs cannot account for the observed 72 Hz signal in GW170817 event.Furthermore,we determined that quark-pairing effects play a crucial role in enabling SQSs to satisfy the necessary conditions for producing these types of echoes.