Hybrid stars and quark hadron phase transition in chiral colour dielectric model

We investigate the properties of hybrid stars consisting of quark matter in the core and hadron matter in outer region. The hadronic equation of state (EOS) is calculated by using nonlinear Walecka model. Strange baryons are included in the hadronic EOS calculation. The chiral colour dielectric (CCD) model, in which quarks are confined dynamically, is used to calculate quark matter EOS. We find that the phase transition from hadron to quark matter is possible in a narrow range of the parameters of nonlinear Walecka and CCD models. The transition is strong or weak first order depending on the parameters used. The EOS thus obtained, is used to study the properties of hybrid stars. We find that the calculated hybrid star properties are similar to those of pure neutron stars.     

Phase Transitions in Neutron Stars Within Modified Quark-Meson Coupling Model

K^- condensation and quark deconfinement phase transitions in neutron stars are investigated. We use the modified quark-meson coupling model for hadronic phase and the MIT bag model for quark phase. With the equation of state (EOS) solved self-consistently, we discuss the properties of neutron stars. We find that the EOS of pure hadron matter with condensed K^- phase should be ruled out by the redshift for star EXO0748-676, while EOS containing unpaired quark matter phase with B^1/4 being about 180 MeV could be consistent with both this observation and the best measured mass of star PSR 1913+16. But if the recent inferred massive star among Terzan 5 with M>1.68M_๏ is confirmed, all the present EOSes with condensed phase and deconfined phase would be ruled out.     

Phase transition to color-flavor-locked matter and condensation of Goldstone bosons in neutron star matter

Deconfinement phase transition and condensation of Goldstone bosons in neutron star matter are investigated in a chiral hadronic model (also referred as to the FST model) for the hadronic phase (HP) and in the color-flavor-locked (CFL) quark model for the deconfined quark phase. It is shown that the hadronic-CFL mixed phase (MP) exists in the center of neutron stars with a small bag constant, while the CFL quark matter cannot appear in neutron stars when a large bag constant is taken. Color superconductivity softens the equation of state (EOS) and decreases the maximum mass of neutron stars compared with the unpaired quark matter. The K⁰ condensation in the CFL phase has no remarkable contribution to the EOS and properties of neutron star matter. The EOS and the properties of neutron star matter are sensitive to the bag constant B, the strange quark mass m_s and the color superconducting gap Δ. Increasing B and m_s or decreasing Δ can stiffen the EOS which results in the larger maximum masses of neutron stars.     

Influence of medium effects on the rotating hybrid stars

A hybrid star with a pure quark core,a hadron crust and a mixed phase between the two is considered.The relativistic mean field model for hadron matter and the effective mass bag model for quark matter are used to construct the equation of state for hybrid stars.The influences of medium effects that are parameterized by the strong coupling constant have been discussed on the configuration of rotating stars.The strong coupling constant is a prominent factor that influences the properties of rotating hybrid stars.     

Phase Structure in a Quark Mass Density-and-Temperature-Dependent Model

The phase diagram of bulk quark matter in equilibrium with a finite hadronic gas is studied. Different from previous investigations, we treat the quark phase with the quark mass density-and-temperature-dependent model to take the strong quark interaction into account, while the hadron phase is treated by hard core repulsion factor. It is found that the phase diagram in this model is, in several aspects, different from those in the conventional MIT bag model, especially at high temperature. The new phase diagram also has strong effects on the mass-radius relation of compact hybrid stars.     

中子星内部强子-夸克相变的有限尺度效应研究

在致密星体内部极高密度条件下,强子物质可能发生退禁闭相变成为夸克物质,即强子-夸克相变。这种相变过程对于中子星的性质有着重要影响。考虑库仑能和表面能的影响,即有限尺度效应,相变过程中的混杂相包含了被称为pasta相的几何结构。强子-夸克共存相的平衡条件是通过求总能量的最小值得到的。采用相对论平均场（RMF）模型来描述强子物质相,采用Nambu-Jona-Lasinio（NJL）模型来描述夸克物质相。有限尺度效应一定程度上增加了中子星的最大质量,增加幅度取决于强子-夸克表面张力的大小。有限尺度效应能够降低混杂相的范围,其结果介于Gibbs结构和Maxwell结构的结果之间。研究结果表明,中子星中可能包含一个混杂相的核心部分,其大小受到表面张力等参数的影响。It is generally considered that hadron matter may undergo a deconfinement phase transition becoming quark matter at very high density in massive neutron stars. This hadron-quark phase transition has important impact on neutron stars, which has received much attention. We consider finite-size effect in this phase transition process, which contains the impact of Coulomb energy and surface energy. By including this effect, the mixed phase forms the pasta structures. The equilibrium conditions for coexisting hadronic and quark phases are derived by minimizing the total energy including the surface and Coulomb contributions. We employ the relativistic mean-field(RMF) model to describe the hadronic phase, while the Nambu-Jona-Lasinio(NJL) model is used for the quark phase. We conclude that the finite-size effect will raise the stiffness of EOS, and then increase the maximum mass of neutron stars, which depend on the value of surface tension. Our results show that finite-size effects can significantly reduce the region of the mixed phase, and the results lie between those from the Gibbs and Maxwell constructions. We show that a massive star may contain a mixed phase core and its size depends on the surface tension of the hadron-quark interface.     

Spin polarised nuclear matter and its application to neutron stars

An equation of state (EOS) of nuclear matter with explicit inclusion of a spin-isospin dependent force is constructed from a finite range, momentum and density dependent effective interaction. This EOS is found to be in good agreement with those obtained from more sophisticated models for unpolarised nuclear matter. Introducing spin degrees of freedom, it is found that it is possible for neutron matter to undergo a ferromagnetic transition at densities realisable in the core of neutron stars. The maximum mass and the surface magnetic field of the neutron star can be fairly explained in this model. Since finding quark matter rather than hadronic matter at the core of neutron stars is a possibility, the proposed EOS is also applied to the study of hybrid stars. It is found using the bag model picture that one can in principle describe both the mass as well as the surface magnetic field of hybrid stars satisfactorily.     

Equation of state in hybrid stars and the stability window of quark matter

Properties of hybrid stars with a mixed phase composed of asymmetric nuclear matter and strange quark matter are studied. The quark phase is investigated by the quark quasiparticle model with a self-consistent thermodynamic and statistical treatment. We present the stability windows of the strange quark matter with respect to the interaction coupling constant versus the bag constant. We find that the appearance of the quark–hadron mixed phases is associated with the meta-stable or unstable regions of the pure quark matter parameters. The mass–radius relation of the hybrid star is dominated by the equation of state of quark matter rather than nuclear matter. The contour plots of the maximum mass of the hybrid star are shown in the plane of the coupling constant and the bag constant.     

Influences of the bag constant on properties of hybrid stars

Influences of the bag constant on the properties of hybrid stars are investigated by using relativistic mean field theory and the MIT bag model to describe the hadron phase and quark phase in the interior of neutron stars, respectively. Our results indicate that the onset of hadron-quark phase transition is put off and the appearance of hyperon species is increased with the increase in bag constant. As a result, the hybrid star equation of state for a mixed phase range stiffens whereas that of the quark phase range softens, and the gravitational mass as well as the corresponding radius of hybrid stars are increased obviously. The gravitational mass of a hybrid star is increased from 1.42 Mo (M<,⊙> is solar mass) to 1.63M<,⊙> and the corresponding radius is changed from 9.1 km to 12.2 km when the bag constant (B<'1/4>) is increased from 170 MeV to 200 MeV. It is interesting to find that hybrid star equations of state become non-smooth when the TM2 parameter sets in the framework of relativistic mean field theory used to describe the hadronic matter, and consequently, the third family of compact stars appear in the mass-radius relations of hybrid stars in the narrow scope of the bag constant from 175 MeV to 180 MeV. These show that the choice of the bag constant in the MIT bag model has significant influence on the properties of hybrid stars.     

36Cl and41Ca depth profiles in a Hiroshima granite stone and the Dosimetry System 1986

Hybrid stars composed of a strange matter core surrounded by neutron matter are investigated. We apply star models based on phenomenological equations of state (EOS) from nuclear reactions including a phase transition between the hadronic phase and the quark gluon plasma. For specific equations of state hybrid stars might exist. While the nuclear part of the EOS has only a minor influence on the properties of hybrid stars, the EOS for the quark gluon phase has a crucial impact on the existence of such objects.     

The influence of medium effects on the gross structure of hybrid stars

We investigate the influence of medium effects on the structure of hybrid stars, i.e. neutron stars possessing a quark matter core. We found that medium effects in quark matter reduce the extent of a pure quark matter phase in the interior of a hybrid star significantly in favor of a mixed phase of quark and hadronic matter. Over a wide range of the strong coupling constant — which parameterizes the influence of medium effects — quark matter is able to exist at least in a mixed phase in the interior of neutron stars.     

Properties of hybrid stars in an extended MIT bag model

The properties of hybrid stars are investigated in the framework of the relativistic mean field theory (RMFT) and an MIT bag model with density-dependent bag constant to describe the hadron phase (HP) and quark phase (QP), respectively. We find that the density-dependent B(p) decreases with baryon density p; this decrement makes the strange quark matter become more energetically favorable than ever, which makes the threshold densities of the hadron-quark phase transition lower than those of the original bag constant case. In this case, the hyperon degrees of freedom can not be considered. As a result, the equations of state of a star in the mixed phase (MP) become softer whereas those in the QP become stiffer, and the radii of the star obviously decrease. This indicates that the extended MIT bag model is more suitable to describe hybrid stars with small radii.     

Magnetized color flavor locked state and compact stars

The stability of the color flavor locked phase in the presence of a strong magnetic field is investigated within the phenomenological MIT bag model, taking into account the variation of the strange quark mass, the baryon density, the magnetic field, as well as the bag and gap parameters. It is found that the minimum value of the energy per baryon in a color flavor locked state at vanishing pressure is lower than the corresponding one for unpaired magnetized strange quark matter and, as the magnetic field increases, the energy per baryon decreases. This implies that magnetized color flavor locked matter is more stable and could become the ground state inside neutron stars. The mass-radius relation for such stars is also studied.     

Influences of the bag constant on properties of hybrid stars

Influences of the bag constant on the properties of hybrid stars are investigated by using relativistic mean field theory and the MIT bag model to describe the hadron phase and quark phase in the interior of neutron stars, respectively. Our results indicate that the onset of hadron-quark phase transition is put off and the appearance of hyperon species is increased with the increase in bag constant. As a result, the hybrid star equation of state for a mixed phase range stiffens whereas that of the quark phase range softens, and the gravitational mass as well as the corresponding radius of hybrid stars are increased obviously. The gravitational mass of a hybrid star is increased from 1.42 M_⊙ (M_⊙ is solar mass) to 1.63 M_⊙ and the corresponding radius is changed from 9.1 km to 12.2 km when the bag constant (B^1/4) is increased from 170 MeV to 200 MeV. It is interesting to find that hybrid star equations of state become non-smooth when the TM2 parameter sets in the framework of relativistic mean field theory used to describe the hadronic matter, and consequently, the third family of compact stars appear in the mass-radius relations of hybrid stars in the narrow scope of the bag constant from 175 MeV to 180 MeV. These show that the choice of the bag constant in the MIT bag model has significant influence on the properties of hybrid stars.     

包含暗物质的强子夸克混合星

研究了含有暗物质的夸克核心混合星的观测属性。用相对论平均场理论和有效质量口袋模型分别描述夸克核心的混合星物质内强子相和夸克相,用Gibbs相平衡条件描述强子-夸克混合相,研究了由于包含强、弱相互作用的费米子暗物质对混合星质量、半径、引力红移、自转频率和转动惯量等整体观测属性的影响。结果表明,在强、弱相互作用下,暗物质粒子质量大于等于0.5 GeV时暗物质会使混合星的状态方程比无暗物质时有一定软化,相应的混合星最大质量减少。当调节暗物质粒子质量研究表明,随着暗物质粒子质量的增大,夸克核心的混合星物质的状态方程变软,混合星的质量、半径变小,并且引力红移、自转频率和转动惯量等整体观测属性也明显依赖于暗物质粒子的质量。当暗物质粒子质量0.1 GeV时,包含强、弱作用暗物质的混合星质量达到2.0 M_⊙和2.8 M_⊙（其中M_⊙为太阳质量）,说明大质量脉冲星PSR J1859-0131和J1931-01可能是包含小质量暗粒子暗物质的强子夸克的混合星。整体观测属性的计算结果均在中子星的天文观察数据范围内,也说明强子夸克的混合星内可能包含暗物质。The observational properties of quark core hybrid star contain dark matter are studied. The influences of containing of strongly or weakly interacting dark matter to global observational features of hybrid stars, mass, radius, gravitational red-shift, rotational period and moment of inertia are studied by using relativistic mean field theory to describe hadron phase, effective mass bag model to quark phase, and Gibbs phase equilibrium conditions to hadron-quark mixed phase respectively. Our results indicate that, both in the strong and weak interacting case, the equation of state for hybrid star matter contain dark matter become softer than that of without dark matter while the mass of dark matter particles larger than 0.5 GeV, which leads to the decrease of the mass and corresponding radius of hybrid star. With the increase of the dark matter particle mass, the equation of state for hybrid star matter become softer, this cause the decrease of the mass and radius of hybrid star obviously. The gravitational red-shift and the rotational period, obviously increase of the moment of inertia of the hybrid stars are influenced by the dark matter particle mass. When the dark matter particle mass is equal to 0.1 GeV, the masses of the star with strong and weak interacting dark matter reach to 2.0 M_⊙ and 2.8 M_⊙(M_⊙ is the solar mass), this result indicates that the giant mass PSR, J1859-0131 and J1931-01, can be a hadron-quark hybrid star and containing dark matter with small dark particle mass. The computational results of all above global observational features of hybrid stars are in the range of astronomical observation data, these also indicate that hybrid star with quark core may contains dark matter.     

Deconfinement Phase Transition Including Perturbative QCD Corrections in （Proto）neutron Star Matter

Deconlinement phase transition and neutrino trapping in （proto）neutron star matter are investigated in a chiral hadronic model （also referred to as the FST model） for the hadronic phase （HP） and in the color-flavor-locked （CFL） quark model for the deconlined quark phase. We include a perturbative QCD correction parameter αs in the CFL quark matter equation of states. It is shown that the CFL quark core with K^0 condensation forms in neutron star matter with the large value of αs. If the small value of αs is taken, hyperons suppress the CFL quark phase and the liP is dominant in the high-density region of （proto）neutron star matter. Neutrino trapping makes the fraction of the CFL quark matter decrease compared with those without neutrino trapping. Moreover, increasing the QCD correction parameter as or decreasing the bag constant B and the strange quark mass ms can make the fraction of the CFL quark matter increase, simultaneously, the fraction of neutrino in protoneutron star matter increases, too. The maximum masses and the corresponding radii of （proto）neutron stars are not sensitive to the QCD correction parameter αs.     

超子耦合常数对混合星性质的影响

用相对论平均场理论描述强子物质, 用NJL模型描述夸克物质研究了超子耦合常数对混合星性质的影响. 结果表明, 随着超子耦合常数的增大, 强子-夸克相变密度变小, 混合相区域的状态方程变硬, 中子星的最大质量及对应的半径变大. 超子耦合常数由0.73增到1.0时, 混合星最大质量由1.68M_⊙增至1.84M_⊙, 相应的半径由11.4km变到12.5km. 该夸克模型下不同强子参数组对应的混合星性质也有较明显的差异. 可知, 其适合于描述大质量而小夸克核心的混合星.     

Hadron-quark phase coexistence in a hybrid MIT-Bag model

The phase transition of hadronic to quark matter and the boundaries of the hadron-quark coexistence phase are studied within the two Equation of State (EoS) models. The relativistic effective mean-field approach with constant and density-dependent meson-nucleon couplings is used to describe hadronic matter, and the MIT-Bag model is adopted to describe quark matter. The boundaries of the mixed phase for different Bag constants are obtained solving the Gibbs equations. We notice that the dependence on the Bag parameter of the critical temperatures (at zero chemical potential) can be well reproduced by a fermion ultrarelativistic quark gas model, without contribution from the hadron part. At variance, the critical chemical potentials (at zero temperature) are very sensitive to the EoS of the hadron sector. Hence, the contribution of the hadronic interaction is much more relevant for the determination of the transition to the quark-gluon plasma at finite baryon density and low T . Moreover, in the low-temperature and finite chemical potential region no solutions of the Gibbs conditions are existing for small Bag-constant values, B < (135 MeV)⁴ . Isospin effects in asymmetric matter appear important in the high chemical-potential regions at lower temperatures, of interest for the inner-core properties of neutron stars and for heavy-ion collisions at intermediate energies.     

Hybrid stars

Recently there have been important developments in the determination of neutron star masses which put severe constraints on the composition and equation of state (EOS) of the neutron star matter. Here we study the effect of quark and nuclear matter mixed phase on mass radius relationship of neutron stars employing recent models from two classes of EOS’s and discuss their implications.     

Influence of hadronic hard core radius on detonations and deflagrations in quark matter

The parameters for deflagration and detonations transitions between baryon-rich quark matter and hadronic matter are calculated at high densities and low temperatures. The equation of state of hadronic matter takes into account the hard core repulsion character of nuclear forces and the bag pressure is included in the quark phase. The transition is considered first directly from the quark phase to the hadronic phase. It is found that the velocity of the front separating the quark and nuclear phases as well as the energy flux are substantially larger than in the case where no hard core repulsion is taken into account. Most of the calculated quantities are only weakly dependent on the temperature in the region considered. The transitions from the quark phase to the mixed phase and from the mixed phase to the hadronic phase are also considered. No realistic solutions are found for the case where the temperature remains zero throughout the transition. At small temperatures and high densities solutions are obtained where the transition involves only minimal superheating. The energy flux for such a transition is small.