Hadron-quark phase transition in neutron stars

We study the hadron-quark phase transition in the interior of neutron stars. The relativistic mean field (RMF) theory is adopted to describe the hadronic matter phase, while the Nambu-Jona-Lasinio (NJL) model is used for the quark matter phase. We investigate the influence of the hadronic equation of state on the phase transition and neutron star properties. It is found that a neutron star possesses a large population of hyperons, but it is not dense enough to possess a pure quark core. Whether or not the mixed phase of hadronic and quark matter appears in the center of neutron stars depends on the RMF parameters used in the calculation.     

Influence of the nuclear equation of state on the hadron-quark phase transition in neutron stars

We study the hadron-quark phase transition in the interior of neutron stars, and examine the influence of the nuclear equation of state on the phase transition and neutron star properties. The relativistic mean field theory with several parameter sets is used to construct the nuclear equation of state, while the     

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.     

Crust-core properties of neutron stars in the Nambu–Jona-Lasinio model

We adopt the Nambu–Jona-Lasinio(NJL) model to study the crust-core transition properties in neutron stars(NSs). For a given momentum cutoff and symmetry energy of saturation density in the NJL model, decreasing the slope of the symmetry energy gives rise to an increase in the crust-core transition density and transition pressure.Given the slope of the symmetry energy at saturation density, the transition density and corresponding transition pressure increase with increasing symmetry energy. The increasing trend between the fraction of the crustal moment of inertia and the slope of symmetry energy at saturation density indicates that a relatively large momentum cutoff of the NJL model is preferred. For a momentum cutoff of 500 Me V, the fraction of the crustal moment of inertia clearly increases with the slope of symmetry energy at saturation density. Thus, at the required fraction(7%) of the crustal moment of inertia, the NJL model with momentum cutoff of 500 Me V and a large slope of the symmetry energy of saturation density can give the upper limit of the mass of the Vela pulsar to be above 1.40 M_⊙.     

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.     

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.     

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 EX00748-676, while EOS containing unpaired quark matter phase with B1/4 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.     

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.     

色味连锁物质的稳定态及其相变

简要介绍和评述了色味连锁物质的稳定态及其相变,指出高密强相互作用物质由于夸克配对出现了一些奇异相。重点介绍色味连锁（CFL）物质及其中的Goldstone-mode凝聚现象。在考虑奇异数对应化学势μs≠0的情况下,CFL物质中K^0和K^-0都可能发生凝聚。随着重子数密度的增高,强作用物质呈现出丰富相结构,在核物质相与CFL相之间可能存在其它相,但最简单的可能相变过程是直接从核物质相变为CFL物质。这种相变可有两种过程,即两相间仅存在一个极小界面或出现两相混合区域。另外还重点讨论了K^-介子凝聚对相变的影响。Quark matter at high density has a rich phase structure. Goidstone-mode may condense in the color-flavor-locked （CFL） phase matter. We review the stability of CFL phase and its phase transition, as well as the effect of nonzero strangeness chemical potential on the CFL phase of dense quark matter. It is pointed out that, depending on the value of μs, both K^0 and K^-0 may condense in the CFL matter. As a function of quark chemical potential, other phases may intervene between the nuclear-matter and CFL phase. The simplest possibility, however, is a transition between nuclear and CFL matter. Such a transition could occur either at a single sharp interface or through a mixed phase region. The effect of discontinuous K^- meson condensation on the phase transition is also discussed. [     

Rotochemical heating in hybrid stars with modified Urca reactions in operation

We have recently shown that, as a compact star containing mixed-phase matter slows down, the compression can cause deconfinement phase transition, and thus enhance the chemical deviations and raise the chemical heating efficiency. In a previous study, only the direct Urca processes in nucleon and quark matter were considered. In this work, we extend the previous analysis to the case where the much slower modified Urca processes operate in nucleon matter. We find a fast promotion in the surface effective temperature of hybrid stars, and that the cooling process is dominated by both the nucleon and quark channels.     

Quark deconfinement in neutron star cores

Whether or not the deconfined quark phase exists in neutron star cores is an open question. We use two realistic effective quark models, the three-flavor Nambu-Jona-Lasinio model and the modified quark-meson coupling model, to describe the neutron star matter. We show that the modified quark-meson coupling model, which is fixed by reproducing the saturation properties of nuclear matter, can be consistent with the experimental constraints from nuclear collisions. After constructing possible hybrid equations of state (EOSes) with an unpaired or color superconducting quark phase with the assumption of the sharp hadron-quark phase transition, we discuss the observational constraints from neutron stars on the EOSes. It is found that the neutron star with pure quark matter core is unstable and the hadronic phase with hyperons is denied, while hybrid EOSes with a two-flavor color superconducting phase or unpaired quark matter phase are both allowed by the tight and most reliable constraints from two stars Ter 5 I and EXO 0748-676. And the hybrid EOS with an unpaired quark matter phase is allowed even compared with the tightest constraint from the most massive pulsar star PSR J0751+1807.     

Neutron stars in relativistic hadron-quark models

Neutron star properties are computed in relativistic models that contain both hadron and quark degrees of freedom. Neutron matter is assumed to have a low-density phase described by quantum hadrodynamics (QHD) and a high-density phase described by quantum chromodynamics (QCD). Several different QHD models and approximations are employed; all use parameters that reproduce the binding energy and density of equilibrium nuclear matter. Calculated neutron star properties depend primarily on the high-density equation of state and cannot be inferred from the symmetry energy or compressibility of equilibrium nuclear matter. If interactions are neglected in the QCD phase, the density of the hadron-quark phase transition is determined by one free parameters, which is the energy/volume needed to create a “bubble” that confines the quarks and gluons. Observed neutron star masses do not constrain this parameter, but stable neutron stars with quark cores can exist only for a limited range of parameter values. When second-order gluon-exchange corrections are included in the QCD phase, these conclusions are unchanged, and the parameter values that lead to stable hadronquark stars are restricted even further.     

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.     

Neutron star in the presence of strong magnetic field

Compact stars such as neutron stars (NS) can have either hadronic or exotic states like strange quark or colour superconducting matter. Stars can also have a quark core surrounded by hadronic matter, known as hybrid stars (HS). The HS is likely to have a mixed phase in between the hadron and the quark phases. Observational results suggest huge surface magnetic field in certain NS. Therefore, we study here the effect of strong magnetic field on the respective equation of states (EOS) of matter under extreme conditions. We further study the hadron–quark phase transition in the interiors of NS giving rise to HS in the presence of strong magnetic field. The hadronic matter EOS is described based on RMF theory and we include the effects of strong magnetic fields leading to Landau quantization of the charged particles. For quark phase, we use the simple Massachusetts Institute of Technology (MIT) bag model, assuming density-dependent bag pressure and magnetic field. The magnetic field strength increases from the surface to the centre of the star. We construct the intermediate mixed phase using Glendenning conjecture. The magnetic field softens the EOS of both the matter phases. We finally study, the mass–radius relationship for such types of mixed HS, calculating their maximum mass, and compare them with the recent observations of pulsar PSR J1614-2230, which is about 2 solarmass.     

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.