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 $Λ(M)$ 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 $Λ(R)$ relations are in accordance with the latest astrophysical constraints from NICER and Ligo/VIRGO observations, respectively.
Hyperon ($Y$) mixing in neutron-star matter brings about a remarkable softening of the equation of state (EoS) and the maximum mass is reduced to a value far less than $2M_{\odot}$. One idea to avoid this "hyperon puzzle in neutron stars" is to assume that the many-body repulsions work universally for every kind of baryons. The other is to take into account the quark deconfinement phase transitions from a hadronic EoS to a sufficiently stiff quark-matter EoS. In the present approach, both effects are handled in a common framework. As well as the hadronic matter, the quark matter with the two-b…
Inspired by the excluded volume model for isospin symmetric quarkyonic matter, we construct an `excluded volume' model for a charge neutral quarkyonic phase whose hadronic sector contains only neutrons. We refer to this model as quarkyonic neutron matter. We compute the equation of state for this model and solve the Tolman-Oppenhermer-Volkoff equations to obtain mass and radius relations relevant for neutron stars. The most straightforward extension of the model for symmetric quarkyonic matter to quarkyonic neutron matter does not satisfy the mass radius constraints from neutron star measureme…
The structured hadron-quark mixed phase, known as the pasta phase, is expected to appear in the core of massive neutron stars. Motivated by the recent advances in astrophysical observations, we explore the possibility of the appearance of quarks inside neutron stars and check its compatibility with current constraints. We investigate the properties of the hadron-quark pasta phases and their influences on the equation of state (EOS) for neutron stars. In this work, we extend the energy minimization (EM) method to describe the hadron-quark pasta phase, where the surface and Coulomb contributions…
Neutron stars were first posited in the early thirties, and discovered as pulsars in late sixties; however, only recently are we beginning to understand the matter they contain. This talk describes the continuing development of a consistent picture of the liquid interiors of neutron stars, driven by four advances: observations of two heavy neutron stars with masses $\simeq$ 2.0 solar masses; inferences of masses and radii simultaneously for an increasing number of neutron stars in low mass X-ray binaries, and future determinations via the NICER observatory; the observation of the binary neutro…
The detection of gravitational waves from GW170817 has provided a new opportunity to constrain the equation of state (EOS) of neutron stars. In this article, we investigate the possible existence of quarks inside the neutron star core in the context of GW170817. The nucleon phase is treated within the relativistic nuclear mean-field approach where we have employed a fully comprehensive set of available models, and the quark phase is described in the Bag model. We show that the nucleonic EOSs which are inconsistent with the tidal deformability bound become consistent when phase transition to qu…
We study the QCD phase diagram using a non-local SU(3) NJL model with vector interactions among quarks. We analyze several thermodynamic quantities such as entropy and specific heat, and study the influence of vector interactions on the thermodynamic properties of quark matter. Upon imposing electric charge neutrality and baryon number conservation on the field equations, we compute models for the equation of state of the inner cores of proto-neutron stars providing a non-local treatment of quark matter for astrophysics.
Comment on "Three-dimensional hydrodynamic simulations of the combustion of a neutron star into a quark star"
如果奇异物质是绝对稳定的，那么普通的原子核就会衰变为奇异核，而中子星则会转化为奇异星。普通核的寿命在实验上被限制在$\sim 10^{33}$年以上，而亚稳态中子星的寿命取决于中子星的质量，可以超过宇宙的年龄。因此，中子星和奇异星可以在宇宙中共存。我们指出，M。Herzog和F. K. Roepke在Phys. Rev. D 84，083002（2011）[arXiv：1109.0539]中的研究集中在奇异物质参数空间中的一个区域，在该区域中，低质量中子星和奇异星共存，而大质量中子星在天文时间尺度上是不稳定的，寿命很短。
The rotating neutron star properties are studied with a phase transition to quark matter. The density-dependent relativistic mean-field model (DD-RMF) is employed to study the hadron matter, while the Vector-Enhanced Bag model (vBag) model is used to study the quark matter. The star matter properties like mass, radius,the moment of inertia, rotational frequency, Kerr parameter, and other important quantities are studied to see the effect on quark matter. The maximum mass of rotating neutron star with DD-LZ1 and DD-MEX parameter sets is found to be around 3$M_{\odot}$ for pure hadronic phase an…
The Quark-Hadron Chiral Parity-Doublet model (Q$χ$P) is applied to calculate compact star properties in the presence of a deconfinement phase transition. Within this model, a consistent description of nuclear matter properties, chiral symmetry restoration, and a transition from hadronic to quark and gluonic degrees of freedom is possible within one unified approach. We find that the equation of state obtained is consistent with recent perturbative quantum chromodynamics (QCD) results and is able to accommodate observational constraints of massive and small neutron stars. Furthermore, we show t…
In this contribution, we summarize our recent studies on the chiral invariant mass and the chiral condensates in neutron star matter. We construct a unified equations of state assuming the crossover phase transition from hadronic matter described by a parity doublet model to quark matter by an Nambu--Jona-Lasinio type quark model. We first show that the chiral invariant mass is constrained to be 600 MeV $\lesssim m_0 \lesssim$ 900 MeV from recent observations of neutron stars. We then determine the density dependence of the chiral condensate in the crossover description, and show that the chir…
In this paper, we use a three flavor non-local Nambu--Jona-Lasinio (NJL) model, an~improved effective model of Quantum Chromodynamics (QCD) at low energies, to investigate the existence of deconfined quarks in the cores of neutron stars. Particular emphasis is put on the possible existence of quark matter in the cores of rotating neutron stars (pulsars). In contrast to non-rotating neutron stars, whose particle compositions do not change with time (are frozen in), the type and structure of the matter in the cores of rotating neutron stars depends on the spin frequencies of these stars, which o…
With the recent findings from various astrophysical results hinting towards possible existence of strange quark matters with the baryonic resonances such as $Λ^0, Σ^0, Ξ, Ω$ in the core of neutron stars, we investigate the MSW effect, in general, in quark matter. We find that the resonance condition for the complete conversion of down-quark to strange quark requires estremely large matter density ($ρ_u \simeq 10^{5}\,\mbox{fm}^{-3} $). Nonetheless the neutron stars provide a best condition for the conversion to be statistically significant which is of the same order as is expected from imposin…
In the first part of this paper, we investigate the possible existence of a structured hadron-quark mixed phase in the cores of neutron stars. This phase, referred to as the hadron-quark pasta phase, consists of spherical blob, rod, and slab rare phase geometries. Particular emphasis is given to modeling the size othis phase in rotating neutron stars. We use the relativistic mean-field theory to model hadronic matter and the non-local three-flavor Nambu-Jona-Lasinio model to describe quark matter. Based on these models, the hadron-quark pasta phase exists only in very massive neutron stars, wh…
We present a much improved equation of state for neutron star matter, QHC19, with a smooth crossover from the hadronic regime at lower densities to the quark regime at higher densities. We now use the Togashi et al.~equation of state (Togashi:2017), a generalization of the Akmal-Pandharipande-Ravenhall equation of state of uniform nuclear matter, in the entire hadronic regime; the Togashi equation of state consistently describes non-uniform as well as uniform matter, and matter at beta equilibrium without the need for an interpolation between pure neutron and symmetric nuclear matter. We descr…
We describe charge-neutral neutron star matter in $β-$equilibrium using hybrid equations of state, where a first-order phase transition from hadronic to quark matter is realized. The hadronic matter is described in a model-independent way by a Taylor expansion around saturation density $n_0$, while the three-flavor NJL model is used for the quark matter. Exploring the present uncertainty on the empirical parameters of nuclear matter and the parameter space of the NJL model, we construct two datasets of thermodynamically consistent and causal hybrid EoSs, compatible with astrophysical observati…
In this paper, we find the heat capacity of the magnetic dual chiral density wave (MDCDW) phase of dense quark matter and use it to explore the feasibility of this phase for a neutron star interior. MDCDW is a spatially inhomogeneous phase of quark matter known to be favored at intermediate densities over the chirally symmetric phase and the color-flavor-locked superconducting phase. By comparing our result to the lower limit of the core heat capacity established from observations of transiently accreting neutron stars, we show that the heat capacity of MDCDW quark matter is well above that lo…
We examine the effects of the isovector-vector coupling and hypercharge-vector coupling in quark matter on hadron-quark coexistence in neutron-star matter. The relativistic mean field theory with the TM1 parameter set and an extended TM1 parameter set are used to describe hadronic matter, and the Nambu-Jona-Lasinio model with scalar, isoscalar-vector, isovector-vector and hypercharge-vector couplings is used to describe deconfined quark matter. The hadron-quark phase transition is constructed via the Gibbs conditions for phase equilibrium. The isovector-vector and hypercharge-vector couplings …
We study the equation of state of neutron-star matter including the effects of isovector-vector coupling in quark matter. We employ the relativistic mean-field theory with an extended TM1 parameter set to describe hadronic matter and the SU(3) Nambu-Jona-Lasinio model with isovector-vector and hypercharge-vector couplings to describe the quark matter. The deconfinement hadron-quark phase transition is constructed under Gibbs phase equilibrium conditions. It is found that the isovector-vector and hypercharge-vector couplings in quark matter enhance the symmetry energy and hypercharge symmetry e…
The theory governing the strong nuclear force, Quantum Chromodynamics, predicts that at sufficiently high energy densities hadronic nuclear matter undergoes a deconfinement transition to a new phase of quarks and gluons. Although this has been observed in ultrarelativistic heavy-ion collisions, it is currently an open question whether quark matter exists inside neutron stars. By combining astrophysical observations and theoretical ab-initio calculations in a model-independent way, we find that the inferred properties of matter in the cores of neutron stars with mass corresponding to 1.4 solar …
Matter state inside neutron stars is an exciting problem in astrophysics, nuclear physics and particle physics. The equation of state (EOS) of neutron stars plays a crucial role in the present multimessenger astronomy, especially after the event of GW170817. We propose a new neutron star EOS "QMF18" from the quark level, which describes well robust observational constraints from free-space nucleon, nuclear matter saturation, heavy pulsar measurements and the tidal deformability of the very recent GW170817 observation. For this purpose, we employ the quark-mean-field (QMF) model, allowing one t…
We construct an equation of state (EOS) for neutron stars by interpolating hadronic EOS at low density and quark EOS at high density. A hadronic model based on the parity doublet structure is used for hadronic matter and a quark model of Nambu--Jona-Lasinio type is for quark matter. We assume crossover between hadronic matter and quark matter in the the color-flavor locked phase. The nucleon mass of the parity doublet model has a mass associated with the chiral symmetry breaking, and a chiral invariant mass $m_0$ which is insensitive to the chiral condensate. The value of $m_0$ affects the nuc…
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 …
We study the hadron-quark mixed phase, which may occur in the interior of neutron stars. The relativistic mean-field model is employed to describe the hadronic phase, while the Nambu--Jona-Lasinio model is used for the quark phase. We examine the effects of nuclear symmetry energy in the hadronic phase and repulsive vector interaction in the quark phase. For the treatment of hadron-quark mixed phase, we describe and compare four methods: (1) energy minimization method; (2) coexisting phases method; (3) Gibbs construction; and (4) Maxwell construction. The finite-size effects like surface and C…
Using the quark-meson coupling model with the cloudy bag, we construct the equation of state for neutron stars with hyperons in SU(3) flavor symmetry. The hyperfine interaction due to the gluon exchange and the pion-cloud effect inside a baryon is taken into account in vacuum and nuclear matter. We investigate how the quark degrees of freedom and the exchanges of gluon and pion between two quarks affect the properties of nuclear and neutron-star matter. It is found that the variation of baryon substructure in matter plays an important role in supporting massive neutron stars.
We aim at drawing the hadron-quark phase transition line in the QCD phase diagram by using the two phase model (TPM) in which the entanglement Polyakov-loop extended Nambu--Jona-Lasinio (EPNJL) model with vector-type four-quark interaction is used for the quark phase and the relativistic mean field (RMF) model is for the hadron phase. Reasonable TPM is constructed by using lattice QCD data and neutron star observations as reliable constraints. For the EPNJL model, we determine the strength of vector-type four-quark interaction at zero quark chemical potential from lattice QCD data on quark num…
We review the prospects for detecting quark matter in neutron star cores. We survey the proposed signatures and emphasize the importance of data from neutron star mergers, which provide access to dynamical properties that operate on short timescales that are not probed by other neutron star observables.
A quark-meson coupling model based on the quark model proposed by Bogoliubov for the description of the quark dynamics is developed and applied to the description of neutron stars. Starting from a su(3) symmetry approach, it is shown that this symmetry has to be broken in order to satisfy the constraints set by the hypernuclei and by neutron stars. The model is able to describe observations such as two solar mass stars or the radius of canonical neutron stars within the uncertainties presently accepted. If the optical potentials for $Λ$ and $Ξ$ hyperons in symmetric nuclear matter at saturatio…
By a new approach introducing a "3-window model" and constructing phenomenologically an equation of state for the hadron-quark (HQ) transition region, possible maximum mass of neutron stars (NSs) is discussed. It is found that neutron stars (NSs) with HQ transition core are able to have a mass exceeding two-solar mass, consistent with massive NSs recently observed.
This study is performed with the aim of gaining insights into the possible applicability of the quark-hadron continuity concept, not only in the idealized case of three-flavor symmetric quark matter, but also for the transition from neutron matter to two-flavor quark matter. A key issue is the continuity between neutron superfluidity and a corresponding superfluid quark phase produced by $d$-quark pairing. Symmetry arguments are developed and relevant dynamical mechanisms are analyzed. It is pointed out that the $^3P_2$ superfluidity in dense neutron matter has a direct analogue in the $^3P_2$…
Based on an equivparticle model, we investigate the in-medium quark condensate in neutron stars. Carrying out a Taylor expansion of the nuclear binding energy to the order of $ρ^3$, we obtain a series of EOSs for neutron star matter, which are confronted with the latest nuclear and astrophysical constraints. The in-medium quark condensate is then extracted from the constrained properties of neutron star matter, which decreases non-linearly with density. However, the chiral symmetry is only partially restored with non-vanishing quark condensates, which may vanish at a density that is out of rea…
We consider Quarkyonic Matter to naturally explain the observed properties of neutron stars. We argue that such matter might exist at densities close to that of nuclear matter and at the onset, the pressure and the sound velocity in Quarkyonic matter increase rapidly. In the limit of large number of quark colors $N_c$, this transition is characterized by a discontinuous change in pressure as a function of baryon number density. We make a simple model of Quarkyonic matter and show that generically the sound velocity is a non-monotonic function of density -- it reaches a maximum at relatively lo…
Quasi-normal oscillation modes of neutron stars provide a means to probe their interior composition using gravitational wave astronomy. We compute the frequencies and damping times of composition-dependent core g-modes of neutron stars containing quark matter employing linearized perturbative equations of general relativity. We find that ignoring background metric perturbations due to the oscillating fluid, as in the Cowling approximation, underestimates the g-mode frequency by up to 10% for higher mass stars, depending on the parameters of the nuclear equation of state and how the mixed phase…
We investigate the surface tension $σ$ and the curvature energy $γ$ of quark matter drops in the MIT bag model with vector interactions. Finite size corrections to the density of states are implemented by using the multiple reflection expansion (MRE) formalism. We find that $σ$ and $γ$ are strongly enhanced by new terms arising from vector interactions. With respect to the noninteracting case they are increased by a large factor, which can be as high as $\sim 10$ when the vector coupling constant $g$ varies within the range used in the literature. This behavior may have major consequences for …
In part one of this paper, we use a non-local extension of the 3-flavor Polyakov-Nambu-Jona-Lasinio model, which takes into account flavor-mixing, momentum dependent quark masses, and vector interactions among quarks, to investigate the possible existence of a spinodal region (determined by the vanishing of the speed of sound) in the QCD phase diagram and determine the temperature and chemical potential of the critical end point. In part two of the paper, we investigate the quark-hadron composition of baryonic matter at zero as well as non-zero temperature. This is of great topical interest fo…
Alice and Boojums are both representative characters created by Lewis Carroll. We show that they possibly meet in cores of rotating neutron stars. Recent studies of quark-hadron continuity suggest that neutron superfluid matter can connect smoothly to two-flavor symmetric quark matter at high densities. We study how this can be maintained in the presence of the vortices. In the neutron matter, quantized superfluid vortices arise. In the two-flavor dense quark matter, vortices carrying color magnetic fluxes together with fractionally quantized superfluid circulations appear as the most stable c…
We study the finite-size effects, like the surface and Coulomb energies, on the hadron-quark mixed phase in neutron stars. The equilibrium conditions for coexisting hadronic and quark phases are derived by minimizing the total energy including the surface and Coulomb contributions, which are different from the Gibbs conditions without finite-size effects. We employ the relativistic mean-field model to describe the hadronic phase, while the Nambu-Jona-Lasinio model with vector interactions is used for the quark phase. It is found that finite-size effects can significantly reduce the region of t…
