Neutron star interiors provide the opportunity to probe properties of cold dense matter in the QCD phase diagram. Utilizing models of dense matter in accord with nuclear systematics at nuclear densities, we investigate the compatibility of deconfined quark cores with current observational constraints on the maximum mass and tidal deformability of neutron stars. We explore various methods of implementing the hadron-to-quark phase transition, specifically, first-order transitions with sharp (Maxwell construction) and soft (Gibbs construction) interfaces, and smooth crossover transitions. We find that within the models we apply, hadronic matter has to be stiff for a first-order phase transition and soft for a crossover transition. In both scenarios and for the equations of state we employed, quarks appear at the center of pre-merger neutron stars in the mass range $\approx 1.0-1.6\,{\rm M}_{\odot}$, with a squared speed of sound $c^2_{\rm QM}\gtrsim 0.4$ characteristic of strong repulsive interactions required to support the recently discovered neutron star masses $\geq 2\,{\rm M}_{\odot}$. We also identify equations of state and phase transition scenarios that are consistent with the bounds placed on tidal deformations of neutron stars in the recent binary merger event GW170817. We emphasize that distinguishing hybrid stars with quark cores from normal hadronic stars is very difficult from the knowledge of masses and radii alone, unless drastic sharp transitions induce distinctive disconnected hybrid branches in the mass-radius relation.
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…
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…
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.
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…
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…
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…
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…
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} $). Nonetheless the neutron stars provide a best condition for the conversion to be statistically significant which is of the same order as is expected from imposin…
Comment on "Three-dimensional hydrodynamic simulations of the combustion of a neutron star into a quark star"
如果奇异物质是绝对稳定的，那么普通的原子核就会衰变为奇异核，而中子星则会转化为奇异星。普通核的寿命在实验上被限制在$\sim 10^{33}$年以上，而亚稳态中子星的寿命取决于中子星的质量，可以超过宇宙的年龄。因此，中子星和奇异星可以在宇宙中共存。我们指出，M。Herzog和F. K. Roepke在Phys. Rev. D 84，083002（2011）[arXiv：1109.0539]中的研究集中在奇异物质参数空间中的一个区域，在该区域中，低质量中子星和奇异星共存，而大质量中子星在天文时间尺度上是不稳定的，寿命很短。
In the first part of this paper, we investigate the possible existence of a structured hadron-quark mixed phase in the cores of neutron stars. This phase, referred to as the hadron-quark pasta phase, consists of spherical blob, rod, and slab rare phase geometries. Particular emphasis is given to modeling the size othis phase in rotating neutron stars. We use the relativistic mean-field theory to model hadronic matter and the non-local three-flavor Nambu-Jona-Lasinio model to describe quark matter. Based on these models, the hadron-quark pasta phase exists only in very massive neutron stars, wh…
The rotating neutron star properties are studied with a phase transition to quark matter. The density-dependent relativistic mean-field model (DD-RMF) is employed to study the hadron matter, while the Vector-Enhanced Bag model (vBag) model is used to study the quark matter. The star matter properties like mass, radius,the moment of inertia, rotational frequency, Kerr parameter, and other important quantities are studied to see the effect on quark matter. The maximum mass of rotating neutron star with DD-LZ1 and DD-MEX parameter sets is found to be around 3$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…
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…
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 …
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 …
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…
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…
As neutron stars merge they can approach very high nuclear density. Here, we summarized recent results for the evolution and gravitational wave emission from binary neutron star mergers using a a variety of nuclear equations of state with and without a crossover transition to quark matter. We discuss how the late time gravitational wave emission from binary neutron star mergers may possibly reveal the existence of a crossover transition to quark matter.
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 …
We review the equation of state of matter in neutron stars from the solid crust through the liquid nuclear matter interior to the quark regime at higher densities. We focus in detail on the question of how quark matter appears in neutron stars, and how it affects the equation of state. After discussing the crust and liquid nuclear matter in the core we briefly review aspects of microscopic quark physics relevant to neutron stars, and quark models of dense matter based on the Nambu--Jona-Lasinio framework, in which gluonic processes are replaced by effective quark interactions. We turn then to …
We have studied the spin-down induced phase transition in cold, isolated neutron stars in this work. After birth, as the star slows down, its central density rises and crosses the critical density of phase transition, and a quark core is seeded inside the star. Intermediate mass stars are more likely to have a quark seeding in their lifetime at birth. Smaller neutron stars do not have a quark core and remain neutron stars throughout their life, whereas in massive stars, a quark core exists at their center from birth. In intermediate and massive stars, the quark core grows further as the star s…
It is well known that the equation of state (EoS) of compact objects like neutron and quark stars is not determined despite there are several sophisticated models to describe it. From the electromagnetic observations, summarized in \cite{Lattimer01}, and the recent observation of gravitational waves from binary neutron star inspiral GW170817 \cite{Abbott2017_etal} and GW190425 \cite{Abbott2019}, it is possible to make an estimation of the range of masses and so constraint the mass of the neutron and quark stars, determining not only the best approximation for the EoS, but which kind of stars w…
The fundamental constituent of matter at high temperature and density has intrigued physicists for quite some time. Recent results from heavy-ion colliders have enriched the Quantum Chromodynamics phase diagram at high temperatures and low baryon density. However, the phase at low temperatures and finite (mostly intermediate) baryon density remain unexplored. Theoretical Quantum Chromodynamics calculation predicts phase transition from hadronic matter to quark matter at such densities. Presently, the best laboratories available to probe such densities lie at the core of neutron stars. Recent r…
