We construct a set of equations of state (EoS) of dense and hot matter with a 1st order phase transition from a hadronic system to a deconfined quark matter state. In this two-phase approach, hadrons are described using the relativistic mean field theory with different parametrisations and the deconfined quark phase is modeled using vBag, a bag-type model extended to include vector interactions as well as a simultaneous onset of chiral symmetry restoration and deconfinement. This feature results in a non-trivial connection between the hadron and quark EoS, modifying the quark phase beyond its onset density. We find that this unique property has an impact on the predicted hybrid (quark core) neutron star mass--radius relations.
We derive the empirical formulas for the neutron star mass and gravitational redshift as a function of the central density and specific combination of the nuclear saturation parameters, which are applicable to the stellar models constructed with the central density up to threefold nuclear saturation density. Combining the both empirical formulas, one also estimates the neutron star radius. In practice, we find that the neutron star mass (radius) can be estimated within $\sim 10\%$ (a few percent) accuracy by comparing the mass and radius evaluated with our empirical formulas to those determine…
Taking into account the terrestrial experiments and the recent astrophysical observations of neutron stars and gravitational-wave signals, we impose restrictions on the equation of state (EoS) for isospin-asymmetric nuclear matter. Using the relativistic mean-field model with SU(3) flavor symmetry, we investigate the impacts of effective nucleon mass, nuclear incompressibility, and slope parameter of nuclear symmetry energy on the nuclear and neutron-star properties. It is found that the astrophysical information of massive neutron stars and tidal deformabilities as well as the nuclear experim…
We study the cooling of isolated neutron stars with particular regard to the importance of nuclear pairing gaps. A microscopic nuclear equation of state derived in the Brueckner-Hartree-Fock approach is used together with compatible neutron and proton pairing gaps. We then study the effect of modifying the gaps on the final deduced neutron star mass distributions. We find that a consistent description of all current cooling data can be achieved and a reasonable neutron star mass distribution can be predicted employing the (slightly reduced by about 40\%) proton 1S0 Bardeen-Cooper-Schrieffer (B…
Neutron stars are unique laboratories to probe matter in extreme conditions, not accessible in terrestrial laboratories. Here, we discuss the modelling of the neutron-star equation of state, particularly in connection with recent constraints coming from both nuclear physics (experiments and ab-initio calculations) and astrophysical observations.
A compressible liquid-drop approach adjusted to uniform matter many-body calculations based on chiral EFT interactions and to the experimental nuclear masses is used to investigate the neutron star crust properties. Eight chiral EFT hamiltonians and a representative phenomenological force (SLy4) are confronted. We show that some properties of the crust, e.g. clusters mass, charge, and asymmetry, are mostly determined by symmetric matter properties close to saturation density and are therefore mainly constrained by experimental nuclear masses, while other properties, e.g., energy per particle, …
Neutron stars are valuable laboratories for the study of dense matter. Recent observations have uncovered both massive and low-mass neutron stars and have also set constraints on neutron star radii. The largest mass measurements are powerfully influencing the high-density equation of state because of the existence of the neutron star maximum mass. The smallest mass measurements, and the distributions of masses, have implications for the progenitors and formation mechanisms of neutron stars. The ensemble of mass and radius observations can realistically restrict the properties of dense matter, …
We report a new microscopic equation of state (EOS) of dense symmetric nuclear matter, pure neutron matter, and asymmetric and $β$-stable nuclear matter at zero temperature using recent realistic two-body and three-body nuclear interactions derived in the framework of chiral perturbation theory (ChPT) and including the $Δ(1232)$ isobar intermediate state. This EOS is provided in tabular form and in parametrized form ready for use in numerical general relativity simulations of binary neutron star merging. Here we use our new EOS for $β$-stable nuclear matter to compute various structural proper…
We investigate the cooling of neutron stars with relativistic and non-relativistic models of dense nuclear matter. We focus on the effects of uncertainties originated from the nuclear models, the composition of elements in the envelope region, and the formation of superfluidity in the core and the crust of neutron stars. Discovery of $2 M_\odot$ neutron stars PSR J1614-2230 and PSR J0343+0432 has triggered the revival of stiff nuclear equation of state at high densities. In the mean time, observation of a neutron star in Cassiopeia A for more than 10 years has provided us with very accurate da…
Low-mass neutron stars are directly associated with the nuclear saturation parameters because their central density is definitely low. We have already found a suitable combination of nuclear saturation parameters for expressing the neutron star mass and gravitational redshift, i.e., $η\equiv (K_0L^2)^{1/3}$ with the incompressibility for symmetric nuclear matter, $K_0$, and the density-dependent nuclear symmetry energy, $L$. In this study, we newly find another suitable combination given by $η_τ\equiv (-K_τL^5)^{1/6}$ with the isospin dependence of incompressibility for asymmetric nuclear matt…
We present predictions for neutron star tidal deformabilities obtained from a Bayesian analysis of the nuclear equation of state, assuming a minimal model at high-density that neglects the possibility of phase transitions. The Bayesian posterior probability distribution is constructed from priors obtained from microscopic many-body theory based on realistic two- and three-body nuclear forces, while the likelihood functions incorporate empirical information about the equation of state from nuclear experiments. The neutron star crust equation of state is constructed from the liquid drop model, a…
In order to systematically examine the possible maximum mass of neutron stars, which is one of the important properties characterizing the physics in high-density region, I construct neutron star models by adopting phenomenological equations of state with various values of nuclear saturation parameters for low-density region, which are connected to the equation of state for high-density region characterized by the possible maximum sound velocity in medium. I derive an empirical formula for the possible maximum mass of neutron star. If massive neutron stars are observed, it could be possible to…
We investigate the effects of the symmetry energy on nuclear pasta phases and the crust-core transition in neutron stars. We employ the relativistic mean-field approach and the coexisting phases method to study the properties of pasta phases presented in the inner crust of neutron stars. It is found that the slope of the nuclear symmetry energy at saturation density plays an important role in the crust-core transition and pasta phase properties. The correlation between the symmetry energy slope and the crust-core transition density obtained in this study is consistent with those obtained by ot…
We present a simple model for electron transport in a possible layer of exotic nuclear clusters (in the so called nuclear pasta layer) between the crust and liquid core of a strongly magnetized neutron star. The electron transport there can be strongly anisotropic and gyrotropic. The anisotropy is produced by different electron effective collision frequencies along and across local symmetry axis in domains of exotic ordered nuclear clusters and by complicated effects of the magnetic field. We also calculate averaged kinetic coefficients in case local domains are freely oriented. Possible appli…
Brueckner theory is used to investigate the in-medium properties of a $Λ$-hyperon in nuclear and neutron matter, based on hyperon-nucleon interactions derived within SU(3) chiral effective field theory (EFT). It is shown that the resulting $Λ$ single-particle potential $U_Λ(p_Λ=0,ρ)$ becomes strongly repulsive for densities $ρ$ of two-to-three times that of normal nuclear matter. Adding a density-dependent effective $ΛN$-interaction constructed from chiral $ΛNN$ three-body forces increases the repulsion further. Consequences of these findings for neutron stars are discussed. It is argued that …
We consider the thermal conductivity, shear viscosity, and momentum relaxation rates in the nucleon cores of the neutron stars. We study how the choice of the nuclear interaction and the model for three-body forces may affect these transport coefficients calculated within the Brueckner-Hartree-Fock many-body nuclear theory. We find that at relatively large densities the model dependence of the results is substantial. In addition we provide the analytical approximations which allow to incorporate our results in practical simulations.
Neutron star structure and nuclear matter properties from a general Walecka-type model with Bayesian analysis
School of Frontier Sciences, Nanjing University（前沿科学学院，南京大学）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（基础物理与数学学院，杭州高等研究院，中国科学院大学）
We calculate the equation of state of neutron matter with realistic two- and three-nucleon interactions using quantum Monte Carlo techniques, and illustrate that the short-range three-neutron interaction determines the correlation between neutron matter energy at nuclear saturation density and higher densities relevant to neutron stars. Our model also makes an experimentally testable prediction for the correlation between the nuclear symmetry energy and its density dependence -- determined solely by the strength of the short-range terms in the three neutron force. The same force provides a sig…
Now 50 years since the existence of the neutron star crust was proposed, we review the current understanding of the nuclear physics of the outer layers of accreting neutron stars. Nuclei produced during nuclear burning replace the nascent composition of the neutron star ocean and crust. Non-equilibrium nuclear reactions driven by compression alter the outer thermal structure and chemical composition, leaving observable imprints on astronomical phenomena. As observations of bursting neutron stars and cooling neutron stars have increased, the recent volume of astronomical data allows new insight…
Neutron stars -- compact objects with masses similar to that of our Sun but radii comparable to the size of a city -- contain the densest form of matter in the universe that can be probed in terrestrial laboratories as well as in earth- and space-based observatories. The historical detection of gravitational waves from a binary neutron star merger has opened the brand new era of multimessenger astronomy and has propelled neutron stars to the center of a variety of disciplines, such as astrophysics, general relativity, nuclear physics, and particle physics. The main input required to study the …
We explore constraints on the equation of state (EOS) of neutron-rich matter based on microscopic calculations up to nuclear densities and observations of neutron stars. In a previous work we showed that predictions based on modern nuclear interactions derived within chiral effective field theory and the observation of two-solar-mass neutron stars result in a robust uncertainty range for neutron star radii and the EOS over a wide range of densities. In this work we extend this study, employing both the piecewise polytrope extension from Hebeler et al. as well as the speed of sound model of Gre…
The determination of the equation of state (EOS) for nuclear matter has been one of the biggest problems in nuclear astrophysics, because the EOS is essential for determining the properties of neutron stars. To constrain the density-dependence of the nuclear symmetry energy, several nuclear experiments, e.g., reported by the S$π$RIT and PREX-II collaborations, have recently been performed. However, since their uncertainties are still large, additional constraints such as astronomical observations must be crucial. In addition, it is interesting to see the effect of their reported value on neutr…
We model the cooling of hybrid neutron stars combining a microscopic nuclear equation of state in the Brueckner-Hartree-Fock approach with different quark models. We then analyze the neutron star cooling curves predicted by the different models and single out the preferred ones. We find that the possibility of neutron p-wave pairing can be excluded in our scenario.
X-ray observations of the neutron star in the Cas A supernova remnant over the past decade suggest the star is undergoing a rapid drop in surface temperature of $\approx$ $2-5.5\%$. One explanation suggests the rapid cooling is triggered by the onset of neutron superfluidity in the core of the star, causing enhanced neutrino emission from neutron Cooper pair breaking and formation (PBF). Using consistent neutron star crust and core equations of state (EOSs) and compositions, we explore the sensitivity of this interpretation to the density dependence of the symmetry energy $L$ of the EOS used, …
Understanding the equation of state of dense QCD matter remains a major challenge in both nuclear physics and astrophysics. Neutron star observations from electromagnetic and gravitational wave spectra provide critical insights into the behavior of dense neutron-rich matter. The next generation of telescopes and gravitational wave observatories will offer even more detailed observations of neutron stars. Utilizing deep learning techniques to map neutron star mass and radius observations to the equation of state allows for its accurate and reliable determination. This work demonstrates the feas…
We study the dark matter effects on the nuclear matter parameters characterising the equation of states of super dense neutron-rich nucleonic-matter. The observables of the nuclear matter, i.e. incompressibility, symmetry energy and its higher-order derivatives in the presence dark matter for symmetric and asymmetric nuclear matter are analysed with the help of an extended relativistic mean-field model. The calculations are also extended to beta-stable matter to explore the properties of the neutron star. We analyse the dark matter effects on symmetric nuclear matter, pure neutron matter and n…
Nuclear matter and finite nuclei exhibit the property of superfluidity by forming Cooper pairs. We review the microscopic theories and methods that are being employed to understand the basic properties of superfluid nuclear systems, with emphasis on the spatially extended matter encountered in neutron stars, supernova envelopes, and nuclear collisions. Our survey of quantum many-body methods includes techniques that employ Green functions, correlated basis functions, and Monte Carlo sampling of quantum states. With respect to empirical realizations of nucleonic and hadronic superfluids, this r…
One of the most significant challenges involved in efforts to understand the equation of state of dense neutron-rich matter is the uncertain density dependence of the nuclear symmetry energy. Because of its broad impact, pinning down the density dependence of the nuclear symmetry energy has been a longstanding goal of both nuclear physics and astrophysics. Recent observations of neutron stars, in both electromagnetic and gravitational-wave spectra, have already constrained significantly the nuclear symmetry energy at high densities. Training deep neural networks to learn a computationally effi…
A unified chiral mean field approach is presented for QCD thermodynamics in a wide range of temperatures and densities. The model simultaneously gives a satisfactory description of lattice QCD thermodynamics and fulfills nuclear matter and astrophysical constraints. The resulting equation of state can be incorporated in relativistic fluid-dynamical simulations of heavy-ion collisions and neutron stars mergers. Access to different regions of the QCD phase diagram can be obtained in simulations of heavy-ion data and observations of neutron star mergers.
The nuclear symmetry energy plays a key role in determining the equation of state of dense, neutron-rich matter, which governs the properties of both terrestrial nuclear matter as well as astrophysical neutron stars. A recent measurement of the neutron skin thickness from the PREX collaboration has lead to new constraints on the slope of the nuclear symmetry energy, L, which can be directly compared to inferences from gravitational-wave observations of the first binary neutron star merger inspiral, GW170817 In this paper, we explore a new regime for potentially constraining the slope, L, of th…
Nuclear matter and compact neutron stars are studied in the framework of the non-linear derivative (NLD) model which accounts for the momentum dependence of relativistic mean-fields. The generalized form of the energy-momentum tensor is derived which allows to consider different forms of the regulator functions in the NLD Lagrangian. The thermodynamic consistency of the NLD model is demonstrated for arbitrary choice of the regulator functions. The NLD approach describes the bulk properties of the nuclear matter and compares well with microscopic calculations and Dirac phenomenology. We further…
Using a extended version of the Quantum Hadrodynamics (QHD), I propose a new microscopic equation of state (EoS) able to correctly reproduce the main properties of symmetric nuclear matter at the saturation density, as well produce massive neutron stars and satisfactory results for the radius and the tidal parameter $Λ$. I show that even when hyperons are present, this EoS is able to reproduce at least 2.00 solar masses neutron star. The constraints about the radius of a $2.00M_\odot$ and the minimum mass that enable direct Urca effect are also checked.
Common-envelope evolution is important in the formation of neutron star binaries within the isolated binary formation channel. As a neutron star inspirals within the envelope of a primary massive star, it accretes and spins up. Because neutron stars are in the strong-gravity regime, they have a substantial relativistic mass deficit, i.e., their gravitational mass is less than their baryonic mass. This effect causes some fraction of the accreted baryonic mass to convert into neutron star binding energy. The relativistic mass deficit also depends on the nuclear equation of state, since more comp…
In this lecture, we give a first introduction to neutron stars, based on fundamental physical principles. After outlining their amazing macroscopic properties, as obtained from observations, we infer the extreme conditions of matter in their interiors. We then describe two crucial physical phenomena which characterize compact stars, gravitational stability of strongly degenerate matter and neutronization of nuclear matter with increasing density, and explain how the formation and properties of neutron stars are a consequence of the extreme compression of matter under gravity. Finally, we descr…
I review holographic models for (dense and cold) nuclear matter, neutron stars, and their mergers. I start by a brief general discussion on current knowledge of cold QCD matter and neutron stars, and go on discussing various approaches to model cold nuclear and quark matter by using gauge/gravity duality, pointing out their strengths and weaknesses. Then I focus on recent results for a complex bottom-up holographic framework (V-QCD), which also takes input from lattice QCD results, effective field theory, and perturbative QCD. Dense nuclear matter is modeled in V-QCD through a homogeneous non-…
Thermal Spin Polarization Driven by Nuclear Spin-Orbit Coupling in Neutron Star Pasta
The University of Tokyo（东京大学）；RIKEN Nishina Center（理化学研究所仁科中心）；Quark Nuclear Science Institute, The University of Tokyo（东京大学夸克核科学研究所）；Institute for Advanced Research, Nagoya University（名古屋大学高等研究院）；Department of Physics, Nagoya University（名古屋大学物理系）；Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学项目（iTHEMS））；Nonequilibrium Quantum Statistical Mechanics RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR)（理化学研究所前沿研究集群（CPR）非平衡量子统计力学理化学博雅研究团队）；Center for Spintronics Research Network, Keio University（庆应义塾大学自旋电子学研究网络中心）；Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学卡弗里理论科学研究院）；Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University（广岛大学先进理工学研究学院物理学项目）；Hiroshima Astrophysical Science Center, Hiroshima University（广岛大学广岛天体物理科学中心）；Department of Physics, Chiba Institute of Technology (CIT)（千叶工业大学物理系）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子力研究机构先进科学研究中心）
In the past few years, new observations of neutron stars and neutron-star mergers have provided a wealth of data that allow one to constrain the equation of state of nuclear matter at densities above nuclear saturation density. However, most observations were based on neutron stars with masses of about 1.4 solar masses, probing densities up to $\sim$ 3-4 times the nuclear saturation density. Even higher densities are probed inside massive neutron stars such as PSR J0740+6620. Very recently, new radio observations provided an update to the mass estimate for PSR J0740+6620 and X-ray observations…
Nuclear reactions may affect gravitational-wave signals from neutron-star mergers, but the impact is uncertain. In order to quantify the effect, we compare two numerical simulations representing intuitive extremes. In one case reactions happen instantaneously. In the other case, they occur on timescales much slower than the evolutionary timescale. We show that, while the differences in the two gravitational-wave signals are small, they should be detectable by third-generation observatories. To avoid systematic errors in equation of state parameters inferred from observed signals, we need to ac…
