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 experimental data plays an important role to restrict the EoS for neutron stars. Especially, the softness of the nuclear EoS due to the existence of hyperons in the core gives stringent constraints on those physical quantities. Furthermore, it is possible to put limits on the curvature parameter of nuclear symmetry energy by means of the nuclear and astrophysical calculations.
After a brief historical overview of superfluidity in connection with neutron matter and cold fermionic atoms, we discuss the commonalities between these two systems as well as their relevance to the physics of neutron star crusts. We then present the methodological tools we use to attack the many-body problem, comparing Quantum Monte Carlo to mean-field theory and to the analytic expectations at weak coupling. We review recent results on the equation of state and the pairing gap of cold atoms and neutron matter and contrast them with a variety of calculations by other groups. We conclude by g…
Recent observations of neutron stars with gravitational waves and X-ray timing provide unprecedented access to the equation of state (EoS) of cold dense matter at densities difficult to realize in terrestrial experiments. At the same time, predictions for the EoS with reliable uncertainty estimates from chiral effective field theory ($χ$EFT) bound our theoretical ignorance. In this work, we analyze astrophysical data using a nonparametric representation of the neutron-star EoS conditioned on $χ$EFT to directly constrain the underlying physical properties of the compact objects. We discuss how …
We present the first astrophysical measurement of the pressure of cold matter above nuclear saturation density, based on recently determined masses and radii of three neutron stars. The pressure at higher densities are below the predictions of equations of state that account only for nucleonic degrees of freedom, and thus present a challenge to the microscopic theory of neutron star matter.
Observations of neutron stars (NSs) by the LIGO-Virgo and NICER collaborations have provided reasonably precise measurements of their various macroscopic properties. In this paper, we employ a Bayesian framework to combine them and place improved joint constraints on the properties of NS equation of state (EoS). We use a hybrid EoS formulation that employs a parabolic expansion-based nuclear empirical parameterization around the nuclear saturation density augmented by a generic 3-segment piecewise polytrope model at higher densities. Within the $90 \%$ credible level this parameterization pred…
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…
A set of hadronic equations of state (EoSs) derived from relativistic density functional theory and constrained by terrestrial experiments, astrophysical observations, in particular by the GW170817 event, and chiral effective field theory ($χ$EFT) of neutron matter is used to explore the sensitivity of the EoS parameterization on the few nuclear matter characteristics defined at the saturation density. We find that the gross properties of compact stars are most sensitive to the isoscalar skewness coefficient $Q_{\text{sat}}$ and the isovector slope coefficient $L_{\text{sym}}$ around saturatio…
We present a Bayesian analysis to constrain the equation of state of dense nucleonic matter by exploiting the available data from symmetric nuclear matter at saturation and from observations of compact X-ray sources and from the gravitational wave event GW170817. For the first time, such analysis is performed by using a class of models, the relativistic mean field models, which allow to consistently construct an equation of state in a wide range of densities, isospin asymmetries and temperatures. The selected class of models contains five nuclear physics empirical parameters at saturation for …
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.
Heavy-ion reactions provide a unique means to investigate the equation of state (EOS) of neutron-rich nuclear matter, especially the density dependence of the nuclear symmetry energy $E_{sym}(ρ)$. The latter plays an important role in understanding many key issues in both nuclear physics and astrophysics. Recent analyses of heavy-ion reactions have already put a stringent constraint on the $E_{sym}(ρ)$ around the saturation density. This subsequently allowed us to constrain significantly the radii and cooling mechanisms of neutron stars as well as the possible changing rate of the gravitationa…
Ever since the discovery of neutron stars it has been realized that they serve as probes of a physical regime that cannot be accessed in laboratories: strongly degenerate matter at several times nuclear saturation density. Existing nuclear theories diverge widely in their predictions about such matter. It could be that the matter is primarily nucleons, but it is also possible that exotic species such as hyperons, free quarks, condensates, or strange matter may dominate this regime. Astronomical observations of cold high-density matter are necessarily indirect, which means that we must rely on …
We show that the gravitational binding energy of a neutron star of a given mass is correlated with the slope of the nuclear symmetry energy at 1-2 times nuclear saturation density for equations of state without significant softening (i.e., those that predict maximum masses $M_{\rm max} > 1.44M_{\odot}$ in line with the largest accurately measured neutron star mass). Applying recent laboratory constraints on the slope of the symmetry energy to this correlation we extract a constraint on the baryon mass of the lower mass member of the double pulsar binary system, PSR J0737-3039B. We compare with…
In view of new constraints put forth by recent observations and measurements in the realm of astrophysics and nuclear physics, we update the non-linear realization of the sigma model as to reflect such constraints. By doing this, we obtain new equations of state that may be used to describe neutron stars. Such equations of state are obtained by investigating different ways by which the vector mesons self-interact. Furthermore, we also investigate the role played by the delta mesons in the model. As a result, we are able to develop equations of state that are in better agreement with data, such…
Determining the Equation of State (EOS) of dense neutron-rich nuclear matter is a shared goal of both nuclear physics and astrophysics. Except possible phase transitions, the density dependence of nuclear symmetry \esym is the most uncertain part of the EOS of neutron-rich nucleonic matter especially at supra-saturation densities. Much progresses have been made in recent years in predicting the symmetry energy and understanding why it is still very uncertain using various microscopic nuclear many-body theories and phenomenological models. Simultaneously, significant progresses have also been m…
Pulsars are among the most mysterious astrophysical objects in the Universe and are believed to be rotating neutron stars formed in supernova explosions. They are unique testing grounds of dense matter theories and gravitational physics and also provide links among nuclear physics, particle physics and General Relativity. Neutron stars may exhibit some of the most extreme and exotic characteristics that could not be found elsewhere in the Universe. Their properties are largely determined by the equation of state (EOS) of neutron-rich matter, which is the chief ingredient in calculating neutron…
Within an isospin- and momentum-dependent hadronic transport model it is shown that the recent FOPI data on the $π^-/π^+$ ratio in central heavy-ion collisions at SIS/GSI energies (Willy Reisdorf {\it et al.}, NPA {\bf 781}, 459 (2007)) provide circumstantial evidence suggesting a rather soft nuclear symmetry energy \esym at $ρ\geq 2ρ_0$ compared to the Akmal-Pandharipande-Ravenhall prediction. Some astrophysical implications and the need for further experimental confirmations are discussed.
Within both dynamical and thermodynamical approaches using the equation of state for neutron-rich nuclear matter constrained by the recent isospin diffusion data from heavy-ion reactions in the same sub-saturation density range as the neutron star crust, the density and pressure at the inner edge separating the liquid core from the solid crust of neutron stars are determined to be 0.040 fm$^{-3}$ $\leq ρ_{t}\leq 0.065$ fm$^{-3}$ and 0.01 MeV/fm$^{3}$ $\leq P_{t}\leq 0.26$ MeV/fm$^{3}$, respectively. These together with the observed minimum crustal fraction of the total moment of inertia allow …
Explosive astrophysical systems, such as supernovae or compact star binary mergers, provide conditions where strange quark matter can appear. The high degree of isospin asymmetry and temperatures of several MeV in such systems may cause a transition to the quark phase already around saturation density. Observable signals from the appearance of quark matter can be predicted and studied in astrophysical simulations. As input in such simulations, an equation of state with an integrated quark matter phase transition for a large temperature, density and proton fraction range is required. Additional…
Nuclear symmetry energy $E_{\rm{sym}}(ρ)$ at density $ρ$ is normally expanded or simply parameterized as a function of $χ=(ρ-ρ_0)/3ρ_0$ in the form of $E_{\rm{sym}}(ρ)\approx S+Lχ+2^{-1}K_{\rm{sym}}χ^2+6^{-1}J_{\rm{sym}}χ^3+\cdots$ using its magnitude $S$, slope $L $, curvature $K_{\rm{sym}}$ and skewness $J_{\rm{sym}}$ at the saturation density $ρ_0$ of nuclear matter. Much progress has been made in recent years in constraining especially the $S$ and $L$ parameters using various terrestrial experiments and astrophysical observations. However, such kind of expansions/parameterizations do not c…
An ambitious goal of the astrophysical community is not only to constrain the equation of state (EOS) of neutron star (NS) matter by confronting it with astrophysics observations, but ultimately also to infer the NS composition. Nevertheless, the composition of the NS core is likely to remain uncertain unless we have an accurate determination of the nuclear symmetry energy at supra saturation density ($ρ>ρ_0$). We investigate how the nucleonic direct Urca (dUrca) processes can be used as an effective probe to constraint the high density nuclear symmetry energy. A large number of minimally cons…
We search for possible correlations between neutron star observables and thermodynamic quantities that characterize high density nuclear matter. We generate a set of model-independent equations of state describing stellar matter from a Taylor expansion around saturation density. Each equation of state which is a functional of the nuclear matter parameters is thermodynamically consistent, causal and compatible with astrophysical observations. We find that the neutron star tidal deformability and radius are strongly correlated with the pressure, the energy density and the sound velocity at diffe…
The equation of state (EOS) of dense matter is an essential ingredient for numerical simulations of core-collapse supernovae and neutron star mergers. The properties of matter near and above nuclear saturation density are uncertain, which translates into uncertainties in astrophysical simulations and their multi-messenger signatures. Therefore, a wide range of EOSs spanning the allowed range of nuclear interactions are necessary for determining the sensitivity of these astrophysical phenomena and their signatures to variations in input microphysics. We present a new set of finite temperature E…
We report microscopic calculation of key $β$-decay properties for some of the crucial waiting point species having neutron closed magic shells 50 and 82. Our calculation bear astrophysical significance vis-á-vis speeding of the $r$-process. The $β$-decay properties include half-lives, energy rates of $β$-delayed neutrons and their emission probabilities, both under terrestrial and stellar conditions. We perform a pn-QRPA calculation with a separable multi-shell interaction and include both allowed and unique first-forbidden (U1F) transitions in our calculation. We compare our results with prev…
The symmetry energy and its density dependence are pivotal for many nuclear physics and astrophysics applications, as they determine properties ranging from the neutron-skin thickness of nuclei to the crust thickness and the radius of neutron stars. Recently, PREX-II reported a value of $0.283\pm0.071$ fm for the neutron-skin thickness of $^{208}$Pb, $R_{\rm skin}^{^{208}\text{Pb}}$, implying a symmetry-energy slope parameter $L$ of $106\pm37$ MeV, larger than most ranges obtained from microscopic calculations and other nuclear experiments. We use a nonparametric equation of state representati…
The secondary component of the GW190814 event left us with a question, "whether it is a supermassive neutron star or lightest black-hole?". Recently, Fattoyev et al. have obtained an energy density functional (EDF) named as BigApple, which reproduces the mass of the neutron star is 2.60 $M_\odot$ which is well consistent with GW190814 data. This study explores the properties of finite nuclei, nuclear matter, and neutron stars by using the BigApple EDF along with four well-known relativistic mean-field forces, namely NL3, G3, IOPB-I, and FSUGarnet. The finite nuclei properties like binding ener…
Bayesian Analysis of the Neutron Star Equation of State and Model Comparison: Insights from PSR J0437+4715, PSR J0614+3329, and Other Multi-Physics Data
Universidad Andrés Bello（安德斯·贝略大学）；The Chinese University of Hong Kong, Shenzhen (CUHKShenzhen)（香港中文大学（深圳））
本文通过贝叶斯分析，利用多物理数据约束中子星方程 of 状态参数，发现Skyrme模型在综合数据下表现最佳，确定了对称能量参数和中子星半径、潮汐变形性等关键结果。
We summarize the current status on constraining the density dependence of the symmetry energy from terrestrial laboratory measurements and astrophysical observations. While the value $E_{sym}({ρ_{0}})$ and density slope $L$ of the symmetry energy at saturation density $ρ_{0}$ can vary largely depending on the data or methods, all the existing constraints are essentially consistent with $E_{sym}({ρ_{0}}) = 31 \pm 2$ MeV and $L = 50 \pm 20$ MeV. The determination of the supra-saturation density behavior of the symmetry energy remains a big challenge.
Bayesian inferences on covariant density functionals from multimessenger astrophysical data: The impacts of likelihood functions of low density matter constraints
Recent analyses of several isospin effects in heavy-ion reactions have allowed us to constrain the density dependence of nuclear symmetry energy at sub-saturation densities within a narrow range. Combined with constraints on the Equation of State (EOS) of symmetric nuclear matter obtained previously from analyzing the elliptic flow in relativistic heavy-ion collisions, the EOS of neutron-rich nuclear matter is thus partially constrained. Here we report effects of the partially constrained EOS of neutron-rich nuclear matter on the mass-radius correlation, moment of inertia, elliptical deformati…
Significant progress has been made in recent years in constraining nuclear symmetry energy at and below the saturation density of nuclear matter using data from both terrestrial nuclear experiments and astrophysical observations. However, many interesting questions remain to be studied especially at supra-saturation densities. In this lecture note, after a brief summary of the currently available constraints on nuclear symmetry energy near the saturation density we first discuss the relationship between the symmetry energy and the isopin and momentum dependence of the single-nucleon potential …
Significant progress has been made in recent years in constraining the density dependence of nuclear symmetry energy using terrestrial nuclear laboratory data. Around and below the nuclear matter saturation density, the experimental constraints start to merge in a relatively narrow region. At supra-saturation densities, there are, however, still large uncertainties. After summarizing the latest experimental constraints on the density dependence of nuclear symmetry energy, we highlight a few recent studies examining imprints of nuclear symmetry energy on the binding energy, energy release durin…
Interpreting high-energy, astrophysical phenomena, such as supernova explosions or neutron-star collisions, requires a robust understanding of matter at supranuclear densities. However, our knowledge about dense matter explored in the cores of neutron stars remains limited. Fortunately, dense matter is not only probed in astrophysical observations, but also in terrestrial heavy-ion collision experiments. In this work, we use Bayesian inference to combine data from astrophysical multi-messenger observations of neutron stars and from heavy-ion collisions of gold nuclei at relativistic energies w…
Considering the non-Newtonian gravity proposed in the grand unification theories, we show that the stability and observed global properties of neutron stars can not rule out the super-soft nuclear symmetry energies at supra-saturation densities. The degree of possible violation of the Inverse-Square-Law of gravity in neutron stars is estimated using an Equation of State (EOS) of neutron-rich nuclear matter consistent with the available terrestrial laboratory data.
The nucleardatapy toolkit for simple access to experimental nuclear data, astrophysical observations, and theoretical predictions
Facility for Rare Isotope Beams, Michigan State University（密歇根州立大学稀有同位束设施）；Université de Toulouse, CNES, UPS-OMP（图卢兹大学, 法国国家空间研究中心, 图卢兹第三大学/观测物理研究所）；International Research Laboratory on Nuclear Physics and Astrophysics, Michigan State University and CNRS（密歇根州立大学和法国国家科学研究中心核物理与天体物理学国际研究实验室）；Institute of Nuclear and Particle Physics (INPP), Ohio University（俄亥俄大学核与粒子物理研究所）；Departamento de Física e Laboratório de Computação Científica Avançada e Modelamento (Lab-CCAM), Instituto Tecnológico de Aeronáutica, DCTA（巴西航空技术学院应用科学与建模高级计算实验室）；Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论部）；Department of Physics, University of Guelph（圭尔夫大学物理系）；Institut für Physik und Astronomie, Universität Potsdam（波茨坦大学物理与天文研究所）；IRAP, CNRS（法国国家科学研究中心研究天体物理研究所）；Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Dipartimento di Fisica e Astronomia “Ettore Majorana”, Università di Catani（意大利国家核物理研究院卡塔尼亚分部, 卡塔尼亚大学“埃托雷·马约拉纳”物理与天文学系）
We observe photons and neutrinos from stars. Based on these observations, complemented by measurements of cosmic rays energies and composition, we have been able to constrain several models for the Big Bang and for stellar evolution. But that is not enough. We also need to help this effort with laboratory experiments. We are still far from being able to reproduce stellar environments in a terrestrial laboratory. But in many cases we can obtain accurate nuclear reaction rates needed for modeling primordial nucleosynthesis and hydrostatic burning in stars. The relevant reactions are difficult to…
The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions and astrophysical phenomena. A recently developed quantum statistical (QS) approach that takes the formation of clusters into account predicts low density symmetry energies far above the usually quoted mean field limits. A consistent description of the symmetry energy has been developed that joins the correct low-density limit with values calculated from quasi-particle approaches valid near the saturation density. The results are confronted with experimental values for …
