Background:The microscopic composition and properties of infinite hadronic matter at a wide range of densities and temperatures have been subjects of intense investigation for decades. The equation of state (EoS) relating pressure, energy density, and temperature at a given particle number density is essential for modeling compact astrophysical objects such as neutron stars, core-collapse supernovae, and related phenomena, including the creation of chemical elements in the universe. The EoS depends not only on the particles present in the matter, but, more importantly, also on the forces acting among them. Because a realistic and quantitative description of infinite hadronic matter and nuclei from first principles in not available at present, a large variety of phenomenological models has been developed in the past several decades, but the scarcity of experimental and observational data does not allow a unique determination of the adjustable parameters. Purpose: It is essential for further development of the field to determine the most realistic parameter sets and to use them consistently. Recently, a set of constraints on properties of nuclear matter was formed and the performance of 240 nonrelativistic Skyrme parametrizations was assessed [M. Dutra et al., Phys. Rev. C 85, 035201 (2012)] in describing nuclear matter up to about three times nuclear saturation density. In the present work we examine 263 relativistic-mean-field (RMF) models in a comparable approach. These models have been widely used because of several important aspects not always present in nonrelativistic models, such as intrinsic Lorentz covariance, automatic inclusion of spin, appropriate saturation mechanism for nuclear matter, causality, and, therefore, no problems related to superluminal speed of sound in medium. Method: Three different sets of constraints related to symmetric nuclear matter, pure neutron matter, symmetry energy, and its derivatives were used. The first set (SET1) was the same as used in assessing the Skyrme parametrizations. The second and third sets (SET2a and SET2b) were more suitable for analysis of RMF and included, up-to-date theoretical, experimental and empirical information. Results: The sets of updated constraints (SET2a and SET2b) differed somewhat in the level of restriction but still yielded only 4 and 3 approved RMF models, respectively. A similarly small number of approved Skyrme parametrizations were found in the previous study with Skyrme models. An interesting feature of our analysis 0556-2813/2014/90(5)/055203 (35) 055203-1 ©2014 American Physical Society M. DUTRA et al.PHYSICAL REVIEW C 90, 055203 (2014) has been that the results change dramatically if the constraint on the volume part of the isospin incompressibility (K τ,v ) is eliminated. In this case, we have 35 approved models in SET2a and 30 in SET2b. Conclusions: Our work provides a new insight into application of RMF models to properties of nuclear matter and brings into focus their problematic proliferation. The assessment performed in this wo...

The uncertainties in neutron star radii and crust properties due to our limited knowledge of the equation of state are quantitatively analyzed. We first demonstrate the importance of a unified microscopic description for the different baryonic densities of the star. If the pressure functional is obtained matching a crust and a core equation of state based on models with different properties at nuclear matter saturation, the uncertainties can be as large as ∼30 % for the crust thickness and 4% for the radius. Necessary conditions for causal and thermodynamically consistent matchings between the core and the crust are formulated and their consequences examined. A large set of unified equations of state for purely nucleonic matter is obtained based on twenty-four Skyrme interactions and nine relativistic mean-field nuclear parametrizations. In addition, for relativistic models fifteen equations of state including a transition to hyperonic matter at high density are presented. All these equations of state have in common the property of describing a 2M star and of being causal within stable neutron stars. Spans of ∼3 and ∼4 km are obtained for the radius of, respectively, 1.0M and 2.0M stars. Applying a set of nine further constraints from experiment and ab initio calculations the uncertainty is reduced to ∼1 and 2 km, respectively. These residual uncertainties reflect lack of constraints at large densities and insufficient information on the density dependence of the equation of state near the nuclear matter saturation point. The most important parameter to be constrained is shown to be the symmetry energy slope L. Indeed, this parameter exhibits a linear correlation with the stellar radius, which is particularly clear for small mass stars around 1.0M . The other equation-of-state parameters do not show clear correlations with the radius, within the present uncertainties. Potential constraints on L, the neutron star radius, and the equation of state from observations of thermal states of neutron stars are also discussed. The unified equations of state are made available in the Supplemental Materials and via the CompOSE database.

In the present work we use the large-Nc approximation to investigate quark matter described by the SU(2) Nambu-Jona-Lasinio model subject to a strong magnetic field. The Landau levels are filled in such a way that usual kinks appear in the effective mass and other related quantities. β-equilibrium is also considered and the macroscopic properties of a magnetar described by this quark matter is obtained. Our study shows that the magnetar masses and radii are larger if the magnetic field increases but only very large fields (≥ 10 18 G) affect the EoS in a non negligible way.

The possibility to draw links between the isospin properties of nuclei and the structure of compact stars is a stimulating perspective. In order to pursue this objective on a sound basis, the correlations from which such links can be deduced have to be carefully checked against model dependence. Using a variety of nuclear effective models and a microscopic approach, we study the relation between the predictions of a given model and those of a Taylor density development of the corresponding equation of state: this establishes to what extent a limited set of phenomenological constraints can determine the core-crust transition properties. From a correlation analysis, we show that (a) the transition density ρt is mainly correlated with the symmetry energy slope L, (b) the proton fraction Yp,t with the symmetry energy and symmetry energy slope (J, L) defined at saturation density, or, even better, with the same quantities defined at ρ = 0.1 fm −3 , and (c) the transition pressure Pt with the symmetry energy slope and curvature (L, Ksym) defined at ρ = 0.1 fm −3 .

We perform a systematic analysis of the density dependence of the nuclear symmetry energy within the microscopic Brueckner-Hartree-Fock (BHF) approach using the realistic Argonne V18 nucleon-nucleon potential plus a phenomenological three body force of Urbana type. Our results are compared thoroughly to those arising from several Skyrme and relativistic effective models.The values of the parameters characterizing the BHF equation of state of isospin asymmetric nuclear matter fall within the trends predicted by those models and are compatible with recent constraints coming from heavy ion collisions, giant monopole resonances or isobaric analog states.In particular we find a value of the slope parameter L = 66.9 MeV, compatible with recent experimental constraints from isospin diffusion, L = 88 ± 25 MeV. The correlation between the neutron skin thickness of neutron-rich isotopes and the slope, L, and curvature, K sym , parameters of the symmetry energy is studied. Our BHF results are in very good agreement with the correlations already predicted by other authors using non-relativistic and relativistic effective models. The correlations of these two parameters and the neutron skin thickness with the transition density from non-uniform to β-stable matter in neutron stars are also analyzed. Our results confirm that there is an inverse correlation between the neutron skin thickness and the transition density.PACS numbers: 21.65.Cd; 21.65.Ef; 21.65.Mn 2 A well-grounded understanding of the properties of isospin-rich nuclear matter is a necessary ingredient for the advancement of both nuclear physics and astrophysics. Isospin asymmetric nuclear matter is present in nuclei, especially in those far away from the stability line, and in astrophysical systems, particularly in neutron stars. A major scientific effort is being carried out at an international level to study experimentally the properties of asymmetric nuclear systems. Laboratory measurements, such as those running or planned to run in the existing or the next-generation, radioactive ion beam facilities at CSR (China), FAIR (Germany), RIKEN (Japan), SPIRAL2/GANIL (France) and the upcoming FRIB (USA), can probe the behavior of the symmetry energy close and above saturation density [1]. Moreover, the 208 Pb Radius Experiment (PREX), scheduled to run at JLab in early 2010, should provide a very accurate measurement of the neutron skin thickness in lead via parity violating electron scattering [2]. Astrophysical observations of compact objects are also a window into both the bulk and the microscopic properties of nuclear matter at extreme isospin asymmetries [3]. The symmetry energy determines to a large extent the composition of β-stable matter and therefore the structure and mass of a neutron star [4].The empirical knowledge gathered from all these sources should be helpful in identifying the major issues arising when the isospin content of nuclear systems is altered. Reliable theoretical investigations of neutron-rich (and possibly proton-rich) systems are...