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.

Constraints set on key parameters of the nuclear matter equation of state (EoS) by the values of the tidal deformability, inferred from GW170817, are examined by using a diverse set of relativistic and non-relativistic mean field models. These models are consistent with bulk properties of finite nuclei as well as with the observed lower bound on the maximum mass of neutron star ∼ 2 M⊙. The tidal deformability shows a strong correlation with specific linear combinations of the isoscalar and isovector nuclear matter parameters associated with the EoS. Such correlations suggest that a precise value of the tidal deformability can put tight bounds on several EoS parameters, in particular, on the slope of the incompressibility and the curvature of the symmetry energy. The tidal deformability obtained from the GW170817 and its UV/optical/infrared counterpart sets the radius of a canonical 1.4 M⊙ neutron star to be 11.82 R1.4 13.72 km.

Background: The recent accurate measurement of the mass of two pulsars close to or above 2 M has raised the question of whether such large pulsar masses allow for the existence of exotic degrees of freedom, such as hyperons, inside neutron stars. Purpose: In the present work, we will investigate, within a phenomenological relativistic mean field approach, how the existing hypernuclei properties may constrain the neutron star equation of state and confront the neutron star maximum masses obtained with equations of state calibrated to hypernuclei properties with the astrophysical 2 M constraint. Method: The study is performed using a relativistic mean field approach to describe both the hypernuclei and the neutron star equations of state. Unified equations of state are obtained. A set of five models that describe 2 M when only nucleonic degrees of freedom are employed. Some of these models also satisfy other well-established laboratory or theoretical constraints. Results: The-meson couplings are determined for all the models considered, and the potential in symmetric nuclear matter and matter at saturation are calculated. Maximum neutron star masses are determined for two values of the-ω meson coupling, g ω = 2g ωN /3 and g ω = g ωN , and a wide range of values for g φ. Hyperonic stars with the complete baryonic octet are studied, restricting the coupling of the and hyperons to the ω, ρ, and σ mesons due to the lack of experimental data, and maximum star masses calculated. Conclusions: We conclude that, within a phenomenological relativistic mean field approach, the currently available hypernuclei experimental data and the lack of constraints on the asymmetric equation of state of nuclear matter at high densities set only a limited number of constraints on the neutron star matter equation of state using the recent 2 M observations. It is shown that the potential in symmetric nuclear matter takes a value of ∼30−32 MeV at saturation for the g ω coupling given by the SU(6) symmetry, being of the order of the values generally used in the literature. On the other hand, the potential in matter varies between −14 and −8 MeV, taking for vector mesons couplings the SU(6) values, at variance with generally employed values between −1 and −5 MeV. If the SU(6) constraint is relaxed and the vector meson couplings to hyperons are kept to values not larger than those of nucleons, then values between −13 and +9 MeV are obtained.

Context. The existence of 2 M pulsars puts very strong constraints on the equation of state (EOS) of neutron stars (NSs) with hyperon cores, which can be satisfied only by special models of hadronic matter. The radius-mass relation for these models is sufficiently specific that it could be subjected to an observational test with future X-ray observatories. Aims. We want to study the impact of the presence of hyperon cores on the radius-mass relation for NS. We aim to find out how, and for which particular stellar mass range, a specific relation R(M), where M is the gravitational mass, and R is the circumferential radius, is associated with the presence of a hyperon core. Methods. We consider a set of 14 theoretical EOS of dense matter, based on the relativistic mean-field approximation, allowing for the presence of hyperons in NSs. We also discuss a recent EOS based on non-relativistic G-matrix theory yielding NSs with hyperonic cores and M > 2 M . We seek correlations between R(M) and the stiffness of the EOS below the hyperon threshold needed to pass the 2 M test. Results. For NS masses 1.0 < M/M < 1.6, we get R > 13 km, because of a very stiff pre-hyperon segment of the EOS. At nuclear density (n 0 = 0.16 fm −3 ), the pressure is significantly higher than a robust upper bound obtained recently using chiral effective field theory. Conclusions. If massive NSs do have a sizable hyperon core, then according to current models the radii for M = 1.0−1.6 M are necessarily >13 km. If, on the contrary, a NS with a radius R (obs) < 12 km is observed in this mass domain, then sizable hyperon cores in NSs, as we model them now, are ruled out. Future X-ray missions with <5% precision for a simultaneous M and R measurement will have the potential to solve the problem with observations of NSs. Irrespective of this observational test, present EOS allowing for hyperons that fulfill condition M max > 2 M yield a pressure at nuclear density that is too high relative to up-to-date microscopic calculations of this quantity.

We discuss the thermalization process of the neutron star's crust described by solving the heat-transport equation with a microscopic input for the specific heat of baryonic matter. The heat equation is solved with initial conditions specific to a rapid cooling of the core. To calculate the specific heat of inner-crust baryonic matter, that is, nuclear clusters and unbound neutrons, we use the quasiparticle spectrum provided by the Hartree-Fock-Bogoliubov approach at finite temperature. In this framework, we analyze the dependence of the crust thermalization on pairing properties and on cluster structure of inner-crust matter. It is shown that the pairing correlations reduce the crust thermalization time by a large fraction. The calculations show also that the nuclear clusters have a non-negligible influence on the time evolution of the surface temperature of the neutron sta

We examine the correlations of neutron star radii with the nuclear matter incompressibility, symmetry energy, and their slopes, which are the key parameters of the equation of state (EoS) of asymmetric nuclear matter. The neutron star radii and the EoS parameters are evaluated using a representative set of 24 Skyrme-type effective forces and 18 relativistic mean field models, and two microscopic calculations, all describing 2M⊙ neutron stars. Unified EoSs for the inner-crust-core region have been built for all the phenomenological models, both relativistic and non-relativistic. Our investigation shows the existence of a strong correlation of the neutron star radii with the linear combination of the slopes of the nuclear matter incompressibility and the symmetry energy coefficients at the saturation density. Such correlations are found to be almost independent of the neutron star mass in the range 0.6-1.8M⊙. This correlation can be linked to the empirical relation existing between the star radius and the pressure at a nucleonic density between one and two times saturation density, and the dependence of the pressure on the nuclear matter incompressibility, its slope and the symmetry energy slope. The slopes of the nuclear matter incompressibility and the symmetry energy coefficients as estimated from the finite nuclei data yield the radius of a 1.4M⊙ neutron star in the range 11.09-12.86 km.PACS numbers: 21.65.+f, 21.30.Fe, 26.60.+c The bulk properties of neutron stars are mainly governed by the behaviour of the equation of state (EoS) of highly asymmetric dense matter. The correlations of the various EoS parameters of asymmetric nuclear matter with the different properties of neutron star, such as the crust-core transition density and pressure, radii, maximum mass and cooling rate, have been studied [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The crust-core transition density is strongly correlated with the slope of the symmetry energy, L 0 , at saturation density (ρ 0 ∼ 0.16 fm −3 ) [5,6,11]. However, the transition pressure is found to be strongly correlated with a linear combination of the slope and curvature of the symmetry energy at the sub-saturation density (ρ = 0.1 fm −3 ) [7,11,12]. The simultaneous determination of mass and radius of low-mass neutron stars can better constrain the product of nuclear matter incompressibility and symmetry energy slope parameter [13].The correlations of the neutron star radii of different masses with the EoS parameters have been investigated extensively. The covariance analysis, based on a single model, suggests the existence of strong correlations of the radii of low-mass neutron stars (M NS ∼ 0.6-1.2M ⊙ ) with the symmetry energy slope parameter L 0 [10], the correlations becoming weaker with the increase of the neutron star mass. Similar analysis for the correlations of the radii with the symmetry energy slope over a wider range of densities was performed for two different models, having different behaviours on the density dependence of the symmetry energy, a...

Context. Few unified equations of state for neutron star matter, in which core and crust are described using the same nuclear model, are available. However the use of non-unified equations of state with simplified matching between the crust and core has been shown to introduce uncertainties in the radius determination, which can be larger than the expected precision of the next generation of X-ray satellites. Aims. We aim to eliminate the dependence of the radius and mass of neutron stars on the detailed model for the crust and on the crust-core matching procedure. Methods. We solved the approximate equations of the hydrostatic equilibrium for the crust of neutron stars and obtained a precise formula for the radius that only depends on the core mass and radius, the baryon chemical potential at the core-crust interface, and at the crust surface. For a fully accreted crust one needs, additionally, the value of the total deep crustal heating per one accreted nucleon. Results. For typical neutron star masses, the approximate approach allows us to determine the neutron star radius with an error ∼0.1% (∼10 m, equivalent to a 1% inaccuracy in the crust thickness). The formalism applies to neutron stars with a catalyzed or a fully accreted crust. The difference in the neutron star radius between the two models is proportional to the total energy release due to deep crustal heating. Conclusions. For a given model of dense matter describing the neutron star core, the radius of a neutron star can be accurately determined independent of the crust model with a precision much better than the ∼5% precision expected from the next generation of X-ray satellites. This allows us to circumvent the problem of the radius uncertainty that may arise when non-unified equations of state for the crust and core are used.

Abstract.A set of theoretical mass-radius relations for rigidly rotating neutron stars with exotic cores, obtained in various theories of dense matter, is reviewed. Two basic observational constraints are used: the largest measured rotation frequency (716 Hz) and the maximum measured mass (2M ). The present status of measuring the radii of neutron stars is described. The theory of rigidly rotating stars in general relativity is reviewed and limitations of the slow rotation approximation are pointed out. Mass-radius relations for rotating neutron stars with hyperon and quark cores are illustrated using several models. Problems related to the non-uniqueness of the crust-core matching are mentioned. Limits on rigid rotation resulting from the mass-shedding instability and the instability with respect to the axisymmetric perturbations are summarized. The problem of instabilities and of the back-bending phenomenon are discussed in detail. Metastability and instability of a neutron star core in the case of a first-order phase transition, both between pure phases, and into a mixed-phase state, are reviewed. The case of two disjoint families (branches) of rotating neutron stars is discussed and generic features of neutron-star families and of core-quakes triggered by the instabilities are considered.