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 $\sim 30$ % 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 $2M_{\odot }$ star and of being causal within stable neutron stars. Spans of $\sim 3$ and $\sim 4$ km are obtained for the radius of, respectively, $1.0M_{\odot }$ and $2.0M_{\odot }$ stars. Applying a set of nine further constraints from experiment and ab initio calculations the uncertainty is reduced to $\sim 1$ 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 $1.0M_{\odot }$. 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 nonrelativistic 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 $\approx 2M_{\odot }$. 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 and infrared counterpart sets the radius of a canonical $1.4M_{\odot }$ neutron star to be $11.82\le R_{1.4}\le 13.72\mathrm{km}$.

Background: The recent accurate measurement of the mass of two pulsars close to or above $2{\mathrm{M}}_{\odot }$ 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.

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 $2M_{\odot }$ neutron stars. Unified EoSs for the inner-crust–core region have been built for all the phenomenological models, both relativistic and nonrelativistic. 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 $0.6\text{–}1.8M_{\odot }$. 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 $1.4M_{\odot }$ neutron star in the range $11.09\text{–}12.86$ km.

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> 2M ⊙. 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.

For core-collapse and neutron star merger simulations, it is important to have adequate equations of state which describe dense and hot matter as realistically as possible. We present two newly constructed equations of state including the entire baryon octet, compatible with the main constraints coming from nuclear physics, both experimental and theoretical. One of the equations of state describes cold β-equilibrated neutron stars with a maximum mass of 2 Msun. Results obtained with the new equations of state are compared with the ones of DD2Y, the only existing equation of state containing the baryon octet and satisfying the above constraints. The main difference between our new equations of state and DD2Y is the harder symmetry energy of the latter. We show that the density dependence of the symmetry energy has a direct influence on the amount of strangeness inside hot and dense matter and, consequently, on thermodynamic quantities. We expect that these differences affect the evolution of a proto-neutron star or binary neutron star mergers. We propose also several parameterisations based on the DD2 and SFHo models calibrated to Lambda hypernuclei that satisfy the different constraints.