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.

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...

From empirically determined values of some of the characteristic constants associated with homogeneous nuclear matter at saturation and subsaturation densities, within the framework of a Skyrme-inspired energy density functional, we construct an equation of state (EoS) of nuclear matter.This EoS is then used to predict values of density slope parameters of symmetry energy L(ρ), isoscalar incompressibility K(ρ), and a few related quantities. The close consonance of our predicted values with the currently available ones for the density dependence of symmetry energy and incompressibility gleaned from diverse approaches offers the possibility that our method may help in settling their values in tighter bounds. Extrapolation of our EoS at supranormal densities shows that it is in good harmony with the one extracted from experimental data.

The spinodal instabilities in hot asymmetric nuclear matter and some important critical parameters derived thereof are studied by using six different families of relativistic mean-field models. The slopes of the symmetry energy coefficient vary over a wide range within each family. The critical densities and proton fractions are more sensitive to the symmetry energy slope parameter at temperatures much below its critical value (T c ∼ 14−16 MeV). The spread in the critical proton fraction at a given symmetry energy slope parameter is noticeably larger near T c , indicating that the equation of state of warm asymmetric nuclear matter at subsaturation densities is not sufficiently constrained. The distillation effects are sensitive to the density dependence of the symmetry energy at low temperatures which tend to wash out with increasing temperature.

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The model dependence and the symmetry energy dependence of the core-crust transition properties for the neutron stars are studied using three different families of systematically varied extended relativistic mean field model. Several forces within each of the families are so considered that they yield wide variations in the values of the nuclear symmetry energy asym and its slope parameter L at the saturation density. The core-crust transition density is calculated using a method based on random-phase-approximation. The core-crust transition density is strongly correlated, in a model independent manner, with the symmetry energy slope parameter evaluated at the saturation density. The pressure at the transition point dose not show any meaningful correlations with the symmetry energy parameters at the saturation density. At best, pressure at the transition point is correlated with the symmetry energy parameters and their linear combination evaluated at the some sub-saturation density. Yet, such correlations might not be model independent. The correlations of core-crust transition properties with the symmetry energy parameter are also studied by varying the symmetry energy within a single model. The pressure at the transition point is correlated once again with the symmetry energy parameter at the sub-saturation density.

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