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Background: The nuclear symmetry energy $E_{sym}(rho)$ encodes information about the energy necessary to make nuclear systems more neutron-rich. While its slope parameter L at the saturation density $rho_0$ of nuclear matter has been relatively well constrained by recent astrophysical observations and terrestrial nuclear experiments, its curvature $K_{rm{sym}}$ characterizing the $E_{sym}(rho)$ around $2rho_0$ remains largely unconstrained. Over 520 calculations for $E_{sym}(rho)$ using various nuclear theories and interactions in the literature have predicted several significantly different $K_{rm{sym}}-L$ correlations. Purpose: If a unique $K_{rm{sym}}-L$ correlation of $E_{sym}(rho)$ can be firmly established, it will enable us to progressively better constrain the high-density behavior of $E_{sym}(rho)$ using the available constraints on its slope parameter L. We investigate if and by how much the different $K_{rm{sym}}-L$ correlations may affect neutron star observables. Method: A meta-model of nuclear Equation of States (EOSs) with three representative $K_{rm{sym}}-L$ correlation functions is used to generate multiple EOSs for neutron stars. We then examine effects of the $K_{rm{sym}}-L$ correlation on the crust-core transition density and pressure as well as the radius and tidal deformation of canonical neutron stars. Results:The $K_{rm{sym}}-L$ correlation affects significantly both the crust-core transition density and pressure. It also has strong imprints on the radius and tidal deformability of canonical neutron stars especially at small L values. The available data from LIGO/VIRGO and NICER set some useful limits for the slope L but can not distinguish the three representative $K_{rm{sym}}-L$ correlations considered.
The slope of the nuclear symmetry energy at saturation density $L$ is pointed out as a crucial quantity to determine the mass and width of neutron-star crusts. This letter clarifies the relation between $L$ and the core-crust transition. We confirm t
The radii and tidal deformabilities of neutron stars are investigated in the framework of relativistic mean-field (RMF) model with different density-dependent behaviors of symmetry energy. To study the effects of symmetry energy on the properties of
A number of observed phenomena associated with individual neutron star systems or neutron star populations find explanations in models in which the neutron star crust plays an important role. We review recent work examining the sensitivity to the slo
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