Background: The nuclear symmetry energy $E_{\mathrm{sym}}\left(\rho \right)$ encodes information about the energy necessary to make nuclear systems more neutron rich. It is currently poorly known especially at suprasaturation densities but has broad impacts on properties of neutron stars and on nuclear structure and reactions. 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 $K_{\mathrm{sym}}$ characterizing the $E_{\mathrm{sym}}\left(\rho \right)$ around $2{\rho }_0$ remains largely unconstrained. Over 520 calculations for $E_{\mathrm{sym}}\left(\rho \right)$ using various nuclear theories and interactions in the literature have predicted several significantly different $K_{\mathrm{sym}}\text{−}L$ correlations.

Purpose: If a unique $K_{\mathrm{sym}}\text{−}L$ correlation of $E_{\mathrm{sym}}\left(\rho \right)$ can be firmly established, it will enable us to progressively constrain the high-density behavior of $E_{\mathrm{sym}}\left(\rho \right)$ using the available and better constrained slope parameter $L$. We investigate if and by how much the different $K_{\mathrm{sym}}\text{−}L$ correlations may affect neutron star observables. We also examine if LIGO/VIRGO's observation of tidal deformability using gravitational waves from GW170817 and NICER's recent extraction of neutron star radius using high-precision x-rays can distinguish the different $K_{\mathrm{sym}}\text{−}L$ correlations predicted.

Methods: A metamodel of nuclear equations of state (EOSs) with three representative $K_{\mathrm{sym}}\text{−}L$ correlation functions is used to generate multiple EOSs for neutron stars. We then examine effects of the $K_{\mathrm{sym}}\text{−}L$ correlation on the crust-core transition density and pressure as well as the radius and tidal deformation of canonical neutron stars.

Results: We found that the $K_{\mathrm{sym}}\text{−}L$ 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 cannot distinguish the three representative $K_{\mathrm{sym}}\text{−}L$ correlations considered.

Conclusions: The $K_{\mathrm{sym}}\text{−}L$ correlation is important for understanding properties of neutron stars. More precise and preferably independent measurements of the radius and tidal deformability from multiple observables of neutron stars have the strong potential to help pin down the curvature-slope correlation and thus the high-density behavior of nuclear symmetry energy.

• Received 26 August 2020
• Revised 20 September 2020
• Accepted 1 October 2020

DOI:https://doi.org/10.1103/PhysRevC.102.045807