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Background: The nuclear symmetry energy $E_{sym}(\rho)$ encodes informationabout the energy necessary to make nuclear systems more neutron-rich. While itsslope parameter L at the saturation density $\rho_0$ of nuclear matter has beenrelatively well constrained by recent astrophysical observations andterrestrial nuclear experiments, its curvature $K_{\rm{sym}}$ characterizingthe $E_{sym}(\rho)$ around $2\rho_0$ remains largely unconstrained. Over 520calculations for $E_{sym}(\rho)$ using various nuclear theories andinteractions 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 toprogressively better constrain the high-density behavior of $E_{sym}(\rho)$using the available constraints on its slope parameter L. We investigate if andby how much the different $K_{\rm{sym}}-L$ correlations may affect neutron starobservables. Method: A meta-model of nuclear Equation of States (EOSs) withthree representative $K_{\rm{sym}}-L$ correlation functions is used to generatemultiple EOSs for neutron stars. We then examine effects of the$K_{\rm{sym}}-L$ correlation on the crust-core transition density and pressureas well as the radius and tidal deformation of canonical neutron stars.Results:The $K_{\rm{sym}}-L$ correlation affects significantly both thecrust-core transition density and pressure. It also has strong imprints on theradius and tidal deformability of canonical neutron stars especially at small Lvalues. The available data from LIGO/VIRGO and NICER set some useful limits forthe slope L but can not distinguish the three representative $K_{\rm{sym}}-L$correlations considered.

physical review. c

Curvature-slope correlation of nuclear symmetry energy and its imprints  on the crust-core transition, radius and tidal deformability of canonical  neutron stars