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What can we learn about the density dependence of nuclear symmetry energy$E_{\rm{sym}}(\rho )$ from precise measurements of the radius ($R_{\rm{1.4}}$)and/or tidal polarizability ($\Lambda_{1.4}$) of canonical neutron stars (NSs)with a mass of 1.4 M$_\odot$? With the $E_{\rm{sym}}(\rho )$ parameterizedusing three parameters $L$, $K_{\rm{sym}}$, and $J_{\rm{sym}}$ which have theasymptotic meaning of being respectively the slope, curvature, and skewness ofsymmetry energy at saturation density, we found that, while both the$R_{\rm{1.4}}$ and $\Lambda_{1.4}$ depend strongly on the slope $L$, the$K_{\rm{sym}}$ and $J_{\rm{sym}}$ parameters characterizing the high-densitybehavior of $E_{\rm{sym}}(\rho )$ also play appreciable roles. Thus, there isnot a simple relation between the $\Lambda_{\rm{1.4}}$/$R_{\rm{1.4}}$ and $L$alone. Precise measurements of just the $\Lambda_{\rm{1.4}}$ and $R_{\rm{1.4}}$can not completely determine the $E_{\rm{sym}}(\rho )$ but limit combinationsof its parameters. In particular, stringent constraints approximatelyindependent of the $J_{\rm{sym}}$ on the $L$-$K_{\rm{sym}}$ correlations can beobtained. However, infinite combinations of the larger (smaller) $L$ andsmaller (larger) $K_{\rm{sym}}$ can lead to the same $\Lambda_{\rm{1.4}}$ and$R_{\rm{1.4}}$. Additional observables including those from terrestrial nuclearexperiments are thus necessary to break this degeneracy in order to completelydetermine the density dependence of nuclear symmetry energy $E_{\rm{sym}}(\rho)$.

Delineating Effects of Nuclear Symmetry Energy on the Radii and Tidal Polarizabilities of Neutron Stars