Delineating effects of nuclear symmetry energy on the radii and tidal polarizabilities of neutron stars

What can we learn about the density dependence of nuclear symmetry energy E sym ( ) from precise measurements of the radius (R1.4) and/or tidal polarizability (Λ1.4) of canonical neutron stars with a mass of 1.4 M ? With the E sym ( ) parameterized using three parameters L, Ksym, and Jsym which have the asymptotic meaning of being respectively the slope, curvature, and skewness of symmetry energy at saturation density, we found that, while both the R1.4 and Λ1.4 depend strongly on the slope L, the Ksym and Jsym parameters characterizing the high-density behavior of Esym( ) also play appreciable roles. Thus, there is not a simple relation between the Λ1.4/R1.4 and L alone. Precise measurements of just the Λ1.4 and R1.4 cannot completely determine the Esym( ) but limit combinations of its parameters. In particular, stringent constraints approximately independent of the Jsym on the L-Ksym correlations can be obtained. However, infinite combinations of the larger (smaller) L and smaller (larger) Ksym can lead to the same Λ1.4 and R1.4. Additional observables including those from terrestrial nuclear experiments are thus necessary to break this degeneracy in order to completely determine the density dependence of nuclear symmetry energy Esym( ).