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

TL;DR

This paper investigates how measurements of neutron star radii and tidal polarizabilities can inform us about the density dependence of nuclear symmetry energy, highlighting the roles of various parameters and the need for additional data.

Contribution

It introduces a parameterization of symmetry energy using three parameters and analyzes their effects on neutron star observables, revealing degeneracies and the necessity of supplementary measurements.

Findings

Both radius and tidal polarizability depend on slope parameter L.

High-density parameters K_sym and J_sym significantly influence observables.

Additional terrestrial experiments are needed to fully constrain symmetry energy parameters.

Abstract

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 $E_{\rm{sym}}(\rho )$ parameterized using three parameters $L$, $K_{\rm{sym}}$, and $J_{\rm{sym}}$ 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 $R_{\rm{1.4}}$ and $\Lambda_{1.4}$ depend strongly on the slope $L$, the $K_{\rm{sym}}$ and $J_{\rm{sym}}$ parameters characterizing the high-density behavior of $E_{\rm{sym}}(\rho )$ also play appreciable roles. Thus, there is not 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 combinations of its parameters. In particular, stringent constraints approximately independent of the $J_{\rm{sym}}$ on the $L$-$K_{\rm{sym}}$ correlations can be obtained. However, infinite combinations of the larger (smaller) $L$ and smaller (larger) $K_{\rm{sym}}$ can lead to the same $\Lambda_{\rm{1.4}}$ and $R_{\rm{1.4}}$. 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 $E_{\rm{sym}}(\rho )$.