The key factor to determine the relation between radius and tidal deformability of neutron stars: slope of symmetry energy

TL;DR

This study investigates how the slope of symmetry energy influences the relationship between neutron star radius and tidal deformability, revealing that the slope parameter is the dominant factor in this relation.

Contribution

It demonstrates that the slope of symmetry energy primarily determines the radius-tidal deformability relation of neutron stars, regardless of other high-order symmetry energy parameters.

Findings

The $R_{1.4} \,\sim\, \Lambda_{1.4}$ relation is consistent across variations in high-order symmetry energy parameters.

The slope of symmetry energy $L$ is the main factor affecting the $R$-$\Lambda$ relation.

The established relation for 1.4 $M_\odot$ neutron stars does not hold for more massive stars.

Abstract

The constraints on tidal deformability $\Lambda$ of neutron stars are first extracted from GW170817 by LIGO and Virgo Collaborations but the relation between radius $R$ and tidal deformability $\Lambda$ is still nuder debate. Using an isospin-dependent parameterized equation of state (EOS), we study the relation between $R$ and $\Lambda$ of neutron stars and its dependence on parameters of symmetry energy $E_{\rm sym}$ and EOS of symmetric nuclear matter $E_0$ when the mass is fixed as $1.4$ $M_\odot$, $1.0$ $M_\odot$, and $1.8$ $M_\odot$, respectively. We find that, though the changes of high order parameters of $E_{\rm sym}$ and $E_0$ can shift the individual values of $R_{1.4}$ and $\Lambda_{1.4}$ to different values, the $R_{1.4}\sim\Lambda_{1.4}$ relation approximately locates at the same fitted curve. The slope of symmetry energy $L$ plays the dominated role in determining the $R_{1.4}\sim\Lambda_{1.4}$ relation. By checking the mass dependence of $R\sim\Lambda$ relation, the well fitted $R\sim\Lambda$ relation for 1.4 $M_\odot$ is broken for massive neutron stars.