Effect of symmetry energy on properties of rapidly rotating neutron stars and universal relations

TL;DR

This study explores universal relations for rapidly rotating neutron stars at the mass-shedding limit, demonstrating their robustness across various equations of state and implications for gravitational wave observations.

Contribution

It provides explicit universal relations for rotating neutron stars at the Keplerian limit, accounting for variations in symmetry energy and skewness parameters, and assesses their accuracy.

Findings

Universal relations hold within 10% deviation at the Keplerian limit.

Relations are more accurate (~1%) in slow rotation compared to rapid rotation.

Results support the use of universal relations in gravitational wave modeling.

Abstract

We investigated universal relations for compact stars rotating at the Keplerian (mass-shedding) limit, which is highly relevant for understanding the rapidly rotating objects formed in the aftermath of a neutron star-neutron star merger. Our analysis is based on a set of nucleonic equations of state (EoSs) featuring systematic variations in the symmetry energy slope parameter $L_{\rm sym}$ and the isoscalar skewness parameter $Q_{\rm sat}$, varied within ranges that are broadly consistent with current laboratory and astrophysical constraints. The global observable properties of isolated maximally rotating stars are examined, focusing on the mass-radius relation, moment of inertia, quadrupole moment, and the Keplerian (maximum) rotation frequency, as well as their variations in the $L_{\rm sym}$-$Q_{\rm sat}$ parameter space. Next, we demonstrate that, in the limit of Keplerian rotation, universal relations remain valid across the same set of EoSs characterized by varying $L_{\rm sym}$ and $\Qsat$. In particular, we present explicit results for the moment of inertia ($I$) and quadrupole moment ($Q$) as functions of compactness, as well as for the moment of inertia-quadrupole moment relation. All of these relations exhibit excellent universality, with deviations typically within a range from a few percent to 10\% across a wide range of parameters. Additionally, we verify for our set of EoSs that the universality of $I$-$Q$ holds to higher accuracy (at the level of 1\%) in the slow-rotation approximation compared with the Kepler limit, where the relative error increases up to $\lesssim 10\%$. Our findings support the applicability of $I$-Love-$Q$-type universal relations in observational modeling of maximally rotating compact stars and the gravitational wave emitted by them.