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 $L_{\mathrm{sym}}$ and the isoscalar skewness parameter $Q_{\mathrm{sat}}$, 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 $L_{\mathrm{sym}}\text{−}{Q}_{\mathrm{sat}}$ 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 $L_{\mathrm{sym}}$ and $Q_{\mathrm{sat}}$. 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 $I\text{−}Q$ 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, when accounting for significant variation in the symmetry energy and high-density behavior of the nuclear EoS.

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• Neutron stars & pulsars
• Stars