Investigating the I-Love-Q and w-mode Universal Relations Using Piecewise Polytropes

TL;DR

This paper explores universal relations among neutron star properties, extending previous models with piecewise polytropes, including twin stars, and introduces new empirical relations involving the complex frequency of the w-mode.

Contribution

It extends I-Love-Q relations to include twin stars and proposes new empirical relations involving the w-mode frequency, enhancing understanding of neutron star universality.

Findings

Second-branch relations are less tight than first-branch.

Relations tighten with higher minimum maximum mass.

New empirical relations between I, λ, Q, and w-mode frequency are comparable in tightness.

Abstract

Neutron stars are expected to have a tight relation between their moment of inertia ($I$), tidal deformability ($\lambda$, which is related to the Love number), and rotational mass quadrupole moment ($Q$) that is nearly independent of the unknown equation of state (EoS) of cold dense matter. These and similar relations are often called "universal", and they have been used for various applications including analysis of gravitational wave data. We extend these studies using piecewise polytropic representations of dense matter, including for so-called twin stars that have a second branch of stability at high central densities. The second-branch relations are less tight, by a factor of $\sim 3$, than the relations found in the first stable branch. We find that the relations on both branches become tighter when we increase the lower limit to the maximum mass for the EoS under consideration. We also propose new empirical relations between $I$, $\lambda$, $Q$, and the complex frequency $\omega=\omega_R+i\omega_I$ of the fundamental axial $w$-mode, and find that they are comparably tight to the I-Love-Q correlations.