Unveiling the universality of I-Love-Q relations

TL;DR

This paper investigates the universal I-Love-Q relations in compact stars, attributing their universality to the incompressible limit and demonstrating their robustness across different equations of state and star types.

Contribution

The study provides numerical and analytical evidence linking the I-Love-Q relations' universality to the incompressible limit, explaining their weak dependence on the equation of state.

Findings

Universality is due to the incompressible limit of the relations.

Modern stiff equations of state support universality for neutron and quark stars.

Low-mass neutron stars show more sensitivity to the equation of state, but quark stars still follow the incompressible limit.

Abstract

The recent discovery of the universal I-Love-Q relations connecting the moment of inertia, tidal deformability, and the spin-induced quadrupole moment of compact stars is intriguing and totally unexpected. In this paper, we provide numerical evidence showing that the universality can be attributed to the incompressible limit of the I-Love-Q relations. The fact that modern equations of state are stiff, with an effective adiabatic index larger than about two, above the nuclear density range is the key to establishing the universality for neutron stars and quark stars with typical compactness from about 0.1 to 0.3. On the other hand, the I-Love-Q relations of low-mass neutron stars near the minimum mass limit depend more sensitively on the underlying equation of state because these stars are composed mainly of softer matter at low densities. However, the I-Love-Q relations for low-mass quark stars can still be represented accurately by the incompressible limit. We also study the I-Love relation connecting the moment of inertia and tidal deformability analytically in Newtonian gravity and show why the I-Love-Q relation is weakly dependent on the underlying equation of state and can be attributed to its incompressible limit.