Universality and stationarity of the I-Love relation for self-bound stars

TL;DR

This paper analytically investigates the I-Love relation for self-bound stars, demonstrating its universality and stationarity near incompressible stars, and providing a new physical explanation for this universal behavior.

Contribution

It formulates perturbative expansions for self-bound stars and analytically shows the I-Love relation's universality and stationarity near incompressible stars, offering a novel physical insight.

Findings

The I-Love relation is stationary with respect to EOS variations near incompressible stars.

The moment of inertia and tidal deformability of self-bound stars are approximately equal to those of incompressible stars with adjusted compactness.

The universality of the I-Love relation is due to the proximity of self-bound stars to incompressible stars.

Abstract

The emergence of the I-Love-Q relations, revealing that the moment of inertia, the tidal Love number (deformability) and the spin-induced quadrupole moment of compact stars are, to high accuracy, interconnected in a universal way disregarding the wide variety of equations of state (EOSs) of dense matter, has attracted much interest recently. However, the physical origin of these relations is still a debatable issue. In the present paper, we focus on the I-Love relation for self-bound stars (SBSs) such as incompressible stars and quark stars. We formulate perturbative expansions for the moment of inertia, the tidal Love number (deformability) and the I-Love relation of SBSs. By comparing the respective I-Love relations of incompressible stars and a specific kind of SBSs, we show analytically that the I-Love relation is, to relevant leading orders in stellar compactness, stationary with respect to changes in the EOS about the incompressible limit. Hence, the universality of the I-Love relation is indeed attributable to the proximity of compact stars to incompressible stars, and the stationarity of the relation as unveiled here. We also discover that the moment of inertia and the tidal deformability of a SBS with finite compressibility are, to leading order in compactness, equal to their counterparts of an incompressible star with an adjusted compactness, thus leading to a novel explanation for the I-Love universal relation.