I-Love relation for incompressible stars and realistic stars

TL;DR

This paper analytically derives the I-Love relation for incompressible stars using recursive post-Minkowskian expansion, demonstrating its accuracy in approximating realistic neutron and quark stars across various mass ranges.

Contribution

It introduces an analytical derivation of the I-Love relation for incompressible stars, providing a new approach to understand universality in compact star properties.

Findings

The derived I-Love relation accurately predicts realistic star behavior.

Incompressible star models closely approximate realistic neutron star relations.

The formula applies from Newtonian limit to maximum mass limit.

Abstract

In spite of the diversity in the equations of state of nuclear matter, the recently discovered I-Love-Q relations [Yagi and Yunes, Science {\bf 341}, 365 (2013)], which relate the moment of inertia, tidal Love number (deformability) and the spin-induced quadrupole moment of compact stars, hold for various kinds of realistic neutron stars and quark stars. While the physical origin of such universality is still a current issue, the observation that the I-Love-Q relations of incompressible stars can well approximate those of realistic compact stars hints at a new direction to approach the problem. In this paper, by establishing recursive post-Minkowskian expansion for the moment of inertia and the tidal deformability of incompressible stars, we analytically derive the I-Love relation for incompressible stars and show that the so obtained formula can be used to accurately predict the behavior of realistic compact stars from the Newtonian limit to the maximum mass limit.