Rotation-dependent $I$-Love-$Q$-$\delta M$ relations in perturbation theory

TL;DR

This paper reformulates the $I$-Love-$Q$ relations in perturbation theory to depend on observable mass instead of static mass, enhancing their practical applicability in astrophysics.

Contribution

It introduces a new formulation of the $I$-Love-$Q$ relations that relies on observable mass, making these relations more accessible for empirical use.

Findings

Reformulated $I$-Love-$Q$ relations depend on observable mass.

The new relations are derived using perturbation theory.

Enhanced potential for observational inference of stellar properties.

Abstract

The so-called $I$-Love-$Q$ relations link some normalized versions of the moment of inertia, the Love number, and the quadrupole moment of a star. These relations, in principle, enable the inference of two of the quantities given the third. However, their use has been limited because the normalized versions of the multipole moments rely on the static mass derived from the Tolman-Oppenheimer-Volkoff equation, which is not directly observable. In this work, using perturbation theory, we find that the $I$-Love-$Q$ relations can also be formulated in terms of an alternative set of normalized quantities that do not depend on the static mass, but on the actual (observable) mass.