Improving the inference of the stellar quantities using the extended $I$-Love-$Q$-$\delta M$ relations

TL;DR

This paper reviews and compares methods for inferring stellar quantities using extended $I$-Love-$Q$-$oldsymbol{ m extdelta M}$ relations, improving accuracy over traditional $I$-Love-$Q$ relations especially for faster rotating stars.

Contribution

It introduces and evaluates an extended set of $I$-Love-$Q$-$oldsymbol{ m extdelta M}$ relations that better infer stellar parameters without assuming slow rotation.

Findings

The extended relations improve inference accuracy for rotating stars.

Numerical comparisons show advantages over traditional methods.

The approach is applicable to a wider range of stellar rotation rates.

Abstract

In relativistic Astrophysics the $I$-Love-$Q$ relations refer to approximately EoS-independent relations involving the moment of inertia, Love number, and quadrupole moment through some quantities that are normalised by the mass $M_0$ of the background configuration of the perturbative scheme. Since $M_0$ is not an observable quantity, this normalisation hinders the direct applicability of the relations. A common remedy assumes that $M_0$ coincides with the actual mass of the star $M_S$; however, this approximation is only adequate for very slow rotation (when the dimensionless spin parameter is $\chi_S<0.1$). The more accurate alternative approach, based on the $I$-Love-$Q$-$\delta M$ set of relations, circumvents this limitation by enabling the inference of $M_0$. Here we review both approaches and provide numerical comparisons.