$I$-Love-$Q$, and $\delta M$ too: The role of the mass in universal relations of compact stars

In the study of rotating neutron stars the $I$-Love-$Q$ relations refer to the existence of various approximate, equation of state-independent relations involving the moment of inertia, the Love number and the quadrupole moment. These relations are relevant for observational astrophysics, since they allow (in theory) the inference of any two quantities within the $I$-Love-$Q$ triad out of the third one alone. However, the quantities involved in the relations are, in fact, normalized by a parameter $M_0$ that arises in the usual perturbative analytical approach as the mass of the background configuration. Since $M_0$ is not the mass of the rotating star $M_S$, it is not an observational quantity, which may affect the application of the relations to actual observations. This situation is usually ignored in most studies by taking $M_0$ to be the mass of the star, an approximation that can, in some cases, be inconsistent. In this paper we extract the value of $M_0$ using an $\textit{extended}$ version of the universal relations that involve a fourth parameter, $\delta M$, proportional to the difference $M_S-M_0$. We analyze to which degree this extended set of relations yields a more precise inference of compact star properties and equation of state parameters.
Comment: 15 pages, 6 figures, 4 tables