Improving the inference of the stellar quantities using the extended I -Love- Q-δM relations

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 χs < 0.1). The more accurate alternative approach, based on the I -Love- Q-δM set of relations, circumvents this limitation by enabling the inference of M 0 . Here we review both approaches and provide numerical comparisons.