Completion of the universal I-Love-Q relations in compact stars including the mass.

In a recent paper, we applied a rigorous perturbed matching framework to show the amendment of the mass of rotating stars in Hartle's model. Here, we apply this framework to the tidal problem in binary systems. Our approach fully accounts for the correction to the Love numbers needed to obtain the universal I--Love--Q relations. We compute the corrected mass versus radius configurations of rotating quark stars, revisiting a classical paper on the subject. These corrections allow us to find a universal relation involving the second-order contribution to the mass δM. We thus complete the set of universal relations for the tidal problem in binary systems, involving four perturbation parameters, namely I, Love, Q and δM. These relations can be used to obtain the perturbation parameters directly from observational data. [ABSTRACT FROM AUTHOR]