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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]

Hartle's model for slowly rotating stars has been extensively used to compute equilibrium configurations of slowly rotating stars to second order in perturbation theory in general relativity, given a barotropic equation of state. A recent study based on the modern theory of perturbed matchings concludes that the functions in the (first and second order) perturbation tensors can always be taken as continuous at the surface of the star, except for the second-order function m0. This function presents a jump at the surface of the star proportional to the discontinuity of the energy density there. This concerns only a particular outcome of the model: the change in mass δM. In this paper, the amended change in mass is calculated for the case of constant density stars. [ABSTRACT FROM AUTHOR]