Takuya Katagiri, Gowtham Rishi Mukkamala, Kent Yagi

Quasi-universal relations are known to exist among various neutron star observables that do not depend sensitively on the underlying nuclear matter equations of state. For example, some of these relations imply that the tidally induced multipole moments are approximately characterized by the electric-type quadrupolar tidal deformability. Such relations can be used to reduce the number of independent tidal parameters in gravitational-waveform modeling, thereby allowing us to infer extreme nuclear matter properties more accurately and test General Relativity in an insensitive manner to uncertainties in nuclear physics. We present a comprehensive theoretical investigation into approximate universality of neutron stars. Our approach employs a semi-analytic relativistic stellar interior model, which extends the Tolman VII solution, thereby enabling a refined exploration of the tidal properties of nonrotating stars within a semi-analytic framework. The derived power-law relations among various tidal deformabilities -- referred to as the universal Love relations -- agree well with expressions in previous work found empirically. We elucidate how the equation-of-state dependence is suppressed in a particular combination of macroscopic physical parameters induced by perturbations and demonstrate that the relation between the moment of inertia and electric-type quadrupolar tidal deformability (I-Love relation) rests on the same underlying mechanism. Our findings indicate that the approximate universality of neutron stars can be attributed to low compressibility, consistent with some of the previous studies on the possible origin of the universality.