Multipolar universal relations between f -mode frequency and tidal deformability of compact stars

Though individual stellar parameters of compact stars usually demonstrate obvious dependence on the equation of state (EOS), EOS-insensitive universal formulas relating these parameters remarkably exist. In the present paper, we explore the interrelationship between two such formulas, namely the f-I relation connecting the f-mode quadrupole oscillation frequency ω₂ and the moment of inertia I, and the I-Love-Q relations relating I, the quadrupole tidal deformability λ₂, and the quadrupole moment Q, which have been proposed by Lau, Leung, and Lin [Astrophys. J. 714, 1234 (2010)] and Yagi and Yunes [Science 341, 365 (2013)], respectively. A relativistic universal relation between ωₗ and λₗ with the same angular momentum l=2,3,, the so-called ``diagonal f-Love relation'' that holds for realistic compact stars and stiff polytropic stars, is unveiled here. An in-depth investigation in the Newtonian limit is further carried out to pinpoint its underlying physical mechanism and hence leads to a unified f-I-Love relation. We reach the conclusion that these EOS-insensitive formulas stem from a common physical origin---compact stars can be considered as quasiincompressible when they react to slow time variations introduced by f-mode oscillations, tidal forces and rotations.