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

摘要

Though individual stellar parameters of compact stars usually demonstrateobvious dependence on the equation of state (EOS), EOS-insensitive universalformulas relating these parameters remarkably exist. In the present paper, weexplore the interrelationship between two such formulas, namely the $f$-$I$relation connecting the $f$-mode quadrupole oscillation frequency $\omega_2$and the moment of inertia $I$, and the $I$-Love-$Q$ relations relating $I$, thequadrupole tidal deformability $\lambda_2$, and the quadrupole moment $Q$,which have been proposed by Lau, Leung, and Lin [Astrophys. J. {\bf 714}, 1234(2010)] and Yagi and Yunes [Science {\bf 341}, 365 (2013)], respectively. Arelativistic universal relation between $\omega_l$ and $\lambda_l$ with thesame angular momentum $l=2,3,\ldots$, the so-called "diagonal $f$-Loverelation" that holds for realistic compact stars and stiff polytropic stars, isunveiled here. An in-depth investigation in the Newtonian limit is furthercarried out to pinpoint its underlying physical mechanism and hence leads to aunified $f$-$I$-Love relation. We reach the conclusion that theseEOS-insensitive formulas stem from a common physical origin --- compact starscan be considered as quasiincompressible when they react to slow timevariations introduced by $f$-mode oscillations, tidal forces and rotations.