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

TL;DR

This paper uncovers universal, EOS-insensitive relations linking the f-mode frequency, moment of inertia, and tidal deformability of compact stars, revealing a common physical origin rooted in their quasi-incompressible nature.

Contribution

It establishes a unified, relativistic relation between f-mode frequency and tidal deformability, deepening understanding of compact star properties independent of the EOS.

Findings

Discovery of a relativistic universal relation between $oldsymbol{oldsymbol{ extit{ extbf{f}}}}$-mode frequency and tidal deformability.

Unification of various EOS-insensitive formulas through a common physical mechanism.

Validation of the relations for realistic compact stars and stiff polytropic models.

Abstract

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 $\omega_2$ and the moment of inertia $I$, and the $I$-Love-$Q$ relations relating $I$, the quadrupole 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. A relativistic universal relation between $\omega_l$ and $\lambda_l$ with the same angular momentum $l=2,3,\ldots$, 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.