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

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 $l=2,3,\dots$, 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.

Minor changes to match the published version

References in corpus (12)

• Neutron Star Observations: Prognosis for Equation of State Constraints
• Tidal Love numbers of neutron stars
• Constraining neutron star tidal Love numbers with gravitational wave detectors
• Relativistic theory of tidal Love numbers
• Constraints on the Symmetry Energy Using the Mass-Radius Relation of Neutron Stars
• I-Love-Q, Spontaneously: Slowly Rotating Neutron Stars in Scalar-Tensor Theories
• Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics
• Quadrupole Moments of Rapidly Rotating Compact Objects in Dilatonic Einstein-Gauss-Bonnet Theory
• Gravitational wave asteroseismology with fast rotating neutron stars
• Why I-Love-Q
• Toward Realistic and Practical No-Hair Relations for Neutron Stars in the Non-Relativistic Limit
• Determination of the internal structure of neutron stars from gravitational wave spectra

Cited by in corpus (3)

• Dynamical Tides in General Relativity: Effective Action and Effective-One-Body Hamiltonian
• Multipole moments in scalar-tensor theory of gravity
• Tidal Love numbers and moment-Love relations of polytropic stars