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$f$-Mode oscillations and the gravitational response of compact stars with analytic equations of state

Kilar Zhang, Alessandro Parisi, C. Vásquez Flores, Chian-Shu Chen

TL;DR

This work studies compact stars described by analytic EOS drawn from holographic QCD (WSS instanton gas) and self-interacting dark matter, focusing on masses, radii, tidal deformabilities, and fundamental ($f$-mode) oscillations. By combining Tolman–Oppenheimer–Volkoff structure, static tidal perturbations, and Lindblom–Detweiler nonradial oscillation theory, the authors derive mass–radius curves, tidal Love numbers, and $f$-mode frequencies and damping times for two representative EOS. They show that these analytic EOS can reproduce broad observational constraints and provide transparent scaling relations between microphysics and gravitational-wave observables. The results underscore the potential of multi-messenger data to constrain exotic dense-matter models and motivate extensions to include rotation, finite temperature, and magnetic effects.

Abstract

We apply analytical models to study the property of neutron stars and dark stars. With the aim of exploring the global observable properties of those compact stars, we investigate the total masses and radii, the tidal deformabilities and especially the fundamental (f -) mode oscillations. While we choose two typical models in this work, this method applies to any analytical equations of state. By comparing with the multi-messenger observations, one can constrain the corresponding parameters in those models.

$f$-Mode oscillations and the gravitational response of compact stars with analytic equations of state

TL;DR

This work studies compact stars described by analytic EOS drawn from holographic QCD (WSS instanton gas) and self-interacting dark matter, focusing on masses, radii, tidal deformabilities, and fundamental (-mode) oscillations. By combining Tolman–Oppenheimer–Volkoff structure, static tidal perturbations, and Lindblom–Detweiler nonradial oscillation theory, the authors derive mass–radius curves, tidal Love numbers, and -mode frequencies and damping times for two representative EOS. They show that these analytic EOS can reproduce broad observational constraints and provide transparent scaling relations between microphysics and gravitational-wave observables. The results underscore the potential of multi-messenger data to constrain exotic dense-matter models and motivate extensions to include rotation, finite temperature, and magnetic effects.

Abstract

We apply analytical models to study the property of neutron stars and dark stars. With the aim of exploring the global observable properties of those compact stars, we investigate the total masses and radii, the tidal deformabilities and especially the fundamental (f -) mode oscillations. While we choose two typical models in this work, this method applies to any analytical equations of state. By comparing with the multi-messenger observations, one can constrain the corresponding parameters in those models.
Paper Structure (6 sections, 31 equations, 6 figures)

This paper contains 6 sections, 31 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Analytic models for equation of states
  3. Tidal deformability equations
  4. Nonradial oscillation equations
  5. Discussion and Conclusions
  6. The Lindblom-Detweiler equations

Figures (6)

  • Figure 1: Mass radius relation for a holographic compact star with the EOS given in Eq. (\ref{['eos1']}). We consider different values of $\ell$, changing this parameter it is possible to span a large range of values of mass and radius.
  • Figure 2: Mass radius relation for a dark star with the EOS given in Eq. (\ref{['eos2']}).
  • Figure 3: TLN-Mass relation for the EOS given in Eq. (\ref{['eos1']}).
  • Figure 4: TLN-Mass relation for the EOS given in Eq. (\ref{['eos2']}).
  • Figure 5: Frequency and damping time of the fundamental mode as a function of the stellar mass for the EOS given in Eq. (\ref{['eos1']}). We use different values of the parameter $\ell$.
  • ...and 1 more figures