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New perspectives on neutron star and black hole spectroscopy and dynamic tides

Sayan Chakrabarti, Térence Delsate, Jan Steinhoff

TL;DR

This paper develops an effective-field-theory framework to model dynamical tidal interactions of compact objects in General Relativity by encoding quadrupole dynamics in a frequency-dependent linear response function F(ω). It shows that nonrotating neutron stars admit a harmonic-oscillator interpretation of their internal tidal degrees of freedom, allowing a transparent resonance-based description of tides, while Black Holes exhibit horizon-induced absorption and a vanishing leading Love number. The authors derive F(ω) via a matching procedure between interior perturbations and exterior Regge-Wheeler/MST solutions, obtaining a two-pole NS fit that captures the main dynamical features and discussing regularization issues that motivate dimensional regularization. The framework unifies Love numbers and dynamical tides, with clear implications for gravitational-wave modeling (e.g., EOB) and potential insights into neutron-star oscillation spectra and black-hole physics.

Abstract

We elaborate on a powerful tidal interaction formalism where the multipole dynamics is kept generic and encoded in a linear response function. This response function is the gravitational counterpart of the atomic spectrum and can become of similar importance with the rise of gravitational wave astronomy. We find that the internal dynamics of nonrotating neutron stars admit a harmonic oscillator formulation yielding a simple interpretation of tides. A preliminary investigation of the black holes case is given. Our results fill the gap between Love numbers and dynamic tides.

New perspectives on neutron star and black hole spectroscopy and dynamic tides

TL;DR

This paper develops an effective-field-theory framework to model dynamical tidal interactions of compact objects in General Relativity by encoding quadrupole dynamics in a frequency-dependent linear response function F(ω). It shows that nonrotating neutron stars admit a harmonic-oscillator interpretation of their internal tidal degrees of freedom, allowing a transparent resonance-based description of tides, while Black Holes exhibit horizon-induced absorption and a vanishing leading Love number. The authors derive F(ω) via a matching procedure between interior perturbations and exterior Regge-Wheeler/MST solutions, obtaining a two-pole NS fit that captures the main dynamical features and discussing regularization issues that motivate dimensional regularization. The framework unifies Love numbers and dynamical tides, with clear implications for gravitational-wave modeling (e.g., EOB) and potential insights into neutron-star oscillation spectra and black-hole physics.

Abstract

We elaborate on a powerful tidal interaction formalism where the multipole dynamics is kept generic and encoded in a linear response function. This response function is the gravitational counterpart of the atomic spectrum and can become of similar importance with the rise of gravitational wave astronomy. We find that the internal dynamics of nonrotating neutron stars admit a harmonic oscillator formulation yielding a simple interpretation of tides. A preliminary investigation of the black holes case is given. Our results fill the gap between Love numbers and dynamic tides.

Paper Structure

This paper contains 20 sections, 64 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Effective Action
  3. Perturbed compact objects
  4. EFT Calculation
  5. Results
  6. Conclusions
  7. Formulas and Implementations
  8. NS Perturbation Equations
  9. Preliminaries
  10. Master Equations
  11. Boundary Conditions and Series
  12. Analytic Solutions from Mano:Suzuki:Takasugi:1996
  13. Solutions to the RW Equation
  14. Recurrence Relation for $a_n^{\nu}$
  15. Normalization of Analytic Solutions and Wronskian
  16. ...and 5 more sections

Figures (1)

  • Figure 1: Propagator of the quadrupole in minimal subtraction (MS). The dots are some selected numeric data points, the solid line is the fit (\ref{['fitF']}) and (\ref{['fitmu']}). For the circles the logarithmic scale dependence was ignored ($\mu_0 \sim \omega$) and for the crosses only the leading order in (\ref{['Fresult']}) was taken into account. This shows that the $\epsilon^2$ corrections in (\ref{['Fresult']}) are essential for a good fit, while the corrections from $\mu_0$ start to contribute only beyond the f-mode.