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Tail-induced spin-orbit effect in the gravitational radiation of compact binaries

Luc Blanchet, Alessandra Buonanno, Guillaume Faye

TL;DR

This work advances analytical gravitational-wave modeling for spinning compact binaries by deriving spin-orbit tail effects at $3$PN in the energy flux and at $2.5$PN/$3$PN in the waveform, thereby yielding accurate $3$PN phasing corrections for quasi-circular inspirals. The authors integrate tail integrals within the multipolar post-Newtonian framework, account for spin precession through a moving triad, and verify consistency with the test-particle limit against black-hole perturbation theory. The results enhance template fidelity for parameter estimation and NR comparisons, supporting improved predictions through the inspiral and merger phases. Future directions include completing non-tail SO couplings at $2$PN/$3$PN orders and extending computations to higher gravitational modes to further refine analytical templates.

Abstract

Gravitational waves contain tail effects which are due to the back-scattering of linear waves in the curved space-time geometry around the source. In this paper we improve the knowledge and accuracy of the two-body inspiraling post-Newtonian (PN) dynamics and gravitational-wave signal by computing the spin-orbit terms induced by tail effects. Notably, we derive those terms at 3PN order in the gravitational-wave energy flux, and 2.5PN and 3PN orders in the wave polarizations. This is then used to derive the spin-orbit tail effects in the phasing through 3PN order. Our results can be employed to carry out more accurate comparisons with numerical-relativity simulations and to improve the accuracy of analytical templates aimed at describing the whole process of inspiral, merger and ringdown.

Tail-induced spin-orbit effect in the gravitational radiation of compact binaries

TL;DR

This work advances analytical gravitational-wave modeling for spinning compact binaries by deriving spin-orbit tail effects at PN in the energy flux and at PN/PN in the waveform, thereby yielding accurate PN phasing corrections for quasi-circular inspirals. The authors integrate tail integrals within the multipolar post-Newtonian framework, account for spin precession through a moving triad, and verify consistency with the test-particle limit against black-hole perturbation theory. The results enhance template fidelity for parameter estimation and NR comparisons, supporting improved predictions through the inspiral and merger phases. Future directions include completing non-tail SO couplings at PN/PN orders and extending computations to higher gravitational modes to further refine analytical templates.

Abstract

Gravitational waves contain tail effects which are due to the back-scattering of linear waves in the curved space-time geometry around the source. In this paper we improve the knowledge and accuracy of the two-body inspiraling post-Newtonian (PN) dynamics and gravitational-wave signal by computing the spin-orbit terms induced by tail effects. Notably, we derive those terms at 3PN order in the gravitational-wave energy flux, and 2.5PN and 3PN orders in the wave polarizations. This is then used to derive the spin-orbit tail effects in the phasing through 3PN order. Our results can be employed to carry out more accurate comparisons with numerical-relativity simulations and to improve the accuracy of analytical templates aimed at describing the whole process of inspiral, merger and ringdown.

Paper Structure

This paper contains 17 sections, 86 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Motivation
  3. Notation
  4. Wave generation formalism
  5. Expression of the radiative moments
  6. Computing the tail integrals
  7. Applications to spinning binaries
  8. Spin vectors for point-like objects
  9. Multipole moments with spin-orbit effects
  10. Equations of motion with spin-orbit effects
  11. Evolution of the triad $\{\bm{n}, \bm{\lambda}, \bm{\ell}\}$
  12. Computation of the waveform
  13. Energy flux and orbital phasing
  14. Conclusion
  15. 3PN spin terms in the equations of motion
  16. ...and 2 more sections

Figures (2)

  • Figure 1: We show (i) the source frame defined by the orthonormal basis $(\bm{x},\bm{y},\bm{z})$, (ii) the instantaneous orbital plane which is described by the orthonormal basis $(\bm{x}_\ell, \bm{y}_\ell, \bm{\ell})$, (iii) the moving triad $(\bm{n},\bm{\lambda},\bm{\ell})$, and (iv) the direction of the total angular momentum $\bm{J}$ (agreeing by definition with the $z$--direction). Dashed lines show projections into the $x\hbox{--}y$ plane.
  • Figure 2: Similar as Fig. \ref{['figure:SourceFramePhase']} but with the direction of the source $\bm{N}$ indicated together with a choice of convention for the two polarization vectors $\bm{P}$ and $\bm{Q}$.