Next-to-leading tail-induced spin-orbit effects in the gravitational radiation flux of compact binaries

TL;DR

This paper completes the spin-orbit tail analysis by deriving the 4PN tail-induced contributions to the gravitational-wave energy flux and orbital phasing for quasi-circular compact binaries within the multipolar post-Newtonian framework. It develops an analytical spin-orbit dynamics solution and uses it to evaluate the hereditary tail integrals, showing that only tail terms contribute at this order for circular orbits and that the results align with Kerr perturbation theory in the test-mass limit. The findings enable more faithful PN templates for both ground-based and space-based detectors, though horizon-absorption and higher-order spin terms remain to be integrated for full waveform precision. Overall, the work significantly refines the phasing model and the expected GW cycles, supporting improved parameter estimation in observational data.

Abstract

The imprint of non-linearities in the propagation of gravitational waves --- the tail effect --- is responsible for new spin contributions to the energy flux and orbital phasing of spinning black hole binaries. The spin-orbit (linear in spin) contribution to this effect is currently known at leading post-Newtonian order, namely 3PN for maximally spinning black holes on quasi-circular orbits. In the present work, we generalize these tail-originated spin-orbit terms to the next-to-leading 4PN order. This requires in particular extending previous results on the dynamical evolution of precessing compact binaries. We show that the tails represent the only spin-orbit terms at that order for quasi-circular orbits, and we find perfect agreement with the known result for a test particle around a Kerr black hole, computed by perturbation theory. The BH-horizon absorption terms have to be added to the PN result computed here. Our work completes the knowledge of the spin-orbit effects to the phasing of compact binaries up to the 4PN order, and will allow the building of more faithful PN templates for the inspiral phase of black hole binaries, improving the capabilities of ground-based and space-based gravitational wave detectors.

Figures (1)

• Figure 1: Geometric definitions to describe the precessional motion of the binary, identical to the ones used in Paper I. The conserved angular momentum $\bm{J}$ gives a fixed direction $\bm{z}$, completed with two constant unit vectors $\bm{x}$ and $\bm{y}$ forming with $\bm{z}$ an orthonormal triad; $\bm{\ell}$ is the normal to the instantaneous orbital plane (shown in yellow), described by the Euler angles $\alpha,\iota$, and defines the auxiliary vectors $\bm{x}_{\ell}$, $\bm{y}_{\ell}$, see Eqs. \ref{['eq:defxlyl']}. The position of the unit separation vector $\bm{n}$ defines the third Euler angle $\Phi$, and the moving triad is completed by $\bm{\lambda}=\bm{\ell}\times\bm{n}$.