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

Gravitational waves contain tail effects which are due to the backscattering 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.

Figure 1

We show (i) the source frame defined by the orthonormal basis $(\mathit{x},\mathit{y},\mathit{z})$, (ii) the instantaneous orbital plane which is described by the orthonormal basis $({\mathit{x}}_{\ell },{\mathit{y}}_{\ell },\mathbf{\ell })$, (iii) the moving triad $(\mathit{n},\mathit{\lambda },\mathbf{\ell })$, and (iv) the direction of the total angular momentum $\mathit{J}$ (agreeing, by definition, with the $z$ direction). Dashed lines show projections into the $x-y$ plane.

Figure 2

Similar to Fig. 1 but with the direction of the source $\mathit{N}$ indicated together with a choice of convention for the two polarization vectors $\mathit{P}$ and $\mathit{Q}$.