Momentum recoil in the relativistic two-body problem: Higher-order tails

In the description of the relativistic two-body interaction, together with the effects of energy andangular momentum losses due to the emission of gravitational radiation, one has to take into account alsothe loss of linear momentum, which is responsible for the recoil of the center-of-mass of the system. Wecompute higher-order tail (i.e., tail-of-tail and tail-squared) contributions to the linear momentum fluxfor a nonspinning binary system either along hyperboliclike or ellipticlike orbits. The correspondingorbital averages are evaluated at their leading post-Newtonian approximation, using harmoniccoordinates and working in the Fourier domain. The final expressions are given in a large-eccentricity(or large-angular momentum) expansion along hyperboliclike orbits and in a small-eccentricityexpansion along ellipticlike orbits. We thus complete a previous analysis focusing on both energyand angular momentum losses [Phys. Rev. D 104, 104020 (2021)], providing brick-type results whichwill be useful, e.g., in the high-accurate determination of the radiated impulses of the two bodiesundergoing a scattering process.