Spin-spin effects in radiating compact binaries

TL;DR

The paper advances the understanding of gravitational radiation reaction in spinning compact binaries on eccentric orbits by incorporating spin-spin interactions at $2^{\text{nd}}$ PN order using a generalized true anomaly parametrization for the radial motion. It derives both instantaneous and secular (time-averaged) losses of energy and the magnitude of the orbital angular momentum, revealing self-interaction spin terms and expressing results in terms of the angular-average $\bar{L}$ and spin geometry. The approach yields closed-form secular contributions to $\langle dE/dt \rangle$ and $\langle dL/dt \rangle$ that complement existing spin-orbit results, providing a more complete picture of radiation back-reaction for eccentric, spinning binaries. These results are essential for accurate waveform modeling and interpretation of gravitational-wave signals from such systems, with implications for parameter estimation and tests of general relativity.

Abstract

The dynamics of a binary system with two spinning components on an eccentric orbit is studied, with the inclusion of the spin-spin interaction terms appearing at the second post-Newtonian order. A generalized true anomaly parametrization properly describes the radial component of the motion. The average over one radial period of the magnitude of the orbital angular momentum $\bar{L}$ is found to have no nonradiative secular change. All spin-spin terms in the secular radiative loss of the energy and magnitude of orbital angular momentum are given in terms of $\bar{L}$ and other constants of the motion. Among them, self-interaction spin effects are found, representing the second post-Newtonian correction to the 3/2 post-Newtonian order Lense-Thirring approximation.