Spin-spin effects in radiating compact binaries

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 L̄ 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 L̄ 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.