Spin-spin effects in radiating compact binaries

TL;DR

This paper analyzes the effects of spin-spin interactions on the dynamics and radiative losses of eccentric compact binary systems, including new second post-Newtonian order corrections.

Contribution

It introduces a generalized true anomaly parametrization and derives spin-spin effects on orbital angular momentum and energy loss at second post-Newtonian order.

Findings

Average orbital angular momentum has no secular change.

Spin-spin effects influence radiative energy and angular momentum loss.

Self-interaction spin effects are identified as second post-Newtonian corrections.

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.