Second post-Newtonian radiative evolution of the relative orientations of angular momenta in spinning compact binaries

TL;DR

This paper derives the second post-Newtonian order equations governing the evolution of spin and orbital angular momentum orientations in eccentric spinning compact binaries, revealing the specific contributions of spin interactions to radiative angular changes.

Contribution

It provides the first detailed second post-Newtonian order analysis of spin and orbital angular momentum evolution, including spin-spin effects and their impact on binary dynamics.

Findings

Spin-orbit and spin-spin terms influence angular evolution.

Instantaneous radiative changes in spins average out over a radial period.

Spin-spin contributions include two-body and self-interaction effects.

Abstract

The radiative evolution of the relative orientations of the spin and orbital angular momentum vectors ${\bf S}_{{\bf 1}}, {\bf S}_{{\bf 2}}$ and ${\bf L}$, characterizing a binary system on eccentric orbit is studied up to the second post-Newtonian order. As an intermediate result, all Burke-Thorne type instantaneous radiative changes in the spins are shown to average out over a radial period. It is proved that spin-orbit and spin-spin terms contribute to the radiative angular evolution equations, while Newtonian, first and second post-Newtonian terms together with the leading order tail terms do not. In complement to the spin-orbit contribution, given earlier, the spin-spin contribution is computed and split into two-body and self-interaction parts. The latter provide the second post-Newtonian order corrections to the 3/2 order Lense-Thirring description.