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

TL;DR

This work addresses how gravitational radiation reaction alters the relative orientations of the spin vectors $S_1$, $S_2$, and the orbital angular momentum $L$ for eccentric, spinning compact binaries up to $2\mathrm{PN}$ order. It shows that Burke-Thorne instantaneous spin changes average out over a radial period, so secular spin magnitudes remain constant and only orientation-precession terms matter; the secular evolution is driven by spin-orbit and spin-spin effects, with Newtonian, 1PN, 2PN, and tail terms canceling in the angular evolution. The spin-spin sector is computed and decomposed into self-interaction and two-body contributions, yielding a closed set of equations for $\kappa_i$ and $\gamma$ that refine the Lense-Thirring description at $3/2$PN. The results provide explicit, averaged expressions for the SS contributions and establish a consistent framework for incorporating these effects into gravitational-wave templates for eccentric binaries.

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.