Spin effects in gravitational radiation backreaction III. Compact binaries with two spinning components

TL;DR

This paper investigates the secular evolution of eccentric, spinning binary systems in general relativity, including spin effects up to 3/2 post-Newtonian order, revealing eccentricity-induced acceleration in their dynamical evolution.

Contribution

It extends previous models by incorporating spin-orbit and spin-spin effects at higher post-Newtonian order for eccentric binaries, with a novel averaging technique and detailed evolution equations.

Findings

Eccentricity accelerates the evolution of spin and orbital angles.

A simple averaging method using residue theorem is developed.

Closed-form differential equations describe the dissipative evolution.

Abstract

The secular evolution of a spinning, massive binary system in eccentric orbit is analyzed, expanding and generalizing our previous treatments of the Lense-Thirring motion and the one-spin limit. The spin-orbit and spin-spin effects up to the 3/2 post-Newtonian order are considered, both in the equations of motion and in the radiative losses. The description of the orbit in terms of the true anomaly parametrization provides a simple averaging technique, based on the residue theorem, over eccentric orbits. The evolution equations of the angle variables characterizing the relative orientation of the spin and orbital angular momenta reveal a speed-up effect due to the eccentricity. The dissipative evolutions of the relevant dynamical and angular variables is presented in the form of a closed system of differential equations.