Eccentric Motion of Spinning Compact Binaries

TL;DR

This paper develops a perturbative approach to model the eccentric motion of spinning compact binaries, revealing how mass differences influence spin-orbit precession and employing action-angle variables for simplified analysis.

Contribution

It introduces a first-order perturbative solution for eccentric spinning binaries and applies canonical transformations and action-angle variables for analytical tractability.

Findings

Precession effects depend on mass difference and vanish for equal masses or single-spin cases.

The perturbative method accurately captures eccentric spin dynamics.

Canonical transformations simplify the complex Hamiltonian structure.

Abstract

The equations of motion for spinning compact binaries on eccentric orbits are treated perturbatively in powers of a fractional mass-difference ordering parameter. The solution is valid through first order in the mass-difference parameter. A canonical point transformation removes the leading order terms of the spin-orbit Hamiltonian which induce a wiggling precession of the orbital angular momentum around the conserved total angular momentum, a precession which disappears in the case of equal masses or one single spin. Action-angle variables are applied which make a canonical perturbation theory easily treatable.