Spinning compact binary inspiral: Independent variables and dynamically preserved spin configurations

TL;DR

This paper introduces a set of independent variables to effectively track the complex spin evolution of compact binaries during inspiral, revealing that only equal-mass, aligned or antialigned spins allow uniform precession.

Contribution

It develops a new framework for analyzing spin dynamics in binary inspirals up to second post-Newtonian order, identifying special configurations with uniform precession.

Findings

Identifies independent variables for spin evolution analysis.

Proves that only equal-mass, aligned or antialigned spins allow uniform precession.

Provides limitations on configurations in numerical simulations.

Abstract

We establish the set of independent variables suitable to monitor the complicated evolution of the spinning compact binary during the inspiral. Our approach is valid up to the second post-Newtonian order, including leading order spin-orbit, spin-spin and mass quadrupol-mass monopole effects, for generic (noncircular, nonspherical) orbits. Then we analyze the conservative spin dynamics in terms of these variables. We prove that the only binary black hole configuration allowing for spin precessions with equal angular velocities about a common intantaneous axis roughly aligned to the normal of the osculating orbit, is the equal mass and parallel (aligned or antialigned) spin configuration. This analytic result puts limitations on what particular configurations can be selected in numerical investigations of compact binary evolutions, even in those including only the last orbits of the inspiral.