Effective potentials and morphological transitions for binary black-hole spin precession

TL;DR

This paper introduces an effective potential for binary black-hole spin precession, enabling analytical solutions and classification of precession morphologies, which enhances modeling of gravitational waves and final black hole spins.

Contribution

We derive an effective potential at second post-Newtonian order, providing analytical solutions for BBH spin precession and classifying precession morphologies, including new spin-orbit resonances.

Findings

Analytical solutions for spin precession are quasiperiodic.

Classified BBH precession into three morphologies.

Identified new spin-orbit resonances affecting angular momentum.

Abstract

We derive an effective potential for binary black-hole (BBH) spin precession at second post-Newtonian order. This effective potential allows us to solve the orbit-averaged spin-precession equations analytically for arbitrary mass ratios and spins. These solutions are quasiperiodic functions of time: after a fixed period the BBH spins return to their initial relative orientations and jointly precess about the total angular momentum by a fixed angle. Using these solutions, we classify BBH spin precession into three distinct morphologies between which BBHs can transition during their inspiral. We also derive a precession-averaged evolution equation for the total angular momentum that can be integrated on the radiation-reaction time and identify a new class of spin-orbit resonances that can tilt the direction of the total angular momentum during the inspiral. Our new results will help efforts to model and interpret gravitational waves from generic BBH mergers and predict the distributions of final spins and gravitational recoils.