Multi-timescale analysis of phase transitions in precessing black-hole binaries

TL;DR

This paper introduces a multi-scale analytical approach to study the complex spin precession dynamics of binary black holes, revealing phase transitions in their precession morphologies during inspiral.

Contribution

It develops a novel precession-averaged post-Newtonian method that simplifies the analysis of precessing black-hole binaries across different timescales.

Findings

Classified BBH spin precession into three morphologies

Identified phase transitions between precession morphologies during inspiral

Provided an efficient way to model BBH dynamics from large separations

Abstract

The dynamics of precessing binary black holes (BBHs) in the post-Newtonian regime has a strong timescale hierarchy: the orbital timescale is very short compared to the spin-precession timescale which, in turn, is much shorter than the radiation-reaction timescale on which the orbit is shrinking due to gravitational-wave emission. We exploit this timescale hierarchy to develop a multi-scale analysis of BBH dynamics elaborating on the analysis of Kesden et al. (2015). We solve the spin-precession equations analytically on the precession time and then implement a quasi-adiabatic approach to evolve these solutions on the longer radiation-reaction time. This procedure leads to an innovative "precession-averaged" post-Newtonian approach to studying precessing BBHs. We use our new solutions to classify BBH spin precession into three distinct morphologies, then investigate phase transitions between these morphologies as BBHs inspiral. These precession-averaged post-Newtonian inspirals can be efficiently calculated from arbitrarily large separations, thus making progress towards bridging the gap between astrophysics and numerical relativity.