On the equal-mass limit of precessing black-hole binaries

TL;DR

This paper studies the inspiral dynamics of equal-mass precessing black-hole binaries, revealing unique constants of motion and spin behaviors that differ from unequal-mass cases, with implications for gravitational wave modeling.

Contribution

It identifies two constants of motion in equal-mass precessing binaries and characterizes their unique spin and precession dynamics, enhancing understanding of their evolution.

Findings

The spin magnitude and effective spin are conserved constants in equal-mass binaries.

The spin morphology remains constant throughout the inspiral.

Precessional motion occurs on a longer timescale than orbital precession.

Abstract

We analyze the inspiral dynamics of equal-mass precessing black-hole binaries using multi-timescale techniques. The orbit-averaged post-Newtonian evolutionary equations admit two constants of motion in the equal-mass limit, namely the magnitude of the total spin $S$ and the effective spin $\xi$. This feature makes the entire dynamics qualitatively different compared to the generic unequal-mass case, where only $\xi$ is constant while the variable $S$ parametrizes the precession dynamics. For fixed individual masses and spin magnitudes, an equal-mass black-hole inspiral is uniquely characterized by the two parameters $(S,\xi)$: these two numbers completely determine the entire evolution under the effect of radiation reaction. In particular, for equal-mass binaries we find that (i) the black-hole binary spin morphology is constant throughout the inspiral, and that (ii) the precessional motion of the two black-hole spins about the total spin takes place on a longer timescale than the precession of the total spin and the orbital plane about the total angular momentum.