Comparing Post-Newtonian and Numerical-Relativity Precession Dynamics

TL;DR

This paper develops a method to compare precession dynamics in binary black-hole systems between post-Newtonian theory and full numerical relativity, showing good agreement in certain aspects and highlighting differences in others.

Contribution

A new procedure to match and compare precession dynamics predicted by post-Newtonian theory with numerical relativity simulations for binary black holes.

Findings

PN and NR agree within 1° for angular momentum and spin directions during inspiral

Nutation of orbital plane matches well between PN and NR

Spin nutation behavior differs qualitatively between PN and NR near merger

Abstract

Binary black-hole systems are expected to be important sources of gravitational waves for upcoming gravitational-wave detectors. If the spins are not colinear with each other or with the orbital angular momentum, these systems exhibit complicated precession dynamics that are imprinted on the gravitational waveform. We develop a new procedure to match the precession dynamics computed by post-Newtonian (PN) theory to those of numerical binary black-hole simulations in full general relativity. For numerical relativity NR) simulations lasting approximately two precession cycles, we find that the PN and NR predictions for the directions of the orbital angular momentum and the spins agree to better than $\sim 1^{\circ}$ with NR during the inspiral, increasing to $5^{\circ}$ near merger. Nutation of the orbital plane on the orbital time-scale agrees well between NR and PN, whereas nutation of the spin direction shows qualitatively different behavior in PN and NR. We also examine how the PN equations for precession and orbital-phase evolution converge with PN order, and we quantify the impact of various choices for handling partially known PN terms.