Reducing orbital eccentricity of precessing black-hole binaries

TL;DR

This paper presents a new method to reduce orbital eccentricity in precessing binary black-hole simulations by analyzing the orbital frequency derivative, effectively distinguishing between initial eccentricity and spin-induced oscillations.

Contribution

The authors develop and validate a novel eccentricity-removal procedure based on the orbital frequency derivative, improving initial condition accuracy in spinning black-hole binary simulations.

Findings

Successfully reduces eccentricity to below 0.0001 with moderate spins

Effectively distinguishes between eccentricity and spin-induced oscillations

Demonstrates applicability across different mass ratios and spin orientations

Abstract

Building initial conditions for generic binary black-hole evolutions without initial spurious eccentricity remains a challenge for numerical-relativity simulations. This problem can be overcome by applying an eccentricity-removal procedure which consists in evolving the binary for a couple of orbits, estimating the eccentricity, and then correcting the initial conditions. The presence of spins can complicate this procedure. As predicted by post-Newtonian theory, spin-spin interactions and precession prevent the binary from moving along an adiabatic sequence of spherical orbits, inducing oscillations in the radial separation and in the orbital frequency. However, spin-induced oscillations occur at approximately twice the orbital frequency, therefore they can be distinguished from the initial spurious eccentricity, which occurs at approximately the orbital frequency. We develop a new removal procedure based on the derivative of the orbital frequency and find that it is successful in reducing the eccentricity measured in the orbital frequency to less than 0.0001 when moderate spins are present. We test this new procedure using numerical-relativity simulations of binary black holes with mass ratios 1.5 and 3, spin magnitude 0.5 and various spin orientations. The numerical simulations exhibit spin-induced oscillations in the dynamics at approximately twice the orbital frequency. Oscillations of similar frequency are also visible in the gravitational-wave phase and frequency of the dominant mode.