Reducing orbital eccentricity in binary black hole simulations

TL;DR

This paper develops a method to generate low-eccentricity initial data for binary black hole simulations, improving the accuracy of gravitational wave predictions by reducing orbital eccentricity.

Contribution

The authors extend the quasi-equilibrium initial-data method to include non-zero radial velocities, enabling the creation of low-eccentricity binary black hole initial data.

Findings

Low-eccentricity initial data reduce orbital eccentricity in simulations.

Eccentricity decay matches Peters (1964) predictions.

Gravitational waveforms are largely unaffected by initial eccentricity.

Abstract

Binary black hole simulations starting from quasi-circular (i.e., zero radial velocity) initial data have orbits with small but non-zero orbital eccentricities. In this paper the quasi-equilibrium initial-data method is extended to allow non-zero radial velocities to be specified in binary black hole initial data. New low-eccentricity initial data are obtained by adjusting the orbital frequency and radial velocities to minimize the orbital eccentricity, and the resulting ($\sim 5$ orbit) evolutions are compared with those of quasi-circular initial data. Evolutions of the quasi-circular data clearly show eccentric orbits, with eccentricity that decays over time. The precise decay rate depends on the definition of eccentricity; if defined in terms of variations in the orbital frequency, the decay rate agrees well with the prediction of Peters (1964). The gravitational waveforms, which contain $\sim 8$ cycles in the dominant l=m=2 mode, are largely unaffected by the eccentricity of the quasi-circular initial data. The overlap between the dominant mode in the quasi-circular evolution and the same mode in the low-eccentricity evolution is about 0.99.