Numerical black hole initial data with low eccentricity based on post-Newtonian orbital parameters

TL;DR

This paper develops a method to generate low-eccentricity initial data for black hole binary simulations using post-Newtonian parameters, improving accuracy especially for spinning and unequal mass systems.

Contribution

It compares different post-Newtonian methods and demonstrates that the effective-one-body Hamiltonian yields lower eccentricity initial data, especially for spinning black holes.

Findings

Eccentricity is lower with the effective-one-body approach.

Eccentricity increases with mass ratio and spin.

Effective-one-body Hamiltonian performs better for spinning binaries.

Abstract

Black hole binaries on non-eccentric orbits form an important subclass of gravitational wave sources, but it is a non-trivial issue to construct numerical initial data with minimal initial eccentricity for numerical simulations. We compute post-Newtonian orbital parameters for quasi-spherical orbits using the method of Buonanno, Chen and Damour (2006) and examine the resulting eccentricity in numerical simulations. Four different methods are studied resulting from the choice of Taylor-expanded or effective-one-body Hamiltonians, and from two choices for the energy flux. The eccentricity increases for unequal masses and for spinning black holes, but remains smaller than that obtained from previous post-Newtonian approaches. The effective-one-body Hamiltonian offers advantages for decreasing initial separation as expected, but in the context of this study also performs significantly better than the Taylor-expanded Hamiltonian for binaries with spin.