High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants

TL;DR

This paper presents highly accurate numerical simulations of black-hole binaries to compute gravitational-wave fluxes and compares these results with various post-Newtonian approximants, improving waveform modeling for gravitational wave detection.

Contribution

It provides the first detailed comparison of numerical relativity results with multiple post-Newtonian models, including EOB, and demonstrates how tuning model parameters can significantly reduce phase differences.

Findings

Pade flux does not improve convergence but is closer to numerical results.

EOB models better match numerical flux and phase than Taylor or Pade models.

Tuning EOB parameters can reduce phase difference below numerical error.

Abstract

Expressions for the gravitational wave (GW) energy flux and center-of-mass energy of a compact binary are integral building blocks of post-Newtonian (PN) waveforms. In this paper, we compute the GW energy flux and GW frequency derivative from a highly accurate numerical simulation of an equal-mass, non-spinning black hole binary. We also estimate the (derivative of the) center-of-mass energy from the simulation by assuming energy balance. We compare these quantities with the predictions of various PN approximants (adiabatic Taylor and Pade models; non-adiabatic effective-one-body (EOB) models). We find that Pade summation of the energy flux does not accelerate the convergence of the flux series; nevertheless, the Pade flux is markedly closer to the numerical result for the whole range of the simulation (about 30 GW cycles). Taylor and Pade models overestimate the increase in flux and frequency derivative close to merger, whereas EOB models reproduce more faithfully the shape of and are closer to the numerical flux, frequency derivative and derivative of energy. We also compare the GW phase of the numerical simulation with Pade and EOB models. Matching numerical and untuned 3.5 PN order waveforms, we find that the phase difference accumulated until $M \omega = 0.1$ is -0.12 radians for Pade approximants, and 0.50 (0.45) radians for an EOB approximant with Keplerian (non-Keplerian) flux. We fit free parameters within the EOB models to minimize the phase difference, and confirm degeneracies among these parameters. By tuning pseudo 4PN order coefficients in the radial potential or in the flux, or, if present, the location of the pole in the flux, we find that the accumulated phase difference can be reduced - if desired - to much less than the estimated numerical phase error (0.02 radians).