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

## 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, nonspinning 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; nonadiabatic 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 0.50more »

- Authors:

- Theoretical Astrophysics 130-33, California Institute of Technology, Pasadena, California 91125 (United States)
- Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, Maryland 20742 (United States)
- Center for Radiophysics and Space Research, Cornell University, Ithaca, New York, 14853 (United States)

- Publication Date:

- OSTI Identifier:
- 21250921

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 78; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.78.104020; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ACCURACY; BLACK HOLES; CENTER-OF-MASS SYSTEM; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; CONVERGENCE; ENERGY BALANCE; FORECASTING; GRAVITATIONAL WAVES; MASS; NUMERICAL SOLUTION; POTENTIALS; WAVE FORMS

### Citation Formats

```
Boyle, Michael, Pfeiffer, Harald P., Scheel, Mark A., Buonanno, Alessandra, Pan Yi, Kidder, Lawrence E., and Mroue, Abdul H.
```*High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants*. United States: N. p., 2008.
Web. doi:10.1103/PHYSREVD.78.104020.

```
Boyle, Michael, Pfeiffer, Harald P., Scheel, Mark A., Buonanno, Alessandra, Pan Yi, Kidder, Lawrence E., & Mroue, Abdul H.
```*High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants*. United States. doi:10.1103/PHYSREVD.78.104020.

```
Boyle, Michael, Pfeiffer, Harald P., Scheel, Mark A., Buonanno, Alessandra, Pan Yi, Kidder, Lawrence E., and Mroue, Abdul H. Sat .
"High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants". United States. doi:10.1103/PHYSREVD.78.104020.
```

```
@article{osti_21250921,
```

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

author = {Boyle, Michael and Pfeiffer, Harald P. and Scheel, Mark A. and Buonanno, Alessandra and Pan Yi and Kidder, Lawrence E. and Mroue, Abdul H.},

abstractNote = {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, nonspinning 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; nonadiabatic 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 the presence of degeneracies among these parameters. By tuning the 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 at M{omega}=0.1 can be reduced--if desired--to much less than the estimated numerical phase error (0.02 radians)},

doi = {10.1103/PHYSREVD.78.104020},

journal = {Physical Review. D, Particles Fields},

number = 10,

volume = 78,

place = {United States},

year = {Sat Nov 15 00:00:00 EST 2008},

month = {Sat Nov 15 00:00:00 EST 2008}

}