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

Boyle, Michael and Buonanno, Alessandra and Kidder, Lawrence E. and Mroué, Abdul H. and Pan, Yi and Pfeiffer, Harald P. and Scheel, Mark A. (2008) High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants. Physical Review D, 78 (10). Art. No. 104020. ISSN 2470-0010. doi:10.1103/PhysRevD.78.104020.

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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 Padé models; nonadiabatic effective-one-body (EOB) models]. We find that Padé summation of the energy flux does not accelerate the convergence of the flux series; nevertheless, the Padé flux is markedly closer to the numerical result for the whole range of the simulation (about 30 GW cycles). Taylor and Padé 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 Padé and EOB models. Matching numerical and untuned 3.5 PN order waveforms, we find that the phase difference accumulated until Momega=0.1 is -0.12 radians for Padé 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 Momega=0.1 can be reduced—if desired—to much less than the estimated numerical phase error (0.02 radians).

Item Type:Article
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Kidder, Lawrence E.0000-0001-5392-7342
Pfeiffer, Harald P.0000-0001-9288-519X
Additional Information:© 2008 The American Physical Society. (Received 25 April 2008; published 18 November 2008) We thank Emanuele Berti, Lee Lindblom, Etienne Racine, Bangalore Sathyaprakash, Saul Teukolsky, and Kip Thorne for informative discussions. We also thank Emanuele Berti and Eric Poisson for providing us the numerical data of the GW flux in the test-mass limit case. We thank Thibault Damour and Alessandro Nagar for clarifications on the "nontuned" EOB model used in Ref. [18]. A.B. and Y.P. acknowledge support from NSF Grant No. PHY-0603762, and A.B. also acknowledges support from the Alfred P. Sloan Foundation. M.B., L.K., A.M., H.P., and M.S. are supported in part by grants from the Sherman Fairchild Foundation to Caltech and Cornell, and from the Brinson Foundation to Caltech; by NSF Grants No. PHY-0601459, No PHY-0652995, No. DMS-0553302, and NASA Grant No. NNG05GG52G at Caltech; by NSF Grants No. PHY-0652952, No. DMS-0553677, No. PHY-0652929, and NASA Grant No. NNG05GG51G at Cornell.
Funding AgencyGrant Number
National Science FoundationPHY-0603762
Alfred P. Sloan FoundationUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Brinson FoundationUNSPECIFIED
National Science FoundationPHY-0601459
National Science FoundationPHY-0652995
National Science FoundationDMS-0553302
National Science FoundationPHY-0652952
National Science FoundationDMS-0553677
National Science FoundationPHY-0652929
Issue or Number:10
Record Number:CaltechAUTHORS:BOYprd08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12419
Deposited By: Archive Administrator
Deposited On:25 Nov 2008 18:09
Last Modified:08 Nov 2021 22:28

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