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Binary black hole coalescence in the large-mass-ratio limit: The hyperboloidal layer method and waveforms at null infinity

Bernuzzi, Sebastiano and Nagar, Alessandro and Zenginoğlu, Anıl (2011) Binary black hole coalescence in the large-mass-ratio limit: The hyperboloidal layer method and waveforms at null infinity. Physical Review D, 84 (8). Art. No. 084026. ISSN 2470-0010.

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We compute and analyze the gravitational waveform emitted to future null infinity by a system of two black holes in the large-mass-ratio limit. We consider the transition from the quasiadiabatic inspiral to plunge, merger, and ringdown. The relative dynamics is driven by a leading order in the mass ratio, 5PN-resummed, effective-one-body (EOB), analytic-radiation reaction. To compute the waveforms, we solve the Regge-Wheeler-Zerilli equations in the time-domain on a spacelike foliation, which coincides with the standard Schwarzschild foliation in the region including the motion of the small black hole, and is globally hyperboloidal, allowing us to include future null infinity in the computational domain by compactification. This method is called the hyperboloidal layer method, and is discussed here for the first time in a study of the gravitational radiation emitted by black hole binaries. We consider binaries characterized by five mass ratios, ν=10^(-2,-3,-4,-5,-6), that are primary targets of space-based or third-generation gravitational wave detectors. We show significative phase differences between finite-radius and null-infinity waveforms. We test, in our context, the reliability of the extrapolation procedure routinely applied to numerical relativity waveforms. We present an updated calculation of the final and maximum gravitational recoil imparted to the merger remnant by the gravitational wave emission, v_kick^(end)/(cν^2)=0.04474±0.00007 and v_(kick)^(max)/(cν^2)=0.05248±0.00008. As a self-consistency test of the method, we show an excellent fractional agreement (even during the plunge) between the 5PN EOB-resummed mechanical angular momentum loss and the gravitational wave angular momentum flux computed at null infinity. New results concerning the radiation emitted from unstable circular orbits are also presented. The high accuracy waveforms computed here could be considered for the construction of template banks or for calibrating analytic models such as the effective-one-body model.

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Additional Information:© 2011 American Physical Society. Received 27 July 2011; published 13 October 2011. We thank Thibault Damour for useful inputs. We are also grateful to Ryuichi Fujita for making available to us his data for circular orbits. S.B. is supported by DFG Grant SFB/Transregio 7 "GravitationalWave Astronomy." S. B. thanks IHES for hospitality and support during the development of this work. A. Z. acknowledges support by the NSF Grant No. PHY-1068881, and by a Sherman Fairchild Foundation grant to California Institute of Technology. Computations were performed on the MERLIN cluster at IHES. The authors thank Francois Bachelier for computer assistance.
Funding AgencyGrant Number
DFG SFB/Transregio 7
Sherman Fairchild FoundationUNSPECIFIED
Issue or Number:8
Classification Code:PACS: 04.30.Db, 04.25.Nx, 95.30.Sf, 97.60.Lf
Record Number:CaltechAUTHORS:20111122-091921776
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Official Citation:Binary black hole coalescence in the large-mass-ratio limit: The hyperboloidal layer method and waveforms at null infinity Sebastiano Bernuzzi, Alessandro Nagar, and Anıl Zenginoğlu Published 13 October 2011 (22 pages) 084026
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27906
Deposited By: Ruth Sustaita
Deposited On:22 Nov 2011 18:09
Last Modified:03 Oct 2019 03:27

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