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Ineffectiveness of Padé resummation techniques in post-Newtonian approximations

Mroué, Abdul H. and Kidder, Lawrence E. and Teukolsky, Saul A. (2008) Ineffectiveness of Padé resummation techniques in post-Newtonian approximations. Physical Review D, 78 (4). Art. No. 044004. ISSN 2470-0010. doi:10.1103/PhysRevD.78.044004.

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We test the resummation techniques used in developing Padé and effective one body (EOB) waveforms for gravitational wave detection. Convergence tests show that Padé approximants of the gravitational wave energy flux do not accelerate the convergence of the standard Taylor approximants even in the test mass limit, and there is no reason why Padé transformations should help in estimating parameters better in data analysis. Moreover, adding a pole to the flux seems unnecessary in the construction of these Padé-approximated flux formulas. Padé approximants may be useful in suggesting the form of fitting formulas. We compare a 15-orbit numerical waveform of the Caltech-Cornell group to the suggested Padé waveforms of Damour et al. in the equal mass, nonspinning quasicircular case. The comparison suggests that the Padé waveforms do not agree better with the numerical waveform than the standard Taylor based waveforms. Based on this result, we design a simple EOB model by modifiying the Taylor-expanded EOB model of Buonanno et al., using the Taylor series of the flux with an unknown parameter at the fourth post-Newtonian order that we fit for. The 4PN parameter incorporates higher order effects of the radiation reaction. This simple EOB model generates a waveform having a phase difference of only 0.002 radians with the numerical waveform, much smaller than 0.04 radians the phase uncertainty in the numerical data itself. An EOB Hamiltonian can make use of a Padé transformation in its construction, but this is the only place Padé transformations seem useful.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Kidder, Lawrence E.0000-0001-5392-7342
Teukolsky, Saul A.0000-0001-9765-4526
Additional Information:© 2008 The American Physical Society. Received 15 May 2008; published 4 August 2008. It is a pleasure to acknowledge useful discussions with Emanuele Berti, Michael Boyle, Alessandra Buonanno, Lee Lindblom, Harald P. Pfeiffer, Yi Pan, Mark A. Scheel, and Nicolás Yunes. We thank Jihad Touma for helpful discussions about Padé approximants, Harald P. Pfeiffer and Michael Boyle for providing the numerical data of the flux in the equal mass case, and Eric Poisson for providing the numerical data of the flux in the test mass limit. This work was supported in part by grants from the Sherman Fairchild Foundation to Cornell; by NSF Grant Nos. PHY-0652952, DMS-0553677, PHY-0652929, and NASA Grant No. NNG05GG51G at Cornell.
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Issue or Number:4
Classification Code:PACS numbers: 04.25.dg, 04.25.Nx, 04.30.Db
Record Number:CaltechAUTHORS:20180606-084613563
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86821
Deposited By: Tony Diaz
Deposited On:06 Jun 2018 16:40
Last Modified:15 Nov 2021 20:42

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