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title: "Ineffectiveness of Padé resummation techniques in post-Newtonian approximations"
authors:
- "Abdul H. Mroué"
- "Lawrence E. Kidder"
- "Saul A. Teukolsky"
jref: "Phys. Rev. D 78, 044004 (2008)"
- "Mroue, Abdul H."
- "Kidder, Lawrence E."
- "Teukolsky, Saul A."
jref: "Phys.Rev.D 78, 044004 (2008)"
doi: "10.1103/PhysRevD.78.044004"
date: 2008-05-15
arxiv: "0805.2390"
used_spec: true
abstract: |
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
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
quasi-circular 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 ET 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. This simple EOB model
quasi-circular 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 ET 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. 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.
can make use of a Padé transformation in its construction, but
this is the only place Padé transformations seem useful.
---

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