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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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