Ineffectiveness of Pade resummation techniques in post-Newtonian approximations

We test the resummation techniques used in developing Pade and effective one body (EOB) waveforms for gravitational wave detection. Convergence tests show that Pade 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 Pade transformations should help in estimating parameters better in data analysis. Moreover, adding a pole to the flux seems unnecessary in the construction of these Pade-approximated flux formulas. Pade 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 Pade waveforms of Damour et al. in the equal mass, nonspinning quasicircular case. The comparison suggests that the Pade waveforms do not agree better with the numerical waveform than the standard Taylor based waveforms. Based on this result, we design a simple ECB model by modifying 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 Pade transformation in its construction, but this is the only place Pade transformations seem useful.