Ineffectiveness of Padé resummation techniques in post-Newtonian approximations

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 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 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.

arXiv comment13 pages, 7 figures. added some references

References in corpus (56)

• Evolution of Binary Black Hole Spacetimes
• Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
• Effective one-body approach to general relativistic two-body dynamics
• Gravitational wave extraction from an inspiraling configuration of merging black holes
• Transition from inspiral to plunge in binary black hole coalescences
• Coalescence of Two Spinning Black Holes: An Effective One-Body Approach
• Gravitational-Radiation Damping of Compact Binary Systems to Second Post-Newtonian order
• The Last Three Minutes: Issues in Gravitational Wave Measurements of Coalescing Compact Binaries
• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions
• Calibration of Moving Puncture Simulations
• Improved filters for gravitational waves from inspiralling compact binaries
• Dimensional regularization of the gravitational interaction of point masses
• A Comparison of search templates for gravitational waves from binary inspiral
• Toward faithful templates for non-spinning binary black holes using the effective-one-body approach
• Transition from inspiral to plunge in precessing binaries of spinning black holes
• 3rd post-Newtonian higher order Hamilton dynamics for two-body point-mass systems
• Faithful Effective-One-Body waveforms of small-mass-ratio coalescing black-hole binaries
• Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
• Solving Einstein's Equations With Dual Coordinate Frames
• Reducing orbital eccentricity in binary black hole simulations
• General relativistic dynamics of compact binaries at the third post-Newtonian order
• Binary black-hole evolutions of excision and puncture data
• Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
• Where post-Newtonian and numerical-relativity waveforms meet
• Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem
• Comparing Effective-One-Body gravitational waveforms to accurate numerical data
• Using Full Information When Computing Modes of Post-Newtonian Waveforms From Inspiralling Compact Binaries in Circular Orbit
• The 2.5PN gravitational wave polarisations from inspiralling compact binaries in circular orbits
• Unequal Mass Binary Black Hole Plunges and Gravitational Recoil
• Detection template families for gravitational waves from the final stages of binary--black-hole inspirals: Nonspinning case
• Equivalence between the ADM-Hamiltonian and the harmonic-coordinates approaches to the third post-Newtonian dynamics of compact binaries
• Consistency of post-Newtonian waveforms with numerical relativity
• The last orbit of binary black holes
• Gravitational Recoil during Binary Black Hole Coalescence using the Effective One Body Approach
• On the multipole expansion of the gravitational field
• New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity
• The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part
• On the equations of motion of point-particle binaries at the third post-Newtonian order
• Gravitational Waves by a Particle in Circular Orbits around a Schwarzschild black hole -5.5 Post-Newtonian Formula-
• Gravitational radiation from a particle in circular orbit around a black hole. VI. Accuracy of the post-Newtonian expansion
• Equation of motion for relativistic compact binaries with the strong field point particle limit: Third post-Newtonian order
• Gravitational radiation reaction and balance equations to post-Newtonian order
• Filling the holes: Evolving excised binary black hole initial data with puncture techniques
• Gravitational waves from black hole binary inspiral and merger: The span of third post-Newtonian effective-one-body templates
• Equation of motion for relativistic compact binaries with the strong field point particle limit : the second and half post-Newtonian order
• A comparison of search templates for gravitational waves from binary inspiral - 3.5PN update
• An explicit harmonic code for black-hole evolution using excision
• Accurate Evolution of Orbiting Binary Black Holes
• A quasi-physical family of gravity-wave templates for precessing binaries of spinning compact objects: Application to double-spin precessing binaries
• Final spin of a coalescing black-hole binary: an Effective-One-Body approach
• Accuracy of the Post-Newtonian Approximation: Optimal Asymptotic Expansion for Quasi-Circular, Extreme-Mass Ratio Inspirals
• Relativistic black hole-neutron star binaries in quasiequilibrium: effects of the black hole excision boundary condition
• Introductory lectures on the Effective One Body formalism
• Binary black holes on a budget: Simulations using workstations
• Improved gravitational waveforms from spinning black hole binaries

Cited by in corpus (17)

• High-accuracy waveforms for binary black hole inspiral, merger, and ringdown
• Post-Newtonian corrections to the gravitational-wave memory for quasicircular, inspiralling compact binaries
• Tracking the precession of compact binaries from their gravitational-wave signal
• Comparison of Numerical and Post-Newtonian Waveforms for Generic Precessing Black-Hole Binaries
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• The Samurai Project: verifying the consistency of black-hole-binary waveforms for gravitational-wave detection
• High accuracy simulations of black hole binaries:spins anti-aligned with the orbital angular momentum
• Conservative self-force correction to the innermost stable circular orbit: comparison with multiple post-Newtonian-based methods
• Status of black-hole-binary simulations for gravitational-wave detection
• Comparison of high-accuracy numerical simulations of black-hole binaries with stationary phase post-Newtonian template waveforms for Initial and Advanced LIGO
• Length requirements for numerical-relativity waveforms
• Uncertainty in hybrid gravitational waveforms: Optimizing initial orbital frequencies for binary black-hole simulations
• Numerical black hole initial data with low eccentricity based on post-Newtonian orbital parameters
• Accuracy of the post-Newtonian approximation. II. Optimal asymptotic expansion of the energy flux for quasicircular, extreme mass-ratio inspirals into a Kerr black hole
• Spinning compact binary inspiral: Independent variables and dynamically preserved spin configurations
• Numerical relativity simulations in the era of the Einstein Telescope
• Periastron Advance in Neutron Star - Black Hole Binaries