A New Template Family For The Detection Of Gravitational Waves From Comparable Mass Black Hole Binaries

Abstract

In order to improve the phasing of the comparable-mass waveform as we approach the last stable orbit for a system, various re-summation methods have been used to improve the standard post-Newtonian waveforms. In this work we present a new family of templates for the detection of gravitational waves from the inspiral of two comparable-mass black hole binaries. These new adiabatic templates are based on re-expressing the derivative of the binding energy and the gravitational wave flux functions in terms of shifted Chebyshev polynomials. The Chebyshev polynomials are a useful tool in numerical methods as they display the fastest convergence of any of the orthogonal polynomials. In this case they are also particularly useful as they eliminate one of the features that plagues the post-Newtonian expansion. The Chebyshev binding energy now has information at all post-Newtonian orders, compared to the post-Newtonian templates which only have information at full integer orders. In this work, we compare both the post-Newtonian and Chebyshev templates against a fiducially exact waveform. This waveform is constructed from a hybrid method of using the test-mass results combined with the mass dependent parts of the post-Newtonian expansions for the binding energy and flux functions. Our results show that the Chebyshev templates achieve extremely high fitting factors at all PN orders and provide excellent parameter extraction. We also show that this new template family has a faster Cauchy convergence, gives a better prediction of the position of the Last Stable Orbit and in general recovers higher Signal-to-Noise ratios than the post-Newtonian templates.

Final published version. Accepted for publication in Phys. Rev. D

References in corpus (8)

• Total recoil: the maximum kick from nonspinning black-hole binary inspiral
• Faithful Effective-One-Body waveforms of small-mass-ratio coalescing black-hole binaries
• Binary black hole merger dynamics and waveforms
• How to move a black hole without excision: gauge conditions for the numerical evolution of a moving puncture
• The last orbit of binary black holes
• Gravitational Recoil during Binary Black Hole Coalescence using the Effective One Body Approach
• Spin-orbit interactions in black-hole binaries
• Modelling the post-Newtonian test-mass gravitational wave flux function for compact binary systems using Chebyshev polynomials

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• Impact of the second order self-forces on the dephasing of the gravitational waves from quasi-circular extreme mass-ratio inspirals
• 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