Improved resummation of post-Newtonian multipolar waveforms from circularized compact binaries

Details Improved resummation of post-Newtonian multipolar waveforms from circularized compact binaries Improved resummation of post-Newtonian multipolar waveforms from circularized compact binaries

2008-11-13

arxiv.org/abs/0811.2069v2

Phys.Rev.D79:064004,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

31 pages, 12 figures. Minor modifications. Published in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.79.064004

We improve and generalize a resummation method of post-Newtonian multipolar waveforms from circular compact binaries introduced in Refs. \cite{Damour:2007xr,Damour:2007yf}. One of the characteristic features of this resummation method is to replace the usual {\it additive} decomposition of the standard post-Newtonian approach by a {\it multiplicative} decomposition of the complex multipolar waveform $h_{\lm}$ into several (physically motivated) factors: (i) the "Newtonian" waveform, (ii) a relativistic correction coming from an "effective source", (iii) leading-order tail effects linked to propagation on a Schwarzschild background, (iv) a residual tail dephasing, and (v) residual relativistic amplitude corrections $f_{\lm}$. We explore here a new route for resumming $f_{\lm}$ based on replacing it by its $\ell$-th root: $\rho_{\lm}=f_{\lm}^{1/\ell}$. In the extreme-mass-ratio case, this resummation procedure results in a much better agreement between analytical and numerical waveforms than when using standard post-Newtonian approximants. We then show that our best approximants behave in a robust and continuous manner as we "deform" them by increasing the symmetric mass ratio $\nu\equiv m_1 m_2/(m_1+m_2)^2$ from 0 (extreme-mass-ratio case) to 1/4 (equal-mass case). The present paper also completes our knowledge of the first post-Newtonian corrections to multipole moments by computing ready-to-use explicit expressions for the first post-Newtonian contributions to the odd-parity (current) multipoles.

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