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

We improve and generalize a resummation method of post-Newtonian multipolar waveforms from circular (nonspinning) compact binaries introduced in Refs. 1, 2. One of the characteristic features of this resummation method is to replace the usual additive decomposition of the standard post-Newtonian approach by a multiplicative decomposition of the complex multipolar waveform h_ 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_. We explore here a new route for resumming f_ based on replacing it by its -th root: _=f_^1/. 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 m₁m₂/ (m₁+m₂) ^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.