Post-Newtonian factorized multipolar waveforms for spinning, non-precessing black-hole binaries

TL;DR

This paper extends the factorized resummation of gravitational waveforms to spinning black-hole binaries, improving agreement with numerical solutions and aiding the development of more accurate gravitational wave templates.

Contribution

It introduces a generalized factorized resummation method for spinning black holes, enhancing waveform accuracy for non-precessing binaries across a range of spins and velocities.

Findings

Factorized amplitudes agree well with numerical results up to high spins and velocities.

Resummation improves agreement over standard post-Newtonian approximants.

New higher-order post-Newtonian terms are computed for subdominant modes.

Abstract

We generalize the factorized resummation of multipolar waveforms introduced by Damour, Iyer and Nagar to spinning black holes. For a nonspinning test-particle spiraling a Kerr black hole in the equatorial plane, we find that factorized multipolar amplitudes which replace the residual relativistic amplitude f_{l m} with its l-th root, \rho_{l m} = f_{l m}^{1/l}, agree quite well with the numerical amplitudes up to the Kerr-spin value q \leq 0.95 for orbital velocities v \leq 0.4. The numerical amplitudes are computed solving the Teukolsky equation with a spectral code. The agreement for prograde orbits and large spin values of the Kerr black hole can be further improved at high velocities by properly factoring out the lower-order post-Newtonian contributions in \rho_{l m}. The resummation procedure results in a better and systematic agreement between numerical and analytical amplitudes (and energy fluxes) than standard Taylor-expanded post-Newtonian approximants. This is particularly true for higher-order modes, such as (2,1), (3,3), (3,2), and (4,4) for which less spin post-Newtonian terms are known. We also extend the factorized resummation of multipolar amplitudes to generic mass-ratio, non-precessing, spinning black holes. Lastly, in our study we employ new, recently computed, higher-order post-Newtonian terms in several subdominant modes, and compute explicit expressions for the half and one-and-half post-Newtonian contributions to the odd-parity (current) and even-parity (odd) multipoles, respectively. Those results can be used to build more accurate templates for ground-based and space-based gravitational-wave detectors.