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

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 ${f}_{\ensuremath{\ell}m}$ with its $\ensuremath{\ell}$th root, ${\ensuremath{\rho}}_{\ensuremath{\ell}m}={f}_{\ensuremath{\ell}m}^{1/\ensuremath{\ell}}$, agree quite well with the numerical amplitudes up to the Kerr-spin value $q\ensuremath{\le}0.95$ for orbital velocities $v\ensuremath{\le}0.4$. 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 ${\ensuremath{\rho}}_{\ensuremath{\ell}m}$. 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, nonprecessing, 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.