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Journal Article

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


Buonanno,  Alessandra
Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;
Maryland Center for Fundamental Physics & Joint Space-Science Institute, Department of Physics, University of Maryland;

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Pan, Y., Fujita, R., Buonanno, A., Racine, E., & Tagoshi, H. (2011). Post-Newtonian factorized multipolar waveforms for spinning, non-precessing black-hole binaries. Physical Review D, 83(6): 064003. doi:10.1103/PhysRevD.83.064003.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0015-83CA-9
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.