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Abstract

We complete the post-Newtonian (PN) prediction at the 3.5PN order for the
spin contributions to the gravitational waveforms emitted by inspiraling
compact binaries, in the case of quasi-circular, equatorial orbits, where both
spins are aligned with the orbital angular momentum. Using results from the
multipolar post-Minkowskian wave generation formalism, we extend previous works
that derived the dynamics and gravitational-wave energy flux and phasing, by
computing the full waveform decomposed in spin-weighted spherical harmonics.
This new calculation requires the computation of multipolar moments of higher
multipolar order, new quadratic-in-spin contributions to the hereditary tail
terms entering at the 3.5PN order, as well as other non-linear interactions
between moments. When specialized to the test-mass limit, our results are
equivalent to those obtained in the literature for the waveform emitted by a
test-mass in equatorial, circular orbits around a Kerr black hole. We also
compute the factorized modes for use in effective-one-body waveform models,
correcting the 2.5PN nonspinning and 3PN quadratic-in-spin terms in the (2,1)
mode used in current models.