Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries: Ready-to-use gravitational waveforms

Abstract

We provide ready-to-use time-domain gravitational waveforms for spinning compact binaries with precession effects through 1.5 post-Newtonian (PN) order in amplitude, and compute their mode decomposition using spin-weighted $\ensuremath{-}2$ spherical harmonics. In the presence of precession, the gravitational-wave modes $(\ensuremath{\ell},m)$ contain harmonics originating from combinations of the orbital frequency and precession frequencies. We find that the gravitational radiation from binary systems with large mass asymmetry and large inclination angle can be distributed among several modes. For example, during the last stages of inspiral, for some maximally spinning configurations, the amplitude of the (2, 0) and (2, 1) modes can be comparable to the amplitude of the (2, 2) mode. If the mass ratio is not too extreme, the $\ensuremath{\ell}=3$ and $\ensuremath{\ell}=4$ modes are generally 1 or 2 orders of magnitude smaller than the $\ensuremath{\ell}=2$ modes. Restricting ourselves to spinning, nonprecessing compact binaries, we apply the stationary-phase approximation and derive the frequency-domain gravitational waveforms including spin-orbit and spin(1)-spin(2) effects through 1.5PN and 2PN order, respectively, in amplitude, and 2.5PN order in phase. Since spin effects in the amplitude through 2PN order affect only the first and second harmonics of the orbital phase, they do not extend the mass reach of gravitational-wave detectors. However, they can interfere with other harmonics and lower or raise the signal-to-noise ratio depending on the spin orientation. These ready-to-use waveforms could be employed in the data analysis of the spinning, inspiraling binaries as well as in comparison studies at the interface between analytical and numerical relativity.