Exciting black hole modes via misaligned coalescences: II. The mode content of late-time coalescence waveforms

Abstract

Using inspiral and plunge trajectories we construct with a generalized Ori-Thorne algorithm, we use a time-domain black hole perturbation theory code to compute the corresponding gravitational waves. The last cycles of these waveforms are a superposition of Kerr quasinormal modes. In this paper, we examine how the modes' excitations vary as a function of source parameters, such as the larger black hole's spin and the geometry of the smaller body's inspiral and plunge. We find that the mixture of quasinormal modes that characterize the final gravitational waves from a coalescence is entirely determined by the spin $a$ of the larger black hole, an angle $I$ which characterizes the misalignment of the orbital plane from the black hole's spin axis, a second angle $\theta_{\rm fin}$ which describes the location at which the small body crosses the black hole's event horizon, and the direction sgn$(\dot\theta_{\rm fin})$ of the body's final motion. If these large-mass-ratio results hold at less extreme mass ratios, then measuring multiple ringdown modes of binary black hole coalescence gravitational waves may provide important information about the source's binary properties, such as the misalignment of the orbit's angular momentum with black hole spin. This may be particularly useful for large mass binaries, for which the early inspiral waves are out of the detectors' most sensitive band.