Modeling ringdown: Beyond the fundamental quasinormal modes

Abstract

While black hole perturbation theory predicts a rich quasinormal mode structure, technical challenges have limited the numerical study of excitations to the fundamental, lowest order modes caused by the coalescence of black holes. Here, we present a robust method to identify quasinormal mode excitations beyond the fundamentals within currently available numerical relativity waveforms. In applying this method to waveforms of 68 initially nonspinning black hole binaries, of mass ratios $1\ensuremath{\mathbin:}1$ to $15\ensuremath{\mathbin:}1$, we find not only the fundamental quasinormal mode amplitudes, but also overtones, and evidence for second order quasinormal modes. We find that the mass-ratio dependence of quasinormal mode excitation is very well modeled by a post-Newtonian-like sum in symmetric mass ratio. Concurrently, we find that the mass-ratio dependence of some quasinormal mode excitations is qualitatively different from their post-Newtonian inspired counterparts, suggesting that the imprints of nonlinear merger are more evident in some modes than in others. We present new fitting formulas for the related quasinormal mode excitations, as well as for remnant black hole spin and mass. We also discuss the relevance of our results in terms of gravitational wave detection and characterization.