  While black hole perturbation theory predicts a rich quasi-normal 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 quasi-normal mode
excitations beyond the fundamentals within currently available numerical
relativity waveforms. In applying this method to waveforms of initially
non-spinning black hole binaries, of mass ratios 1 to 15, we find not only the
fundamental quasi-normal mode amplitudes, but also overtones, and evidence for
2nd order quasi-normal modes. We find that the mass-ratio dependence of
quasi-normal 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 quasi-normal modes 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 quasi-normal 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.
