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The analytical understanding of quasinormal mode ringing requires an accurateknowledge of the Green's function describing the response of the black hole toexternal perturbations. We carry out a comprehensive study of quasinormal modeexcitation for Kerr black holes. Relying on the formalism developed by Mano,Suzuki and Takasugi, we improve and extend previous calculations of thequasinormal mode residues in the complex frequency plane ("excitation factors"B_q). Using these results we compute the "excitation coefficients" C_q(essentially the mode amplitudes) in the special case where the source of theperturbations is a particle falling into the black hole along the symmetryaxis. We compare this calculation with numerical integrations of theperturbation equations, and we show quantitatively how the addition of higherovertones improves the agreement with the numerical waveforms. Our resultsshould find applications in models of the ringdown stage and in theconstruction of semianalytical template banks for gravitational-wave detectors,especially for binaries with large mass ratios and/or fast-spinning blackholes.

Quasinormal ringing of Kerr black holes. II. Excitation by particles falling radially with arbitrary energy