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In general relativity, when two black holes merge they produce a rotating(Kerr) black hole remnant. According to perturbation theory, the remnant emits"ringdown" radiation: a superposition of exponentials with characteristiccomplex frequencies that depend only on the remnant's mass and spin. While thegoal of the black hole spectroscopy program is to measure the quasinormal modefrequencies, a knowledge of their amplitudes and phases is equally important todetermine which modes are detectable, and possibly to perform additionalconsistency checks. Unlike the complex frequencies, the amplitudes and phasesdepend on the properties of the binary progenitors, such as the binary massratio and component spins. In this paper we develop a fitting algorithmdesigned to reliably identify the modes present in numerical simulations and toextract their amplitudes and phases. We apply the algorithm to over 500 binaryblack hole simulations from the public SXS numerical relativity simulationcatalog, and we present fitting formulas for the resulting mode amplitudes andphases as functions of the properties of the progenitors. Crucially, ouralgorithm allows for the extraction of not only prograde fundamental modes andovertones, but also retrograde modes and second-order modes. We unveilinteresting relations for the amplitude ratios of different modes. The fittingcode and interactive versions of some of the plots are publicly available. Theresults presented in this paper can be updated as more and better simulationsbecome available.

Extracting linear and nonlinear quasinormal modes from black hole merger simulations