Using gravitational waves to probe the geometry of the ringing remnant black hole formed in a binary black hole coalescence is a well-established way to test Einstein’s theory of general relativity. However, doing so requires knowledge of when the predictions of black hole perturbation theory, i.e., quasinormal modes (QNMs), are a valid description of the emitted gravitational wave as well as what the amplitudes of these excitations are. In this work, we develop an algorithm to systematically extract QNMs from the ringdown of black hole merger simulations. Our algorithm improves upon previous ones in three ways: it fits over the two-sphere, enabling a complete model of the strain; it performs a reverse search in time for QNMs using a more robust nonlinear least squares routine called varpro; and it checks the variance of QNM amplitudes, which we refer to as “stability,” over an interval matching the natural timescale of each QNM. Using this algorithm, we not only demonstrate the stability of a multitude of QNMs and their overtones across the parameter space of quasicircular, nonprecessing binary black holes, but we also identify new quadratic QNMs that may be detectable in the near future using ground-based interferometers. Furthermore, we provide evidence which suggests that the source of remnant black hole perturbations is roughly independent of the overtone index in a given angular harmonic across binary parameter space, at least for overtones with $n\lesssim 2$. This finding may hint at the spatiotemporal structure of ringdown perturbations in black hole coalescences, as well as the regime of validity of perturbation theory in the ringdown of these events.

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• Classical black holes
• Gravitation
• Gravitational wave sources
• Gravitational waves
• Numerical relativity
• Numerical simulations in gravitation & astrophysics
• Numerical techniques