Learning about black hole binaries from their ringdown spectra

The coalescence of two black holes generates gravitational waves that carry detailed information about the properties of those black holes and their binary configuration. The final coalescence cycles are in the form of a {\it ringdown}: a superposition of quasi-normal modes of the merged remnant black hole. Each mode has an oscillation frequency and decay time that in general relativity is determined by the remnant's mass and spin. Measuring the frequency and decay time of multiple modes makes it possible to measure the remnant's mass and spin, and to test the waves against the predictions of gravity theories. In this {\it Letter}, we show that the relative amplitudes of these modes encodes information about a binary's {\it geometry}. Focusing on the large mass-ratio limit, which provides a simple-to-use tool for effectively exploring parameter space, we demonstrate how a binary's geometry is encoded in the relative amplitudes of these modes, and how to parameterize the modes in this limit. Although more work is needed to assess how well this carries over to less extreme mass ratios, our results indicate that measuring multiple ringdown modes from coalescence may aid in measuring important source properties, such as the misalignment of its members' spins and orbit.