Merging binary black holes exhibit a ringdown phase in which they primarily emit gravitational waves in the shape of damped sinusoids corresponding to quasinormal modes of the Kerr remnant. In general, each mode carries 4 degrees of freedom encoding amplitude and phase information. When the modes are excited with equatorial reflection symmetry, as is the case for black hole mergers with spins (anti)aligned to the orbital angular momentum, the symmetry constrains 2 degrees of freedom. As a result, the relationship between polarization amplitudes and phases in each mode is fixed by the viewing (inclination) angle to the equatorial plane. We use such a constrained model to fit the ringdown signals of both nonprecessing and precessing systems such as GW150914 and GW190521, respectively. We show that we can measure the degree of circular polarization and handedness of ringdown signals like those of GW150914, even if only the two LIGO detectors are available; such a polarization measurement can be translated into an inferred source inclination assuming the reflection symmetry above, again using the ringdown signal alone. On the other hand, the constrained polarization model is insufficient to capture the polarization structure of signals from precessing systems, leading to biases in the inferred mode frequencies and amplitudes. We explore the magnitude of this effect by fitting GW190521-like injections with the restricted model, finding weaker predictive accuracy relative to the arbitrary-polarization model and potentially significant systematic biases. As our detectors continue to improve, using the correct polarization model is increasingly important to avoid biased ringdown measurements.

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• Gravitational wave sources
• Gravitational waves