The gravitational radiation from the ringdown of a binary black hole merger is described by the solution of the Teukolsky equation, which predicts both the temporal dependence and the angular distribution of the emission. Many studies have explored the temporal feature of the ringdown wave through black hole spectroscopy. In this work, we further study the spatial distribution, by introducing a global fitting procedure over both temporal and spatial dependencies, to propose a more complete test of general relativity. We show that spin-weighted spheroidal harmonics are the better representation of the ringdown angular emission patterns compared to spin-weighted spherical harmonics. The differences are distinguishable in numerical relativity waveforms. We also study the correlation between progenitor binary properties and the excitation of quasinormal modes, including higher-order angular modes, overtones, prograde, and retrograde modes. Specifically, we show that the excitation of retrograde modes is dominant when the remnant spin is antialigned with the binary orbital angular momentum. This study seeks to provide an analytical strategy and inspire the future development of ringdown tests using real gravitational wave events.

• Received 8 October 2021
• Accepted 14 December 2021

DOI:https://doi.org/10.1103/PhysRevD.105.024016