Overtones and nonlinearities in binary black hole ringdowns

Matthew Giesler; Sizheng Ma; Keefe Mitman; Naritaka Oshita; Saul A. Teukolsky; Michael Boyle; Nils Deppe; Lawrence E. Kidder; Jordan Moxon; Kyle C. Nelli; Harald P. Pfeiffer; Mark A. Scheel; William Throwe; Nils L. Vu

doi:10.1103/PhysRevD.111.084041

Overtones and nonlinearities in binary black hole ringdowns

Matthew Giesler ^1,*, Sizheng Ma ², Keefe Mitman ³, Naritaka Oshita ^4,5,6, Saul A. Teukolsky ^1,3, Michael Boyle ¹, Nils Deppe^1,7, Lawrence E. Kidder ¹, Jordan Moxon ³ et al.

Kyle C. Nelli ³, Harald P. Pfeiffer ⁸, Mark A. Scheel ³, William Throwe ¹, and Nils L. Vu ³

¹Cornell Center for Astrophysics and Planetary Science, Cornell University, Ithaca, New York 14853, USA
²Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L2Y5, Canada
³Theoretical Astrophysics 350-17, California Institute of Technology, Pasadena, California 91125, USA
⁴Center for Gravitational Physics and Quantum Information (CGPQI), Yukawa Institute for Theoretical Physics (YITP), Kyoto University, 606-8502, Kyoto, Japan
⁵The Hakubi Center for Advanced Research, Kyoto University, Yoshida Ushinomiyacho, Sakyo-ku, Kyoto 606-8501, Japan
⁶RIKEN iTHEMS, Wako, Saitama, 351-0198, Japan
⁷Department of Physics, Cornell University, Ithaca, New York 14853, USA
⁸Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476 Potsdam, Germany

^*Contact author: mgiesler@tapir.caltech.edu

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Phys. Rev. D 111, 084041 – Published 16 April, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.084041

Abstract

Using high-accuracy numerical relativity waveforms, we confirm the presence of numerous overtones of the $ℓ = 2$ , $m = 2$ quasinormal mode early in the ringdown of binary black hole mergers. We do this by demonstrating the stability of the mode amplitudes at different fit times, ruling out the possibility that a linear superposition of modes unphysically fits a highly nonlinear part of the waveform. We also find a number of previously unidentified subdominant second-order quasinormal modes in the (2, 2) mode. Even though these modes are mathematically nonlinear, they nevertheless confirm the validity of perturbation theory as a good approximation for describing much of the ringdown.

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Overtones and nonlinearities in binary black hole ringdowns

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Overtones and nonlinearities in binary black hole ringdowns

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