Constraining the Quadratic-mode Amplitude Coupling in GW250114
Abstract
Detecting quadratic quasi-normal modes in black hole ringdowns would provide evidence for nonlinear gravitational dynamics, while measuring their properties would enable tests of the corresponding predictions of general relativity. Specifically, second-order black hole perturbation theory predicts that their amplitudes scale with the product of the amplitudes of their parent linear modes, with a coupling coefficient that depends on the spin of the remnant black hole. This mode-specific coupling coefficient has not yet been directly measured from gravitational wave data. Here, we use Bayesian inference on the GW250114 ringdown, modeled with the $220$, $221$, and 220×220 modes, to infer the amplitude-coupling coefficient of the 220×220 mode. The inferred coefficient is consistent with predictions from numerical relativity fits and second-order perturbation theory; no comparison shows a deviation exceeding $1.3 σ$. Although the current data cannot distinguish among these spin-dependent predictions, this measurement establishes a basis for more stringent observational tests of nonlinear gravitational dynamics in black-hole ringdowns.
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BibTeX
@misc{yang2026constraining,
title = {{Constraining the Quadratic-mode Amplitude Coupling in GW250114}},
author = {Yuxin Yang and Changfu Shi and Yi-Ming Hu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28953},
eprint = {2609.28953},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28953},
}
RIS
TY - UNPB
TI - Constraining the Quadratic-mode Amplitude Coupling in GW250114
AU - Yuxin Yang
AU - Changfu Shi
AU - Yi-Ming Hu
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.28953
UR - https://arxiv.org/abs/2609.28953
AB - Detecting quadratic quasi-normal modes in black hole ringdowns would provide evidence for nonlinear gravitational dynamics, while measuring their properties would enable tests of the corresponding predictions of general relativity. Specifically, second-order black hole perturbation theory predicts that their amplitudes scale with the product of the amplitudes of their parent linear modes, with a coupling coefficient that depends on the spin of the remnant black hole. This mode-specific coupling coefficient has not yet been directly measured from gravitational wave data. Here, we use Bayesian inference on the GW250114 ringdown, modeled with the $220$, $221$, and 220×220 modes, to infer the amplitude-coupling coefficient of the 220×220 mode. The inferred coefficient is consistent with predictions from numerical relativity fits and second-order perturbation theory; no comparison shows a deviation exceeding $1.3 σ$. Although the current data cannot distinguish among these spin-dependent predictions, this measurement establishes a basis for more stringent observational tests of nonlinear gravitational dynamics in black-hole ringdowns.
ER -