A nonlinear voice from GW250114 ringdown

Abstract: The detection of quadratic quasi-normal modes would provide a direct probe into black hole nonlinear perturbations. We report the first observational evidence of a set of quadratic quasi-normal modes in the gravitational-wave ringdown of a binary black hole merger. Analyzing the signal from GW250114, we detect six nonlinear modes from the quadratic coupling of the fundamental $(2,2,0)$ mode and its first two overtones. At 5 final mass ($M_\mathrm{f}$) after the merger, the evidence for these nonlinear modes reaches a Bayes factor of 74. To single out these contributions, we employ recent theoretical progress to compute the waveforms and subtract the corresponding nonlinear modes from a numerical relativity surrogate waveform. Our data analysis uses a novel method that incorporates inspiral-merger inference results as a highly constraining prior for the ringdown inference. We further perform a test allowing for phenomenological deviations for the theoretically predicted amplitudes of the quadratic modes. The results show that an amplitude of zero is excluded at $3.0~σ$ significance level, while the theoretical expectation is consistent with the inference. This detection marks a first step towards observationally characterizing nonlinear perturbations in the ringdown of a black hole.