A nonlinear voice from GW250114 ringdown

Abstract

Gravitational-wave astronomy, by detecting ripples in spacetime, has opened a new window to observe compact objects and probe theories of gravity in the nonlinear strong-field regime. The ringdown signal of a binary black hole merger contains a superposition of damped sinusoids known as quasi-normal modes (Ref.[1]), whose frequencies are completely determined by the mass and spin of the remnant black hole and form the basis of black hole spectroscopy (Refs.[2-4]). A crucial prediction yet to be observationally confirmed is the existence of quadratic quasi-normal modes, which represent fundamental properties associated with wave-wave coupling in general relativity, and the leading mode is predicted to be detectable with next-generation ground-based detectors (Refs.[5-7]) using traditional methods. Here we show the first observational evidence for a set of quadratic quasi-normal modes in the ringdown of the binary black hole merger GW250114, the loudest gravitational-wave event detected to date, enabled by a novel analysis. These nonlinear modes result from the quadratic coupling of the linear $(2,2,n)$ modes with $n\leq3$. Starting the analysis at a time corresponding to four times the remnant mass ($M_\mathrm{f}$) after the merger, the evidence for their presence reaches a Bayes factor of 62. A phenomenological test allowing these modes to deviate from the theoretical prediction rejects the zero-amplitude hypothesis at a significance of 3.4 $σ$, while the inferred amplitude and complex frequency are consistent with the prediction of general relativity. This finding provides the first observational evidence of gravitational wave-wave interaction and extends black hole spectroscopy from the linear to the nonlinear regime. It also establishes a new direction for testing the fundamental nonlinear structure of general relativity with the most extreme gravity.