A nonlinear voice from GW250114 ringdown

TL;DR

The paper tackles the detection of nonlinear perturbations in black hole ringdowns by identifying quadratic QNMs, which arise from second-order GR effects. It introduces a hierarchical Bayesian method that uses gating and inpainting to separate inspiral-merger and ringdown data, employing the inspiral-merger inference as an informative prior for the ringdown. The ringdown modeling relies on NRSur7dq4 for linear modes and computes six quadratic QNMs from couplings of $ (2,2,n) $ with $ n \in \{0,1,2\} $, which are then subtracted to quantify their presence. Applied to GW250114, the approach yields a Bayes factor of $74$ for including the six quadratic modes starting at $5\,M_\mathrm{f}$ after merger, with the inferred quadratic amplitude consistent with GR predictions and zero amplitude excluded at $3\sigma$. This work establishes a pathway to observationally characterize nonlinear GR effects in black hole ringdown and motivates future analyses, including stacking multiple events to enhance sensitivity.

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.

Figures (6)

• Figure 1: The coupling coefficient $\mathcal{R}_{22n\times22m}$ from different coupling channels as a function remnant spin, obtained by solving the reduced second-order Teukolsky equation through a hyperboloidal slicing Khera:2024bjs.
• Figure 2: Comparison of the $(4,4)$ multiple of the numerical relativity simulations SXS:BBH:3617 and various quadratic modes. The sum of 3, 6 and 10 quadratic QNM involves overtone couplings up to $(2,2,1)$, $(2,2,2)$ and $(2,2,3)$, respectively. In the inset plot, we show a fit using only the linear $(4,4,0)$ and $(4,4,1)$ modes, where the match achieves $89\%$. A fit by further adding the 6 quadratic modes would increase the match to $97\%$.
• Figure 3: Bayes factors comparing two ringdown models against a baseline that removes the $(4,4)$ mode. Starting at 5 $M_\mathrm{f}$, the full model including both linear and quadratic QNM is favored with a Bayes factor of 74 compared with the linear-only model.
• Figure 4: Whitened data and maximum-likelihood waveform model for the ringdown analysis starting at 5 $M_\mathrm{f}$ after the merger.
• Figure 5: Posterior distribution for the fractional deviation $\delta {A}$ of the quadratic mode amplitudes from the theoretical prediction. The dashline represents the 90% credible interval. A zero amplitude of quadratic modes is excluded with 3.0 $\sigma$. The theoretical expectation value consistent with the posterior at the 1% quantile.