Ringdown Analysis of GW250114 with Orthonormal Modes

Abstract

GW250114 is the loudest gravitational-wave event to date observed by the LIGO-Virgo-KAGRA Collaboration. Owing to its high signal-to-noise ratio (SNR), previous analyses based on quasinormal mode (QNM) superpositions have suggested evidence of the fundamental and the first overtone of the $\ell=m=2$ mode in this event. However, QNMs are not orthogonal and the inclusion of multiple QNMs induces correlations among them, which can hinder the robust identification of subdominant QNMs. To address this challenge, we apply an analysis based on orthonormalized QNMs [arXiv:2507.12376] to GW250114. We find that, in the model including three $\ell=m=2$ QNMs up to the second overtone, the first overtone of the $\ell=m=2$ mode is more strongly supported than in previous nonorthogonal analyses, with the inferred significance increasing from $82.5\%$ to $99.9\%$. Furthermore, we estimate deviations from the Kerr prediction using the orthonormal QNM framework and find no significant deviation, consistent with previous analyses. These results demonstrate that the orthonormal QNM framework provides a more robust way to identify subdominant modes in high-SNR ringdown signals, highlighting its potential for future gravitational-wave observations.

Figures (6)

• Figure 1: Posterior distributions of the amplitudes of the 220 and 221 modes for the 220+221 (blue) and 220+221+222 (orange) models, evaluated for different analysis start times $\Delta t$. The left (right) panel shows the results from ringdown (the semianalytic method). The circles, thick vertical lines, and thin vertical lines represent the medians, 50%, and 90% credible intervals, respectively. The gray lines and shaded regions represent the means, 50%, and 90% credible intervals of the amplitudes predicted from the posterior of the 220+221 model at $\Delta t=6\,t_{M_f}$ (vertical dotted line), assuming exponential decay with the QNM damping time. Note that, in the orthonormal analysis (right panel), the basis functions no longer correspond to simple exponentially damped sinusoids. As a result, the amplitudes constructed from their coefficients (see Eq. \ref{['eq:orthonormal_amplitude']}) exhibit oscillatory behavior. The hatched regions indicate exclusion at the $3\sigma$ (top panel) and $2\sigma$ (bottom panel) credible levels.
• Figure 2: Posterior distributions for the remnant BH's mass, spin, and mode amplitudes for the 220+221 (blue) and 220+221+222 (orange) models, evaluated at $\Delta t=6\,t_{M_f}$. The left (right) panel shows the results from the nonorthogonal (orthonormal) analysis. Contours indicate the $1\sigma$ (39.3%), $2\sigma$ (86.5%), and $3\sigma$ (98.9%) credible regions. Black contours show the 90% credible regions obtained from the IMR analysis using NRSur7dq4Varma:2019csw, with black lines indicating their mean values ($M_f=68.1\,M_{\odot}$, $\chi_f=0.68$).
• Figure 3: OVL between the posterior distributions of QNM amplitudes obtained from the 220+221+222 model and those predicted from the 220+221 fit at $\Delta t=6\,t_{M_f}$ (black dash-dotted line). Circles and squares denote the OVL obtained from the orthonormal and nonorthogonal analyses, respectively. Green and red markers correspond to the $(2,2,0)$ and $(2,2,1)$ modes, respectively. The darker markers correspond to the time points after the reference time $6\,t_{M_f}$ at which the 220+221 model in the orthonormal analysis indicates the presence of the $(2,2,0)$ and $(2,2,1)$ modes at the $3\sigma$ and $2\sigma$ levels, respectively.
• Figure 4: Posterior distributions of the deviation parameters $\delta f_{221}$ and $\delta\gamma_{221}$ obtained from the orthonormal analysis (light blue) and the nonorthogonal analysis (purple). The black dotted lines indicate the Kerr prediction, $\delta f_{221}=\delta\gamma_{221}=0$. The remnant mass $M_f$ and spin $\chi_f$ are marginalized over.
• Figure 5: Posterior distributions for the remnant BH's mass, spin, and mode amplitudes for the 220+221 signal. Blue (orange) distributions correspond to the 220+221 (220+221+222) model. The left (right) panel shows the results from the nonorthogonal (orthonormal) analysis. Contours indicate the $1\sigma$ (39.3%), $2\sigma$ (86.5%), and $3\sigma$ (98.9%) credible regions. Black lines indicate the injected values.