Accuracy of ringdown models calibrated to numerical relativity simulations

TL;DR

This work systematically assesses the accuracy of NR-calibrated ringdown models (London, Cheung, TEOBPM) by computing time-domain mismatches with NR waveforms from the SXS catalog for non-precessing, quasi-circular binaries. The authors employ a time-domain mismatch formalism based on a PSD-derived autocovariance and derive starting-time criteria for each model, revealing that Cheung generally yields the smallest mismatches for many modes while TEOBPM performs best for the dominant $(2,2)$ at early times; higher-order harmonics remain challenging. Their results provide practical guidelines and an interpolation tool to select optimal ringdown starting times across parameter space, with direct implications for current LVK analyses and future detectors. The study also highlights the need to improve modeling of higher harmonics and mode mixing, and discusses extensions to precession and eccentricity to ensure robustness across broader binary configurations.

Abstract

The ''ringdown'' stage of gravitational-wave signals from binary black hole mergers, mainly consisting of a superposition of quasinormal modes emitted by the merger remnant, is a key tool to test fundamental physics and to probe black hole dynamics. However, ringdown models are known to be accurate only in the late-time, stationary regime. A key open problem in the field is to understand if these models are robust when extrapolated to earlier times, and if they can faithfully recover a larger portion of the signal. We address this question through a systematic time-domain calculation of the mismatch between non-precessing, quasi-circular ringdown models parameterised by the progenitor binary's degrees of freedom and full numerical relativity inspiral-merger-ringdown waveforms from the Simulating eXtreme Spacetimes (SXS) simulation catalog. For the best-performing models, the mismatch is typically in the range $[10^{-6}, 10^{-4}]$ for the $(\ell,|m|)= (2,2)$ harmonic, and $[10^{-4}, 10^{-2}]$ for higher-order modes. Our findings inform ongoing observational searches for quasinormal modes, and underscore the need for improved modeling of higher-order modes to meet the sensitivity requirements of future gravitational-wave detectors.

Figures (20)

• Figure 1: ACF as a function of time in the range $t=[0,~4]\,{\rm s}$, where $T$ is the observation time. The inset shows the truncated ACF in the time range $[t_{\rm s},t_{\rm e}]$, of length $N$.
• Figure 2: Mismatches between the NR waveforms and the London (blue), Cheung (red), and TEOBPM (green) models as a function of the starting time $t^{(2,2)}_{\rm peak}$, in units of the remnant mass. The left column refers to $(\ell,|m|)=(2,2)$, and the right column to $(\ell,|m|)=(3,3)$. In both cases, the origin of the starting time is taken to be the peak of the $(2,2)$ waveform, $t^{(2,2)}_{\rm peak}$. Different rows refer to representative non-spinning NR simulations with varying mass ratios. Dashed vertical black lines mark the time delay $\Delta t^{(\ell,|m|)}$ between the peak of the $(\ell,|m|)$ multipole and the peak of the $(2,2)$ multipole, as defined in Eq. \ref{['delay']}.
• Figure 3: Histograms of mismatches, computed with the simulation set $\mathcal{I}_{\rm tot - C}$, of the London (blue), the Cheung (red), and TEOBPM (green) models at different $(\ell,|m|)$, reported on the different rows. On the columns instead, moving from left to right, are reported the different starting times, defined with repspect to the given $(\ell,|m|)$ mode, from $0$ to $20$M, at steps of $5$M.
• Figure 4: Number of simulations $N_{\rm cross}$ that can cross a given mismatch threshold for different $(\ell,|m|)$ harmonics, computed at the minimum starting time at which the mismatch threshold is achieved.
• Figure 5: Histograms of the starting times $t_{\rm start, eq}^{(\ell,|m|)}$ such that the Cheung (red) and London (blue) model mismatches are equal to the TEOBPM model mismatches, as defined in Eq. \ref{['cross_t_start']}.