GW231123 ringdown: interpretation as multimodal Kerr signal

TL;DR

The paper analyzes GW231123 as a ringdown-dominated gravitational-wave signal and demonstrates that multimodal quasinormal mode (QNM) fits, particularly two-mode Kerr models, provide statistically preferred descriptions over single-mode fits across a broad range of start times. Remnant mass and spin estimates from these two-mode fits align with NRSur7dq4 when the modes are identified as the prograde fundamental $(\ell,m)=(2,2)$ and $(2,0)$, though alternative identifications such as $(2,2)$ and $(2,1)$ and three-mode fits including an overtone can offer better cross-time consistency and Kerr-spectrum agreement. Tests allowing deviations from Kerr show Kerr-consistent frequencies within roughly $\pm10\%$ at the $90\%$ credible level for suitable configurations, but potential systematic differences with NRSur7dq4 highlight the need for caution in interpreting GR tests and remnant properties. The results underscore the value of QNM-based analyses as complementary probes to inspiral-merger-ringdown (IMR) models, potentially revealing NRSur7dq4 systematics and guiding future population studies, with the data release providing extensive QNM posteriors for alternative fits. The study also finds that the $\ell,m,n=(2,2,1)$ overtone can improve cross-time consistency, and that the physically plausible 210 QNM may be a meaningful alternative to NRSur7dq4 in certain parameter regimes.

Abstract

GW231123 is a short-duration, low-frequency gravitational wave signal consistent with a binary black hole coalescence and dominated by the merger-ringdown regime due to the high mass of the source. We demonstrate that fits of this ringdown signal using two quasinormal modes are statistically preferred over single-mode fits, for a broad range of fit start times. We also find that two-mode fits give remnant mass and spin measurements consistent with those of the inspiral-merger-ringdown model NRSur7dq4, whereas one-mode fits struggle to do so. Agreement of our fits with those of NRSur7dq4 is achieved by labeling the two quasinormal modes as the ${(\ell,m)=(2,2)}$ and ${(2,0)}$ Kerr prograde fundamental modes. However, we find some indications that fits with the ${(2,1)}$ quasinormal mode instead of the ${(2,0)}$ mode may describe the data better, hinting at possible NRSur7dq4 error or other systematics. When fitting at early times near the estimated peak strain, we find that the inclusion of a third mode, an ${(\ell,m,n)=(2,2,1)}$ prograde overtone, improves consistency with fits at later times. Finally, we perform a test of general relativity by searching for deviations from the Kerr frequency spectrum. Setting issues of systematics aside, we validate the Kerr frequency and damping rate spectrum to within $\pm10\%$ at the 90$\%$ credible level using a fundamental mode fit, and we also report $\pm8\%$ constraints using a model with fundamental modes and an overtone fit at times near the peak strain. Understanding the systematic errors that may be affecting the most accurate analyses of GW231123 is crucial in the context of population and binary formation studies -- our ${(2,1)}$ mode fits return a significantly higher remnant mass and spin than all available inspiral-merger-ringdown models including NRSur7dq4, and this difference in parameter estimates may have astrophysical implications.

Figures (15)

• Figure 1: To quantify statistical goodness of fit, we use the Leave-One-Out Cross-Validation (LOO) LOO_PaperLOO_FAQ, which is approximately related to the chi-squared test as ${{\rm LOO}\approx-\frac{1}{2}\chi^2}$ plus a penalty term which depends on the leverage of individual data points. Following Ref. mclatchie2024efficient, LOO differences greater than 4 are very significant. We deem differences of 1 to be our minimum for noteworthy statistical significance. The error bars indicate differences between LOO of each less-favored model and the top model at a given fit time, and are computed with the compare method in the arviz package arviz_2019. Peak strain statistical timing uncertainty from NRSur7dq4 is $\pm 0.9~t_M$, shown as a grey band. Top: When fitting free damped sinusoids without Kerr frequency constraints, we find significant preference for two modes over one when the fits start as late as 14 $t_M$, and no preference for three modes over two. Bottom: LOO of plausible Kerr models which we found to have the best-constrained non-zero amplitudes. Again, we find significant preference for two modes over one. Within two-mode models, LOO differences in favor of the {220, 210} over the {220, 200} model have expectation values greater than 1 and statistical significance of at least $1\sigma$ as late as $8~t_M$. When fitting three-mode models with an overtone, there is little LOO improvement if fitting post-peak. However, the {220, 210, 221} model is strongly preferred before the peak strain time. This is at odds with the behavior of the free sinusoid models, which had no preference for three-mode fits. The results when replacing the 221 with the 211 or 201 are similar (not shown), although at certain pre-peak times (in particular $6~t_M$) the 221 is still significantly preferred.
• Figure 2: When simultaneously fitting two free damped sinusoids over a wide range of fit start times, the mode frequencies and damping rates remain broadly consistent with the parameters of ${\ell=2}$ fundamental QNMs implied by NRSur7dq4 remnant mass and spin measurements. The frequency and damping rate of modes are shown on the x and y axes respectively. Colors correspond to different fitted sinusoids, and transparency is related to the fit start time as shown in the colorbar. 90% credible contours shown for all posteriors. The NRSur7dq4 QNM distributions are inferred using the qnm package qnmpackage_Stein.
• Figure 3: Frequency and damping rate of single-mode Kerr fits, as well as their amplitudes. Top: See Fig. \ref{['fig:damped_sinusoid_fgamma']} caption for figure conventions. When fitting a single Kerr mode, consistency with NRSur7dq4 is not found until $22~t_M$, after the point at which single-mode fits are equivalent to multi-mode fits in terms of LOO, as shown in Fig. \ref{['fig:LOOfig']}. Bottom: QNM amplitudes. Errorbars on each scatterpoint indicate 68% and 95% highest density interval (HDI). We extrapolate the amplitude from the fit at 16 $t_M$ (as indicated by dashed line), the earliest time where single-mode fits are equivalent to multi-mode fits in terms of LOO, as shown in Fig. \ref{['fig:LOOfig']}. We show the $1\sigma$ uncertainty of the extrapolated exponential decay of the 220 QNM as a colored band. This extrapolation is only consistent with fit times after $16~t_M$. The amplitude of a single-mode Kerr fit is consistent with being non-zero at $2\sigma$ until $28~t_M$.
• Figure 4: The frequency and damping rate of fits with two fundamental Kerr modes. See Fig. \ref{['fig:damped_sinusoid_fgamma']} for figure conventions. Top: We find that {220, 200} fits are consistent with NRSur7dq4 and also self-consistent over time, starting from 4 $t_M$. We do not find another combination of well-measured fundamental QNMs consistent with NRSur7dq4. Bottom: The {220, 210} model is similarly self-consistent over time but not in agreement with NRSur7dq4.
• Figure 5: Frequency and damping rate of Kerr models with overtones. See Fig. \ref{['fig:damped_sinusoid_fgamma']} caption for figure conventions. Left: We find that {220, 200, 2$m$1} fits are consistent with NRSur7dq4 and also self-consistent over time, starting from 0 $t_M$. While the above figure shows only the three-mode model with the 221 as the included overtone, similarly consistent results are obtained with the 211 and 201 QNMS. Right: While {220, 210, 2$m$1} fits are inconsistent with NRSur7dq4, the added overtone makes this model self-consistent as early as at least $-8~t_M$ depending on which $m$ index overtone is added.