Measuring Eccentricity and Addressing Waveform Systematics in GW231123

Abstract

The gravitational-wave event GW231123_135430 is the heaviest binary black hole system observed by the LIGO--Virgo--KAGRA Collaboration to date, with the initial analysis indicating the individual black hole masses lie within or above the theorized pair-instability mass gap of roughly $60$--$130\,M_\odot$. The inference further suggests that both black holes possess high spins, measured to be $0.90^{+0.10}_{-0.19}$ and $0.80^{+0.20}_{-0.51}$. Therefore, the observation of this event suggests the formation of black holes from channels beyond the standard stellar collapse. However, different waveform models yield significantly different parameter estimates, possibly due to missing physics in the models used in inference. In this work, we carry out a reanalysis of GW231123 using a physically complete model, accounting for both spin precession and eccentricity. Our analysis shows that this event does not exhibit strong evidence for eccentricity and the exclusion of eccentricity has minimal impact on inference. Furthermore, for GW231123-like systems, even eccentricities as large as $0.15$ at $10$ Hz do not yield a confident nonzero eccentricity measurement. Through a zero-noise injection recovery study, we show that the observed discrepancies in the parameter estimates can be explained by disagreement in the waveform models at strong spin precession, with the degree of parameter bias in the zero-noise runs being comparable to that observed for the real signal. We also show that inference performed with an eccentric, aligned-spin waveform model can yield a confident nonzero eccentricity measurement due to the degeneracy between eccentricity and spin precession. Bayesian model selection, however, rules out this interpretation in favor of the eccentric, spin precessing hypothesis, which supports zero eccentricity -- a conclusion we confirm with additional zero-noise injection-recovery tests.

Figures (4)

• Figure 1: GW231123 results: One- and two-dimensional marginal posterior distributions for the detector-frame component masses (left), the total mass and mass ratio (middle), and the spin magnitudes (right) obtained using the three waveform models (TEOB, NRSur, SEOB). Each contour shows the $90\%$ credible intervals for the joint two-dimensional marginal posterior distribution. TEOBResumS-Dalı́ is used to analyze this event under two hypotheses: eccentric, spin precessing (TEOB) and quasicircular, spin precessing (TEOB-P).
• Figure 2: Eccentricity posterior distributions for GW231123 and GW231123-like synthetic injections (Part I: measuring eccentricity): One-dimensional marginal posterior distribution for $e_{10}$ obtained by analyzing GW231123 with TEOB. For comparison, we also show posteriors for zero-noise injections at the TEOB maximum-likelihood parameters with three different injected eccentricities. Only the injection with $e_{10}=0.15$ yields a posterior whose $90\%$ highest-density interval excludes zero and displays a distinct peak away from zero. The dashed vertical lines represent the $90\%$ high-density intervals.
• Figure 3: Impact of systematics due to strong spin precession for GW231123-like signals: One- and two-dimensional marginal posterior distributions for the detector-frame component masses (left), the total mass and mass ratio (middle), and the spin magnitudes (right) obtained using the three waveform models (TEOB, NRSur, SEOB). This figure shows that the impact of waveform systematics at the strong spin precession regime is substantial and demonstrates that the waveform models disagree in the high-likelihood region relevant for GW231123. Each contour shows the $90\%$ credible intervals for the joint two-dimensional marginal posterior distribution. The dashed lines and the stars denote the injected values.
• Figure 4: Eccentricity posterior distributions for GW231123 and GW231123-like synthetic injection (Part II: exploring the eccentricity spin precession degeneracy): One-dimensional marginal posterior distribution for $e_{10}$ obtained by analyzing GW231123 with TEOB-E. For comparison, we also show the posterior for a zero-noise injection at the TEOB maximum-likelihood point, with $e_{10}=0.0,~\chi_\text{p}=0.77$. Also shown is the posterior obtained by analyzing the event with TEOB using an extended $e_{10}$ range of $0.0-0.7$. For the zero-noise injection, the analysis with TEOB-E yields a confident, but incorrect, nonzero eccentricity measurement, demonstrating the degeneracy between eccentricity and spin precession. The dashed vertical lines indicate the $90\%$ highest-density intervals.