Distinguishing the origin of eccentric black-hole mergers with gravitational-wave spin measurements

TL;DR

This paper tackles the question of how to identify the formation channel of eccentric binary black hole mergers using gravitational-wave spin measurements. It contrasts two spin-orientation scenarios—uncorrelated spins and mutual alignment with random orbital orientation—and forecasts the ability of current and future detectors to distinguish them via Bayes factors applied to $\chi_{\rm eff}$ distributions. The study finds that next-generation detectors (ET/CE) could distinguish the correct channel with high confidence for modest eccentric-merger fractions, while current LVK runs may require more detections. It also investigates the dynamical evolution of $\chi_{\rm eff}$ and spin tilts during eccentric inspirals, concluding that $\chi_{\rm eff}$ is approximately conserved and that tilt evolution preserves isotropy for uncorrelated spins but drives aligned spins to maintain mutual alignment in their tilts, with implications for spin-based formation-channel discrimination.

Abstract

It remains an open question whether the binary black hole mergers observed with gravitational-wave detectors originate from the evolution of isolated massive binary stars or were dynamically driven by perturbations from the environment. Recent evidence for non-zero orbital eccentricity in a handful of events is seen as support for a non-negligible fraction of the population experiencing external driving of the merger. However, it is unclear from which formation channel eccentric binary black-hole mergers would originate: dense star clusters, hierarchical field triples, active galactic nuclei, or wide binaries in the Galaxy could all be culprits. Here, we investigate whether the spin properties of eccentric mergers could be used to break this degeneracy. Using the fact that different formation channels are predicted to either produce eccentric mergers with mutually aligned or randomly oriented black-hole spins, we investigate how many confident detections would be needed in order for the two models to be statistically distinguishable. If a few percent of binary black hole mergers retain measurable eccentricity in the bandwidth of ground-based detectors, we report a $\sim40\,\%$ chance that we could confidently distinguish both models after the fifth observing run of the LIGO-Virgo-KAGRA detector network, $\sim80\,\%$ for LIGO A#, and $\sim98\,\%$ for the Einstein Telescope and Cosmic Explorer.

Figures (5)

• Figure 1: Left panel: Distribution of $\chi_{\rm eff}$ for mutually aligned spin directions (red) and random spin directions (teal). Dotted lines indicate equal-mass ($q=1$) and maximally spinning BBHs ($\chi_1=\chi_2=1$), solid lines assume an extended mass ratio distribution and a spin magnitude distribution that peaks at lower values, which are consistent with previous GW detections (see text). Black markers show three eccentric BBH merger candidates identified by 2024arXiv240414286G (from bottom to top: GW200129, GW190701, and GW200208_22) and orange markers show four candidates identified by 2022ApJ...940..171R (from bottom to top: GW200208_22, GW190521, GW190620, and GW191109). The commonly identified candidate GW200208_22 is highlighted by a filled marker Romero-Shaw2025. Right panel: Sketch of uncorrelated (top) and mutually aligned black-hole spins of eccentric mergers (bottom).
• Figure 2: Bayes factor distributions that compare the mutually aligned and uncorrelated model. The red histogram assumes GW detections of systems with mutually aligned spins and indicates the confidence for preferring the aligned model over the uncorrelated model. Conversely, the teal histogram assumes GW detections of systems with uncorrelated spins and indicates the confidence for preferring the uncorrelated spin model over the mutually aligned spin model. Thus, in either cases a large Bayes factor ($\log_{10}\mathcal{B}\gtrsim1/2$) indicates that we would correctly infer the spin properties of the underlying population. Solid and dashed vertical lines indicate the medians and 5th/95th percentiles of the distributions, respectively. We assume an eccentric BBH fraction of $\xi_{\rm ecc}=0.05$, a measurement uncertainty for $\chi_{\rm eff}$ of $\sigma_{\chi_{\rm eff}}=0.2$ for LVK O5 and A# and $\sigma_{\chi_{\rm eff}}=0.02$ for ET/CE, and vary between each panel the total number of detections between $2,100$ (LVK O5), $10^4$ (A#), and $10^5$ (ET/CE).
• Figure 3: Percentiles of the Bayes factor distributions as a function of the eccentric BBH fraction $\xi_{\rm ecc}$. We assume that $\chi_{\rm eff}$ will be measured with an uncertainty of $\sigma_{\chi_{\rm eff}}=0.2$ for LVK O5 and A# and $\sigma_{\chi_{\rm eff}}=0.02$ for ET/CE. As in Fig. \ref{['fig:2']}, solid and dashed lines indicate the median and 5th/95th percentiles, respectively. The vertical yellow dotted lines indicate the eccentric fraction of events identified by 2024arXiv240414286G (3 of 57 analysed events; "Gupte+") and by 2022ApJ...940..171R (4 of 62 analysed events; "RS+"), respectively.
• Figure 6: Distribution of the maximum difference $\max_{t>0}|\chi_{\rm eff}(t) - \chi_{\rm eff}(0)|$ of $\chi_{\rm eff}$ during the inspirals of our BBH sample with initially aligned spins and high eccentricity. The inset exemplifies the time evolution of $\chi_{\rm eff}$ of a typical system.
• Figure 7: Distribution of the cosine of spin tilt angles, $\cos\theta_1$ (left panels) and $\cos\theta_2$ (right panels). We assume spin tilts to be either mutually aligned (teal) or uncorrelated (maroon) at formation. Distributions at detection ($f_{\rm GW} = 10$ Hz) and BBH formation ($f_{\rm GW} = 0.95$ Hz) are shown as filled and dashed histogram, respectively. We assume either maximally spinning BH (top panels) or spin magnitudes extracted from a Beta distribution as in Fig. \ref{['fig:2']} (bottom panels).