Hierarchical Triples vs. Globular Clusters: Binary black hole merger eccentricity distributions compete and evolve with redshift

TL;DR

This work addresses how measurable BBH merger eccentricities reflect their formation environments and how these eccentricity distributions evolve with redshift, a key question for next-generation detectors. It contrasts two channels—globular clusters and wide-field hierarchical triples—using detailed population synthesis: GC dynamics via the Cluster Monte Carlo Catalog and triple evolution via secular evolution in TRES with non-secular AR-CHAIN integration, all mapped to redshift through metallicity- and SFR-dependent weighting. The main findings show that, while GC mergers dominate the overall BBH merger rate, hierarchical field triples dominate the population of detectable eccentric mergers up to $z\sim4$, with triples contributing at least about 30% of eccentric mergers across a broad redshift range; metallicity and delay-time distributions shape these trends and remain robust under model variations. Overall, eccentric GW mergers are not exclusive to dense environments; the distinct redshift evolution of eccentricity distributions offers a practical avenue to disentangle formation channels and to map GC formation and field triple demographics with future detectors.

Abstract

The formation mechanisms of merging binary black holes (BBHs) observed by the LIGO-Virgo-KAGRA collaboration remain uncertain. Detectable eccentricity provides a powerful diagnostic for distinguishing between different formation channels, but resolving their eccentricity distributions requires the detection of a large number of eccentric mergers. Future gravitational wave detectors such as the Einstein Telescope and Cosmic Explorer will detect tens of thousands of BBH mergers out to redshifts $z \ge 10$, making it critical to understand the redshift-dependent evolution of eccentricity distributions. We simulate this evolution for two key channels: dynamical assembly in globular clusters (GCs), which leads to rapid, eccentric mergers; and hierarchical triples in the field, where three-body dynamics can induce eccentricity in the inner binary. When considering all BBH mergers, the GC channel dominates overall, consistent with previous studies. However, when focusing on mergers with detectable eccentricity in next-generation detectors, we find that hierarchical triples dominate the eccentric merger rate at $0\le z \le 4$, with GC mergers becoming competitive at higher redshifts. Across all model variations, eccentric mergers in the local Universe ($z\lesssim 1$) have significant contributions from field triples, challenging the common view that such systems primarily form in dense environments. We show that, regardless of cluster and stellar evolution uncertainties, hierarchical triples contribute at least 30 per cent of eccentric mergers across a large range of redshifts.

Figures (9)

• Figure 1: The eccentricity distributions from GCs (top panel) and wide field triples (bottom panel) at three different metallicities, $Z$. In both cases we highlight the contributions from different sub-channels. For the GC channel, we distinguish the processes introduced in detail in Section \ref{['sec:GC_channel']}. For field triples, we distinguish sources that have experienced non-secular evolution, and systems in which purely secular processes led to the merger of the inner BBH. In all panels the grey histograms, showing the entire contribution from one channel, have been normalised to unity. The formation efficiency of GW sources relative to that at $Z=0.02$, $\epsilon_{\mathrm{GW}}$, is shown in each panel.
• Figure 2: The eccentricity distributions of BBH mergers from GCs (upper panel) and wide field triples (lower panel) at three different observed redshifts, $z_{\rm obs}$. We adopt three different definitions for eccentricity extracted at 10 Hz: $e^{\rm W03, src}_{\rm 10Hz}$ and $e^{\rm W03}_{\rm 10Hz}$, eccentricity based on the prescription of Wen2003, in the source frame and redshifted to the detector frame, respectively; and $e^{\rm 2PN}_{\rm 10Hz}$, detector-frame eccentricity based on the prescription of Vijaykumar2024. For each redshift $z_{\rm obs}$, we show the predicted merger rate density for the specific formation channel. We have normalised each histogram due to merger rate density at $z_{\rm obs}$.
• Figure 3: The cumulative eccentricity distribution from GCs (upper panels) and wide field triples (lower panel) at three different redshifts. We adopt three different definitions for eccentricity extracted at 10 Hz; see the caption of Fig. \ref{['fig:ft_ecc_z']} and Section \ref{['sec:detected_eccentricity']} for details. We show three different detectable eccentricity thresholds: $e^{\rm 2G}_{\rm det}$ = 0.05, the eccentricity threshold for 2G detectors, which is only shown for $z_{\rm obs} = 0$; $e^{\rm A\#}_{\rm det} = 10^{-3}$, our optimistic estimated eccentricity threshold for LIGO A$\#$; and finally $e^{\rm XG}_{\rm det} = 10^{-4}$, an optimistic estimate for XG detectors Lower:Eccentricity:2018.
• Figure 4: The total merger rate of BBHs from wide field triples (blue) and GCs (green) as a function of redshift for the three different model variations considered in this paper (see Table \ref{['tab:model_variations']}). This includes all mergers, not just those that are detectably eccentric.
• Figure 5: We highlight the robustness of our main results to uncertainties by showing the detectably-eccentric merger rates assuming thresholds of $e_{\rm10Hz}> 0.05$ (right panel), $e_{\rm10Hz}> 10^{-4}$ (left panel) and $e_{\rm10Hz}> 10^{-3}$ (middle panel) for different model variations: fiducial (upper panel), GCmax (middle panel), TRIPLEmax (lower panel). For each panel, we denote different eccentricity definitions with different linestyles: $e^{\rm W03, src}_{\rm 10Hz}$, source-frame eccentricity based on the prescription of Wen2003 (solid), $e^{\rm W03}_{\rm 10Hz}$, detector-frame eccentricity based on the prescription of Wen2003 (dashed, and $e^{\rm 2PN}_{\rm 10Hz}$, detector-frame eccentricity based on the prescription of Vijaykumar2024 (dotted).