Population Properties of Binary Black Holes with Eccentricity

The improved sensitivity of Gravitational-Wave detectors and the development of eccentric waveform models enable us to explore the growing catalog of gravitational-wave events with measurable eccentricity. This opens new opportunities to gain insight into the formation channels and evolutionary pathways of compact binary systems using eccentricity. However, most recent population analyses have been limited to quasi-circular binaries, primarily due to constraints in waveform modeling and sensitivity estimates. We are now entering an era where both of these limitations are being addressed, allowing for a more comprehensive investigation of eccentric binary populations. In this work, we perform the first population inference analysis that simultaneously fits the mass, spin, redshift, and eccentricity distribution. Specifically, we use source-parameter estimation provided by the Rapid Iterative FiTting (RIFT) framework using the SEOBNRv5EHM waveform model, and a default O4a population model extended to include eccentricity. We find population properties broadly consistent with conclusions obtained in previous analyses assuming quasi-circular binaries. Consistent with our conclusions about each event, we bound the branching ratio for eccentric events to be below $0.0239$ at $90%$ confidence with our fiducial eccentricity mixture models. Using four different parametric population models for eccentricity, we point out that the rate of eccentric events is weakly constrained by observations and highly model-dependent.

💡 Research Summary

This paper presents the first comprehensive population inference analysis of binary black hole (BBH) mergers that simultaneously fits the distributions of mass, spin, redshift, and orbital eccentricity using gravitational-wave (GW) observations. The advent of improved detector sensitivity and the development of accurate eccentric waveform models, like SEOBNRv5EHM, has opened a new window to probe the formation channels of compact binaries, as measurable eccentricity in the GW band is a potential signature of recent dynamical interactions.

The analysis focuses on 139 confident BBH events from the O3 and O4a observing runs. For each event, source parameter estimation was performed using the RIFT framework with the eccentric SEOBNRv5EHM waveform model. Subsequently, a hierarchical Bayesian analysis was conducted using the GWKokab inference engine to infer the underlying astrophysical population. The population model extended the default GWTC-4 model (Broken Power Law + 2 Peaks for mass, Power Law for redshift, Skew-Normal for effective spin) by incorporating four different parametric models to describe the distribution of orbital eccentricity (defined at a reference frequency of 10 Hz). A key simplifying assumption was that the detection probability is independent of eccentricity, based on earlier studies suggesting weak sensitivity dependence for BBHs at low eccentricities.

The primary findings are threefold. First, the overall population properties (mass, spin, redshift distributions) inferred when allowing for eccentricity are broadly consistent with those found in previous analyses that assumed quasi-circular orbits. This indicates that the inclusion of eccentricity does not drastically alter our understanding of the bulk BBH population. Second, and most significantly, the analysis places an upper limit on the fraction of detectable BBH mergers that possess significant eccentricity. Using fiducial mixture models, the branching ratio for eccentric events is constrained to be less than 0.0239 (2.39%) at 90% confidence. This low upper limit suggests that dynamical formation channels imparting significant eccentricity in the LIGO-Virgo band are not the dominant pathway for the observed BBH mergers. Third, the study highlights that the inferred rate or fraction of eccentric events is only weakly constrained by current observations and is highly dependent on the chosen parametric model for the eccentricity distribution. This model dependence underscores the need for more eccentric candidate events and more flexible population models in the future.

In conclusion, this work marks a pivotal step into the era of multi-dimensional GW population studies including orbital eccentricity. It demonstrates the methodology and provides initial constraints, while clearly outlining that future advancements—through more detections, improved waveform models, better understanding of selection effects for eccentric signals, and the use of non-parametric population models—will be crucial to precisely measure the eccentric population and robustly discriminate between different binary black hole formation channels.