Eccentricity as a Magnifying Glass: Precision Population Inference Enabled by Eccentric Neutron Star--Black Hole Mergers

Technical Summary: Eccentricity as a Magnifying Glass: Precision Population Inference Enabled by Eccentric Neutron Star–Black Hole Mergers

Problem Statement
The formation history of neutron star–black hole (NSBH) systems remains a central open question in astrophysics, specifically regarding whether these systems originate primarily from isolated binary evolution or dynamical interactions. While isolated evolution typically produces circular orbits, dynamical interactions can retain measurable orbital eccentricity. Recent analyses of the gravitational-wave (GW) event GW200105 suggest measurable eccentricity, implying alternative formation channels may exist. Furthermore, eccentricity modifies GW waveforms by introducing higher harmonics and altering time-frequency evolution, which can break parameter degeneracies and reduce uncertainties on intrinsic source parameters (e.g., masses and spins). The paper investigates how these "eccentricity-enhanced" parameter measurements propagate to population-level inference, potentially revealing formation histories that are obscured in quasi-circular analyses.

Methodology
The authors construct simulated NSBH populations to test the impact of eccentricity on population inference under the assumptions of the fifth LIGO–Virgo–KAGRA (LVK) observing run (O5).

• Population Simulation: They simulate a population of dynamically assembled binaries where black hole (BH) spin tilts are isotropically distributed and neutron star (NS) spins are negligible. Component masses are drawn from specific distributions: a fiducial "Double-peaked" NS mass model (motivated by Galactic observations) and an intermediate-metallicity BH mass model ($Z_2$). The true eccentricities are drawn from a fiducial distribution scaling as $p(\log e) \propto e^{-12/19}$ over the interval $0.1 \le e \le 0.9$.
• Detection and Parameter Estimation (PE): Systems are selected based on a signal-to-noise ratio (SNR) threshold of 8, assuming A+ design sensitivity. To model the benefits of eccentricity, the authors do not simulate full waveform injections for every event but instead apply a scaling factor to the measurement uncertainties. Motivated by previous work (Tibrewal et al. 2026), they assume eccentric systems ($e \sim 0.1\text{--}0.25$) yield a factor of 10 reduction in uncertainties for the symmetric mass ratio ($\eta$) and effective spin ($\chi_{\text{eff}}$) compared to quasi-circular binaries.
• Hierarchical Bayesian Analysis: The authors generate synthetic posterior samples for luminosity distance, component masses, $\chi_{\text{eff}}$, and eccentricity. They then perform hierarchical Bayesian inference using the dynesty nested sampling algorithm to compare different population models. They calculate Bayesian evidences and Bayes factors to quantify the support for complex models (e.g., Double-peaked NS mass, specific metallicity distributions) over simpler alternatives.

Key Contributions and Results
The study quantifies how improved parameter precision from eccentric mergers enhances four specific areas of population inference:

1. Identification of Spin–Orbit Misalignment:
   Negative values of the effective spin parameter ($\chi_{\text{eff}}$) are a signature of spin–orbit misalignment, consistent with dynamical assembly. The authors find that with reduced uncertainties in the Eccentric scenario, the fraction of systems where $\chi_{\text{eff}} < -2\sigma_{\chi_{\text{eff}}}$ (providing clear evidence of misalignment) increases from $\sim 22\%$ (Circular) to $\sim 43\%$ (Eccentric). This implies that for an isotropically distributed population, a spin–orbit misaligned event could be confidently identified every $\sim 2.5$ eccentric NSBH detections.

2. Resolving Neutron Star Mass Structure:
   The authors compare the fiducial Double-peaked NS mass model against a simpler Uniform model. In the Circular scenario, even with 30 detections, the Uniform model is not significantly disfavored due to large mass uncertainties obscuring the underlying structure. In the Eccentric scenario, the Bayes factor favoring the Double-peaked model increases significantly with the number of detections. With 30 detections, the support for the Double-peaked model is stronger by a factor of $\sim 7.5$ compared to the Circular case. Additionally, constraints on the minimum ($m_{\text{min}}^{\text{NS}}$) and maximum ($m_{\text{max}}^{\text{NS}}$) NS masses tighten by factors of $\sim 2$ and $\sim 2.5$, respectively.

3. Distinguishing BH Progenitor Metallicity:
   The study tests the ability to distinguish between BH mass distributions arising from different progenitor metallicities ($Z_1$, $Z_2$, $Z_3$). Using the intermediate-metallicity model ($Z_2$) as the ground truth, the Eccentric scenario provides systematically stronger support for the correct model. For the comparison between $Z_2$ and the high-metallicity model ($Z_3$), the Bayes factor in favor of $Z_2$ increases by up to a factor of $\sim 10^{14}$ at 30 detections compared to the Circular scenario. The improvement is more modest ($\sim 4\times$) for the $Z_2$ vs. $Z_1$ comparison, reflecting the greater similarity between those mass distributions.

4. Recovering the Eccentricity Distribution:
   The authors investigate the recovery of the proposed universal eccentricity distribution slope ($a = -12/19$) for dynamical channels. Using hierarchical inference on the slope parameter $a$, they demonstrate that both the accuracy and precision of the inferred posterior improve as the number of detections increases, converging toward the injected value.

Significance and Claims
The paper claims that eccentric NSBH mergers act as a "magnifying glass" for population studies. By simultaneously tracing non-isolated formation (via eccentricity) and sharpening measurements of intrinsic parameters, these events offer unique insights into compact binary origins.

• Observational Reach: The authors estimate that an O5 run could yield $\sim 10$ eccentric NSBH detections. They argue this sample size is sufficient to begin testing formation scenarios, such as identifying spin–orbit misalignment and distinguishing NS mass distribution structures.
• Population Constraints: The results suggest that eccentricity-enhanced measurements can tighten constraints on NS nuclear matter properties (via $m_{\text{max}}^{\text{NS}}$) and provide robust probes of stellar evolution processes related to BH progenitor metallicity.
• Validation of Models: The study demonstrates that the proposed population-level eccentricity distribution for dynamical channels can be tested and potentially verified by the end of the O5 run.

The authors maintain a modest tone, noting that while eccentricity measurements can be sensitive to waveform and prior assumptions, a sample of confidently identified eccentric systems provides a valuable opportunity to test formation-related population properties. They emphasize that the constraining power improves progressively with the number of detections, with larger catalogs yielding progressively sharper constraints than the $\sim 10$ detection baseline.