Multiband gravitational wave observations of eccentric escaping binary black holes from globular clusters

Stellar-mass binary black holes (sBBHs) formed in globular clusters (GCs) are promising sources for multiband gravitational wave (GW) observations, particularly with low- and middle-frequency detectors. These sBBHs can retain detectable eccentricities when they enter the sensitivity bands of low-frequency GW observatories. We study multiband GW observations of eccentric sBBHs that escape from GC models simulated with the MOCCA code, focusing on how low- and middle-frequency detectors can constrain their eccentricities and other parameters. Using Monte Carlo simulations, we generate ten realizations of cosmic sBBHs by combining the MOCCA sample with a cosmological model for GC formation and evolution. We then assess their detectability and the precision of parameter estimation. Our results show that LISA, Taiji, the LISA-Taiji network (LT), and AMIGO could detect $0.8\pm0.7$, $11.6\pm2.0$, $15.4\pm2.7$, and $7.9\pm1.3$ escaping sBBHs, respectively, over four years, while LT-AMIGO could detect $20.6\pm3.0$ multiband sBBHs in the same period. LT and AMIGO can measure initial eccentricities with relative errors of approximately $10^{-6}-2\times10^{-4}$ and $10^{-3}-0.7$, respectively. Joint LT-AMIGO observations have a similar ability to estimate eccentricities as LT alone.

💡 Research Summary

This paper investigates the prospects for multiband gravitational‑wave (GW) observations of eccentric stellar‑mass binary black holes (sBBHs) that have escaped from globular clusters (GCs). The authors use a large suite of 268 GC models simulated with the MOCCA (Monte Carlo Cluster) code, which spans a wide range of initial masses, radii, binary fractions, metallicities, and includes both single‑population and two‑population clusters. MOCCA follows long‑term two‑body relaxation and dynamical encounters via the FEWBODY few‑body integrator, but does not incorporate post‑Newtonian corrections; therefore, direct high‑eccentricity mergers occurring during resonant encounters are not captured, while the population of escaping BBHs is well represented.

From the MOCCA outputs the authors extract all BBHs that are ejected from their host clusters. They then embed these binaries into a cosmological model of GC formation and evolution (ΛCDM with H₀=67.9 km s⁻¹ Mpc⁻¹) to generate ten independent realizations of the cosmic sBBH population. Each realization provides a mock catalog of thousands of escaping BBHs with masses, orbital frequencies, and eccentricities at the moment they leave the cluster.

The detectability analysis focuses on low‑frequency space‑based detectors (LISA and Taiji) and a deci‑Hertz instrument (AMIGO). The authors compute signal‑to‑noise ratios (S/N) for each binary using the appropriate detector sensitivity curves, adopting S/N thresholds of 8 for LISA/Taiji and 10 for AMIGO. They also consider the LISA‑Taiji network (LT) and a joint LT‑AMIGO configuration. Over a four‑year observation period the expected numbers of detections are:

• LISA: 0.8 ± 0.7 binaries,
• Taiji: 11.6 ± 2.0 binaries,
• LT network: 15.4 ± 2.7 binaries,
• AMIGO: 7.9 ± 1.3 binaries,
• LT‑AMIGO combined: 20.6 ± 3.0 multiband detections.

Most of the detectable systems retain measurable eccentricities (e₀ ≈ 10⁻³–10⁻²) when they enter the milli‑Hertz band, making them ideal for probing dynamical formation channels. Parameter‑estimation accuracy is evaluated with the Fisher information matrix. The LT network alone can measure the initial eccentricity with relative uncertainties ranging from 10⁻⁶ to 2 × 10⁻⁴, while AMIGO alone yields uncertainties of 10⁻³ to 0.7. The joint LT‑AMIGO observation provides eccentricity constraints comparable to LT alone, because the low‑frequency data dominate the eccentricity measurement, whereas the deci‑Hertz data improve mass and distance estimates.

Key insights include: (i) escaping BBHs from GCs preserve detectable eccentricities at low frequencies, offering a clear signature of dynamical formation; (ii) multiband observations dramatically increase the number of observable events and tighten parameter constraints, especially for eccentricity; (iii) the combination of space‑based milli‑Hertz detectors with a deci‑Hertz instrument is especially powerful for building a statistically robust sample of dynamical BBHs. The study highlights the importance of detector network design for future GW astronomy and suggests that incorporating post‑Newtonian dynamics in future GC simulations would further refine predictions, particularly for in‑cluster high‑eccentricity mergers.