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

TL;DR

This work investigates multiband gravitational-wave observations of eccentric stellar-mass BBHs that escape globular clusters, building a realistic cosmic population by combining MOCCA GC simulations (268 models) with a GC formation-rate history. By computing signal-to-noise ratios across low-, middle-, and joint-frequency detectors and employing an eccentric waveform within a Fisher-matrix framework, the study quantifies detectability and parameter-estimation precision for networks such as LISA, Taiji, LT, AMIGO, and their combinations. It finds that LT-AMIGO offers the largest multiband detections (around $24.8$ over 4 years) and that initial eccentricities can be measured with relative precision as tight as $10^{-6}$–$2 imes10^{-4}$ in LT or LT-AMIGO, while AMIGO alone yields broader constraints; eccentricity information is mainly carried by the low-frequency band. The results highlight the potential of multiband GW observations to illuminate GC-origin sBBHs and differentiate formation channels, but they rely on MOCCA-based dynamics, specific BH-population prescriptions, and idealized Fisher-matrix forecasts, underscoring the need for more comprehensive models and Bayesian analyses in future work.

Abstract

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.

Figures (10)

• Figure 1: Top: Distribution of all MOCCA GC models analyzed in this work, shown in the plane of initial cluster mass versus half-mass radius. Symbol shape shows model type: single population (circle), two populations without time delay (square), and two populations with time delay (triangle). The color of each symbol represents the initial core density (see color bar), while the edge color denotes metallicity. Point size scales with the initial binary fraction, from 7% (smallest) to 95% (largest). Bottom: Core-to-half-mass radius versus cluster mass at 12 Gyr for the 165 MOCCA models that survived to this age; clusters that disrupted earlier are not shown. For comparison, black diamonds indicate observed Milky Way GCs from the Baumgardt2018 catalogue.
• Figure 2: Orbital frequency ($\mathbf{f_{orb}}$) and eccentricity ($\mathbf{e}$) distribution of sBBHs escaping from GC models. Colors indicate the chirp masses of the sBBHs. The top and right-side panels show the distributions of eccentricity and orbital frequency, respectively.
• Figure 3: Distribution of escape timescale ($t_{\rm esc}$: the time from GC formation to sBBH ejection) and merger timescale ($t_{\rm merger}$: the time from escape to sBBH merger) for the sBBHs shown in Figure \ref{['fig:f1']}. The top and right-side panels show the distributions of $t_{\rm merger}$ and $t_{\rm esc}$, respectively. The colors indicate the eccentricities of the sBBHs at escape.
• Figure 4: Merger rate density of escaping sBBHs originating from GCs.
• Figure 5: Parameter distributions of mock escaping sBBHs merging within $500$ years in the millihertz and decihertz bands. The left panel shows the initial eccentricities and orbital frequencies at the time of ejection from their host GC. The right panel shows intrinsic chirp mass ($M_{\rm c}$) and redshift for the sBBHs. Colors indicate the number of sources. The black solid line in the upper part of the right panel shows the observed chirp mass distribution of sBBHs from LVK constraints.