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.