Space-based Gravitational Wave Observatories Will Be Able to Use Eccentricity to Unveil Stellar-mass Binary Black Hole Formation

The measurement of eccentricity would provide strong constraints on the formation channel of stellar-mass binary black holes. However, current ground-based gravitational wave detectors will, in most cases, not be able to measure eccentricity due to orbital circularization. Space-based observatories, in contrast, can determine binary eccentricity at 0.01Hz to $e_{0.01}\gtrsim\mathcal{O}(10^{-4}) $. Directly observing stellar-mass binary black holes with space-based observatories remains a challenging problem. However, observing such systems with ground-based detectors allows the possibility to identify the same signal in archival data from space-based observatories in the years previous. Since ground-based detectors provide little constraints on eccentricity, including eccentricity in the archival search will increase the required number of filter waveforms for the archival search by 5 orders of magnitudes [from $\sim \mathcal{O}(10^3)$ to $\sim \mathcal{O}(10^8)$], and will correspondingly need $ \sim8\times10^5 $ core hours (and $ \sim 10^5$ GB of memory), even for a mild upper limit on eccentricity of $0.1$. In this work, we have constructed the first template bank for an archival search of space-based gravitational wave detectors, including eccentricity. We have demonstrated that even though the inclusion of eccentricity brings extra computational burden, an archival search including eccentricity will be feasible in the time frame of planned space-based observatories, and will provide strong constraints on the eccentricities of stellar-mass binary black holes.