  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.
