Distinguishing Between Formation Channels for Binary Black Holes with LISA

The recent detections of GW150914 and GW151226 imply an abundance of stellar-mass binary-black-hole mergers in the local universe. While ground-based gravitational-wave detectors are limited to observing the final moments before a binary merges, space-based detectors, such as the Laser Interferometer Space Antenna (LISA), can observe binaries at lower orbital frequencies where such systems may still encode information about their formation histories. In particular, the orbital eccentricity and mass of binary black holes in the LISA frequency band can be used together to discriminate between binaries formed in isolation in galactic fields and those formed in dense stellar environments such as globular clusters. In this letter, we explore the orbital eccentricity and mass of binary-black-hole populations as they evolve through the LISA frequency band. Overall we find that there are two distinct populations discernible by LISA. We show that up to ~90% of binaries formed either dynamically or in isolation have eccentricities measurable by LISA. Finally, we note how measured eccentricities of low-mass binary black holes evolved in isolation could provide detailed constraints on the physics of black-hole natal kicks and common-envelope evolution.