eLISA eccentricity measurements as tracers of binary black hole formation

Up to hundreds of black hole binaries individually resolvable by eLISA will coalesce in the Advanced LIGO and Virgo band within 10 yr, allowing for multiband gravitational wave observations. Binaries formed via dynamical interactions in dense star clusters are expected to have eccentricities e(0) similar to 10(-3) - 10(-1) at the frequencies f(0) = 10(-2) Hz where eLISA is most sensitive, while binaries formed in the field should have negligible eccentricity in both frequency bands. We estimate that eLISA should always be able to detect a nonzero e(0) whenever e(0) greater than or similar to 10(-2); if e(0) similar to 10(-3), eLISA should detect nonzero eccentricity for a fraction similar to 90% (similar to 25%) of binaries when the observation time is T-obs = 5 (2) yr, respectively. Therefore eLISA observations of black hole binaries have the potential to distinguish between field and cluster formation scenarios.