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 e₀10^-3-10^-1 at the frequencies f₀=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 e₀ whenever e₀10^-2; if e₀10^-3, eLISA should detect nonzero eccentricity for a fraction 90% (25%) of binaries when the observation time is T₎₁ₒ=5 (2) yr, respectively. Therefore eLISA observations of black hole binaries have the potential to distinguish between field and cluster formation scenarios.