eLISA eccentricity measurements as tracers of binary black hole formation

TL;DR

eLISA can measure the eccentricities of black hole binaries, enabling differentiation between their formation in dense star clusters or in the field based on observed eccentricity levels.

Contribution

This study estimates eLISA's capability to detect nonzero eccentricities in black hole binaries, providing a method to identify their formation channels.

Findings

eLISA can detect eccentricities > 10^{-2} in most cases.

Detection probability depends on observation time and eccentricity magnitude.

Eccentricity measurements can distinguish formation scenarios.

Abstract

Up to hundreds of black hole binaries individually resolvable by eLISA will coalesce in the Advanced LIGO/Virgo band within ten years, allowing for multi-band gravitational wave observations. Binaries formed via dynamical interactions in dense star clusters are expected to have eccentricities $e_0\sim 10^{-3}$-$10^{-1}$ 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 $e_0\gtrsim 10^{-2}$; if $e_0\sim 10^{-3}$, eLISA should detect nonzero eccentricity for a fraction $\sim 90\%$ ($\sim 25\%$) of binaries when the observation time is $T_{\rm obs}=5$ ($2$) years, respectively. Therefore eLISA observations of BH binaries have the potential to distinguish between field and cluster formation scenarios.