  With better statistics and precision, eccentricity could prove to be a useful
tool for understanding the origin and environment of binary black holes.
Hierarchical triples in particular, which might be abundant in globular
clusters and galactic nuclei, could generate observably large eccentricity at
LIGO and future gravitational wave detectors. Measuring the eccentricity
distribution accurately could help us probe the background and the formation of
the mergers. In this paper we continue our previous investigation and improve
our semi-analytical description of the eccentricity distribution of mergers
hierarchical triple systems. Our result, which further reduces the reliance on
numerical simulations, could be useful for statistically distinguishing
different formation channels of observed binary mergers.
