Black Hole Mergers From Globular Clusters Observable by LISA II: Resolved Eccentric Sources and the Gravitational Wave Background

In paper I of this series we showed that a large percentage of the binary black hole (BBH) mergers that form through dynamical interactions in globular clusters will have significant eccentricity in the ~10^{-3}-10^{-1} Hz LISA band. In this work we quantify the evolution of these highly eccentric binaries through the LISA and LIGO bands, and compute the stochastic gravitational wave background from the merging, eccentric population. We find that the population of BBHs that merge in-between three-body encounters inside their cluster (~50% of all cluster-formed BBH mergers) will have measurable eccentricity for their entire lifetime in the LISA band. The population of BBHs that merge during three-body encounters (~5% of all cluster-formed BBH mergers), will be detectable by LIGO with eccentricities of e~0.1. The gravitational wave background from dynamically assembled BBHs encodes a characteristic bump due to the high initial eccentricities of these systems. The location and amplitude of this bump depends on globular cluster properties.