  Orbital eccentricity is one of the most robust discriminators for
distinguishing between dynamical and isolated formation scenarios of binary
black hole mergers using gravitational-wave observatories such as LIGO and
Virgo. Using state-of-the-art cluster models, we show how selection effects
impact the detectable distribution of eccentric mergers from clusters. We show
that the observation (or lack thereof) of eccentric binary black hole mergers
can significantly constrain the fraction of detectable systems that originate
from dynamical environments, such as dense star clusters. After roughly 150
observations, observing no eccentric binary signals would indicate that
clusters cannot make up the majority of the merging binary black hole
population in the local universe (95% credibility). However, if dense star
clusters dominate the rate of eccentric mergers and a single system is
confirmed to be measurably eccentric in the first and second gravitational-wave
transient catalogs, clusters must account for at least 14% of detectable binary
black hole mergers. The constraints on the fraction of detectable systems from
dense star clusters become significantly tighter as the number of eccentric
observations grows and will be constrained to within 0.5 dex once 10 eccentric
binary black holes are observed.
