  We present the first systematic study on how distant weak interactions impact
the dynamical evolution of merging binary black holes (BBHs) in dense stellar
clusters. Recent studies indicate that dense clusters are likely to
significantly contribute to the rate of merging BBHs observable through
gravitational waves (GWs), and that many of these mergers will appear with
notable eccentricities measurable in the LISA and LIGO sensitivity bands. This
is highly interesting, as eccentricity can be used to distinguish between
different astrophysical merger channels. However, all of these recent studies
are based on various Monte Carlo (MC) techniques that only include strong
interactions for the dynamical evolution of BBHs, whereas any binary generally
undergoes orders-of-magnitude more weak interactions than strong. It is well
known that weak interactions primarily lead to a change in the binary's
eccentricity, which for BBHs implies that weak interactions can change their GW
inspiral time and thereby their merger probability. With this motivation, we
perform MC simulations of BBHs evolving in dense clusters under the influence
of both weak and strong interactions. We find that including weak interactions
leads to a notable increase in the number of BBHs that merge inside their
cluster, which correspondingly leads to a higher number of eccentric LISA
sources. These preliminary results illustrate the importance of including weak
interactions for accurately modeling how BBHs merge in clusters, and how to
link their emitted GW signals to their astrophysical environment.
