  Supermassive black hole binaries (BHBs) are expected to be one of the most
powerful sources of low-frequency gravitational waves (GWs) for future
space-borne detectors. Prior to the GW emission stage, BHBs evolving in
gas-poor nuclei shrink primarily through the slingshot ejection of stars
approaching the BHB from sufficiently close distances. Here we address the
possibility that the BHB shrinking rate is enhanced through the infall of a
star cluster (SC) onto the BHB. We present the results of direct summation
N-body simulations exploring different orbits for the SC infall, and we show
that SCs reaching the BHB on non-zero angular momentum orbits (with
eccentricity 0.75) fail to enhance the BHB hardening, while SCs approaching the
BHB on radial orbits reduce the BHB separation by ~10% in less than 10 Myr,
effectively shortening the BHB path towards GWs.
