  Massive black hole binaries (BHBs) are expected to form as the result of
galaxy mergers; they shrink via dynamical friction and stellar scatterings,
until gravitational waves (GWs) bring them to the final coalescence. It has
been argued that BHBs may stall at a parsec scale and never enter the GW stage
if stars are not continuously supplied to the BHB loss cone. Here we perform
several N-body experiments to study the effect of an 80,000 solar masses
stellar cluster (SC) infalling on a parsec-scale BHB. We explore different
orbital elements for the SC and we perform runs both with and without
accounting for the influence of a rigid stellar cusp (modelled as a rigid
Dehnen potential). We find that the semi-major axis of the BHB shrinks by more
than 10 per cent if the SC is on a nearly radial orbit; the shrinking is more
efficient when a Dehnen potential is included and the orbital plane of the SC
coincides with that of the BHB. In contrast, if the SC orbit has non-zero
angular momentum, only a few stars enter the BHB loss cone and the resulting
BHB shrinking is negligible. Our results indicate that SC disruption might
significantly contribute to the shrinking of a parsec-scale BHB only if the SC
approaches the BHB on a nearly radial orbit.
