Star cluster disruption by a massive black hole binary

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 8 × 104M⊙ 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 semimajor axis of the BHB shrinks by ≳ 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 few stars en...