The role of Massive Black Holes in merging star clusters: dynamical evolution, stellar & compact object ejections and gravitational waves

Star clusters can interact and merge in galactic discs, halos, or centers. We present direct N-body simulations of binary mergers of star clusters with $M_{\star} = 2.7 \times 10^4 \: \mathrm{M_{\odot}}$ each, using the N-body code BIFROST with subsystem regularisation and post-Newtonian dynamics. We include 500 $\mathrm{M_{\odot}}$ massive black holes (MBHs) in the progenitors to investigate their impact on remnant evolution. The MBHs form hard binaries interacting with stars and stellar black holes (BHs). A few Myr after the cluster merger, this produces sizable populations of runaway stars ($\sim$800 with $v_{\mathrm{ej}} \gtrsim 50 \mathrm{kms^{-1}}$) and stellar BHs ($\sim$30) escaping within 100 Myr. The remnants lose $\sim30\%$ of their BH population and $\sim3\%$ of their stars, with $\sim$30 stars accelerated to high velocities $\gtrsim 300 \mathrm{kms^{-1}}$. Comparison simulations of isolated clusters with central hard MBH binaries and cluster mergers without MBHs show that the process is driven by MBH binaries, while those with a single 1000 $\mathrm{M_{\odot}}$ MBH in isolated or merging clusters produce fewer runaway stars at lower velocities. Low-eccentricity merger orbits yield rotating remnants ($v_{\mathrm{rot}} \sim 3 \mathrm{kms^{-1}}$) , but probing the presence of MBHs via kinematics alone remains challenging. We expect the binary MBHs to merge within a Hubble time, producing observable gravitational-wave (GW) events detectable by future GW detectors such as the Einstein Telescope and LISA. The results suggest that interactions with low-mass MBH binaries formed in merging star clusters are an important additional channel for producing runaway and high-velocity stars, free-floating stellar BHs and compact objects.