Recoiling Black Holes I. Burst of Observables

Abstract

We aim to investigate the tidal disruption and gravitational wave events shortly after a massive black hole binary merges in the galactic centre and whose remnant black hole is ejected from the galaxy. Using computational methods, black holes of mass $M_{\bullet}=10^{5}$ M$_\odot$ and $4\times10^{5}$ M$_\odot$ embedded in a nuclear star cluster are kicked at velocities of $v_k=300$ and $600$ km s$^{-1}$. Systems are integrated for $0.1$ Myr using a $4$th-order Hermite scheme. The kick instantaneously repopulates the loss cone, producing a strong burst of tidal disruption events and gravitational wave mergers. The anisotropy in the apsidal orientation of bound stars prolongs this burst phase. Rates increase for lower $v_k$, larger $M_{\bullet}$ and for steeper nuclear star cluster density profiles at moment of merger. Assuming binary black holes scour a Bahcall-Wolf density profile during coalescence, ejected remnants with mass between $10^{5}\leq M_{\bullet}$ [M$_\odot] \leq 4\times10^{5}$ generate observable offset events at a forecasted rate of $\dot{N}\lesssim290$ yr$^{-1}$ up to redshift $z=3$. If, at the moment of merger, the milliparsec scales of the nuclear star cluster are described by a shallow density profile ($\gamma=1$), this decreases to $\dot{N}\lesssim30$ yr$^{-1}$. The strong dependence on the initial density profile and recoil kick makes observables powerful probes of the nuclear star cluster post-massive black hole binary coalescence, and provides test for numerical relativity.