n-body dynamics of intermediate mass-ratio inspirals in star clusters

The intermediate mass-ratio inspiral of a stellar compact remnant into an intermediate-mass black hole (IMBH) can produce a gravitational wave (GW) signal that is potentially detectable by current ground-based GW detectors (e.g., Advanced LIGO) as well as by planned space-based interferometers (e.g., eLISA). Here, we present results from a direct integration of the post-Newtonian N-body equations of motion describing stellar clusters containing an IMBH and a population of stellar-mass black holes (BHs) and solar-mass stars. We take particular care to simulate the dynamics closest to the IMBH, including post-Newtonian effects up to an order of 2.5. Our simulations show that the IMBH readily forms a binary with a BH companion. This binary is gradually hardened by transient three-body or four-body encounters, leading to frequent substitutions of the BH companion, while the binary's eccentricity experiences large-amplitude oscillations due to the Lidov–Kozai resonance. We also demonstrate suppression of these resonances by the relativistic precession of the binary orbit. We find an intermediate mass-ratio inspiral in 1 of the 12 cluster models we evolved for ~100 Myr. This cluster hosts a $100{M}_{\odot }$ IMBH embedded in a population of 32 $10{M}_{\odot }$ BH and 32,000 $1{M}_{\odot }$ stars. At the end of the simulation, after ~100 Myr of evolution, the IMBH merges with a BH companion. The IMBH–BH binary inspiral starts in the eLISA frequency window ($\gtrsim 1\,\mathrm{mHz}$) when the binary reaches an eccentricity $1-e\simeq {10}^{-3}$. After $\simeq {10}^{5}$ yr the binary moves into the LIGO frequency band with a negligible eccentricity. We comment on the implications for GW searches, with a possible detection within the next decade.