$N-$body dynamics of Intermediate mass-ratio inspirals in globular clusters

Abstract: 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 order $2.5$. Our simulations show that the IMBH readily forms a binary with a BH companion. This binary is gradually hardened by transient 3-body or 4-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 one of the 12 cluster models we evolved for $\sim 100$ Myr. This cluster hosts a $100 M_\odot$ IMBH embedded in a population of 32 $10M_\odot$ BH and 32,000 $1M_\odot$ stars. At the end of the simulation, after $\sim 100$ Myr of evolution, the IMBH merges with a BH companion. The IMBH--BH binary inspiral starts in the eLISA frequency window ($\gtrsim 1\rm mHz$) when the binary reaches an eccentricity $1-e\simeq 10^{-3}$. After $\simeq 10^5$ years 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.