Formation and Evolution of Compact Binaries Containing Intermediate Mass Black Holes in Dense Star Clusters`

Abstract: We investigate the evolution of star clusters containing intermediate-mass black hole (IMBH) of $300$ to $5000\ \mathrm{M}\odot$, focusing on the formation and evolution of IMBH-stellar mass black holes (SBHs; $M{\rm BH} \lesssim 10^2\ \mathrm{M}_\odot$) binaries. Dense stellar systems like globular clusters (GCs) or nuclear star clusters offer unique laboratories for studying the existence and impact of IMBHs. IMBHs residing in GCs have been under speculation for decades, with their broad astrophysical implications for the cluster's dynamical evolution, stellar population, GW signatures, among others. While existing GW observatories such as the Advanced Laser Interferometer Gravitational-wave Observatory (aLIGO) target binaries with relatively modest mass ratios, $q \lesssim 10$, future observatories such as the Einstein Telescope (ET) and the Laser Interferometer Space Antenna (LISA) will detect intermediate-mass ratio inspirals (IMRIs) with $q > 10$. This work explores the potential for detecting IMRIs adopting these upcoming telescopes. For our experiments, we perform multiple direct $N$-body simulations with IMBHs utilizing Nbody6++GPU, after implementing the GW merger schemes for IMBHs. We then study the statistical properties of the resulting IMRIs, such as the event rates and orbital properties. Assuming that IMRIs with a signal-to-noise ratio $S/N > 8$ are detectable, we derive the following detection rates for each observatory: $\lesssim 0.02\mathrm{yr}^{-1}$ for aLIGO, $\sim 101 - 355 \mathrm{yr}^{-1}$ for ET, $\sim 186 - 200 \mathrm{yr}^{-1}$ for LISA, $\sim 0.24 - 0.34 \mathrm{yr}^{-1}$ for aSOGRO, and $\sim 3880 - 4890 \mathrm{yr}^{-1}$ for DECIGO. Our result confirms the capability of detecting IMRIs with future GW telescopes.