Formation and Evolution of Compact Binaries Containing Intermediate-mass Black Holes in Dense Star Clusters

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Abstract
We investigate the evolution of star clusters containing intermediate-mass black holes (IMBHs) of 300–5000 M ⊙, focusing on the formation and evolution of IMBH–stellar-mass black hole (MBH ≲ 102 M ⊙) binaries. Dense stellar systems like globular clusters (GCs) or nuclear star clusters offer unique laboratories for studying the existence and impacts 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, and gravitational-wave (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 ≲ 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 by 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 ​​> 8 are detectable, we derive the following detection rates for each observatory: ≲0.02 yr−1 for aLIGO, ∼101−355 yr−1 for ET, ∼186−200 yr−1 for LISA, ∼0.24−0.34 yr−1 for aSOGRO, and ∼3880−4890 yr−1 for DECIGO. Our result confirms the capability of detecting IMRIs with future GW telescopes.

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