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Repeated mergers of stellar-mass black holes (BHs) in dense star clusters canproduce intermediate-mass black holes (IMBHs). In particular, nuclear starclusters at the centers of galaxies have deep enough potential wells to retainmost of the BH merger products, in spite of the significant recoil kicks due toanisotropic emission of gravitational radiation. These events can be detectedin gravitational waves (GWs), which represent an unprecedented opportunity toreveal IMBHs. In this paper, we analyze the statistical results of a wide rangeof numerical simulations, which encompass different cluster metallicities,initial BH seed masses, and initial BH spins, and we compute the merger rate ofIMBH binaries. We find that merger rates are in the range$0.01$-$10$\,Gpc$^{-3}$\,yr$^{-1}$ depending on IMBH masses. We also computethe number of multi-band detections in ground-based and space-basedobservatories. Our model predicts that a few merger events per year should bedetectable with LISA, DECIGO, ET, and LIGO for IMBHs with masses $\lesssim1000\msun$, and a few tens of merger events per year with DECIGO, ET, and LIGOonly.

Merger rates of intermediate-mass black hole binaries in nuclear star clusters