Mergers of supermassive and intermediate-mass black holes in galactic nuclei from disruptions of star clusters

Abstract

Gravitational waves (GWs) offer an unprecedented opportunity to survey the sky and detect mergers of compact objects. While intermediate-mass black holes (IMBHs) have not been detected beyond any reasonable doubt with either dynamical or accretion signatures, the GW landscape appears very promising. Mergers of an IMBH with a supermassive black hole (SMBH) will be primary sources for the planned space-based mission LISA and could be observed up to the distant Universe. SMBH-IMBH binaries can be formed as a result of the migration and merger of stellar clusters at the center of galaxies, where an SMBH lurks. We build for the first time a semi-analytical framework to model this scenario, and find that the the comoving merger rate of SMBH-IMBH binaries is $\sim 10^{-4}$ Gpc$^{-3}$ yr$^{-1}$ in the local Universe for a unity IMBH occupation fraction, scales linearly with it, and has a peak at $z\approx 0.5$-$2$. Our model predicts $\sim 0.1$ event yr$^{-1}$ within redshift $z\approx 3.5$ if $10\%$ of the inspiralled star clusters hosted an IMBH, while $\sim 1$ events yr$^{-1}$ for a unity occupation fraction. More than $90\%$ of these systems will be detectable with LISA with a signal-to-noise ratio larger than $10$, promising to potentially find a family of IMBHs.