Intermediate-mass ratio inspirals in merging elliptical galaxies

Close encounters between two initially unbound objects can result in a binary system if enough energy is released as gravitational waves (GWs). We address the scenario in which such encounters occur in merging elliptical galaxies. There is evidence that elliptical galaxies can harbor intermediate-mass black holes. Therefore, these systems are potentially the breeding grounds of sources of gravitational waves corresponding to inspiraling compact objects onto a massive black hole due to the dynamics, the large densities, and the number of compact remnants they contain. We show that this process is efficient for intermediate-mass black holes (IMBHs) with masses ranging from M $\in (10^3,10^5)$ M$_{\odot}$ and results in the formation of intermediate mass-ratio inspirals (IMRIs). We consider a set of IMBHs and smaller black holes with masses $m_2 \in (10,10^3)$ M$_{\odot}$ to estimate the IMRI formation rate. We find rates ranging between 10$^{-8}$ yr$^{-1}$, and 10$^{-5}$ yr$^{-1}$, and the IMRI formation rate per comoving volume in merging galaxies as a function of the redshift. The peak frequencies of the gravitational radiation emitted when these IMRIs are formed are within the detection band of space-borne detectors such as LISA and TianQin; taking into account the observable volume of these detectors, the total amount of IMRI detections per year is significant.