\label{sec:introduction} A majority of all galaxies with masses \(>10^8\msun\) at \(z=0\) are believed to host super-massive black holes (SMBHs) in their cores. In a \(\Lambda\)CDM universe, galaxies at the high end of the galaxy-mass function are merger products of tens to hundreds of such massive galaxies. Even if only a small fraction of merging galaxies hosted an SMBH in their core at the time of merging, it is reasonable to assume that, during a Hubble time of continuous growth, these galaxies they will have substantial phases in which they contain two or more SMBHs at the same time.
Here we look at the merger history of four exemplary galaxies across the galaxy mass spectrum extracted from a cosmological simulation of hierarchical structure formation. We investigate how, after merging with incoming galaxies, SMBHs diffuse into the cores of the hosts and interact with the resident black hole. We show that gravitational interactions of multiple SMBHs is most probable in high-mass galaxies with \(10^{12}<M/\M_sun < 10^{13}\). Galaxies with lower masses have too few mergers with SMBH hosting galaxies. Galaxies with higher masses tend to be too extended, making dynamical friction processes inefficient and hence failing to drive SMBHs into the host galaxy core.
This paper is organized as follows: in Section \ref{sec:methods} we are going to describe the cosmological simulation from which we use the merger history to setup our idealized numerical simulations. We present the few-body integration code, AR-Chain that we used for our simulations of SMBH dynamics, and the modifications we made to this code in order to deal with a host galaxy’s gravitational potential. In Section \ref{sec:results}, we show the results of our four exemplary simulations of galaxies growing with time and acquiring new SMBHs. We analyze how the SMBHs are driven into the core of their new host galaxies and how interaction with the host black hole leads to near-ejections or mergers. The final Section \ref{sec:conclusions} contains a discussion of the result and our conclusions.