Elusive Plunges and Heavy Intermediate-mass-ratio Inspirals from Single and Binary Supermassive Black Holes

The most massive galaxies in the Universe also host the largest supermassive black holes (SMBHs), with masses of $10^9 \: \mathrm{M_{\odot}}$ and above. During their hierarchical assembly, these galaxies have experienced only a few major mergers at low redshift, but have accreted many low-mass galaxies across cosmic time, possibly hosting intermediate mass black holes (IMBHs). If some of these IMBHs migrate to the galactic center, they may form compact subsystems around the central SMBH. We investigate the evolution of such subsystems, consisting of ten $10^5 \: \mathrm{M_{\odot}}$ IMBHs at three different concentrations around a $10^9 \: \mathrm{M_{\odot}}$ SMBH. We evolve these systems both in isolation and in the presence of a companion SMBH, using \texttt{MSTAR}, a regularized integration method including relativistic effects up to post-Newtonian order 3.5PN. Our analysis focuses on gravitational--wave--driven intermediate--mass--ratio inspirals (heavy IMRIs) and direct plunges. We show that perturbations from a secondary SMBH enhance the number of IMBH direct plunges by more than a factor of two, making them the dominant merger channel. These plunges and IMRIs with a central $10^9 \: \mathrm{M_{\odot}}$ SMBH will contribute to SMBH growth but will likely evade detection with future gravitational-wave interferometers and pulsar timing arrays (PTAs). However, for galaxies with lower--mass SMBHs ($M_\bullet \lesssim 10^8 \:\mathrm{M_{\odot}}$), heavy IMRIs will be detectable with the Laser Interferometer Space Antenna (LISA) and can provide direct observational constraints on the existence of IMBHs, while the more numerous plunges will still remain hidden.