Extremely efficient mergers of intermediate mass black hole binaries in nucleated dwarf galaxies

Gravitational waves emitted by merging black holes between $\sim 10^4-10^7~M_\odot$ will be detectable by the Laser Interferometer Space Antenna (LISA) with signal-to-noise ratios of several hundred out to redshift 20. Supermassive black hole ($10^7$~M$_{\odot}$ - $10^{10}$~M$_{\odot}$) binary formation, coalescence and merger within massive galaxies is well-studied. However, low-to-intermediate mass black holes (IMBHs) are hosted by low-mass and dwarf galaxies; it is not trivial to extrapolate black hole merger timescales to this IMBH binary regime, due to the starkly different host galaxy structure, kinematics, and morphology compared to massive galaxy hosts. We perform ultra-high resolution $N$-body simulations to study IMBH dynamics in nucleated dwarf galaxies whose structural parameters are obtained from observations of nearby dwarf galaxies. Starting from 50 parsecs, an IMBH quickly forms a binary. Thereafter, the binary orbit shrinks rapidly due to the high central stellar densities furnished by nuclear star clusters (NSCs). We find high eccentricities ($e \sim 0.4-0.99$) in our suite of IMBH binaries, and residual eccentricity may persist to the LISA regime. IMBH merger times are typically a few hundred million years, with a few exceptionally short merger times for high eccentricities. We find that IMBH-stellar encounters originate predominantly from NSCs, if the NSC-to-IMBH binary mass ratio is greater than 10; otherwise, bulge stars contribute significantly. As the IMBH binary ejects stars, however, the NSCs is disrupted. We conclude that comparable-mass IMBHs merge very efficiently in nucleated dwarf galaxies, making them promising LISA sources, as well as a channel for IMBH growth.