Intermediate-Mass Black Holes in Colliding Clusters: Implications for Lower Frequency Gravitational-Wave Astronomy

Observations suggest that star clusters often form in binaries or larger bound groups. Therefore, mergers between two clusters are likely to occur. If these clusters both harbor an intermediate-mass black hole (IMBH; ~10²-10⁴ M_☉) in their center, they can become a strong source of gravitational waves when the black holes merge with each other. To understand the dynamical processes that operate in such a scenario, we simulate the merger of two stellar clusters each containing 63,000 particles and a central IMBH, using the direct-summation NBODY4 code on special-purpose GRAPE6 hardware. Within ~7 Myr the clusters have merged and the IMBHs constitute a hard binary. The final coalescence happens in ~10⁸ yr. We find that interactions with stars increase the eccentricity of the IMBH binary to about 0.8. Although the binary later circularizes by emission of gravitational waves, the residual eccentricity can be detectable by the Laser Interferometer Space Antenna (LISA) through its influence on the phase of the waves if the last few years of inspiral are observed. For proposed higher frequency space-based missions such as the Big Bang Observer (BBO), whose first purpose is to search for an inflation-generated gravitational waves background in the 10^-1 to 1 Hz range, binary IMBH inspirals would be a foreground noise source. However, we find that the inspiral signals could be characterized accurately enough that they could be removed from the data stream and in the process provide us with detailed information about these astrophysical events.