Binary intermediate-mass black hole mergers in globular clusters

We consider the formation of binary intermediate black holes (BIMBH) in globular clusters (GC), which could happen either in situ or due to the mergers between clusters. We simulate the evolution of the BIMBH orbit (and its subsequent merger) due to stellar ejections. We also take into account the evaporation of GCs due to the tidal field of the host galaxy and two-body relaxation. Our results show that if at least $10^{-3}$ of all GCs become BIMBH hosts and the BIMBH masses are $\sim1\%$ of the GC mass, at least one of the inspiralling (or merging) BIMBHs will be detected by LISA during its 4-year mission lifetime. Most of the detected BIMBHs come 1) from heavy GCs ($\gtrsim3\times10^5M_\odot$), as lower-mass GCs end up being disrupted before their BIMBHs have time to merge, and 2) from redshifts $1<z<3$, assuming that most of GCs form around $z\sim4$ and given that the merger timescale for most BIMBHs is $\sim1$ Gyr. If the BIMBH to GC mass ratio is lower ($\sim10^{-3}$) but the fraction of BIMBH hosts among GCs is higher ($\gtrsim10^{-2}$), some of their mergers will also be detected by LIGO, VIRGO, and KAGRA and the proposed Einstein Telescope.