Eccentric binary black hole mergers in globular clusters hosting intermediate-mass black holes

Abstract: Globular clusters (GCs) may harbour intermediate-mass black holes (IMBHs) at their centres. In these dynamically active environments stellar-mass black holes (SBHs) sink to the center soon after formation, due to dynamical friction and start interacting among themselves and with the central IMBH. Likely, some of the SBHs will form bound systems with the IMBH. A fraction of those will be triple systems composed of binary SBHs and the IMBH acting as a third distant perturber. If the SBH binary orbit is sufficiently inclined it can develop Lidov-Kozai (LK) oscillations, which can drive the system to high eccentricities and eventually to a merger due to gravitational wave (GW) emission on short timescales. In this work, we focus on the dynamics of the IMBH-SBH-SBH triples and illustrate that these systems can be possible sources of GWs. A distinctive signature of this scenario is that a considerable fraction of these mergers are highly eccentric when entering the LIGO band ($10$ Hz). Assuming that $\sim 20\%$ of GCs host IMBHs and a GC density in the range $n_{_{\rm GC}}=0.32$-$2.31\,\mathrm{Mpc}^{-3}$, we have estimated a rate $\Gamma=0.06$-$0.46\,\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ of these events. This suggests that dynamically-driven binary SBH mergers in this scenario could contribute to the merger events observed by LIGO/VIRGO. Full $N$-body simulations of GCs harbouring IMBHs are highly desirable to give a more precise constrain on this scenario.