Parameter space of the CBD lifetime as a function of the CBD mass. Colours indicate final separation with respect to the initial value, final eccentricity, and GW merger fraction for 2.80 M_⊙ + BH binary systems after the resonant interactions between the binary and different CBD models. Hatched grey regions denote the mergers induced by resonant interaction before the formation of the second compact object. As shown in Fig. 10, the double compact merger fraction of 2.80 M_⊙ + BH without any interactions is ∼16%, and around 9% of binaries merge within a Hubble time after binary MT.