Hierarchical Black-Hole Mergers in Multiple Systems: Constrain the Formation of GW190412, GW190814 and GW190521-like events

The merging black-hole (BH) binaries GW190412, GW190814 and GW190521 from the third LIGO/VIRGO observing run exhibit some extraordinary properties, including highly asymmetric masses, significant spin, and component mass in the "mass gap". These features can be explained if one or both components of the binary are the remnants of previous mergers. In this paper, we explore hierarchical mergers in multiple stellar systems, taking into account the natal kick and mass loss due to the supernova explosion (SN) on each component, as well as the merger kick received by the merger remnant. The binaries that have survived the SNe and kicks generally have too wide orbital separations to merge by themselves, but can merge with the aid of an external companion that gives rise to Lidov-Kozai oscillations. The BH binaries that consist of second-generation BHs can also be assembled in dense star clusters through binary interactions. We characterize the parameter space of these BH binaries by merger fractions in an analytical approach. Combining the distributions of the survived binaries, we further constrain the parameters of the external companion, using the analytically formulated tertiary perturbation strength. We find that to produce the three LIGO/VIRGO O3 events, the external companions must be at least a few hundreds $M_\odot$, and fall in the intermediate-mass BH and supermassive BH range. We suggest that GW190412, GW190814 and GW190521 could all be produced via hierarchical mergers in multiples, likely in a nuclear star cluster, with the final merger induced by a massive BH.