Reconstructing the genealogy of LIGO-Virgo black holes

We propose a Bayesian inference framework to predict the merger history of LIGO-Virgo binary black holes, whose binary components may have undergone hierarchical mergers in the past. The framework relies on numerical relativity predictions for the mass, spin, and kick velocity of the remnant black holes. This proposed framework computes the masses, spins, and kicks imparted to the remnant of the parent binaries, given the initial masses and spin magnitudes of the binary constituents. We validate our approach by performing an "injection study" based on a constructed sequence of hierarchically-formed binaries. Noise is added to the final binary in the sequence, and the parameters of the 'parent' and 'grandparent' binaries in the merger chain are then reconstructed. This method is then applied to three GWTC-3 events: GW190521, GW200220₀61928, GW190426₁90642. These events were selected because at least one of the binary companions lies in the putative pair-instability supernova mass gap, in which stellar processes alone cannot produce black holes. Hierarchical mergers offer a natural explanation for the formation of black holes in the pair-instability mass-gap. We use the backward evolution framework to predict the parameters of the parents of the primary companion of these three binaries. Our results indicate that at least one component of these three observed binaries was formed through a prior binary black hole merger. This approach can be readily applied to future high-mass gravitational wave events to predict their formation history under the hierarchical merger assumption.