Evidence for Hierarchical Black Hole Mergers in the Second LIGO-Virgo Gravitational Wave Catalog

We study the population properties of merging binary black holes in the second LIGO-Virgo Gravitational-Wave Transient Catalog assuming they were all formed dynamically in gravitationally bound clusters. Using a phenomenological population model, we infer the mass and spin distribution of first-generation black holes, while self-consistently accounting for hierarchical mergers. Considering a range of cluster masses, we see compelling evidence for hierarchical mergers in clusters with escape velocities ⪆100 km s-1. For our most probable cluster mass, we find that the catalog contains at least one second-generation merger with 99% credibility. We find that the hierarchical model is preferred over an alternative model with no hierarchical mergers (Bayes factor B > 1400) and that GW190521 is favored to contain two second-generation black holes with odds O > 700, and GW190519, GW190602, GW190620, and GW190706 are mixed-generation binaries with O > 10. However, our results depend strongly on the cluster escape velocity, with more modest evidence for hierarchical mergers when the escape velocity is ≲100 km s-1. Assuming that all binary black holes are formed dynamically in globular clusters with escape velocities on the order of tens of km s-1, GW190519 and GW190521 are favored to include a second-generation black hole with odds O > 1. In this case, we find that 99% of black holes from the inferred total population have masses that are less than 49M o˙, and that this constraint is robust to our choice of prior on the maximum black hole mass.