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 ≳100kms−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 ≲100kms−1. Assuming that all binary black holes are formed
dynamically in globular clusters with escape velocities on the order of tens of
kms−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⊙, and that this constraint is robust to our choice
of prior on the maximum black hole mass.Comment: 15 pages, 11 figures, 1 appendi