Star Cluster Population of High Mass Black Hole Mergers in Gravitational Wave Data

Stellar evolution theories predict a gap in the black hole birth mass spectrum as the result of pair instability processes in the cores of massive stars. This gap, however, is not seen in the binary black hole masses inferred from gravitational wave data. One explanation is that black holes form dynamically in dense star clusters where smaller black holes merge to form more massive black holes, populating the mass gap. We show that this model predicts a distribution of the effective and precessing spin parameters, $x_{eff}$ and $x_p$, within the mass gap that is insensitive to assumptions about black hole natal spins and other astrophysical parameters. We analyze the distribution of $x_{eff}$ as a function of primary mass for the black hole binaries in the third gravitational wave transient catalog. We infer the presence of a high mass and isotropically spinning population of black holes that is consistent with hierarchical formation in dense star clusters and a pair-instability mass gap with a lower edge at $44_{-4}^{+6}M_⊙$. We compute a Bayes facto $ℬ >10^4$ relative to models that do not allow for a high mass population with a distinct $x_{eff}$ distribution. Upcoming data will enable us to tightly constrain the hierarchical formation hypothesis and refine our understanding of binary black hole formation.