Black hole genealogy: Identifying hierarchical mergers with gravitational waves

In dense stellar environments, the merger products of binary black hole mergers may undergo additional mergers. These hierarchical mergers are predicted to have higher masses than the first generation of black holes made from stars. The components of hierarchical mergers are expected to have significant characteristic spins $\chi\sim 0.7$. However, since the population properties of first-generation black holes are uncertain, it is difficult to know if any given merger is first-generation or hierarchical. We use observations of gravitational waves to reconstruct the binary black hole mass and spin spectrum of a population containing hierarchical merger events. We employ a phenomenological model that captures the properties of merging binary black holes from simulations of dense stellar environments. Inspired by recent work on the isolated formation of low-spin black holes, we include a zero-spin subpopulation. We analyze binary black holes from LIGO and Virgo's first two observing runs, and find that this catalog is consistent with having no hierarchical mergers. We find that the most massive system in this catalog, GW170729, is mostly likely a first-generation merger, having a $4\%$ probability of being a hierarchical merger assuming a $5 \times 10^5 M_{\odot}$ globular cluster mass. Using our model, we find that $99\%$ of first-generation black holes in coalescing binaries have masses below 44 $M_{\odot}$, and the fraction of binaries with near-zero spin is $0.051^{+0.156}_{-0.048}$ ($90\%$ credible interval). Upcoming observations will determine if hierarchical mergers are a common source of gravitational waves.