2020ApJ...900..177K

In dense stellar environments, the merger products of binary black hole mergers may undergo additional mergers. These hierarchical mergers are naturally expected 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, imprinted by the orbital angular momentum of the previous mergers. 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 including the possibility of hierarchical mergers. We employ a phenomenological model that captures the properties of merging binary black holes from simulations of globular clusters. Inspired by recent work on the 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 x 10⁵M_☉ globular cluster mass. Using our model, we find that 99% of first-generation black holes in coalescing binaries have masses below 44M_☉, and the fraction of binaries with near-zero component spins is less than 0.16 (90% probability). Upcoming observations will determine if hierarchical mergers are a common source of gravitational waves.