Physics-based phenomenological modeling of binary black hole hierarchical formation 1: Synthetic universes from globular cluster simulations for GWTC

Abstract

We iteratively model the GWTC-5.0 binary-black-hole census with three components. First, a physically normalized population from Rapster globular-cluster simulations spans cluster mass, metallicity, formation redshift, compactness, and natal black-hole spin. Hierarchical mergers reproduce higher-mass events and their larger effective-spin dispersion, provided black holes are born with zero natal spin. Second, a phenomenological field (isolated-binary) channel supplies the low-mass, preferentially aligned population. Its inclusion flattens the cluster compactness likelihood, permitting ordinary dense globular-cluster birth radii without requiring nuclear-cluster-like conditions. Finally, residual tension at $15$--$30 M_\odot$ motivates an intermediate-mass isotropic component representing field remnants reprocessed in clusters. This is a hypothesis, not a detection: current numerical support precludes a reliable evidence comparison. Physical normalization converts the high-mass rate into $\hat{f}_{\rm GC}\simeq0.39\%$, with local rates $R_{\rm cl}\simeq9.1$ and $R_{\rm field}\simeq16.0$ Gpc$^{-3}$ yr$^{-1}$. The model predicts linked mass-spectrum breaks near $35$ and $70 M_\odot$, a $q\simeq0.5$ feature from first-plus-second-generation pairings, and a symmetric effective-spin distribution that broadens sharply above $45 M_\odot$. These correlated, mass-resolved predictions can be tested as the gravitational-wave census grows.