The role of migration traps in the formation of binary black holes in AGN disks

Binary black holes (BBHs) forming in the accretion disks of active galactic nuclei (AGNs) represent a promising channel for gravitational-wave production. BBHs are often assumed to form at migration traps, i.e., radial locations where the Type I migration of embedded stellar-mass black holes (BHs) transitions from outward to inward. For this study, we tested this assumption by explicitly simulating the radial migration of BH pairs in AGN disks under different torque prescriptions, including thermal effects and the switch to Type II migration. We mapped where and when binaries form as a function of supermassive BH (SMBH) mass, disk viscosity, and migrating BH mass. We find that, for SMBH masses below $ M_{\bullet}^{\mathrm{thr}} \sim 10^8\,\mathrm{M}_\odot $, the majority of pair-up events occur near migration traps (≳80%). In contrast, for higher SMBH masses, differential migration dominates and off-trap pair-ups can prevail. Certain disk configurations (e.g., α = 0.01, M• < 106 M⊙) present a significant overdensity of pair-ups even in the absence of traps due to traffic-jam accumulations where the gamma profile changes slope sharply. We also investigated hierarchical BBH formation, showing that higher-generation pair-ups cluster more tightly around trap or traffic-jam radii. Our results provide realistic prescriptions for BBH pair-up locations and timescales, highlighting the limitations of assuming fixed BBH formation sites.