Researchers built a new three-dimensional simulation code to study how stellar‑mass black holes behave inside the disks of active galactic nuclei (AGN). AGN are bright, gas‑rich regions around supermassive black holes. The team used the code, called AGNBI, to follow 20,000 black holes orbiting in and near an AGN disk and to simulate the gas forces and close gravitational encounters that control whether pairs form and merge.

The code mixes analytic orbit propagation around the central supermassive black hole with direct N‑body simulation of close interactions. It includes disk effects such as aerodynamic kicks when objects cross the disk, migration torques for objects embedded in the gas, damping of orbital tilt and eccentricity, gas accretion limited by the Eddington rate, and gravitational‑wave driven shrinking of tight binaries. The authors deliberately simulate binary‑single and binary‑binary encounters directly rather than treating them only statistically. For the runs reported here they assumed a standard disk model with an accretion fraction of 0.1 and radiative efficiency of 0.1, and they started with no pre‑existing binaries.

A key result is that binaries form across a wider range of radii than earlier 1D studies suggested. Black holes often migrate toward so‑called migration traps—locations in the disk where the net gas torque is small—and they pair up there. But many of these pairs are quickly broken apart by close encounters with other single or binary black holes. The authors find a broadened ring of formation and merger activity around the trap radius that they call a “scattering belt.” This belt is produced by frequent binary‑single and binary‑binary interactions that move where binaries form and merge.

The simulations also show that the initial orbital shapes of the black holes matter strongly. When the population has non‑zero orbital eccentricities (that is, orbits that are not perfect circles), binary formation and mergers drop by about an order of magnitude compared with a circular population. The paper attributes this to fewer black holes becoming fully embedded in the disk when orbits are eccentric, which reduces the gas‑assisted pairing channel.