Hydrodynamic Simulations of Eccentric Black Hole Encounters in AGN Discs

Abstract: We investigate close encounters between stellar-mass black holes (BHs) in the gaseous discs of active galactic nuclei (AGNs), during which binary black holes (BBHs) may form. We perform a suite of 483 2D adiabatic viscous hydrodynamic simulations within a shearing box prescription using the Eulerian grid code Athena++. We co-evolve the two embedded BHs with the gas. To probe the dependence of capture on non-circular initial conditions, we vary the initial radial separation $b$, the eccentricity $e$ of one of the stellar BHs around the central supermassive black hole, and the eccentric phase angle $φ<em>e$. We consider eccentricities from $e=0$ to $e=0.1$ and compare them with the local disc aspect ratio $h=H/R_0\simeq0.005$. We find that small eccentricities shift the capture window in the parameter space. Eccentricities of order the disc aspect ratio, in particular $e\sim h$--$2h$, produce successful captures at initial separations that do not capture in the circular models. By contrast, systems with $e \gg h$ retain less gas before encounter and have lower capture fractions across the sampled parameter grid. We find that the first periapsis distance is a useful predictor of direct capture. Predicting direct capture for $r</em>{\rm p}&lt;0.1r_H$ correctly classifies $92.7\%$ of Hill sphere encounters. The Hill sphere gas mass helps identify gas-poor failures, but provides no clear additional capture boundary within this suite, in which the initial disc density, temperature, and viscosity parameter are held fixed. Pre-encounter eccentricity modifies gas-assisted BBH formation through its combined effects on the first-encounter geometry and the gas reservoir available for orbital energy dissipation.