Black hole binaries in AGNãccretion discs -II. Gas effects on black hole satellite scatterings

Abstract

The black hole (BH) binaries inãctive galactic nuclei (AGN)ãre expected to form mainly through scattering encounters in theãmbient gaseous medium. Recent simulations, including our own, have confirmed this formation pathway is highly efficient. We perform 3D smoothed particle hydrodynamics (SPH) simulations of BH scattering encounters in AGN discs. Usingã range of impact parameters, we probe the necessary conditions for binary captureãnd ho w dif ferent orbital trajectoriesãffect the dissipati ve ef fects from the gas. We identifyã single range of impact parameters, typically of width ∼0.86 -1.59 binary Hill radii depending on AGN disc density, that reliably leads to binary formation. The periapsis of the first encounter is the primary variable that determines the outcome of the initial scattering. We findãnãssociated power law between the energy dissipatedãnd the periapsis depth to be ΔE ∝ r -b with b = 0.42 ±0.16, where deeper encounters dissipate more energy. Excludingãccretion physics does not significantlyãlter these results. We identify the region of parameter space in initial energy versus impact parameter whereã scattering leads to binary formation. Based on our findings, we provideã ready-to-useãnalytic criterion that utilizes these two pre-encounter parameters to determine the outcome ofãn encounter, withã reliability rate of > 90 per cent. As the criterion is based directly on our simulations, it providesã reliableãnd highly physically moti vãted criterion for predicting binary scattering outcomes which can be used in population studies of BH binariesãnd mergersãround AGN.