[Paper Review] Black Hole Binaries in AGN Accretion Discs II: Gas Effects on Black Hole Satellite Scatterings

Connar Rowan, Henry Whitehead+3 more|arXiv (Cornell University)|Sep 25, 2023

Astrophysical Phenomena and Observations4 citations

TL;DR

This paper presents a physically motivated, 3D smoothed particle hydrodynamics (SPH) simulation of black hole binary formation in active galactic nucleus (AGN) accretion discs, demonstrating that gas drag and gravitational torques during close encounters drive energy dissipation. It derives a predictive analytic criterion based on pre-encounter energy and impact parameter that forecasts binary formation with >90% accuracy, identifying a narrow range of impact parameters (0.86–1.59 binary Hill radii) as most favorable for stable binary capture.

ABSTRACT

The black hole (BH) binaries in active galactic nuclei (AGN) are expected to form mainly through scattering encounters in the ambient 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 disks. Using a range of impact parameters, we probe the necessary conditions for binary capture and how different orbital trajectories affect the dissipative effects from the gas. We identify a single range of impact parameters, typically of width $\sim0.86-1.59$ binary Hill radii depending on AGN disk 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 find an associated power-law between the energy dissipated and the periapsis depth to be $ΔE\propto r^{-b}$ with $b=0.42\pm0.16$, where deeper encounters dissipate more energy. Excluding accretion physics does not significantly alter these results. We identify the region of parameter space in initial energy vs impact parameter where a scattering leads to binary formation. Based on our findings, we provide a ready-to-use analytic criterion that utilises these two pre-encounter parameters to determine the outcome of an encounter, with a reliability rate of >90\%. As the criterion is based directly on our simulations, it provides a reliable and highly physically motivated criterion for predicting binary scattering outcomes which can be used in population studies of BH binaries and mergers around AGN.

Motivation & Objective

• To understand the role of gas in facilitating black hole binary formation through scattering encounters in AGN accretion discs.
• To identify the physical conditions—particularly impact parameters and periapsis distances—under which binary capture occurs efficiently.
• To develop a physically grounded, ready-to-use analytic criterion for predicting binary formation outcomes without requiring full hydrodynamic simulations.
• To quantify the energy dissipation mechanisms (gas drag, gravity, accretion) and their dependence on encounter geometry and disc density.
• To assess the robustness of results when accretion physics is excluded, ensuring the criterion's reliability across different modeling assumptions.

Proposed method

• Conducting 3D smoothed particle hydrodynamics (SPH) simulations of black hole scattering encounters in AGN discs with varying densities and initial conditions.
• Varying impact parameters across a wide range to probe the parameter space of encounter outcomes.
• Measuring energy dissipation during periapsis passages and identifying power-law scaling between dissipated energy and minimum separation (ΔE ∝ r^−b).
• Analyzing three distinct orbital trajectories: left-sided, right-sided, and turnaround encounters, to classify their dynamical behavior and binding efficiency.
• Comparing simulations with and without accretion to isolate the role of accretion vs. gas drag in energy dissipation.
• Deriving an analytic criterion (eq. 34) using pre-encounter parameters—two-Hill-radius energy and one-Hill-radius impact parameter—to predict binary formation with high reliability.

Experimental results

Research questions

• RQ1 What range of impact parameters leads to reliable black hole binary formation in AGN discs?
• RQ2 How does the depth of periapsis passage influence energy dissipation and binary binding?
• RQ3 What is the functional form of the energy dissipation scaling with minimum separation during close encounters?
• RQ4 How do different orbital trajectories (left, right, turnaround) affect the likelihood of binary formation?
• RQ5 Can a simple analytic criterion based on pre-encounter parameters predict binary formation with high accuracy, independent of full hydrodynamic simulation?

Key findings

• A narrow range of impact parameters—0.86 to 1.59 binary Hill radii—consistently leads to successful binary formation across different AGN disc densities.
• Energy dissipation scales with periapsis distance as ΔE ∝ r^−b, with b = 0.42 ± 0.16, indicating stronger dissipation in deeper encounters.
• Right-sided encounters, passing to the right of the inner black hole, are most favorable for binary formation due to optimal gas torque and energy dissipation.
• Excluding accretion physics has minimal impact on outcomes, indicating that gas drag alone captures the essential physics of energy dissipation.
• The derived analytic criterion predicts binary formation with a success rate exceeding 90%, based solely on pre-encounter energy and impact parameter.
• Strong oscillations in energy dissipation due to tidal perturbations of the circumbinary disc are observed, but their low-frequency signature (~10⁻⁷ Hz) lies beyond the sensitivity range of LISA.