[Paper Review] Gas Assisted Binary Black Hole Formation in AGN Discs

Henry Whitehead, Connar Rowan+2 more|arXiv (Cornell University)|Sep 20, 2023

Astrophysical Phenomena and ObservationsPhysics and Astronomy7 citations

TL;DR

This paper uses 345 high-resolution 2D isothermal viscous hydrodynamic simulations in a shearing box to study gas-assisted capture and formation of binary black holes in AGN discs, and derives a capture prescription for semi-analytic models.

ABSTRACT

We investigate close encounters by stellar mass black holes (BHs) in the gaseous discs of active galactic nuclei (AGN) as a potential formation channel of binary black holes (BBHs). We perform a series of 2D isothermal viscous hydrodynamical simulations within a shearing box prescription using the Eulerian grid code Athena++. We co-evolve the embedded BHs with the gas keeping track of the energetic dissipation and torquing of the BBH by gas gravitation and inertial forces. To probe the dependence of capture on the initial conditions, we discuss a suite of 345 simulations spanning local AGN disc density ($ρ_0$) and impact parameter ($b$) space. We identify a clear region in $b - ρ_0$ space where gas assisted BBH capture is efficient. We find that the presence of gas leads to strong energetic dissipation during close encounters between unbound BHs, forming stably bound eccentric BBHs. We find that the gas dissipation during close encounters increases for systems with increased disc density and deeper periapsis passages $r_p$, fitting a power law such that $ΔE \propto ρ_0^αr_p^β$ where $\{α,β\} = \{1.01\pm0.04,-0.43\pm0.03\}$. Alternatively, the gas dissipation is approximately $ΔE = 4.3 M_ ext{d} v_ ext{H} v_p$, where $M_ ext{d} $ is the mass of a single BH minidisc just prior to the encounter when the binary separation is $2r_ ext{H}$ (two binary Hill radii), $v_ ext{H}$ and $v_p$ are the relative BH velocities at $2r_ ext{H}$ and at the first closest approach, respectively. We derive a prescription for capture which can be used in semi-analytical models of AGN. We do not find the dissipative dynamics observed in these systems to be in agreement with the simple gas dynamical friction models often used in the literature.

Motivation & Objective

• Investigate whether gas in AGN discs can induce capture and formation of bound BBHs during close encounters.
• Quantify how gas dissipation during encounters depends on local disc density and encounter geometry (periapsis).
• Identify the region in initial parameter space (b, ρ0) where gas-assisted capture is efficient.
• Derive a semi-analytic capture prescription that can be used in broader AGN BBH formation models.
• Compare gas-driven dissipation mechanisms with simpler gas dynamical friction models and assess modeling implications.

Proposed method

• Perform 2D isothermal viscous hydrodynamics simulations with Athena++ in a shearing box around a central SMBH.
• Embed two equal-mass BHs (25 Msun) with forming minidiscs and track their gas-induced evolution.
• Explore a grid of 345 simulations spanning ambient disc density ρ0 and initial impact parameter b.
• Use adaptive mesh refinement to achieve ≳500 cells per Hill radius to resolve minidiscs and close encounters.
• Compute dissipation diagnostics (epsilon_SMBH and epsilon_gas) and torques to quantify energy and angular momentum exchange.
• Derive a capture criterion and a scaling relation for energy dissipation that can feed semi-analytic BBH formation models.

Experimental results

Research questions

• RQ1 Under what conditions can gas dissipate enough energy during BH encounters to form a bound BBH in AGN discs?
• RQ2 How does gas-induced dissipation scale with disc density and encounter periapsis, and where is capture most efficient in b-ρ0 space?
• RQ3 Can a robust, transferable capture prescription be derived for use in semi-analytic or population synthesis models?
• RQ4 How do gas dynamics compare with simple gas dynamical friction expectations in these encounters?
• RQ5 What are the characteristics (eccentricity, Hill energy) of the formed BBHs and their subsequent evolution under gas torques?

Key findings

• Gas leads to strong energetic dissipation during close encounters, forming stably bound eccentric BBHs.
• Dissipation scales as ΔE ∝ ρ0^α r_p^β with {α,β} = {1.01 ± 0.04, −0.43 ± 0.03}.
• An alternative dissipation prescription is ΔE = 4.3 M_d v_H v_p, with M_d the minidisc mass prior to the encounter and v_H, v_p the relative BH velocities at 2 r_H and at first closest approach.
• Capture is efficient only within a specific region of the initial b–ρ0 parameter space.
• Gas dissipation during the first periapsis is the dominant contributor to hardening, with subsequent passages producing weaker dissipation.
• The dissipative dynamics observed do not fully align with simple gas dynamical friction models often used in literature.