Self-limited Accretion onto Embedded Binaries in a Uniform Medium

We study accretion from a uniform gas at rest onto equal-mass binaries—the binary Bondi problem—as a function of the adiabatic index γ and compactness ξ ≡ R_B/a, where R_B is the Bondi radius of the binary and a is the component separation. We present three-dimensional hydrodynamic simulations spanning ξ = {0.1, 1, 10} at γ = {1, 4/3, 5/3}. Isothermal gas (γ = 1) accretes cooperatively at high compactness, with efficiency (Formula presented) η≡Ṁbinary/ṀBondi→1 for ξ ≫ 1 and a stable sonic surface that screens the orbital modulation. Adiabatic gas (γ > 1) is self-limiting; the orbit drives shocks that generate entropy, producing convective turbulence that suppresses accretion to η ≈ 0.3 (γ = 4/3) and η ≈ 0.1 (γ = 5/3), burying the orbital signature in broadband noise. We derive a stability criterion from first principles; the sonic surface is the separatrix of the Bondi saddle point, and the binary annihilates it in (Formula presented) N∝(γ−1)⁻¹(ξ/ξm−1) orbits, where ξ_m = 4/(5–3γ) is the container threshold at which the sonic surface first encloses the binary, and the (γ − 1)⁻¹ divergence follows from the lack of entropy generation at isothermal shocks. For γ = 5/3, no saddle point exists at any ξ and the neutrally stratified Bondi profile is convectively unstable by a distinct mechanism. The single comparison t_cool versus NT—where T is the orbital period—determines whether an embedded binary accretes cooperatively or throttles its own fuel supply; simulations confirm the analytic thresholds and scaling.