A unified framework for hot accretion flows with finite angular momentum: from Bondi-like to disc-like regimes

Observations of X-ray luminous elliptical galaxies suggest that the accretion rate onto the central supermassive black hole can reach a substantial fraction of the Bondi rate. However, classical accretion theory applicable to such hot accretion flows treats spherically symmetric Bondi accretion and disc-like advection-dominated accretion flows (ADAFs) as two distinct limiting cases, lacking a unified framework for flows with finite angular momentum. In this work, we develop such a framework that continuously connects these two regimes. Our model naturally recovers the Bondi solution in the limit of vanishing angular momentum and approaches the properties of classical ADAFs at high angular momentum, while providing a physically well-defined description of the intermediate regime where neither limiting case is strictly applicable. We further demonstrate that the accretion rate is jointly regulated by the angular momentum of the ambient gas and the gas viscosity. For sufficiently large but physically reasonable viscosity, the accretion rate can remain at a significant fraction of the Bondi rate even in the presence of substantial gas rotation. These results offer a natural explanation for how such accretion rates can be sustained despite finite angular momentum in realistic galactic environments.

💡 Research Summary

This paper addresses a long‑standing gap in the theory of hot accretion onto supermassive black holes (SMBHs): the lack of a unified description that smoothly connects the spherically symmetric Bondi accretion regime (zero angular momentum) with the disc‑like advection‑dominated accretion flow (ADAF) regime (high angular momentum). Observations of X‑ray luminous elliptical galaxies show that the mechanical power of relativistic jets correlates tightly with the Bondi accretion rate, implying that the actual mass inflow onto the SMBH must remain a substantial fraction of the Bondi rate even when the surrounding hot interstellar medium (ISM) possesses non‑negligible rotation. Classical theory, however, treats Bondi and ADAF as mutually exclusive limits; modest rotation introduces a centrifugal barrier that dramatically suppresses the inflow, creating a tension with the observed jet powers.

The authors construct a self‑consistent framework that works in spherical coordinates (r, θ, φ) under the assumptions of steady‑state, axisymmetry, and negligible outflows (v_θ = 0). They retain the full set of hydrodynamic equations: continuity, radial and θ‑components of the momentum equation, the azimuthal angular‑momentum equation, and the energy equation with an advective factor f (typically set to unity for radiatively inefficient flows). Viscous stresses are modeled with the standard α‑prescription, ν = α c_s²/Ω_K, and the gravitational potential is approximated by the Paczyński‑Wiita pseudo‑Newtonian form.

A crucial step is the treatment of the θ‑direction. Equation (4) expresses vertical hydrostatic equilibrium in spherical geometry, balancing the centrifugal force (which points toward the equator) against the pressure gradient. By assuming that the radial velocity v_r, azimuthal velocity v_φ, and sound speed c_s are independent of θ, the authors can integrate the θ‑dependence analytically. This yields explicit expressions for the density and pressure as functions of sin θ, namely ρ(r,θ) = ρ_0(r)