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

TL;DR

The paper develops a unified, theta-integrated framework for hot, radiatively inefficient accretion flows with finite angular momentum, smoothly connecting Bondi-like spherical inflow and disc-like ADAF regimes. By deriving 1D radial equations from full hydrodynamics in spherical coordinates and enforcing appropriate boundary and transonic conditions, the model recovers the Bondi solution in the non-rotating limit and the cylindrical ADAF limit at high rotation, while providing a physically consistent intermediate regime. The accretion rate and sonic radius are shown to be controlled by the ambient angular momentum, the viscosity parameter $\alpha$, and the adopted advection factor, allowing substantial $\dot M$ even with significant rotation, thus offering a natural explanation for observed jet powers in X-ray luminous ellipticals. This framework lays a foundation for studying hot accretion in realistic galactic environments and can be extended to include outflows, magnetic fields, and galactic potentials.

Abstract

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.

Figures (2)

• Figure 1: Accretion rate $\dot{M}$ (left panel) and sonic radius $r_\mathrm{c}$ (right panel) as functions of $\mathcal{L}$, for $\alpha=0.1$, $f=1$, $\gamma=5/3$, and $c_{\mathrm{out}}=10^{-3}c$. The blue, red, and yellow lines correspond to our model, the NF11 model, and the classical ADAF model, respectively. The horizontal axis spans from $\mathcal{L} \ll 1$ to $\mathcal{L} = 272$, the latter corresponding to Keplerian rotation at $r_\mathrm{B}$.
• Figure 2: Accretion rate $\dot{M}$ (left panel) and sonic radius $r_\mathrm{c}$ (right panel) as functions of $\mathcal{L}$ for different values of $\alpha$ in our model: $\alpha=0.01$ (yellow), 0.1 (blue), and 0.4 (purple). Other parameters are $f=1$, $\gamma=5/3$, and $c_{\mathrm{out}}=10^{-3}c$.