Outflows from inflows: the nature of Bondi-like accretion

TL;DR

This paper demonstrates that non-uniform density at the black hole's influence radius transforms the classic Bondi accretion solution into an inflow-outflow pattern, with implications for accretion rates and outflows.

Contribution

It analytically and numerically shows how inhomogeneous density distributions alter the Bondi accretion flow, introducing meridional flows and inflow-outflow solutions.

Findings

Non-uniform density causes meridional flow and inflow-outflow solutions.

Accretion rate remains near the Bondi rate despite inhomogeneity.

Outflow rates can significantly exceed the Bondi accretion rate.

Abstract

The classic Bondi solution remains a common starting point both for studying black hole growth across cosmic time in cosmological simulations and for smaller scale simulations of AGN feedback. In nature, however, there will be inhomogenous distributions of rotational velocity and density along the outer radius ($R_o$) marking the sphere of influence of a black hole. While there have been many studies of how the Bondi solution changes with a prescribed angular momentum boundary condition, they have all assumed a constant density at $R_o$. In this Letter, we show that a non-uniform density at $R_o$ causes a meridional flow and due to conservation of angular momentum, the Bondi solution qualitatively changes into an inflow-outflow solution. Using physical arguments, we analytically identify the critical logarithmic density gradient $|\partial{\ln{\rho}}/\partial{\theta}|$ above which this change of the solution occurs. For realistic $R_o$, this critical gradient is less than 0.01 and tends to 0 as $R_o \rightarrow \infty$. We show using numerical simulations that, unlike for solutions with an imposed rotational velocity, the accretion rate for solutions under an inhomogenous density boundary condition remains constant at nearly the Bondi rate $\dot{M}_B$, while the outflow rate can greatly exceed $\dot{M}_B$.