Generalized Bondi Accretion Flow with and without Outflow

TL;DR

This paper extends Bondi accretion to rotating, viscous flows in the slim-disk regime by solving steady polytropic flows with a viscosity prescription tied to angular shear, across wide ranges of $\\alpha$, $J_{out}$ (via $\\lambda$), and $r_B$. It shows that the dimensionless mass accretion rate $\\dot{m}$ decreases with increasing angular momentum and Bondi radius, with the suppression strength depending on $\\alpha$ and boundary conditions, and that large $r_B$ yields a milder decline so the flow can become Bondi-like at smaller angular momentum. When outflows are included via the ADIOS model, the outer inflow rate $\\dot{m}_0$ can exceed Bondi, but the actual BH accretion rate $\\dot{m}_{BH}$ is suppressed by orders of magnitude, and the angular-momentum dependence weakens at low $\\alpha$. These results imply that black hole growth and feedback energetics depend sensitively on outer-boundary angular momentum and outflow strength, beyond the classic Bondi estimate.

Abstract

The properties of accretion flows are affected by the angular momentum of the accreting gas. M.-G. Park found that the mass accretion rate, specifically, decreases significantly as the gas angular momentum increases. However, R. Narayan & A. C. Fabian found the decrease modest. We investigate global solutions for rotating polytropic flows in a much wider parameter space to understand their general properties within the slim disk approximation and a viscosity description suitable for both low- and high-angular-momentum flows. We find that the mass accretion rate for flows with a small Bondi radius decreases steeply as the gas angular momentum increases, while for those with a large Bondi radius, it decreases gradually. Therefore, the decrease of mass accretion rate due to gas rotation can be significant or mild depending on the Bondi radius. We further investigate global solutions of accretion with outflows using the ADIOS model of R. D. Blandford & M. C. Begelman. Stronger outflows in general slightly increase the mass inflow rate at the outer boundary, but the actual mass accreted into the black hole decreases by orders of magnitude. Stronger outflows also weaken the dependence of the mass accretion rate on the gas angular momentum when the viscosity parameter α is small. The intricate dependence of the mass inflow rate at the outer boundary and the mass accretion rate into the black hole on gas angular momentum will have interesting implications for the growth of black holes and their energy output.

Figures (10)

• Figure 1: Flow profiles of accretion flows with $\gamma = 5/3$, $\alpha = 0.1$, at a Bondi radius of $r_\mathrm{B} = 1.0 \times 10^5 r_\mathrm{s}$, corresponding to $T_\mathrm{out} = 2.7 \times 10^{7} \mathrm{K}$ or $c_\mathrm{s} = 2.2 \times 10^{-3} c$. Different line styles denote different values of the angular momentum: $\lambda=1.0$ for high angular momentum (solid line), $\lambda=0.1$ for intermediate angular momentum (dotted line), and $\lambda = 0.01$ for low angular momentum (dashed line). The grey dashed lines in the panels denote the Keplerian angular velocity (c) and angular momentum (d). The filled circles denote the positions of the critical points.
• Figure 2: (a) The mass accretion rate $\dot{m}$ as a function of angular momentum $\lambda \equiv J_\mathrm{out}/J_\mathrm{B}$ for four different viscosity parameters ($\alpha=0.1, 0.03, 0.01, 0.003$). Different line styles denote flows with different Bondi radii: solid lines for $r_\mathrm{B}=1.0\times 10^5r_\mathrm{s}$ and dashed lines for $r_\mathrm{B} = 2.5 \times 10^3 r_\mathrm{s}$. (b) The mass accretion rate as a function of angular momentum $j_\mathrm{out} \equiv J_\mathrm{out} / (r_\mathrm{s} c)$.
• Figure 3: The mass accretion rate ($\log (\dot{m})$) versus the viscosity parameter ($\log(\alpha)$) for accretion flows with a given $\lambda$. The left and right panels are for accretion flows with $r_\mathrm{B} = 1.0 \times 10^5 r_\mathrm{s}$ and $r_\mathrm{B} = 2.5 \times 10^3 r_\mathrm{s}$, respectively.
• Figure 4: The mass accretion rate as a function of angular momentum parameter in (a) for $\lambda$ and (b) for $j_\mathrm{out}$, for accretion flows with $\gamma=5/3$ and $\alpha = 0.03$ at various Bondi radii. Flow profiles for the accretion flow with specific angular momentum: (c) for $\lambda = 0.1$ and (d) for $j_\mathrm{out} = 35.5$. Different line styles denote different Bondi radii: dotted lines for $r_\mathrm{B} = 1.0 \times 10^3 r_\mathrm{s}$, dashed lines for $r_\mathrm{B} = 2.5 \times 10^3 r_\mathrm{s}$, long-dashed lines for $r_\mathrm{B} = 1.0 \times 10^4 r_\mathrm{s}$, dot-dashed lines for $r_\mathrm{B} = 1.0 \times 10^5 r_\mathrm{s}$, and dot-long-dashed lines for $r_\mathrm{B} = 5.0 \times 10^5 r_\mathrm{s}$. The filled circles in the bottom panels denote the positions of the critical points.
• Figure 5: The mass accretion rate $\dot{m}$ as a function of angular momentum $j_\mathrm{out}$ for accretion flows with $\gamma=5/3$ and four values of $\alpha$ at three Bondi radii. Different line styles denote the accretion flows at $r_\mathrm{B} = 1.0 \times 10^5 r_\mathrm{s}$ (dotted lines), $r_\mathrm{B} = 1.0 \times 10^4 r_\mathrm{s}$ (dashed lines), and $r_\mathrm{B} = 2.5 \times 10^3 r_\mathrm{s}$ (long-dashed lines). Grey lines represent the mass accretion rates approximated by fitting Equations \ref{['eq:gen_P09']} and \ref{['eq:eq_mdot_jout']} for high- and low- angular momentum flows, respectively.