Spherical accretion: Bondi, Michel and rotating black holes

TL;DR

This paper compares classical and relativistic models of spherical gas accretion onto black holes, extends the models to relativistic gases, and investigates how black hole spin affects accretion rates and flow properties.

Contribution

It provides a detailed comparison of Bondi and Michel accretion models across temperature regimes, extends Michel's solution to relativistic gases, and analyzes the impact of black hole spin on accretion in relativistic regimes.

Findings

Michel accretion rate approaches a constant at high temperatures.

Bondi accretion rate decreases with increasing temperature.

Black hole spin reduces accretion rate, especially for relativistic gases.

Abstract

In this work we revisit the steady state, spherically symmetric gas accretion problem from the non-relativistic regime to the ultra-relativistic one. We first perform a detailed comparison between the Bondi and Michel models, and show how the mass accretion rate in the Michel solution approaches a constant value as the fluid temperature increases, whereas the corresponding Bondi value continually decreases, the difference between these two predicted values becoming arbitrarily large at ultra-relativistic temperatures. Additionally, we extend the Michel solution to the case of a fluid with an equation of state corresponding to a monoatomic, relativistic gas. Finally, using general relativistic hydrodynamic simulations, we study spherical accretion onto a rotating black hole, exploring the influence of the black hole spin on the mass accretion rate, the flow morphology and characteristics, and the sonic surface. The effect of the black hole spin becomes more significant as the gas temperature increases and as the adiabatic index $\gamma$ stiffens. For an ideal gas in the ultra-relativistic limit ($\gamma=4/3$), we find a reduction of 10 per cent in the mass accretion rate for a maximally rotating black hole as compared to a non-rotating one, while this reduction is of up to 50 per cent for a stiff fluid ($\gamma=2$).