Spherical accretion: Bondi, Michel, and rotating black holes

Abstract

In this work, we revisit the steady-state, spherically symmetric gas accretion problem from the non-relativistic regime to the ultrarelativistic 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 ultrarelativistic 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 on to 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 γ stiffens. For an ideal gas in the ultrarelativistic limit (γ = 4/3), we find a reduction of 10 per cent in the mass accretion rate for a maximally rotating black hole compared to a non-rotating one, while this reduction is of up to 50 per cent for a stiff fluid (γ = 2).

General Relativistic Hydrodynamics in Discrete Spacetime: Perfect Fluid Accretion onto Static and Spinning Black Holes

“…Following the recent historical exposition of Aguayo-Ortiz, Tejeda, Sarbach and López-Cámara [55], we note that Bondi [11] originally analyzed the case of an infinite, spherically-symmetric distribution of ideal gas with adiabatic exponent Γ, with initially uniform density ρ and pressure P, accreting radially onto a compact object of mass M in Newtonian gravity. Under these assumptions, the steady-state accretion flow in spherical polar coordinates (t, r, θ, φ) is governed by the continuity and radial Euler equations, namely:…”

A dark matter probe in accreting pulsar-black hole binaries

“…The Bondi accretion assumes a spherically symmetric stellar object stationarily accreting a cloud of non-relativistic matter particles. For practical reasons, we will refer to the form in which it is presented in [35] (for a detailed derivation, see appendix A), where the equation reads,…”

“…Where λ M , unlike in the Bondi accretion, depends also on the sound speed of the medium but in general varies between 1 and 2 [35]. Since this accretion rate is extremely small and cannot be observed in the method we propose, we will not elaborate on it.…”

Gravitational-wave Emission from a Primordial Black Hole Inspiraling inside a Compact Star: a Novel Probe for Dense Matter Equation of State

“…For the parameter λ, although there are analytical expressions for EoSs when the adiabatic index is Γ 1 (Richards et al 2021;Aguayo-Ortiz et al 2021), no simple expression is available when Γ < 1 (at the phase transition region of a NS; Potekhin et al 2013) and Γ → ∞ (at the surface of a SS; Xia et al 2021). So, we use a commonly-used value of Γ = 4/3 in our calculations, which naturally gives λ = 1/ √ 2 (Génolini…”