The Magnetohydrodynamics of Convection‐dominated Accretion Flows

Ramesh Narayan,Marek A Abramowicz,Igor V Igumenshchev,Eliot Quataert

doi:10.1086/342159

Abstract

Radiatively inefficient accretion flows onto black holes are unstable due to both an outwardly decreasing entropy (`convection') and an outwardly decreasing rotation rate (the `magnetorotational instability'; MRI). Using a linear magnetohydrodynamic stability analysis, we show that long-wavelength modes are primarily destabilized by the entropy gradient and that such `convective' modes transport angular momentum inwards. Moreover, the stability criteria for the convective modes are the standard Hoiland criteria of hydrodynamics. By contrast, shorter wavelength modes are primarily destabilized by magnetic tension and differential rotation. These `MRI' modes transport angular momentum outwards. The convection-dominated accretion flow (CDAF) model, which has been proposed for radiatively inefficient accretion onto a black hole, posits that inward angular momentum transport and outward energy transport by long-wavelength convective fluctuations are crucial for determining the structure of the accretion flow. Our analysis suggests that the CDAF model is applicable to a magnetohydrodynamic accretion flow provided the magnetic field saturates at a sufficiently sub-equipartition value (plasma beta >> 1), so that long-wavelength convective fluctuations can fit inside the accretion disk. Numerical magnetohydrodynamic simulations are required to determine whether such a sub-equipartition field is in fact obtained.

Highlights

Models of radiatively inefficient accretion flows provide a useful framework for interpreting observations of low-luminosity black hole X-ray binaries and active galactic nuclei
Our analysis suggests that the convection-dominated accretion flow” model (CDAF) model is applicable to a magnetohydrodynamic accretion flow provided the magnetic field saturates at a sufficiently sub-equipartition value (β ≫ 1), so that long-wavelength convective fluctuations with λ/H ≫ β−1/2 can fit inside the accretion disk
We have shown that, when the medium is unstable by the Høiland criteria, long-wavelength instabilities with kvA ≪ Ω are effectively hydrodynamical

Summary

Introduction

Models of radiatively inefficient accretion flows provide a useful framework for interpreting observations of low-luminosity black hole X-ray binaries and active galactic nuclei (see, e.g., Narayan, Mahadevan & Quataert 1998; Quataert 2001; Narayan 2002 for reviews). Balbus & Hawley have argued that, because of the fundamental role played by magnetic fields, hydrodynamic models typically cannot describe the structure of the accretion flow (or differentially rotating systems more generally; e.g., Balbus & Hawley 1998; Balbus 2000; 2001). They have applied this criticism in detail to the CDAF model (Hawley, Balbus, & Stone 2001; Balbus & Hawley 2002; hereafter BH02).

Convective Modes in a Magnetized Differentially Rotating Plasma

The Hydrodynamic Limit

Implications for CDAFs

Conclusion