The Magnetohydrodynamics of Convection-Dominated Accretion Flows

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 with λ/H ≫ β are primarily destabilized by the entropy gradient and that such “convective” modes transport angular momentum inwards (λ is the wavelength of the mode, H is the scale height of the disk, and β is the ratio of the gas pressure to the magnetic pressure). Moreover, the stability criteria for the convective modes are the standard Høiland criteria of hydrodynamics. By contrast, shorter wavelength modes with λ/H ∼ β are primarily destabilized by magnetic tension Permanent Address: Department of Astronomy, Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138