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 MHD stability analysis, we show that long-wavelength modes with lambda/H >> beta(-1/2) are primarily destabilized by the entropy gradient and that such convective modes transport angular momentum inward (lambda is the wavelength of the mode, H is the scale height of the disk, and beta is the ratio of the gas pressure to the magnetic pressure). Moreover, the stability criteria for the "convective" modes are the standard Hoiland criteria of hydrodynamics. By contrast, shorter wavelength modes with lambda/H similar to beta(-1/2) are primarily destabilized by magnetic tension and differential rotation. These "MRI" modes transport angular momentum outward. 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 an MHD accretion flow provided that the magnetic field saturates at a value sufficiently below equipartition (beta >> 1), so that long-wavelength convective fluctuations with lambda/H >> beta(-1/2) can fit inside the accretion disk. Numerical MHD simulations are required to determine whether such a subequipartition field is in fact obtained.