The Magnetohydrodynamics of Convection‐dominated Accretion Flows

Radiatively inefficient accretion flows onto black holes are unstable due toboth an outwardly decreasing entropy (`convection') and an outwardly decreasingrotation rate (the `magnetorotational instability'; MRI). Using a linearmagnetohydrodynamic stability analysis, we show that long-wavelength modes areprimarily destabilized by the entropy gradient and that such `convective' modestransport angular momentum inwards. Moreover, the stability criteria for theconvective modes are the standard Hoiland criteria of hydrodynamics. Bycontrast, shorter wavelength modes are primarily destabilized by magnetictension and differential rotation. These `MRI' modes transport angular momentumoutwards. The convection-dominated accretion flow (CDAF) model, which has beenproposed for radiatively inefficient accretion onto a black hole, posits thatinward angular momentum transport and outward energy transport bylong-wavelength convective fluctuations are crucial for determining thestructure of the accretion flow. Our analysis suggests that the CDAF model isapplicable to a magnetohydrodynamic accretion flow provided the magnetic fieldsaturates at a sufficiently sub-equipartition value (plasma beta >> 1), so thatlong-wavelength convective fluctuations can fit inside the accretion disk.Numerical magnetohydrodynamic simulations are required to determine whethersuch a sub-equipartition field is in fact obtained.Comment: 17 pages including 3 figures. Accepted for publication in ApJ. New appendix and figure were added; some changes of the text were made in response to the referee