Convection‐dominated Accretion Flows

Non-radiating, advection-dominated, accretion flows are convectivelyunstable. We calculate the two-dimensional (r-theta) structure of such flowsassuming that (1) convection transports angular momentum inwards, opposite tonormal viscosity and (2) viscous transport by other mechanisms (e.g., magneticfields) is weak (alpha << 1). Under such conditions convection dominates thedynamics of the accretion flow and leads to a steady state structure that ismarginally stable to convection. We show that the marginally stable flow has aconstant temperature and rotational velocity on spherical shells, a net flux ofenergy from small to large radii, zero net accretion rate, and a radial densityprofile proportional to r-1/2, flatter than the r-3/2 profilecharacteristic of spherical accretion flows. This solution accurately describesthe full two-dimensional structure of recent axisymmetric numerical simulationsof advection-dominated accretion flows, but its relevance to ``real'' flows isless certain.