Convection-dominated accretion flows

Nonradiating advection-dominated accretion flows are convectively unstable in the radial direction. We calculate the two-dimensional (r-θ) structure of such flows assuming that (1) convection transports angular momentum inward, opposite to normal viscosity, and (2) viscous transport by other mechanisms (e.g., magnetic fields) is weak (α ≪ 1). Under such conditions convection dominates the dynamics of the accretion flow and leads to a steady state structure that is marginally stable to convection. We show that the marginally stable flow has a constant temperature and rotational velocity on spherical shells, a net flux of energy from small to large radii, zero net accretion rate, and a radial density profile of ρ ∝ r^-1/2, flatter than the ρ ∝ r^-3/2 profile characteristic of spherical accretion flows. This solution accurately describes the full two-dimensional structure of recent axisymmetric numerical simulations of advection-dominated accretion flows.