Two Dimensional Adiabatic Flows onto a Black Hole: I. Fluid Accretion

When gas accretes onto a black hole, at a rate either much less than or much greater than the Eddington rate, it is likely to do so in an "adiabatic" or radiatively inefficient manner. Under fluid (as opposed to MHD) conditions, the disk should become convective and evolve toward a state of marginal instability. The resulting disk structure is "gyrentropic," with convection proceeding along common surfaces of constant angular momentum, Bernoulli function and entropy, called "gyrentropes." We present a family of two-dimensional, self-similar models which describes the time-averaged disk structure. We then suppose that there is a self-similar, Newtonian torque and that the Prandtl number is large. This torque drives inflow and meridional circulation and the resulting flow is computed. Convective transport will become ineffectual near the disk surface. It is conjectured that this will lead to a large increase of entropy across a "thermal front" which we identify as the effective disk surface and the base of an outflow. The conservation of mass, momentum and energy across this thermal front permits a matching of the disk models to self-similar outflow solutions. We then demonstrate that self-similar disk solutions can be matched smoothly onto relativistic flows at small radius and thin disks at large radius. This model of adiabatic accretion is contrasted with some alternative models that have been discussed recently. The disk models developed in this paper should be useful for interpreting numerical, fluid dynamical simulations. Related principles to those described here may govern the behaviour of astrophysically relevant, magnetohydrodynamic disk models.