On the dynamical foundations of alpha disks

The dynamical foundations of a disk models are described. At the heart of t he viscous formalism of accretion disk models are correlations in the fluct uating components of the disk velocity, magnetic field, and gravitational p otential. We relate these correlations to the large-scale mean flow dynamic s used in phenomenological viscous disk models. MHD turbulence readily lend s itself to the a formalism, but transport by self-gravity does not. Nonloc al transport is an intrinsic property of turbulent self-gravitating disks, which in general cannot be captured by an a model. Local energy dissipation and a-like behavior can be reestablished if the pattern speeds associated with the amplitudes of an azimuthal Fourier decomposition of the turbulence are everywhere close to the local rotation frequency. In this situation, g lobal wave transport must be absent. Shearing box simulations, which employ boundary conditions forcing local behavior, are probably not an adequate t ool for modeling the behavior of self-gravitating disks. As a matter of pri nciple, it is possible that disks that hover near the edge of gravitational stability may behave in accord with a local a model, but global simulation s performed to date suggest matters are not this simple.