On the Dynamical Foundations of Alpha Disks

The dynamical foundations of $\alpha$ disk models are described. At the heart of the viscous formalism of accretion disk models are correlations in the fluctuating components of the disk velocity, magnetic field, and gravitational potential. We relate these correlations to the large scale mean flow dynamics used in phenomenological viscous disk models. MHD turbulence readily lends itself to the $\alpha$ formalsim, but transport by self-gravity does not. Nonlocal transport is an intrinsic property of turbulent self-gravitating disks, which in general cannot be captured by an $\alpha$ model. Local energy dissipation and $\alpha$-like behavior can be re-established 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, global wave transport must be absent. Shearing box simulations, which employ boundary conditions forcing local behavior, are probably not an adequate tool for modeling the behavior of self-gravitating disks. As a matter of principle, it is possible that disks which hover near the edge of gravitational stability may behave in accord with a local $\alpha$ model, but global simulations performed to date suggest matters are not this simple.