On the Dynamical Foundations of α Disks

The dynamical foundations of $\alpha$ disk models are described. At the heartof the viscous formalism of accretion disk models are correlations in thefluctuating components of the disk velocity, magnetic field, and gravitationalpotential. We relate these correlations to the large scale mean flow dynamicsused in phenomenological viscous disk models. MHD turbulence readily lendsitself to the $\alpha$ formalsim, but transport by self-gravity does not.Nonlocal transport is an intrinsic property of turbulent self-gravitatingdisks, which in general cannot be captured by an $\alpha$ model. Local energydissipation and $\alpha$-like behavior can be re-established if the patternspeeds associated with the amplitudes of an azimuthal Fourier decomposition ofthe turbulence are everywhere close to the local rotation frequency. In thissituation, global wave transport must be absent. Shearing box simulations,which employ boundary conditions forcing local behavior, are probably not anadequate tool for modeling the behavior of self-gravitating disks. As a matterof principle, it is possible that disks which hover near the edge ofgravitational stability may behave in accord with a local $\alpha$ model, butglobal simulations performed to date suggest matters are not this simple.Comment: 20 pages, Latex, aasm