VERTICAL OSCILLATIONS IN PROTOSTELLAR DISKS - I - FORMULATION OF THE PROBLEM

Protostellar disks that are relatively massive evolve under the influe nce of spiral-type density perturbations. Radiation from induced verti cal oscillations could slow the rapid growth of these modes while allo wing continued accretion onto the central star. Here I provide a gener al mathematical framework for studying disk evolution in this context. A nondimensional scheme is adopted that separates out the relatively short, dynamical timescale associated with vertical oscillations and o rbital motion from the much longer, evolutionary time required for alt eration of the underlying disk structure. I derive both the axisymmetr ic and nonaxisymmetric modal equations governing the evolution. I also present some general results that will later prove useful, including a perturbative expansion of the disk potential and a careful treatment of the rotation curve near the inner and outer disk edges.