A simplified model for an evolving protoplanetary nebula

The dynamic evolution of a protoplanetary nebula is investigated using analytical solutions of the surface density transport equations. Constant- and so-called beta-viscosity turbulence models are compared with a functional analytical model and the well-known alpha-viscosity formulation. The model presented here is related to a number of simplified disk evolution models but is also associated with beta-viscosity models based on hydrodynamic generation of turbulence. The beta-viscosity model, heretofore used for steady state disks, is shown to be a useful approximation for disk evolution problems.