Hydrodynamical Velocity Fields in Planetary Nebulae
  Based on axi-symmetric hydrodynamical simulations and 3D reconstructions with Shape, we investigate the kinematic signatures of deviations from homologous ("Hubble-type") outflows in some typical shapes of planetary nebulae. We find that, in most situations considered in our simulations, the deviations from a Hubble-type flow are significant and observable. The deviations are systematic and a simple parameterization of them considerably improves morpho-kinematical models of the simulations. We describe such extensions to a homologous expansion law that capture the global velocity structure of hydrodynamical axi-symmetric nebulae during their wind-blown phase. It is the size of the poloidal velocity component that strongly influences the shape of the position velocity diagrams that are obtained, not so much the variation of the radial component. The deviations increase with the degree of collimation of the nebula and they are stronger at intermediate latitudes. We describe potential deformations which these deviations might produce in 3D reconstructions that assume "Hubble-type" outflows. The general conclusion is that detailed morpho-kinematic observations and modeling of planetary nebulae can reveal whether a nebula is still in a hydrodynamically active stage (windy phase) or whether it has reached ballistic expansion. 
W. Steffen, G. Garcia-Segura, N. Koning