The evolution of planetary nebulae

We follow hydrodynamically the evolution of spherical model planetary nebulae subject to different initial conditions and with various central stars, investigating how combinations of central-star mass and asymptotic giant branch mass-loss rate determine the shape and kinematics of a planetary nebula. With this approach we aim at constituting a framework useful for the interpretation of the evolutionary status and previous mass-loss history of observed individual nebulae, making use of their kinematical properties and surface brightness characteristics. In particular, the models are compared with the observed morphologies and kinematics of double shell nebulae. The dynamical structure of all the models is characterized by a more or less complicated shock wave pattern set up by ionization and wind interaction whose combined action results in general in a typical double-shell structure. We have found that models with simple initial structures based on a constant AGB mass-loss rate fail to comply with observed shell morphologies and surface-brightness distributions. A reasonable agreement with the observations is only found for a model where the mass-loss rate is strongly increasing towards the end of the asymptotic giant-branch evolution. Depending on the central star's evolutionary speed and the density of the cool wind expelled along the asymptotic giant-branch, planetary nebulae may never get optically thin. This is primarily the case for the more massive central stars, and this fact offers a rather natural explanation for the long standing problem of the very existence of molecular hydrogen in the immediate vicinity of hot central stars. We also show that distances to planetary nebulae based on expansion parallaxes are systematically too small by a significant amount