The evolution of planetary nebulae

A detailed theoretical study of the basic internal kinematics of planetary nebulae is presented, based on 1D radiation-hydrodynamics simulations of circumstellar envelopes around central stars of 0.595 and 0.696 $M_{\odot}$. By means of observable quantities like radial surface-brightness distributions and emission-line profiles computed from the models, a comparison with real objects was performed and revealed a reasonable agreement. This allowed to draw important conclusions by investigating the kinematics of these models in detail. Firstly, it is shown that the determination of kinematical ages, normally considered to be simple if size and expansion rate of an object are given, can seriously be flawed. Secondly, the expansion law of a planetary nebula is different from what is assumed for deriving spatio-kinematical models. Thirdly and most importantly, our hydrodynamical models help to correctly use existing angular expansion measurements for distance determinations. The mere combination of the angular expansion rates with the spectroscopic expansion velocities leads always to a serious underestimate of the distance, the degree of which depends on the evolutionary state of the object. The necessary correction factor varies between 3 and 1.3. Individual correction factors can be estimated with an accuracy of about 10% by matching our hydrodynamical models to real objects. As a result, revised distances for a few objects with reliable angular expansion rates are presented. But even these corrected distances are not always satisfying: they still appear to be inconsistent with other distance determinations and, even more disturbing, with the accepted theory of post-asymptotic giant branch evolution. As a byproduct of the angular expansion measurements, the transition times from the vicinity of the asymptotic giant branch to the planetary-nebula regime could be estimated. They appear to be shorter than assumed in the present evolutionary calculations