2005A&A...431..963S

We investigate and discuss the expansion properties of planetary nebulae by means of 1D radiation-hydrodynamics models computed for different initial envelope configurations and central star evolutionary tracks. In particular, we study how the expansion depends on the initial density gradient of the circumstellar envelope and show that it is possible to derive information on the very last mass-loss episodes during the star's final evolution along and off the asymptotic giant branch. To facilitate the comparison of the models with real objects, we have also computed observable quantities like surface brightness and emission-line profiles. With the help of newly acquired high-resolution emission-line profiles for a sample of planetary nebulae we show that models with initial envelopes based on the assumption of a stationary wind outflow fail to explain the observed expansion speeds of virtually all of the observed planetary nebulae. Instead it must be assumed that during the very last phase of evolution along the final asymptotic giant branch evolution the mass-loss rate increases in strength, resulting in a much steeper slope of the circumstellar radial density distribution. Under these conditions, the expansion properties of the nebular gas differ considerably from the self-similar solutions found for isothermal conditions. Furthermore, the mass loss must remain at a rather high level until the stellar remnant begins to evolve quickly towards the central star regime. Current theoretical computations of dust-driven mass-loss which are restricted to rather low temperatures cannot be applied during the star's departure from the asymptotic giant branch.