Abstract. 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.

Abstract.A detailed theoretical study of the basic internal kinematics of planetary nebulae is presented, based on 1D radiationhydrodynamics simulations of circumstellar envelopes around central stars of 0.595 and 0.696 M . 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.

Aims. By means of hydrodynamical models we do the first investigations of how the properties of planetary nebulae are affected by their metal content and what can be learned from spatially unresolved spectrograms of planetary nebulae in distant stellar systems. Methods. We computed a new series of 1D radiation-hydrodynamics planetary nebulae model sequences with central stars of 0.595 M surrounded by initial envelope structures that differ only by their metal content. At selected phases along the evolutionary path, the hydrodynamic terms were switched off, allowing the models to relax for fixed radial structure and radiation field into their equilibrium state with respect to energy and ionisation. The analyses of the line spectra emitted from both the dynamical and static models enabled us to systematically study the influence of hydrodynamics as a function of metallicity and evolution. We also recomputed selected sequences already used in previous publications, but now with different metal abundances. These sequences were used to study the expansion properties of planetary nebulae close to the bright cut-off of the planetary nebula luminosity function. Results. Our simulations show that the metal content strongly influences the expansion of planetary nebulae: the lower the metal content, the weaker the pressure of the stellar wind bubble, but the faster the expansion of the outer shell because of the higher electron temperature. This is in variance with the predictions of the interacting-stellar-winds model (or its variants) according to which only the central-star wind is thought to be responsible for driving the expansion of a planetary nebula. Metal-poor objects around slowly evolving central stars become very dilute and are prone to depart from thermal equilibrium because then adiabatic expansion contributes to gas cooling. We find indications that photoheating and line cooling are not fully balanced in the evolved planetary nebulae of the Galactic halo. Expansion rates based on widths of volume-integrated line profiles computed from our radiation-hydrodynamics models compare very well with observations of distant stellar system. Objects close to the bright cut-off of the planetary nebula luminosity function consist of rather massive central stars (>0.6 M ) with optically thick (or nearly thick) nebular shells. The halfwidth-half-maximum velocity during this bright phase is virtually independent of metallicity, as observed, but somewhat depends on the final AGB-wind parameters. Conclusions. The observed expansion properties of planetary nebulae in distant stellar systems with different metallicities are explained very well by our 1D radiation-hydrodynamics models. This result demonstrates convincingly that the formation and acceleration of a planetary nebula occurs mainly because of ionisation and heating of the circumstellar matter by the stellar radiation field, and that the pressure exerted by the shocked stellar wind is less important. Determinations of nebular abundances by means of photoionisa...

Context. The luminosity function of planetary nebulae, in use for about two decades in extragalactic distance determinations, is still subject to controversial interpretations. Aims. The physical basis of the luminosity function is investigated by means of several evolutionary sequences of model planetary nebulae computed with a 1D radiation-hydrodynamics code. Methods. The nebular evolution is followed from the vicinity of the asymptotic-giant branch across the Hertzsprung-Russell diagram until the white-dwarf domain is reached, using various central-star models coupled to different initial envelope configurations. Along each sequence the relevant line emissions of the nebulae are computed and analysed.Results. Maximum line luminosities in Hβ and [O iii] 5007 Å are achieved at stellar effective temperatures of about 65 000 K and 95 000. . . 100 000 K, respectively, provided the nebula remains optically thick for ionising photons. In the optically thin case, the maximum line emission occurs at or shortly after the thick/thin transition. Our models suggest that most planetary nebulae with hotter ( > ∼ 45 000 K) central stars are optically thin in the Lyman continuum, and that their [O iii] 5007 Å emission fails to explain the bright end of the observed planetary nebulae luminosity function. However, sequences with central stars of > ∼ 0.6 M and rather dense initial envelopes remain virtually optically thick and are able to populate the bright end of the luminosity function. Individual luminosity functions depend strongly on the central-star mass and on the variation of the nebular optical depth with time. Conclusions. Hydrodynamical simulations of planetary nebulae are essential for any understanding of the basic physics behind their observed luminosity function. In particular, our models do not support the claim of Marigo et al. (2004, A&A, 423, 995) according to which the maximum 5007 Å luminosity occurs during the recombination phase well beyond 100 000 K when the stellar luminosity declines and the nebular models become, at least partially, optically thick. Consequently, there is no need to invoke relatively massive central stars of, say >0.7 M , to account for the bright end of the luminosity function.