The evolution of planetary nebulae VII. Modelling planetary nebulae of distant stellar systems

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-circle dot 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-circle dot) with optically thick (or nearly thick) nebular shells. The half-width-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 photoionisation modelling may become problematic for those cases where expansion cooling must be considered.