New line-driven mass-loss rate predictions for central stars of planetary nebulae: Luminosity dependence when approaching the Eddington limit

After expelling most of their envelopes, asymptotic giant branch stars turn bluewards in the Hertzsprung-Russel diagram and become hot objects. These objects ionise the surrounding material, possibly creating a planetary nebula. Because they are hot and rather luminous, they are able to launch a line-driven wind. The luminosity dependence of these winds has not yet been studied in detail using global wind models that consistently consider the interaction of the photosphere and the wind. We provide line-driven wind models of the central stars of planetary nebulae focusing on the dependence of these winds on luminosity. While the mass-loss rate is strongly sensitive to stellar luminosity, the terminal velocity increases with effective temperature and only weakly depends on luminosity. The predicted values agree reasonably well with observations, except that observational mass-loss rates show a rather large scatter, and the predicted terminal velocities are slightly lower than observational values. We provide ionising fluxes and show that for stars cooler than approximately 40,kK, the ionising fluxes computed from plane-parallel models are inadequate. The wind efficiency stays rather weak, which implies that the Wolf-Rayet type of central stars is connected with objects with an elevated mass fraction of heavy elements.