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Individual distances to planetary nebulae are of the utmost relevance for ourunderstanding of post-asymptotic giant-branch evolution because they allow aprecise determination of stellar and nebular properties. Also, objects withindividual distances serve as calibrators for the so-called statisticaldistances based on secondary nebular properties. With independently knowndistances, it is possible to check empirically our understanding of theformation and evolution of planetary nebulae as suggested by existinghydrodynamical simulations. We compared the expansion parallaxes that haverecently been determined for a number of planetary nebulae with thetrigonometric parallaxes provided by the Gaia Data Release 2. Except for twoout of 11 nebulae, we found good agreement between the expansion and the Gaiatrigonometric parallaxes without any systematic trend with distance. Therefore,the Gaia measurements also prove that the correction factors necessary toconvert proper motions of shocks into Doppler velocities cannot be ignored.Rather, the size of these correction factors and their evolution with time aspredicted by 1-D hydrodynamical models of planetary nebulae is basicallyvalidated. These correction factors are generally greater than unity and aredifferent for the outer shell and the inner bright rim of a planetary nebula.The Gaia measurements also confirm earlier findings that spectroscopic methodsoften lead to an overestimation of the distance. They also show that evenmodelling of the entire system of star and nebula by means of sophisticatedphotoionization modeling may not always provide reliable results.  The Gaia measurements confirm the basic correctness of the presentradiation-hydrodynamics models, which predict that both the shell and the rimof a planetary nebula are two independently expanding entities.

Confronting expansion distances of planetary nebulae with Gaia DR2 measurements