Confronting expansion distances of planetary nebulae with Gaia DR2
  measurements
  Individual distances to planetary nebulae are of the utmost relevance for our
understanding of post-asymptotic giant-branch evolution because they allow a
precise determination of stellar and nebular properties. Also, objects with
individual distances serve as calibrators for the so-called statistical
distances based on secondary nebular properties. With independently known
distances, it is possible to check empirically our understanding of the
formation and evolution of planetary nebulae as suggested by existing
hydrodynamical simulations. We compared the expansion parallaxes that have
recently been determined for a number of planetary nebulae with the
trigonometric parallaxes provided by the Gaia Data Release 2. Except for two
out of 11 nebulae, we found good agreement between the expansion and the Gaia
trigonometric parallaxes without any systematic trend with distance. Therefore,
the Gaia measurements also prove that the correction factors necessary to
convert proper motions of shocks into Doppler velocities cannot be ignored.
Rather, the size of these correction factors and their evolution with time as
predicted by 1-D hydrodynamical models of planetary nebulae is basically
validated. These correction factors are generally greater than unity and are
different for the outer shell and the inner bright rim of a planetary nebula.
The Gaia measurements also confirm earlier findings that spectroscopic methods
often lead to an overestimation of the distance. They also show that even
modelling of the entire system of star and nebula by means of sophisticated
photoionization modeling may not always provide reliable results.
  The Gaia measurements confirm the basic correctness of the present
radiation-hydrodynamics models, which predict that both the shell and the rim
of a planetary nebula are two independently expanding entities.
