Tests of the Galactic planetary nebula distance scale with the initial
  Gaia parallax distances of their central stars
  We used the "primary dataset" of Gaia Data Release 1 (DR1) to search for
parallax measurements of central stars (CSs) of Galactic planetary nebulae
(PNe), to determine PN distances. We found that a trigonometric parallax is
available for 16 CSs, seven of which with relative uncertainty below 80%. The
limited comparison of these trigonometric distances to other reliable
individual determinations discloses good correlation between the two sets, with
the Gaia parallax distances being lower by a factor of ~0.1 dex in the
logarithmic distances. We tested with the Gaia parallaxes the most popular
Galactic PN distance scales, namely, the physical radius vs. surface
brightness, and the ionized mass vs. inverse optical thickness scales. While
the number of available calibrators may still be too low, and their relative
uncertainties too high, to derive a working distance scale, we were able to
assess the current sample and to reveal the very promising potential of the
future Gaia releases for a recalibration of the distance scale of Galactic PNe.
