The Gaia Data Release 1 parallaxes and the distance scale of Galactic
  planetary nebulae
  In this paper we gauge the potentiality of Gaia in the distance scale
calibration of planetary nebulae (PNe) by assessing the impact of DR1
parallaxes of central stars of Galactic PNe (CSPNe) against known physical
relations. For selected PNe targets with state-of-the-art data on angular sizes
and fluxes, we derive the distance-dependent parameters of the classical
distance scales, i.e., physical radii and ionized masses, from DR1 parallaxes;
we propagate the uncertainties in the estimated quantities and evaluate their
statistical properties in the presence of large relative parallax errors; we
populate the statistical distance scale diagrams with this sample and discuss
its significance in light of existing data and current calibrations.
  We glean from DR1 parallaxes 8 CSPNe with S/N$>$1. We show that this set of
potential calibrators doubles the number of extant trigonometric parallaxes
(from HST and ground-based), and increases by two orders of magnitude the
domain of physical parameters probed previously. We then use the combined
sample of suitable trigonometric parallaxes to fit the
physical-radius-to-surface-brightness relation. This distance scale
calibration, although preliminary, appears solid on statistical grounds, and
suggestive of new PNe physics.
  With the tenfold improvement in PNe number statistics and astrometric
accuracy expected from future Gaia releases the new distance scale, already
very intriguing, will be definitively constrained.
