A new statistical distance scale for planetary nebulae, based on Gaia EDR3

The present work aims to build a new statistical distance scale for planetary nebulae (PNe) based on a rigorous calibration sample. The distances of the calibration sample are derived from the trigonometric parallax method using the recent measurements of Gaia early third data release (Gaia EDR3). The new distance scale is created by applying the well-known linear relationship between the radio surface brightness temperature and the nebular radius. The calibration sample is made up of 96 PNe of accurately computed distances with uncertainties less than $20\%$. Earlier ground- and space-based trigonometric parallaxes of PNe display inconsistency with those of Gaia, particularly the HIPPARCOS results. In addition, these measurements have appreciably lower precision than that of Gaia. When compared to the trigonometric technique, the expansion and kinematic methods exhibited more consistency than the spectroscopic, extinction, gravity, and photo-ionization methods. Furthermore, contrary to earlier results in the literature, the extinction and gravity methods, on average, underestimate and slightly overestimate the PN distances. As a byproduct of extracting the Gaia parallaxes, we detect the radial velocity and variability for 14 and 3 PN central stars (CSs), respectively. To our knowledge, the variability of Hen 2-447 CS has been determined for the first time.