1995A&A...293..541V

We propose to use the correlation between the distance-independent radio continuum brightness temperature and the distance-dependent radius to determine statistical distances to planetary nebulae. This correlation satisfies two objective criteria which define a statistical distance scale: (1) We obtain the same calibration relation for the large sample of Galactic bulge planetary nebulae as for a small sample of non-bulge planetary nebulae with well-determined distances, showing that the method is applicable to different PN populations. (2) The distribution of the distances to the Galactic bulge planetary nebulae is in agreement with the expected distribution of distances around the Galactic center. Distances could be determined to better than a factor 2 for 95% of the planetary nebulae, and on average to an accuracy of about 40%. It is an essential requirement that the optically thin radio flux and corresponding angular diameter be used in calculation of the brightness temperature. We show that the correlation is also reproduced by model calculations of PN evolution. We show that the new calibration of the Daub scale obtained by Cahn et al. (1992A&AS...94..399C) also gives the correct average distance to the large sample of bulge planetary nebulae, but gives a skewed distribution around the Galactic Center. Models show that this is caused by the fact that for young nebulae the Daub curve does not follow evolutionary model tracks.