The distance scale of planetary nebulae

By collecting distances from the literature, a set of 73 planetary nebulae with mean distances of high accuracy is derived. This sample is used for recalibration of the mass-radius relationship, used by many statistical distance methods. An attempt to correct for a statistical peculiarity, where errors in the distances influences the mass{radius relationship by increasing its slope, has been made for the rst time. Distances to PNe in the Galactic Bulge, derived by this new method as well as other statistical methods from the last decade, are then used for the evaluation of these methods as distance indicators. In order of achieving a Bulge sample that is free from outliers we derive new criteria for Bulge membership. These criteria are much more stringent than those used hitherto, in the sense that they also discriminate against background objects. By splitting our Bulge sample in two, one with optically thick (small) PNe and one with optically thin (large) PNe, we nd that our calibration is of higher accuracy than most other calibrations. Dierences between the two subsamples, we believe, are due to the incompleteness of the Bulge sample, as well as the dominance of optical diameters in the \thin" sample and radio diameters in the \thick" sample. Our nal conclusion is that statistical methods give distances that are at least as accurate as the ones obtained from many individual methods. Also, the \long" distance scale of Galactic PNe is conrmed.