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 re calibration of the mass-radius relationship, used by many statistical dista nce methods. An attempt to correct for a statistical peculiarity, where err ors in the distances influences the mass-radius relationship by increasing its slope, has been made for the first time. Distances to PNe in the Galact ic Bulge, derived by this new method as well as other statistical methods f rom the last decade, are then used for the evaluation of these methods as d istance indicators. In order of achieving a Bulge sample that is free from outliers we derive new criteria for Bulge membership. These criteria are mu ch more stringent than those used hitherto, in the sense that they also dis criminate against background objects. By splitting our Bulge sample in two, one with optically thick (small) PNe and one with optically thin (large) P Ne, we find that our calibration is of higher accuracy than most other cali brations. Differences between the two subsamples, we believe, are due to th e incompleteness of the Bulge sample, as well as the dominance of optical d iameters in the "thin" sample and radio diameters in the "thick" sample. Ou r final conclusion is that statistical methods give distances that are at l east as accurate as the ones obtained from many individual methods. Also, t he "long" distance scale of Galactic PNe is confirmed.