The distance scale of planetary nebulae

By collecting distances from the literature, a set of 73 planetarynebulae with mean distances of high accuracy is derived. This sample isused for recalibration of the mass-radius relationship, used by manystatistical distance methods. An attempt to correct for a statisticalpeculiarity, where errors in the distances influences the mass-radiusrelationship by increasing its slope, has been made for the first time.Distances to PNe in the Galactic Bulge, derived by this new method aswell as other statistical methods from the last decade, are then usedfor the evaluation of these methods as distance indicators. In order ofachieving a Bulge sample that is free from outliers we derive newcriteria for Bulge membership. These criteria are much more stringentthan those used hitherto, in the sense that they also discriminateagainst background objects. By splitting our Bulge sample in two, onewith optically thick (small) PNe and one with optically thin (large)PNe, we find that our calibration is of higher accuracy than most othercalibrations. Differences between the two subsamples, we believe, aredue to the incompleteness of the Bulge sample, as well as the dominanceof optical diameters in the ``thin'' sample and radio diameters in the``thick'' sample. Our final conclusion is that statistical methods givedistances that are at least as accurate as the ones obtained from manyindividual methods. Also, the ``long'' distance scale of Galactic PNe isconfirmed.