A new statistical distance scale for planetary nebulae

In the first part of the present article we discuss the consistency among different individual distance methods of Galactic planetary nebulae, while in the second part we develop a new statistical distance scale based on a calibrating sample of well determined distances. A set composed of 315 planetary nebulae with individual distances are extracted from the literature. Inspecting the data set indicates that the accuracy of distances is varying among different individual methods and also among different sources where the same individual method was applied. Therefore, we derive a reliable weighted mean distance for each object by considering the influence of the distance error and the weight of each individual method. The results reveal that the discussed individual methods are consistent with each other, except the gravity method that produces higher distances compared to other individual methods. From the initial data set, we construct a standard calibrating sample consists of 82 objects. This sample is restricted only to the objects with distances determined from at least two different individual methods, except few objects with trusted distances determined from the trigonometric, spectroscopic, and cluster membership methods. In addition to the well determined distances for this sample, it shows a lot of advantages over that used in the prior distance scales. This sample is used to recalibrate the mass-radius and radio surface brightness temperature-radius relationships. An average error of similar to 30 % is estimated for the new distance scale. The newly distance scale is compared with the most widely used statistical scales in literature, where the results show that it is roughly similar to the majority of them within similar to +/- 20 % difference. Furthermore, the new scale yields a weighted mean distance to the Galactic center of 7.6 +/- 1.35 kpc, which in good agreement with the very recent measure of Malkin 2013.