A statistical distance scale for Galactic planetary nebulae

A statistical distance scale is proposed. It is based on the correlation between the ionized mass and the radius and the correlation between the radio continuum surface brightness temperature and the nebular radius. The proposed statistical distance scale is an average of the two distances obtained while using the correlation. These correlations, calibrated based on the 1`32 planetary nebulae with well-determined individual distances by Zhang, can reproduce not only the average distance of a sample of Galactic Bulge planetary nebulae exactly at the distance to the Galactic center, but also the expected Gaussian distribution of their distances around the Galactic center. This new distance scale is applied to 647 Galactic planetary nebulae. It is estimated that this distance scale can be accurate on average to 35%-50%. Our statistical distance scale is in good agreement with the one recently proposed by Van de Steene and Zijlstra. The correlations found in this study can be attributed to the fact that the core mass of the central stars has a very sharp distribution, strongly peaked at approx. 0.6 solar mass. We stress that the scatter seen in the statistical distance scale is likely to be real. The scatter is caused by the fact that the core mass distribution, although narrow and strongly peaked, has a finite width.