A STATISTICAL DISTANCE SCALE FOR GALACTIC PLANETARY-NEBULAE

A statistical distance scale is proposed. It is based on the correlati on between the ionized mass and the radius and the correlation between the radio continuum surface brightness temperature and the nebular ra dius. The proposed statistical distance scale is an average of the two distances obtained using the correlations. These correlations, calibr ated based on the 132 planetary nebulae with well-determined individua l 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 t heir distances around the Galactic center. This new distance scale is applied to 647 Galactic planetary nebulae. It is estimated that this d istance scale can be accurate on average to 35%-50%. Our statistical d istance scale is in good agreement with the one recently proposed by V an 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 similar to 0.6 M.. We stre ss that the scatter seen in the statistical distance scale is likely t o be real. The scatter is caused by the fact that the core mass distri bution, although narrow and strongly peaked, has a finite width.