Spectroscopic investigation of old planetaries V. Distance scales

We use the results of our recent NLTE model atmosphere analysis of central stars of old planetary nebulae (PN) to calculate distances. We perform a comparison with three other methods (trigonometric parallaxes, interstellar NaD lines, and Shklovsky distances) and discuss the problem of the PNe distance scale. The result of the comparison of our spectroscopic distances with the trigonometric distances is that the spectroscopic distances are 55% larger. Since using trigonometric parallaxes with large relative measurement errors can introduce systematic errors, we carried out a Monte Carlo simulation of the biases introduced by selection effects and measurement errors. It turns out that a difference between both distance scales of the observed size is expected for the present day data if the underlying distance scales are identical. Thus our finding is essentially a confirmation of the spectroscopic distance scale! Good agreement is found between the spectroscopic distances and distances derived from the interstellar NaD lines. All three independent methods of distance measurement indicate that the widely used "statistical" distance scales of the Shklovsky type are too short for old PNe. A correlation with nebular radii exists. The most likely explanation is an underestimate of the nebula masses for large PN. Implications for the nebula masses are discussed. Estimates of the PNe space density and birthrate, which are based on Shklovsky type distances, therefore give too large values.