The distances of planetary nebulae: A scale based upon nearby sources

The statistical distances of planetary nebulae (PNe) are known to be notoriously uncertain, differing from each by factors approaching 2, and also from more reliable distances based upon trigonometric and spectroscopic parallaxes, expansion distances, and so forth. We point out that many of these problems arise from the use of inappropriate relations between surface brightness and nebular radius; of incomplete samples of standard sources; and the use of indirect (and/or inaccurate) methods for the evaluation of distances. Many of these problems can be side-stepped, however, where the standard sources are confined to nearby nebulae; planetaries whose distances are less than similar to0.7 kpc or so. We have, using such sources, undertaken a detailed revision of the surface brightness-radius calibration, and thereby de fined a new statistical scale which is consistent with the most direct, recent, and reliable distance measures. This scale is used to determine distances to 448 Population I Galactic planetary nebulae, and the results are compared to alternative statistical scales. It is shown that much of the disparity between the present distance scale and that of Zhang is likely to arise through differences in calibration source distances. It does not (as supposed by previous authors) appear to be a product of selection effects within the nebular samples. A disparity with the van de Steene & Zijlstra distances may arise from differences between Galactic bulge and disk nebulae, while the scales of Daub and Cahn et al. appear to be based upon inappropriate trends between surface brightness and radius. Finally, we discuss the implications of these results for the formation rates of planetary nebulae and determine a galaxy-wide total of PNe N-T = 3.0 x 10(4). The luminosity specific formation rate chi(L) similar to 3 x 10(-11) L.(-1)(,.BOL) appears similar to2.5 times larger than determined in previous analyses, while the rate per unit area of Galactic disk [chi(A)(PNe) similar to 1.6 x 10(3) yr(-1) kpc(-2)] is comparable to the value deduced for white dwarfs.