4. PNe with H-deficient central stars versus other PNe
In this section we compare the PNe having H-deficient nuclei with the rest of the Galactic PN population. The latter sample, for simplicity named "others", includes all the PNe whose central stars have not been found to be H-deficient. Most of the objects in this sample have H-rich PNNi although it cannot be excluded that some of them have yet undetected H-poor central stars. The observational data base for the others comes from the same sources as Table 1.
Fig. 4 compares the distribution of the nebular densities in the case of the H-deficient PNNi with that obtained for the others. The same but for and is shown in Fig. 5 and Fig. 6, respectively. Objects for which only lower limits are known have been excluded from the histograms.
As can be seen from Fig. 4, Fig. 5, and Fig. 6, the distributions for both samples are very similar. Statistical tests of Kolmogorov-Smirnov and of Wilcoxon confirm that there is no statistically important difference between them.
Let us pay more attention to the parts of the distributions corresponding to dense and high surface brightness objects, i.e. log , log , log . These parts are expected to be most complete and least subject to observational selection effects. As it can be seen from Fig. 4, Fig. 5, and Fig. 6 they look very much the same for both samples. The ratio of the H-deficient PNN to the others for log is 15.6%. For the whole samples this ratio is 13.0%. For objects with log the H-deficient proportion is 8.9% against 7.0% for the entire samples. In the case of log the respective figures are exactly 10.1% and 10.1%. This shows that the H-deficient PNNi are not underpopulated (neither overpopulated) among dense, high surface brightness PNe. In other words, the H-deficient stars become observable as PNNi at a similar evolutionary (expansion) stage of the nebulae as the others. This is an important conclusion for the discussion later on in this paper.
Fig. 7 plots versus for the objects from both samples. As shown in Górny et al. (1997a) and Stasinska et al. (1997) this diagram is useful for studying the evolution of PNNi. The objects evolve from the upper-left to the lower-right of the diagram. High mass, fast evolving PNNi are expected to be observed along the upper-right portion of the distribution.
The H-deficient sample presented in Fig. 7 has been devided into three subsamples, i.e. late-[WC] ([WC 11-7]), early-[WC] ([WC 6-2]) and PG 1159 (non-[WC]). Thus the general evolutionary sequence of the H-deficient PNNi, as discussed in the previous section, can be seen from Fig. 7 as well.
The main feature of the diagram displayed in Fig. 7 is that the distribution of the H-deficient PNNi is very much the same as that of the others. There is no region in the diagram where the H-deficient PNNi would be evidently lacking or appearing more often in comparison to the others. It can thus be concluded that the general trend and the rate of evolution of the objects are the same for both samples.
© European Southern Observatory (ESO) 2000
Online publication: October 30, 2000