3. The distribution of PNN masses
Fig. 5 shows the histogram of the PNN mass distribution we find for our sample using =0.2 M . The median, mean and the average deviation of the distribution of PNN masses below 0.94M are indicated in the figure, together with the number of objects. The proportion of objects with derived PNN masses above 0.65M is also indicated. We see that the obtained distribution is very narrow, with more than 80% of the objects having between 0.55 and 0.65M . There are no objects with below 0.555M . This is simply due to the selection effect that stars with smaller masses evolve so slowly that the nebular envelope would disperse before the star gets hot enough to ionize it. On the other hand, as in many of the studies devoted to this problem, we find a long (but not very numerous) tail with PNN masses above 0.65M .
Because the lifetime of the PN phenomenon is depending on , the observed distribution of PN central star masses does not reflect the distribution of masses of post-AGB stars. Using our Fig. 3, we can empirically determine the mass distribution of zero-age post-AGB stars between 0.555M and 0.625M . It is simply obtained by dividing in each mass bin the number of objects by the characteristic time interval between the upper and lower envelope of the bulk of PN ages represented by the two curves in Fig. 3. The resulting distribution is shown in Fig. 6.
It is obviously quite different from the one displayed in Fig. 5, by having a much larger proportion of objects with higher . Because the number of objects in each mass bin above 0.625 M is so small, and because the determinations are so uncertain at such high masses, the distribution of post-AGB star masses above 0.625M cannot be derived quantitatively. Hovewer, the small number of observed PN with 0.65M indicates that there must be a drop in the post-AGB star mass distribution at about this mass.
One must not forget, however, that our determinations were made under the assumption that =0.2M . A different choice for would lead to a different determination of the PNN masses. Fig. 7 shows the histogram of PNN masses we derive under the assumption that =0.1 M , and Fig. 8 shows the histogram obtained under the assumption that =0.4 M . The characteristics of the distributions (median, mean, etc... are indicated in the same way as in Fig. 5). As mentioned above and in GST97, the derived PNN masses are higher for a smaller assumed . Note that also the shape of the PNN mass distributions varies when changing the assumption on . For an assumed of 0.4M , about 30% of the objects lie in the 0.555 0.005M bin.
Undoubtedly, there must be a certain dispersion in the values of of real planetary nebulae. It seems that in the Galactic bulge PN, values around 0.1 - 0.15 M are more probable for the total nebular mass (Stasiska & Tylenda 1994), while in the Magellanic Clouds, PN that are optically thin rather indicate a value of about 0.3M (Barlow 1987). The conclusion of all this is that the true distribution of PN central stars or of zero-age post-AGB stars is impossible to determine accurately in absence of additional observational parameters.
It remains that the distribution of PN central star masses is very narrow, the vast majority of the objects having between 0.55M and 0.65M .
Whether the PN central star mass distribution is compatible with that of white dwarfs is a question which requires a detailed modelling of galactic evolution (similar to the work of Koester & Weidemann 1980, or Yuan 1989), together with an explicit modelling of the biases affecting the observations of white dwarfs and planetary nebulae. Such an enterprise is out of the scope of the present study. For illustrative purposes, we simply compare in Fig. 9 the PNN mass distribution of Fig. 5 and the white dwarf mass distribution as obtained from the works of Bergeron et al. (1992) and Bragaglia et al. (1995). The fact that the white dwarf distributions extends to lower masses than the PNN mass distribution reflects in part the selection effects operating against the observation of planetary nebulae with very slowly evolving nuclei.
© European Southern Observatory (ESO) 1997
Online publication: April 6, 1998