## 5. Mass estimate of the progenitors of the PNeIn order to compare the observed isotopic ratios with the predictions of stellar evolutionary models, we must estimate the mass of the progenitors stars of the PNe. For the present samples, we have followed the procedure adopted in GSTP, consisting of the following steps. (1) We assign to each nebula the best measured distance (or an
average of available distances), the
H flux, the HeII flux
at 4686 Å, the angular size, and the (2) By locating the central star in the - plane, we derive its mass () from comparison with a set of evolutionary tracks (Stanghellini & Renzini 1993). (3) Using the initial mass-final mass relation, we compute the progenitor mass, that is the stellar mass on the main sequence (). The stellar properties adopted for the PNe detected in
Let us examine the uncertainty involved in the final mass calculations. Estimates of the stellar temperature and luminosity given in Table 3 are affected by errors in magnitudes, fluxes, diameters and extinctions. However, these quantities are usually determined with good accuracy (), so that the uncertainty in the derived mass of the central stars does not exceed %, or . The values given in the table do not include errors on the distances to the PN, which can be intrinsically high (up to 50%) but are difficult to estimate on an individual basis. To infer the main sequence masses, we have used the initial mass-final mass relation given by Hervig (1996). This relation differs from that of Weidemann (1987) adopted in GSTP. We preferred Hervig's prescription since it is based on reliable observations of cluster white dwarfs, although the formal errors on the final mass are still substantial, and can amount to about 0.1 . Since we derive initial masses from final masses, the errors on the former quantity can be even larger. Quantitatively, we assign a formal error to the main sequence mass of for low values of the initial mass ( ), and a smaller error ( ) for higher masses. This difference is due to the change of the slope of the initial mass - final mass relation at about 2 : smaller masses are more sensitive to the adopted relation, and the uncertainty is correspondingly larger. © European Southern Observatory (ESO) 2000 Online publication: March 17, 2000 |