ACTA ASTRONOMICA Vol. 43 (1993) pp. 371±380 Comparison of the Masses of Planetary Nebula Nuclei Derived from Different Methods by ; S.K. G o r n y 1;2 , R. Tylenda1 2 , and G.Stasi nska 2 1 Copernicus Astronomical Center, Chopina 12/18, PL-87100 ToruÂn, Poland 2 DAEC, Observatoire de Paris-Meudon, F-92195 Meudon CÂedex, France ABSTRACT We present some results of an extensive and uniform analysis of the planetary nebula nuclei from samples examined by Mendez et al. and Gathier and Pottasch. The present study uses distance independent diagrams. The theoretical tracks have been modi®ed so that they can be directly compared in the diagrams to the observed central star positions. From this comparison the central star masses have been derived. Our results are in contradiction with those from the above cited studies. Possible explanations of the differences are presented. 1. Introduction During recent years numerous studies of the masses of planetary nebula nuclei (PNN) have been undertaken. Most of the authors have come to more or less the same general conclusion, i.e. thatthe PNNmasses are concentrated around0.60M and have a strong cutoff at 0.55 M (SchonbernerÈ 1981, Kaler 1983, Heap and Augensen 1987, Szczerba 1987, 1990, Weidemann 1989, Tylenda and Stasinska 1989, Stasinska and Tylenda 1990, Kaler et al. 1990, Kaler and Jacoby 1990, 1991, Dopita and Meathernigham 1991, Tylenda et al. 1991, Zhang and Kwok 1993). The principal controversy concerns the proportion of massive PNN. Some authors ®nd that the number of PNN above 0.7 M is negligible (e.g. SchonbernerÈ 1981, Weidemann 1989, Tylenda et al. 1991), others obtain an important high-mass tail (e.g. Kaler et al. 1990, Kaler and Jacoby 1990, Dopita and Meathernigham 1991). However, there are authors who came to qualitatively different conclusions than the mentioned above. Mendez et al. (1988, 1990) have obtained PNN masses between 0.65 and 0.90 M for 80% of the objects in their sample. On the other hand, Gathier and Pottasch (1989, hereinafter GP) have constructed an observed H-R diagram from which it can be infered that 50-60% of their PNN have masses 372 A. A. about or below 0.55 M (similar conclusion has also been drawn in Pottasch 1984, Zijlstra and Pottasch 1989 and Pottasch and Acker 1989). The problem is important, since it arises from elaborated studies performed with a great care by their authors. Mendez et al. (1988, 1990) have analyzed the absorption line pro®les in the PNN spectra by means of stellar atmosphere models T g which allowed them to derive e and log These values when compared to the theoretical PNN models have resulted in the PNN masses. In their more recent study Mendez et al. (1992, hereinafter MKH) using a more elaborated version of the PNN model atmospheres have obtained, in most cases, somewhat higher values for the gravities which resulted in lower PNN masses. The problem, however, still remains serious since 80% of the PNN in MKH havemassesbetween 0.64 and 0.73 M which is signi®cantly higher than masses found in other studies and in GP in particular. GP use a rather classic method as they confront the observations to the theoret- ical models in the H-R diagram. The principal particularity and importance of this study is that it uses individually determined distances from Gathier (1987). The authors believe that their distances have an accuracy better than 40%. One can invoke two reasons of the discrepancy between the results of MKH and those of GP. One possibility arises from the fact that the two samples, in the bulk, contain different objects. Therefore it can be suggested that MKH have preferentially selected more luminous and more massive PNN whereas the sample of GP contains a large proportion of low mass objects (see e.g. GP, McCarthy et al. 1990). However, the results obtained in the two studies for two objects in common (NGC 3242 and NGC 7009) are signi®cantly different: the luminosities derived by MKH for these two PNN are factor 30 larger than in GP. The difference is obviously too large and cannot be reconciled within error bars quoted in the two studies. This fact prompts to consider another possibility, i.e. that the bulk of the difference between the PNN masses in MKH and those in GP results from different methods of analysis applied in the two studies. If this is the case then the implication would be that either the PNN masses of MKH are systematically overestimated or the PNN luminosities in GP are, at least for some objects, underestimated or both. This possibility has already been discussed by some authors (e.g. Szczerba 1990, Zhang and Kwok 1993, Tylenda 1993). This paper presents some results of an extensive and uniform analysis of the PN from both samples performed in order to ®nd if there are indications that the two samples are systematically different and in which sense. From basic observational data, such as PNN magnitudes, H ¯ux, radio ¯ux, PN diamaters, etc., we can construct different diagrams in which the observed objects can be compared between them as well as to the theoretical evolutionary models. From these diagrams we can estimate the PNN masses which when confronted to the masses of MKH and GP allows to draw conclusions. Vol. 43 373 2. Observational Parameters and Theoretical Tracks The distances to PN are one of the principal sources of uncertainties while comparing the theoretical PNN models to the observations. Therefore we have concentrated, in the present study, on diagrams using distance independent param- eters. The observational data, i.e. PN diameters, H ¯uxes, radio ¯uxes at 6 cm, HeII 4686 line intensities, central star magnitudes, expansion velocities, have been taken from the ESO-Strasbourg catalogue (Acker et al. 1992). These data have been processed in the usual manner to derive the following parameters: hydrogen T ( ) T ( ) Z Zanstra temperature, Z HI , helium Zanstra temperature, HeII , (both being obtained assuming that the star radiates as a blackbody), parameter f as de®ned T in Tylenda and Stasinska (1989), and radio brightness temperature, b . Then the f observed PNN have been compared to the model PNN on a log T (PNN) ± log T T T ( ) Z diagram and a log b ± log (PNN) diagram constructed separately for HI T ( ) and Z HeII . The PNN evolution for a given mass have been obtained from an interpolation procedure discribed in Stasinska and Tylenda (1993). The procedure is based on the tracks of SchonbernerÈ (1981, 1983) and BlockerÈ and SchonbernerÈ (1991). The tracks from SchonbernerÈ (1981, 1983) have been somewhat modi®ed so they have the zero-age point at the pulsation period of 50 days, similarly as in BlockerÈ and SchonbernerÈ (1991). In order to have theoretical tracks directly comparable to the observed objects in the diagrams, the model PNN have been treated similarily as in Tylenda et al. (1991) or Gorny et al. (1993). Thus we have assumed that each evolving PNN is surrounded by a spherically symmetric, uniform density nebula M V exp of a given mass, neb , expanding at a constant velocity, . The nebular shell thickness relative to the nebular radius is kept constant, and taken equal to 0.3. The star is assumed to radiate as a blackbody. Then the H and He ionization structure of the nebula can be obtained from the ionization equilibrium. This allows to calculate the Zanstra temperatures for the model PNN and the nebular radio brightness temperature. 3. Diagnostic Diagrams Figs. 1 ± 4 show the resultant diagrams. The objects from the MKH sample are represented by ®lled circles. Those from the GP sample are shown as open circles. Partly ®lled squares correspond to the two objects in common. For a number of objects we had only upper limits for HeII 4686. Hence the upper limits T ( ) for Z HeII in Figs. 2 and 4. Curves show the theoretical tracks for given PNN M = V = exp masses. They have been obtained adopting neb 0 2M and 20 km/s. As can be seen from Figs. 1 ± 4 there is a systematic difference in the positions on the diagramsbetweenthe sample of MKH and the sampleof GP. On the average, 374 A. A. T ( ) Fig. 1. The parameter, f against the hydrogen Zanstra temperature, Z HI . Filled circles ± objects from the MKH sample; open circles ± objects from the GP sample; partly ®lled squares ± objects in common; dashed curves ± theoretical tracks for PNN masses from 0.55 M to 0.69 M spaced by 0.01 M . T ( ) Fig. 2. The parameter, f against the helium Zanstra temperature, Z HeII . The same notation as in Fig. 1. Vol. 43 375 T ( ) Fig. 3. The radio brightness temperature, Tb , against the hydrogen Zanstra temperature, Z HI . The same notation as in Fig. 1. T ( ) Fig. 4. The radio brightness temperature, Tb , against the helium Zanstra temperature, Z HeII . The same notation as in Fig. 1. 376 A. A. the former shows lower Zanstra temperatures than the latter. This is certainly due to the observationalselection asMKH pickedup PNN with well developed absorption lines of H and He which takes place at lower effective temperatures. When confronting the observed positions to the theoretical tracks two general conclusions can be drawn from Figs. 1 ± 4. First, contrary to GP we see no PNN lying de®nitively below the track of 0.55 M . Second, the sample of GP lies, on average, within the tracks of higher PNN masses than that of MKH. This is in contradiction to what is expected if the ®ndings of GP and MKH are compared.