ACTA ASTRONOMICA Vol. 43 (1993) pp. 371±380

Comparison of the Masses of 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 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. In order to proceed our analysis more quantitatively we have attempted to derive PNN masses from our diagrams.

4. Estimation of the PNN Masses from our Diagnostic Diagrams

The theoretical tracks displayed in Figs. 1 ± 4 have been obtained adopting

that the model PN has a mass of 0.2 M and expands at 20 km/s. However, the expansion velocities for individual PN are known from the observations. There-

fore, in order to decrease the number of free parameters, while deriving the PNN V

mass for a given object we have used a set of model tracks calculated with exp corresponding to the observed value. Unfortunately the nebular mass cannot be

obtained directly from observations. Thus our PNN masses have been derived

M = assuming neb 0 2 M . However, in order to get an estimate of the error

arising from the uncertainty in the nebular masses we have also obtained the values assuming a nebular mass differing by 0.5 dex, i.e. 0.07 M and 0.6 M .

In this way we have derived for each object up to 4 estimates of the PNN mass M

with uncertainties due to the lack of knowledge of neb . Then we have calculated a ®nal PNN mass as a mean from the individual estimates weighting them inverse proportionally to their uncertainties. The results are given in Table 1 together with the PNN masses from MHK and GP. (The GP masses have been derived from the positions in the H-R diagram of GP and the Schonberner'sÈ tracks.) Considering

the sample of MKH, we ®nd with our method a mean PNN mass of 0.574M with

a dispersion of 0.024 M , while the determinations of MKH give a mean of

0.654 M with a dispersion of 0.042 M . For the GP sample we have obtained a mean PNN mass of 0.614 M and a dispersion of 0.025 M .

5. Discussion

The results of our analysis are in contradiction with the conclusions that can be drawn while comparing the ®ndings of MKH and GP. We have found no evidence suggesting that the sample of MKH consists of more massive objects than that of GP. On the contrary, we have obtained, on average, lower PNN masses for the MKH sample than for the GP sample. Vol. 43 377

Table1

The masses of planetary nebula nuclei [in M ].

PK name mass mass mass our results Mendez et al. Gathier&Pottasch

2+5.1 NGC 6369 .630  .014 .69

3±4.5 NGC 6565 .600 ±  .89

9±5.1 NGC 6629 .550  .004 .67

10+0.1 NGC 6537 ± ± .63

10±1.1 NGC 6578 .590  .012 .54 11±0.2 NGC 6567 .606  .004 .54

25+40.1 IC 4593 .555  .005 .68 34+11.1 NGC 6572 .610  .011 .54

36±57.1 NGC 7293 ± ± .55 37±34.1 NGC 7009 .600  .004 .66 .54

46±4.1 NGC 6803 .582  .006 .56

54±12.1 NGC 6891 .550  .004 .68

60±7.2 NGC 6886 .626  .005 .59

63+13.1 NGC 6720 .610 ± .59 82+7.1 NGC 6884 .623  .006 .54

83+12.1 NGC 6826 .560  .005 .68

84±3.1 NGC 7027 .677  .003 .79

89+0.1 NGC 7026 .628  .004 .56

106±17.1 NGC 7662 .635  .005 .54 107+2.1 NGC 7354 ± ± .56

118±74.1 NGC 246 .590  .007 .56

123+34.1 IC 3568 .564  .003 .66

130+1.1 IC 1747 .610  .004 .54

197+17.1 NGC 2392 .637  .013 .73

206±40.1 NGC 1535 .594  .005 .65

215±24.1 IC 418 .565  .005 .67

220±53.1 NGC 1360 .580  .007 .55

234+2.1 NGC 2440 ± ± .89

243±1.1 NGC 2452 .616  .010 .56

261+32.1 NGC 3242 .608  .004 .66 .54 265+4.1 NGC 2792 .608  .007 .54

272+12.1 NGC 3132 .568  .004 .57

285±14.1 IC 2448 .580  .007 .58

286±4.1 NGC 3211 .643  .010 .66

294+43.1 NGC 4361 .600  .007 .55

294+4.1 NGC 3918 .645  .007 .63

307±3.1 NGC 5189 .613  .010 .57

309±4.2 NGC 5315 .640  .008 .57  315±13.1 He 2-131 .570  .004 .54

316+8.1 He 2-108 .550  .004 .67

320±9.1 He 2-138 .560  .004 .68

325±12.1 He 2-182 .590  .007 .65 326±6.1 He 2-151 .550 ± .67 331±3.1 He 2-162 .550 ± .66

345±8.1 Tc 1 .550  .004 .67

345+0.1 IC 4637 .560  .009 .66

350+4.1 H 2-1 .575  .005 .64

358±0.2 M 1-26 .590  .004 .67 378 A. A.

The main assumption on which our analysis is based is that the evolutionary time scales of the current (Schonberner's)È PNN models are more or less correct. This assumption has not been made neither by MKH nor by GP. Thus the general conclusion is that either these evolutionary time scales are wrong (as suggested by GP or McCarthy etal. 1992)orthatthemassesfromMHK andGParesystematically wrong. Our experiences show that the discrepancy cannot be removed by modi®ng our PN model or rejecting the assumption of the blackbody PNN spectrum. Letus®rst considerthe MKH case. Theonly wayto reconcilethe MHK masses with the observed expansion times of the nebulae is to adopt that the PN formation is ®nished on the AGB well before the zero-age point of the Schonberner'sÈ models

(see also McCarthy et al. 1990). Our preliminary calculations show that a 0.65 M PNN would pass more or less by the positions of the MHK objects in our diagrams if the zero-age point were ®xed at the pulsation period of about 175 days. The post-AGB are observed to pulsate with periods of 40-90 days (e.g. Alcolea and Bujarrabal 1991). Thus a question arises: why the periods above 90 days are so rarely observed? Another consequence of the above modi®cation of the PNN

models is that 90% of the post-AGB, pre-planetary stars should be observed very

T =

close to the AGB, i.e. at log e 3 7 This ®ndings is to be confronted with the statistics of the post-AGB objects.

Fig. 5. The gravities obtained adopting our PNN masses and Teff of MKH against the gravities of MKH. Vol. 43 379

Another explanation of the discrepancy between the MKH masses and ours is that the method of MKH overestimates the PNN masses. This idea is supported by the fact that a more sophisticated version of the model atmosphere used by MKH did in fact lead to an increase in gravities and to a decrease in PNN masses in comparison to the earlier results of Mendez et al. (1988, 1990). One may therefore ask how much the model atmosphere parameters have to be changed in order to obtain an agreement with the PNN masses from the evolutionary time scales. An

example of such an exercise is shown in Fig. 5 which compares the gravities of T

MKH to the gravities obtained adopting our PNN masses and e of MKH. It can

be seen from Fig. 5 that apart from high gravities the difference is systematic. It

g would be necessary to increase log g of MKH, on average, by 0.38 for log 4 5 in order to get an agreement between the masses from both methods. Let us now compare our results to those of GP. The principal discrepancy is that for all objects we have found, PNN masses are equal to or greater than

0.55 M whereas in GP 40% of their sample lies below this limit. We have made

an exercise trying to accelerate the 0.546 M model of SchonbernerÈ (1983) so that it passes through the regions occupied in our diagrams by low mass objects of GP. A PNN model can be accelarated either by moving the zero-age point to a shorter pulsation period (higher effective temperature) or by increasing the post- AGB wind (for detailes see Gorny et al. 1993). If one wants to play with the

zero-age point only then one comes to a conclusion that the PN formation has to

T

be continued up to log e 4 5 in most cases. If we want to stay with a more

=

resonable zero-age point then the required winds correspond to 20 40 if the

T ( ) T ( ) Z diagrams using Z HI are considered (Figs. 1 and 3) or even higher if HeII

is used (Figs. 2 and 4). Since is the ratio of the momentum carried by the wind to that available from the stellar radiation this implies that one has to invoke an extraordinary mechanism for wind generation in low-mass PNN. Therefore, in our opinion the most plausible explanation is that in many cases the PNN luminosities in GP are underestimated, either due to too low effective temperatures or due to too low distances or both.

Acknowledgements. This work was in part supported from the KBN grant No. 2-2114-92-03.

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