We compare in Fig. 3 (click here) the yields predicted by the standard model with those
given by RV for stars formed with initial metallicities
Z = 0.02 (Y = 0.28) and Z = 0.004 (Y = 0.232), respectively.
We take into account the observational fact that HBB takes place in stars
more massive than 
. Accordingly, we use the yields given by RV
in case Z = 0.02 with 
for m > 3.3 
and 
for 
(i.e. their Tables 3 (click here)e and 3 (click here)a, respectively). Similarly,
we use their yields in case Z = 0.004 with 
for m > 3.25 
and 
for m < 3 
(i.e. their tables 3i and 3h). For
Z=0.004 RV did not tabulate results for 
.
Figure 3 (click here) shows that the standard model (pre-AGB evolution as described
in Sect. 3) results in yields which differ from the selected yields of RV
within a factor 2-3. The standard model predicts larger yields
predominantly for AGB stars with 
in case of carbon and oxygen,
and for AGB stars more massive than 
in case of nitrogen.
In this comparison, we have neglected the effect on the resulting yields
of differences (up to 
) in the initial C, N, and O abundances
between the standard model and that of RV.
It was derived in GJ that 
is needed to fit the
observed initial-final mass relation for stars in the Galactic disk
(see Weidemann & Koester 1983). However, the selected yields of RV
were computed for 
while for the standard model
. Therefore, due to the high mass loss rates of AGB
stars much fewer thermal pulses on the AGB occur in the standard model
compared to the RV models. The main part of the observed differences
between the yields predicted by the standard model and those of RV are
probably due to this effect (apart from differences in the detailed
description of evolution along the AGB, in particular the efficiency of third dredge-up).
In conclusion, we find that the selected yields given by RV differ
from those predicted by the standard model by a factor 2-3. In
particular, for high mass AGB stars (
), the effect of
HBB on the nitrogen yields for the selected RV models is much larger
than that for the standard model. This suggests that values of the
mixing length parameter 
may be more appropriate for
massive AGB stars as we will argue below.
We have presented the yields of intermediate mass AGB stars for
appropriate ranges in mass, initial composition, mass loss parameter
, and effects of second dredge-up and HBB. We have
shown that the yields of such stars are determined by their final
stages and are important for the carbon and nitrogen enrichment of the
Galactic disk ISM. In particular, AGB stars account probably for more
than 
of the interstellar nitrogen in the disk (depending on the
shape of the IMF at low and intermediate mass stars).
From the results presented in GJ and GHJ, we argued that the standard
model with 
provides a reasonable
approximation of the yields of intermediate mass AGB stars in the
Galactic disk and the Large Magellanic Cloud. These systems have a
metallicity that differ by only a factor of 2 (e.g. Russell & Dopita
1992). In galaxies with a substantial lower metallicity, one may
expect a lower value of 
to be more appropriate. We
like to emphasize that using a fixed value of 
does
not necessarily mean identical mass loss rates as two stars of the
same initial mass evolve differently in the synthetic model due to the
explicit metallicity dependence of the recipes used.
Direct observational information on the metallicity dependence of mass
loss and element yields in AGB stars is rare. In Groenewegen et
al. (1995), the spectral energy distributions and 
spectra
of three long-period variables (one each in the SMC, LMC and Galaxy)
with roughly the same period were fitted. From the derived ratios of
the dust optical depths in these stars, it was argued that the mass
loss rates of AGB stars in the Galaxy, LMC, and SMC are roughly in the
ratio of 4:3:1. This corroborates that 
could be
similar for AGB stars in the Galaxy and LMC. Furthermore, this
suggests that for AGB stars in low metallicity systems like the SMC
(Z 
0.004), values of 
1-2 may
be more appropriate.
In GHJ, we compared the mean abundances in the envelopes of AGB stars predicted by the standard model with the abundances observed in PNe in the Galactic disk. Here we repeat part of this analysis with improved model input and put emphasis on the differences in the description of pre-AGB evolution between the Geneva models and that outlined in GJ. In particular, we consider in more detail the effects of second dredge-up and HBB on the predicted abundances and address the uncertainties involved.
In the model, the abundances within PNe are estimated by averaging the
abundances in the ejecta of AGB stars over the final 
25000 yr (e.g. Pottasch 1995). We neglect any changes in the ejected
shell abundances during the post-AGB phase, e.g. due to a late thermal
pulse (Schönberner 1983), which is expected to be a rare event, or
due to selective element depletion by dust formation. The latter
process may affect the composition both in the wind of an AGB star and
during the post-AGB phase (e.g. Bond 1992;
van Winckel et al. 1992) but
is neglected here for simplicity.
We assume an upper mass limit of 8 
for stars that ultimately can
become a PN (with final core mass less than 
1.2 
) and ignore
the possibility that not all our model AGB stars will become PNe. In
fact, some of the low-mass AGB stars may evolve so slowly during the
post-AGB phase that the material previously collected in the wind is
dispersed before the central star has become hot enough to ionize this
material. Also, the upper mass limit for AGB stars is matter of debate
and may range between 6 and 
, depending on the critical
mass for carbon ignition in an electron degenerate core and on details
of the stellar mass-loss scenario (cf. GJ; Vassiliadis & Wood 1993;
Hashimoto et al. 1993). Furthermore, we assume a constant value of
yr. In reality, the time during which the mass
accumulated in a PN has been swept up on the AGB may depend on the
mass and initial composition of the progenitor. Nevertheless, we do
not expect that these simplifications will alter our qualitative
conclusions given below.
The observed PNe abundances are taken from various sources, i.e. mainly from Aller & Cryzack (1983), Zuckerman & Aller (1986), Aller & Keyes (1987), and Kaler et al. (1990). The few halo PNe are excluded as the present comparison concentrates on AGB stars in the Galactic disk. Errors in the observed abundances are typically 0.015 in He/H and about 0.2-0.25 dex in all other ratios considered in Fig. 4 (click here).
Figure 4: Planetary nebulae abundances (by number) predicted by the standard
model with pre-AGB evolution according to the Geneva tracks (solid
curves) and according to the recipes outlined in Sect. 3 (dotted
curves). The latter model without HBB is shown for comparison (dashed
curves). Abundances observed in PNe in the Galactic disk are shown by
open circles (data mainly from Aller & Cryzack (1983),
Zuckerman &
Aller (1986), Aller & Keyes (1987), and
Kaler et al. (1990)). Typical errors
in the observations are indicated at the bottom right corner of each panel
The PNe nowadays observed in the Galactic disk probably originate from
AGB stars covering a wide range in initial mass, i.e. 
. This means that the progenitors of these PNe were formed at
galactic ages ranging from about 10-15 Gyr to 50 Myr ago (see e.g.\
Schaller et al. 1992). Therefore, the initial element abundances of
these PN progenitors are expected to differ considerably since the
enrichment of the Galactic disk ISM over this time interval has been
substantial (e.g. Twarog 1980;
Edvardsson et al. 1993). When comparing
the abundances predicted in the envelopes of final stage AGB stars
with those observed in PNe, we take this important effect into account
by incorporating a self-consistent model for the chemical evolution of
the Galactic disk (van den Hoek et al. 1997; GHJ). Since the
metallicity dependent AGB yields and the resulting chemical evolution
of the Galactic disk are mutually dependent, an iterative solution
method was applied. The adopted star formation history (SFR) and
initial mass function (IMF) in this model were derived using
observational constraints to the abundance-abundance variations with
age of stars in the solar neighbourhood, the metallicity and age
distributions of long-living stars as well as constraints to the
current space density and formation rate of several post-main-sequence
star populations.
Resulting abundance-ratios (by number) in PNe are shown in Fig. 4 (click here) in
case of the standard model assuming pre-AGB evolution according to the
Geneva tracks (Tables 2 (click here)-20 (click here)). We verified that the resulting
abundances are insensitive to the adopted PN lifetime up to 
50000 yr. In general, good agreement is found between the
observed and predicted PN abundances despite the uncertainties
involved. We find that the overall trend of the observations is
reproduced well by the standard model independent of the adopted
chemical enrichment history of the Galactic disk. However, some
discrepancies are present between the standard model (with pre-AGB
evolution according to the Geneva tracks) and the observations, in
particular at large values of He/H 
0.15.
For comparison, we show in Fig. 4 (click here) the PN abundances predicted by the
standard model with pre-AGB evolution according to the recipes
outlined in Sect. 3. In this case, the enhanced effect of second
dredge-up can account for massive AGB stars with He/H up to 
0.18
in their envelopes. This suggests that second dredge-up has been
relatively important at least for some of the PNe in our sample with
He/H 
0.15. Alternatively, a substantial fraction of the hydrogen
contained in the outer envelope may have turned into helium. Since
PNe may evolve from a H and/or He-shell burning AGB star, this will
determine the distribution of He/H abundance ratios observed for a
given progenitor mass. We have included in Table 31 (click here) the yields of H
and He for the standard model with second dredge-up as described by RV
(cf. Sect. 3.2) which provides reasonable agreement with the observed
PN abundances of He/H up to 
0.2, in particular for the more
massive PNe.
The effect of HBB on the predicted abundances can be seen in Fig. 4 (click here) by
comparison of the standard model with 
and 1.3 
(i.e. no HBB), respectively. Our results indicate that the standard
model overestimates the effect of HBB on the resulting N/O abundance
ratios in PNe with progenitors mass 
. We note that the
standard model takes into account the maximum effect of HBB as
described by RV so that values of the mixing length parameter 
< 2 in case of RV are probably more appropriate for massive AGB
stars. On the other hand, models without HBB are inconsistent with
the observed N/O abundances as well as with independent observations
discussed in Sect. 4.2. Therefore, the range of N/O abundances
observed in the envelopes of post-AGB stars allows for variations in
the importance of HBB roughly covering the range from 
to 0.9 
. In case of reduced HBB (i.e. 
), the CNO yields of massive stars in Tables 21 (click here)-30 (click here) are more
suitable than those given for the standard model.
The procedure to approximate the effect of HBB in a semi-analytical
way has been described in the Appendix of GJ. Here the basic
parameters were determined by fitting the RV (
, 
) case for which the effect of HBB is largest. Thus, as
the standard model has 
, possible effects of HBB
varying with in particular mass loss were neglected. In fact, the
temperature structure of the envelope is expected to change when the
number of thermal pulses decreases with increasing values of
. This may reduce the amount of HBB occuring in the
convective envelope and affect the resulting abundances as observed
for PNe with log (N/O) 
and He/H 
(cf. Fig. 4 (click here)).
We emphasize that the resulting abundances of PNe do depend strongly on the initial element abundances of their progenitors, i.e. are very sensitive to the detailed chemical enrichment of the Galactic disk. A considerable part of the scatter observed in Fig. 4 (click here) is expected to be caused (in addition to experimental errors) by substantial variations in the initial abundances of PN progenitors due to the inhomogeneous chemical evolution of the Galactic disk ISM (e.g. van den Hoek & de Jong 1997). Furthermore, the progenitors of the PNe nowadays observed in the solar neighbourhood probably have been formed over a large range in galactocentric distance (e.g. Wielen et al. 1996) and thus with a large range in initial metallicity according to the radial abundance gradients in the disk ISM (e.g. Shaver et al. 1983). Therefore, we expect the agreement between the predicted and observed PN abundance-ratios to improve further when averaging over a range in initial composition for a given progenitor mass.
We conclude that the abundance-ratios predicted by the standard model are consistent with the observed abundances in virtually all the PNe in our sample when we allow for plausible variations in strength of second dredge-up and HBB.
The primary application of the stellar yields presented in this paper is probably in galactic chemical evolution studies.
As models with the default parameters for the mass loss on the AGB,
third dredge-up efficiency, and HBB fit many constrains in our
galaxy and the LMC (GJ/GHJ), the corresponding yields (Tables 2 (click here)-20 (click here)) are
probably the most appropriate ones to use. Possible alternatives are
models with less HBB (Tables 21 (click here)-30 (click here)), or using the pre-AGB evolution from the
synthetic model (Table 31 (click here)).
We argued in Sect. 5.2 that the scaling factor 
of the Reimers
law may be different for low metallicities. To simulate this effect one may
want to use the yields for models with 
for Z =
0.004 and 
for Z = 0.001 (Tables 32 (click here)-37 (click here)).
Acknowledgements
We like to thank the referee Georges Meynet for careful reading of the paper and encouraging remarks. It is a pleasure to thank Achim Weiss for his comments on an earlier version of this paper. The research of LBH and MG has been supported under grants 782-372-028 and 782-373-030 by the Netherlands Foundation for Research in Astronomy (ASTRON) which is financially supported by the Netherlands Organisation for Scientific Research (NWO).
Table 2:
Pre-AGB yields for 
">, 
,
and 
">
Table 3:
AGB yields for 
">, 
,
and 
">
Table 4:
Final AGB yields for 
">, 
,
and 
">
Table 5:
Total yields for 
">, 
,
and 
">
Table 6:
Pre-AGB yields for 
">,
">, and 
Table 7:
AGB yields for 
">,
">, and 
Table 8:
Final AGB yields for 
">,
">, and 
Table 9:
Total yields for 
">,
">, and 
Table 10:
Pre-AGB yields for 
">,
">, and 
Table 11:
AGB yields for 
">, 
, and
">
Table 12:
Final AGB yields for 
">,
">, and 
Table 13:
Total yields for 
">,
">, and 
Table 14:
Pre-AGB yields for 
">,
">, and 
Table 15: AGB yields for 
">,
">, and 
Table 16:
Final AGB yields for 
">,
">, and 
Table 17: Total yields for 
">,
">, and 
Table 18: Pre-AGB yields for
">,
">, and 
Table 19:
AGB yields for ">,
">, and
Table 20:
Final AGB yields for 
">, 
,
and 
">
Table 21:
Total yields for 
">,
">, and 
Table 22:
AGB yields for 
">,
">, and 
Table 23:
AGB yields for 
">,
">, and 
Table 24:
AGB yields for 
">,
">, and 
Table 25:
AGB yields for 
">,
">, and 
Table 26:
AGB yields for 
">,
">, and 
Table 27:
Final AGB yields for 
">,
">, and 
Table 28:
AGB yields for 
">,
">, and 
Table 29:
Final AGB yields for 
">,
">, and 
Table 30: AGB yields for 
">,
">, and 
Table 31: Final AGB yields for 
">,
">, and
">
Table 32: Total AGB yields for H, He for synthetic evolution model
Table 33:
AGB yields for 
">,
">, and 
Table 34:
Final AGB yields for 
">,
">, and 
Table 35:
Total yields for 
">,
">, and 
Table 36:
AGB yields for 
">,
">, and 
Table 37: Final AGB yields for 
">,
">, and 
Table 38:
Total yields for 
">,
">, and 
