In Tables 2 (click here)-20 (click here), we present theoretical yields 
for AGB stars in the
mass range 0.8-8 
in case of the standard model (
, 
, 
, and 
) including first, second, and third dredge-up as well
as HBB. We distinguish pre-AGB, AGB, final AGB, and total element
yields at initial metallicities Z = 0.001, 0.004, 0.008, 0.02, and 0.04.
Pre-AGB yields are the yields up to the end of the E-AGB. AGB yields
are the yields on the TP-AGB except for the last 
yr. The final AGB yields are the yields on the TP-AGB integrated over
the last 
yr. This distinction is made to compare with
the abundances in PNe (note that final AGB yields have been omitted if
the AGB lifetime is much smaller than 
yr). In several cases,
stars have final AGB yields that are negligible (because
such massive stars do not always go through the PN stage). For such stars,
the final AGB yields were
omitted in Table 4.
Pre-AGB evolution is based on the Geneva group (e.g. Schaller et al.
1992). These uniform grids of stellar
models are based on up-to-date physical input (e.g. opacities, nuclear
reaction rates, mixing schemes, etc.) and cover the relevant initial
stellar mass range from 0.8 to 8 
as well as initial metallicity from
Z = 0.001-0.04. For stars with 
these tracks have been
computed up to the He flash, for 2 < m <5 
up to the E-AGB, and for
m > 7 
until the end of central C-burning. Recently, Charbonnel et al.
(1996) presented new grids of models covering the evolution (from the zero
age main sequence up to the end of the E-AGB)
of low mass stars with initial masses between 0.8 and 1.7 
born with
metallicities Z = 0.02 and 0.001. We note that these stars were not
evolved through the helium core flash but instead were evolved from
constructed zero-age horizontal branch models (see Charbonnel et al. 1996).
For stars with initial mass above 1.25 
, the Geneva tracks
used are with overshooting and standard mass loss rates (see e.g.\
Schaller et al.). For stars below 1.25 
, the tracks used are
without overshooting (for m = 1.25 
we include yields both for
tracks with and without overshooting). The two 
lines in the tables refer to the 
models both for tracks
with (lower table lines) and without (upper lines) overshooting. Perhaps
the tracks with overshooting are preferred (see Schaller et al. 1992).
We neglect the fact that the Geneva tracks for stars with 
and Z = 0.004, 0.008, and 0.04 end at the helium flash and do
not extent to the end of the E-AGB. However, these low mass stars do
not experience the second dredge-up and are expected not to loose much
mass on the horizontal branch and E-AGB, so that the influence on the
yields is negligible (see Sect. 4.4). The 
star yields
are not included in the total yields tables because for such low-mass stars
the final AGB (PN-phase) yields are relatively uncertain. It would be okay to sum
up the pre-AGB and AGB yields for these stars and use this as the total yield.
In Tables 2 (click here)-20 (click here), we list subsequently the initial mass 
,
element yields 
of H, 
He, 
C, 
C, 
N,
O,
integrated CNO-yield 
, total element integrated yield 
(elements heavier than helium), the total amount of mass returned
, and the stellar mass 
at the end of
each phase.
We consider resulting stellar yields for various choices
of the Reimers mass loss coefficient 
1-5, third
dredge-up efficiency 
, critical core mass for
dredge up 
, and minimum core
mass for HBB 
= 0.8 and 0.9 
(see Sect. 3). We examine
the impact of these quantities as well as of the adopted pre-AGB
evolution model on the predicted yields.
Figure 1 (click here) shows resulting AGB yields for various values of the Reimers
mass-loss parameter 
. The other parameters are
as for the standard model (unless stated otherwise). Low
mass AGB stars (
4 
) predominantly contribute to helium and
carbon. High mass AGB stars are important contributors to helium and
nitrogen (see below). For the standard model, element yields are
smaller by factors typically 2-3 compared to the 
case. Resulting yields increase with decreasing values of
(i.e. smaller mass-loss rates) as a lower value of
results in longer AGB lifetimes and therefore more thermal
pulses (assuming that the amount of dredged-up matter during a thermal
pulse is roughly constant). For large values of 
, the effect of increasing 
on both the AGB lifetimes and
number of thermal pulses becomes negligible and the predicted yields
remain approximately constant.
In general, carbon and oxygen yields increase with decreasing initial metallicity Z (cf. Fig. 1 (click here)). This is due to the fact that dredge-up with subsequent CNO-burning affects more strongly the composition of envelopes with relatively low initial abundances (see e.g. RV). In addition, the core mass at the first thermal pulse is larger at low metallicities (GJ). Therefore, the amount of material dredged-up from the core to the envelope is substantially larger in initially low-Z AGB stars. In contrast, nitrogen yields slightly increase with metallicity as nitrogen is formed during CNO-burning by consumption of C and O. For hydrogen and helium, the sensitivity of the yields to initial metallicity are mainly due to the effect of dredge-up, i.e. post dredge-up processing of H and He is usually low. Note that even small changes in the yields of AGB stars due to variations in initial metallicity can significantly affect the enrichment of the ISM (after weighing by the initial mass function and star formation rate at the time these stars were formed).
We like to emphasize that AGB yields of intermediate mass stars are strongly dependent on the abundances of distinct elements (e.g. C, N, and O) in the galactic ISM from which these stars are formed. In other words, stars with initial element abundances substantially different from those listed in Table 1 (click here) have AGB yields distinct from the yields given in Tables 2 (click here)-20 (click here). We will return to this important point below when model predictions are confronted with abundances observed in PNe in the Galactic disk.
Figure 1: Stellar yields of H, 
He, 
C, 
N, 
O, and
total CNO vs. initial stellar mass for 
= 1 - 5 and initial
compositions (Z, Y) = (0.02, 0.32; solid line) and (0.001, 0.24; dotted).
Parameters values are further as for the standard model (i.e.
= 4)
As discussed before, HBB may prevent or slow down the formation of
carbon stars by the possible destruction of newly dredged up carbon at the
base of the convective envelope. Figure 2 (click here) illustrates that
for low mass AGB stars (m < 4 
), the effect
of HBB is negligible due to the low temperature at the bottom of
their envelopes (GJ). For high mass AGB stars, the effect of HBB
depends on the amount of matter exposed to the high temperatures at the
bottom of their envelopes, the net result being the conversion of carbon and
oxygen to nitrogen. Yields of H, He, and total CNO are not affected by HBB
since basically two reaction chains of the CNO-cycle are involved, i.e.
the CN and ON-cycle.
We compare in Fig. 2 (click here) the resulting yields in case 
= 0.9
(figure labelled HBB)
and 1.3 
(no HBB), respectively. A choice of 
1.3 
or larger results in no HBB as none of the AGB stars in our model
reach such high core masses. In case of HBB, the strong decrease of
the carbon and strong increase in the nitrogen yield can be seen at
masses at 
. In the no HBB case, the stellar yields of
carbon are seen to dominate the total CNO-yields over the entire mass
range.
The effect of changing 
from 0.8 to 0.9 
is that HBB
operates in stars of initial mass 
instead of 
. Since 
= 0.9 
provides a reasonable upper limit to
the minimum stellar mass experiencing HBB, we have included in
Tables 21 (click here)-30 (click here) 
C, 
C, 
N, and 
O yields for stars
more massive than 4 
in case of the standard model with 
=
0.9 
(pre-AGB are as given at the corresponding metallicities in
Tables 2 (click here)-20 (click here)). These yields include the minimum effect of HBB as
inferred from the observations and are somewhat smaller than those given
by the standard model (i.e. 
= 0.8 
).
As discussed earlier, the default choice of 
= 0.8 
is based on our implementation of the RV 
= 2 model but
appears consistent with recent observations of HBB in AGB stars
both in the SMC and LMC as well as recent model calculations on massive
AGB stars. In any case, HBB is required to explain observations. More
observations are needed to investigate any dependence of HBB on metallicity.
Figure 2: Stellar yields of H, 
He, 
C, 
N, 
O, and
total CNO vs. initial stellar mass for the standard model: effect of
varying 1) the amount of HBB (first two columns), 2) the
dredge-up efficiency (center columns), and 3) the critical core mass
for dredge-up (last two columns)
We consider in Fig. 2 (click here) AGB yields for third dredge-up efficiencies 
and 0.9 (i.e. the range allowed for by the observations; GJ). Stellar
yields increase substantially when
is increased, i.e. enhancing the amount of carbon and helium
that is dredged-up and added to the stellar envelope after each
thermal pulse. In addition, the composition of dredged-up material may be
strongly affected by HBB, in particular for high mass stars. In other words,
increasing 
leads to an increase in the carbon yields for low
mass stars and to an increase in nitrogen for high mass stars. Furthermore,
helium yields increase for all stars with initial masses above
which corresponds to the limit of 
.
Yields for extreme values of the minimal core mass for third dredge-up
and 0.60 
, respectively, are shown in
last two columns of Fig. 2 (click here). The effects of varying 
are limited to relatively low mass AGB stars (
2 
).
A larger value of 
implies a higher initial mass for
stars that can turn into carbon stars. This results in negative carbon yields
(corresponding to the depletion of carbon during first dredge-up) over
a larger range in initial mass (helium yields decrease over this mass
range as well). A value of 
as small as 
would imply that all AGB stars end as carbon stars while 
0.61 
would inhibit carbon star formation. Clearly, the third
dredge-up and the precise values of 
and 
are of crucial importance for the formation of carbon stars.
We like to emphasize that the parameter value ranges consistent with the
observations are rather narrow and are mutually correlated
(e.g. in case of 
and 
).
In GJ and GHJ the description of the pre-thermal pulsing AGB evolution was taken from recipes in the literature or fits made to published results. An alternative approach is to directly use stellar evolution tracks, as is done in this study (see above).
In Fig. 3 (click here), we compare for Z = 0.02 and 0.001 the resulting AGB yields in the case of pre-AGB evolution according to the evolution tracks described above with those computed following the recipes from GJ/GHJ. In both cases, the initial stellar composition has been adopted from the Geneva group to comply with the stellar evolution tracks prior to the AGB.
Figure 3: Stellar yields including HBB vs. initial stellar mass of H,
He, 
C, 
N, 
O, and total CNO in case of the standard
model for different treatments of pre-AGB evolution (left and center panels)
and initial metallicities Z = 0.02 (solid line) and 0.004 (dotted line;
yields for Z = 0.001 are similar).
The yields presented by RV (their case 
)
at initial compositions 
= (0.02, 0.32; solid lines) and (0.004, 0.24;
dotted) are shown for comparison (hydrogen yields are not given explicitly
by RV)
Differences between the two sets of yields are found to be very small except for hydrogen and helium where the GJ/GHJ approach predicts higher yields for massive stars. This is traced back to differences in the treatment of the second dredge-up process. We list in Table 31 (click here) the corresponding total AGB yields of H and He for the synthetic GJ/GHJ model (initial metallicities as before). These modified yields can be used when the effect of 2nd dredge up is expected to be more pronounced than that given by the Geneva group (see below). The larger yields also imply higher helium abundances which has interesting consequences for the predicted helium abundances in planetary nebulae (see Sect. 5).
We find that pre-AGB evolution for stars born with metallicity Z = 0.02 is in general unimportant for the total yields of AGB stars, except in case of helium and hydrogen. This confirms our earlier statement that the thermal pulsing AGB is the most important phase in determining the yields of intermediate mass stars (even though initial stellar abundances, effects of overshooting, mixing, and pre-AGB evolution can play a significant role).
We conclude that the resulting AGB yields are most sensitive to the
mass loss parameter 
, the effect of HBB, and the
initial stellar abundances. Variations in the remaining model
parameters result in stellar yields not substantially different from
those predicted by the standard model with 
,
, 
, and 
. Stellar yields for model parameters distinct from that used
for the standard model (e.g. 
, HBB, or initial
abundances) are available upon request. We like to emphasize that small
differences in the predicted AGB yields may be important when integrating
over the initial mass function in galactic chemical evolution models.