Astron. Astrophys. 355, 69-78 (2000)

6. Implications

6.1. Implications on stellar nucleosynthesis

How do we interpret our results on the ¹²C/¹³C  ratios in the framework of stellar nucleosynthesis? To help answering this question, we combine the information provided by the observed ¹²C/¹³C  isotopic ratios with the mass estimates of the progenitors of the PNe, and with the predictions of some representative stellar nucleosynthesis models.

Since the formation of a PN takes place at the end of the AGB phase, the significant comparison is between the observed abundances and those predicted for the stellar ejecta at the AGB tip. Unfortunately, no stellar nucleosynthesis models up to these late phases are available in the literature for stars experiencing deep-mixing. For example, the calculations of Boothroyd & Sackmann (1999) allow to derive the mass dependence of the ¹²C/¹³C  ratio on the stellar surface at the tip of the red giant branch both for the standard case and in the presence of extra-mixing. The standard models indicate that the isotopic ratio has approximately a constant value of 20-23 between and 4 , and then increases steadily at lower masses up to about 28-30 with a small dependence on the stellar metallicity. In the case of extra mixing, the ¹²C/¹³C  ratio displays a sharp drop below  , reaching values of 5-10 at 1 . Similar results have also been obtained by Charbonnel (1994) and Denissenkov & Weiss (1996).

In Fig. 3 we show the distribution of the measured ¹²C/¹³C  ratios in 11 PNe, together with the theoretical values in the ejecta of stars at the tip of the AGB phase. The different curves refer to the models computed in the standard case with no mixing and solar metallicity by FC, HG, and Marigo (1998). Fig. 3 indicates that over the mass interval between 1.5 and 4 the predictions of the HG and Marigo models are in good agreement with each other and indicate a roughly constant value of ¹²C/¹³C 100. The models of FC show significantly lower ratios at 3 and 4 , but have the same qualitative behavior. These results are well understood in terms of the nucleosynthesis occurring during the thermally pulsating AGB phase. In fact, a major phase of ¹²C enrichment of the convective envelope results from the penetration of the convective tongue during thermal pulses (see the discussion in, e.g., FC and HG). At the same time, ¹³C is partially burnt through the ¹³C(,n) reaction at the bottom of the inter-shell region during the inter-pulse phase, as first suggested by Straniero et al. (1995). The combination of these two effects accounts for the high ¹²C/¹³C  ratio in this mass range. On the other hand, more massive AGB stars experience hot bottom burning that progressively leads the ¹²C/¹³C  ratio close to its equilibrium value (4-5).

Fig. 3. 12C/13C  versus progenitor mass of the PNe detected in CO. The filled triangles are the measured PNe, labelled as in Table 3. The uncertainty on the mass is described in the text. The error bar on the derived 12C/13C  ratio is shown in the lower right corner. The three curves are the predicted 12C/13C  ratios in the ejecta of stars at the tip of the asymptotic giant branch (AGB). The dotted curve is from van den Hoek & Groenewegen (1997), the dashed curve is from Forestini & Charbonnel (1997), and the long-dashed curve is from Marigo (1998). All curves are for solar metallicity.

Despite the uncertainties in our measurements, it appears that the standard models produce ¹²C/¹³C  in excess of the values observed in our objects. The only exception is for the two lowest mass stars (0.9 and 1.0 ) computed by HG which agree with the ratios measured in M1-17 and NGC 6781. Although Fig. 3 indicates a marked discrepancy between observed and theoretical values, one should be aware of the sensitivity of the predicted yields on the model assumptions. In particular, the isotopic ratios (not only ¹²C/¹³C ) depend rather strongly on the adopted mass loss rate during the AGB phase, on the third dredge-up efficiency, and on stellar metallicity. Their combined effects have been thoroughly discussed by FC and HG and need not to be repeated here. In general, a shorter phase of mass loss and/or lower mass loss rates tend to decrease the surface ¹²C/¹³C  ratio. However, a more efficient convective penetration results in a higher pollution of the envelope from pulse to pulse and a higher ¹²C/¹³C  ratio. Finally, stars with initial metallicities lower than solar yield higher ¹²C/¹³C  ratios.

Returning to Fig. 3, we see that several PNe lie in the region of the diagram with low ¹²C/¹³C  and low mass. For these objects we should expect the standard models to become inaccurate insofar as they neglect the possible occurrence of mixing mechanisms of non-convective origin which can alter the composition of the stellar ejecta. Low values of the carbon isotopic ratio have also been measured in field population II stars and in globular cluster giant (e.g. Sneden et al. 1986; Gilroy & Brown 1991; Pilachowski et al. 1997) and have provided the motivation to introduce extra-mixing processes in the standard evolution (e.g. Charbonnel 1995). Recently, Charbonnel & do Nascimento (1998) find that more than 90% of a sample of 191 field and cluster red giants presents carbon isotopic ratios inconsistent with those predicted by standard nucleosynthesis.

The observational situation in AGB stars is less clear, because of the extreme sensitivity of the determination of isotopic ratios on excitation temperatures and model atmospheres. For example, Greaves & Holland (1997) have measured a ¹²C/¹³C  ratio varying between 12 and 36 in a sample of 9 carbon stars with high mass-loss rates (  yr^-1), in accordance with similar results previously obtained by Wannier & Sahai (1987) on seven other carbon stars. On the other hand, Lambert et al. (1986) measured the ¹²C/¹³C  ratio in 30 cool carbon stars and found values between 30 and 70. More recently, Ohnaka & Tsuji (1996) report ratios between 20 and 30 for 24 N-type carbon stars in common with the sample of Lambert et al. (1986). These values are about a factor of 2 smaller than those derived by Lambert et al. (see however the discussion in de Laverny & Gustafsson 1998 and Ohnaka & Tsuji 1998), but are consistent with those found for our PN sample. If these samples are representative of the population of both carbon stars and PNe, the low ¹²C/¹³C  ratios provide strong indication that most stars should experience some extra-mixing and deplete ¹²C with respect to ¹³C. According to this conjecture, it appears that in order to match the observations, more realistic stellar models should include additional physical processes to avoid too large ¹²C/¹³C  ratios throughout the latest stages of stellar evolution .

6.2. Implications on Galactic chemical evolution

Theoretical models predict that stars with low values of ¹²C/¹³C  should also have low ³He abundances. In GSTP, we estimated that to obtain consistency between the observed ³He abundances and chemical evolution models, the majority of the Galactic PNe (70%) should have a ¹²C/¹³C  ratio well below the standard value. In this section we test this suggestion using the constraint provided by the ¹²C/¹³C  observations in PNe. Chemical evolution models offer the adequate tool to follow simultaneously the evolution of ¹²C/¹³C  and ³He over the Galactic lifetime.

In Fig. 4 and Fig. 5 we show the evolution of ¹²C/¹³C  and ³He as a function of time in the solar neighborhood (Galactocentric radius  kpc), and as a function of R at the present time ( Gyr), as predicted by models described by Dearborn et al. (1996) and Sandrelli et al. (1998). The two figures correspond to different assumptions on the fraction of low-mass stars experiencing deep mixing in the RGB phase. In both cases, the Galactic evolution of the various isotopes has been computed assuming metallicity-dependent yields. In the upper panels, the solid line corresponds to models adopting the ¹²C and ¹³C yields from BS for stars in the mass range 0.8 - 2.5 , from FC in the range 3 - 6 , and from Woosley & Weaver (1995) for massive stars. The dotted and dashed lines display the results obtained using the same yields as before, except for stars in the mass range 3-6 , where the HG and BS yields, respectively, are adopted. The calculations by BS are the only ones that provide the ¹²C and ¹³C yields for both the standard and the CBP cases. For ³He, the standard yields are taken from Dearborn et al. (1996) and the CBP yields from BS.

Fig. 4. Evolution of 12C/13C  and 3He as a function of time for the solar neighborhood and as a function of Galactocentric radius at the present time. Standard case with no extra mixing. The three curves show the results obtained using the yields for intermediate-mass stars by FC (solid ), by HG (dotted ), and by BS (dashed ). The observational data for 12C/13C  are from: Anders & Grevesse (1989); Henkel et al. (1980); Gardner & Whiteoak (1981); Henkel et al. (1982); Henkel et al. (1985), Langer & Penzias (1993); Wouterloot & Brand (1996). The data on 3He are from Geiss (1993), Gloeckler & Geiss (1996) and Rood et al. (1995).

Fig. 5. Evolution of 12C/13C  and 3He as a function of time for the solar neighborhood and as function of Galactocentric radius at the present time. Case with mixing in 90% of low mass stars. Symbols and observational data are as in Fig. 4.

The behaviour of ³He is typical of the elements produced mainly by low-mass, long-lived stars. ¹²C is a primary element produced by stars of any mass and available for Galactic enrichment already after the explosions of the first massive objects. ¹³C is mostly secondary and its bulk abundance is due to intermediate-mass stars. Therefore, the enrichment of this element in the ISM occurs later than that of ¹²C. This delay causes the decrease of ¹²C/¹³C  visible in Fig. 4 and Fig. 5. The positive radial gradient of ¹²C/¹³C  is also due to the different mass intervals of stars that are producers of the carbon isotopes, and to the higher star formation activity in the inner Galactic regions, independent of the stellar initial mass function. All these effects combined make the relative proportion of ¹³C over ¹²C producers increasingly higher for decreasing Galactocentric distances.

Fig. 4 shows the standard case with no deep mixing, whereas the results with CBP in 90% of stars randomly chosen in the mass range   are displayed in Fig. 5. The hatched regions represent the range of abundances resulting from 50 different cases for the random sorting. As already discussed by GSTP, the overall enrichment of ³He is very sensitive to the assumptions on deep mixing. On the contrary, the variation of ¹²C/¹³C  is marginal, since most of ¹²C and ¹³C is produced by stars more massive than 2.5  which are not affected by deep mixing processes. Thus, altering the amount of ¹²C and ¹³C released by low-mass stars leads to smaller variations in the resulting abundances. For these reasons, the Galactic evolution of ³He is an excellent indicator of the fraction of low-mass stars which should undergo CBP, but that of ¹²C/¹³C  is not. From Fig. 4 and Fig. 5, one can see that the fraction required to reproduce the observed pattern of ³He abundances is up to 90%, in agreement with the finding of Charbonnel & do Nascimento (1998).

As for ¹²C/¹³C, the predicted abundance distributions with time and with Galactocentric distance are roughly consistent with the data regardless of the occurence of extra-mixing. The ¹²C/¹³C  ratio in the Sun cannot be accurately reproduced, and the radial gradient is flatter than the observed one (as deduced from measurements in molecular clouds), independently of the adopted percentage of stars undergoing CBP. Using the yields of FC and BS leads to a better fit of the solar value and to the present distribution of ¹²C/¹³C  in the inner Galactic regions. On the other hand, the models of HG reproduce the local ISM ratio. In all cases, the fraction of low-mass stars experiencing deep mixing does not affect significantly the overall results of the chemical evolution models. Of course, deep mixing alters the values ¹²C/¹³C  in low-mass stars, but the Galactic evolution of ¹²C and ¹³C is mainly governed by stars in which this process is not expected to take place.

© European Southern Observatory (ESO) 2000

Online publication: March 17, 2000
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