Astron. Astrophys. 333, 926-941 (1998)

4. The primordial scenario

In the primordial scenario, star-to-star abundance variations in globular clusters are thought to be produced before or during formation of low mass stars. Possible sources of primordial pollution include winds from massive stars, SNe explosions, winds and planetary nebulae (PNe) ejection by AGB stars and novae. Are any traces of nucleosynthesis yields from the earlier generations of stars seen in globular clusters? If one assumes that protoglobular clusters formed from material having the big bang chemical composition with zero heavy element content, then the answer is definitely yes, since in present-day clusters stars show a wide spectrum of elements heavier than helium, and one is forced to seek such primordial sources.

The first objects to contribute to the self-enrichment of globular clusters are massive stars during hydrostatic mass loss and on their final evolutionary stage - SNeII (we do not consider the hypothesized Very Massive Objects). The modern radiation-driven wind theory (Kudritzki et al. 1991; Jura 1986) predicts, however, that during hydrostatic evolution massive stars with Z = 0 will not lose a considerable amount of their mass (Maeder 1992). Therefore, the only nucleosynthesis yields from the first generation of massive stars are most probably those produced by SNeII and consist mainly of O (and other -elements) (Woosley & Weaver 1995). It is also important to note that as argued by Laird & Sneden (1996) and Carney (1996) there is no evidence for any progressive enrichment of clusters by the SNeIa responsible for the production of the iron-peak elements in Galactic chemical evolution (Timmes et al. 1995, hereafter TWW95) and which chronologically follow SNeII.

The next potential polluters of the intracluster medium are AGB stars. ND95 reported that abundances of the heavy neutron-addition elements, which are presumably produced in the s-process nucleosynthesis in AGB stars rise as [Fe/H] increases in  Cen red giants. Since intermediate mass stars () evolve faster than objects, one expects that some products of nucleosynthesis from intermediate mass AGB stars could also be present in the material captured by contracting low mass stars in globular clusters or accreted by them later.

4.1. Nucleosynthesis yields from SNe

The chemical enrichment history of globular clusters seems to be quite different from the chemical evolution of the bulk of the Galaxy. One of the plausible scenarios of globular cluster formation was proposed by Cayrel (1986) and elaborated upon further by Brown et al. (1991b, 1995). In this scenario massive stars form first in a protocluster's dense core from material having the big bang composition. They evolve rather quickly (on a time scale of years) and explode as SNeII without leaving any remnants. A supershell produced by shocks from the multiple SNe explosions sweeps up and compresses the protocluster material which now consists of a mixture of the big bang and SNeII ejecta compositions. It is this supershell that becomes the birthplace for stars covering the whole mass spectrum. There are a number of arguments, both theoretical and observational, supporting this scenario (see the papers cited above). One of these is the absence of low mass stars having the primordial big bang composition. We shall not, however, discuss here all advantages and disadvantages of different globular clusters formation models. We merely emphasize that both intermediate and low mass stars in globulars were very likely to form out of material polluted by SNeII. Two things are necessary to specify the element abundances in this material: first, mass dependent nucleosynthesis yields from the SNeII whose progenitors had the big bang initial composition, and second, an estimate of dilution of these yields in the supershell.

In Fig. 6 the abundances of some of the SNeII ejecta which are important for our work are presented as functions of the initial mass of the SN progenitor (which is also its final mass because in these calculations stellar winds were not taken into account) for for the models of Woosley & Weaver (1995) as adopted by TWWA (their Sect. 2.4). One should bear that in mind, however, that the ejecta composition of SN models is more uncertain at higher masses; for example, the Na/O production of the 30  models varies by almost a factor of 500 (Woosley & Weaver 1995). The large variations of abundances from star to star are mainly caused by the uncertainty in modelling the explosion and the sensitivity of models to the interaction between various convective zones during the late stages of the evolution. Despite these large random-like abundance variations TWWA argue that after convolution with an appropriate initial mass function and integrating over time one gets quite reasonable results, and indeed they do succeed in reproducing the observed evolutionary changes of abundances for a large number of elements lighter than zinc in a simple model of galactic chemical evolution.

Fig. 6. Abundances of some nuclides ejected by SNeII (following Woosley & Weaver 1995)

The range of masses of the SN progenitors in Fig. 6 is . Following TWWA and Cayrel (1986) we assume that the initial mass function in the protoglobular cluster's dense core was a low mass cutoff Salpeter (1955) power law with a slightly different exponent of (instead of 1.35) which gave the best fit to the observed element evolution. After convolution of the abundances from Fig. 6 with over the range 12 - 40 we find the average abundances ejected by SNeII. The latter are diluted in the supershell by material having the big bang composition. The dilution coefficient can be estimated as the ratio of the local intracluster sound velocity km s^-1 to the initial velocity of the SN's ejecta km s^-1 (Cayrel 1986). This estimate neglects the adiabatic phase of the SN's expansion and takes into account only the "snowplow" phase. In Table 1 the final abundances expected as a result of SNeII explosions and subsequent dilution in the supershell are presented.

Table 1. Abundances expected as the result of SNeII explosions

From these data we draw the following conclusions: (i) the value of [Fe/H] corresponds to that of the most metal-deficient globular clusters; (ii) the values of [ /Fe] are lower than observed in globular clusters which results, in large part, from the overproducton of Fe in the model supernovae (see TWWA); (iii) N is extremely underabundant; (iv) the ²² Ne/Na ratio is far less than the initial one assumed in GCRGs (Sect. 3.1); (v) abundances of ²⁵ Mg and ²⁶ Mg are very low compared to ²⁴ Mg and Al. Inspection of Fig. 6 shows that the conclusion concerning the very low ²⁵ Mg/²⁴ Mg ratio in the primordial mixture is rather robust. We thus have to look for other nucleosynthesis source(s) of ²² Ne, ²⁵ Mg and ²⁶ Mg. TWWA proposed the intermediate mass AGB stars as the main producers of the ²⁵ Mg and ²⁶ Mg isotopes. Our calculations support this idea (see below). As regards N, TWWA reported that its abundance in SNeII ejecta can be much larger if one takes into account some convective overshoot in the low metallicity SNII's progenitor but they also infer that AGB stars can contribute much to the galactic N (and C) production.

4.2. Yields from intermediate mass AGB stars

To take into account the contribution to galactic chemical evolution from intermediate mass AGB stars TWWA made use of the results of parameterized nucleosynthesis calculations by Renzini & Voli (1981) who, however, followed only the evolution of abundances of ¹² C, ¹³ C, ¹⁴ N and ¹⁶ O for . Our calculations supplement those of Renzini & Voli in two respects. First, we consider also the evolution of elements heavier than O and, second, we choose Z as low as 10^-4 and allow different relative distributions of nuclides within Z which turns out to have a pronounced effect on the final abundances.

As a representative of intermediate mass AGB stars we considered a object. Thermal pulses of the helium burning shell started with the core mass . It should be emphasized again that we did not follow the AGB stellar evolution. Instead we considered the parameterized nucleosynthesis in the AGB star following the description of Renzini & Voli (1981) (for more details see Paper II ). The core mass is constrained to remain smaller than the Chandrasekhar limit , but long before could approach some kind of instability is believed to force envelope ejection in the form of a PN which terminates AGB evolution (Renzini 1981; Wagenhuber & Weiss 1994). The exact upper limit for the number of pulses before the PN's ejection is not known. It can be approximately constrained by the observed relation between white dwarf masses and the initial masses of their MS progenitors. Such relations show that intermediate mass stars with lower metallicity may survive longer on the AGB (Weidemann 1987). We have chosen as the limiting number of pulses in our low metallicity AGB nucleosynthesis calculations. This number results in the final core mass . We are aware that the chosen value of N may be overestimated, but smaller values () give the same qualitative (but of course less pronounced quantitative) results. The initial chemical composition is that given in Table 1.

In Fig. 7 the final (i.e. after 400 pulses) surface abundances in the envelope of the AGB star are plotted for three different hot bottom burning (HBB) temperatures: and 100 10⁶ K. It should be noted that the model value of is also very uncertain because it strongly depends on the depth within the HBS which can be reached by the BCE during the interpulse period, with the depth being very sensitive to the poorly known extent of convective overshoot (Lattanzio & Frost 1997). Unfortunately, it is that determines whether ²⁴ Mg is transformed into Al at the BCE (Fig. 7). The initial chemical composition for these calculations was that given in Table 1 (see Sect. 4.1).

Fig. 7. Nucleosynthesis yields of some light nuclides from intermediate mass AGB stars after 400 pulses. The notation HBBT6 signifies that HBB was assumed to occur at the temperature T6 106 K. The atomic mass number 26 corresponds to 26 Mg. The initial chemical composition was that given in Table 1

From Fig. 7 we infer that if HBB is neglected (this approximately corresponds to the results shown by asterisks for K) the main new results (as compared to those obtained by Renzini & Voli (1981)) are considerable increases of the ²² Ne/Na ratio and of the ²⁵ Mg and ²⁶ Mg abundances. The ²² Ne, ²⁵ Mg and ²⁶ Mg isotopes are primarily produced by -capture reactions whereas Na is synthesized in the reactions ²² Ne(n, Ne( Na. Aluminium is not produced during pulses because there are no -capture reactions which result in Al, on the one hand, and the neutron capture cross section for the reaction ²⁶ Mg(n, Mg followed by the beta-decay ²⁷ Mg( Al is very low ( mb), on the other.

In Table 2 we compare the abundances of ²² Ne, Na, ²⁵ Mg and ²⁶ Mg which are achieved in the H-He intershell just after the 400th pulse for three initial compositions: (1) solar; (2) and the relative abundance distribution as described in Sect. 3.1; (3) abundances from Table 1. We see that especially large increases of the ratio ²² Ne/Na and of the ²⁵ Mg and ²⁶ Mg abundances are obtained for the third mixture, which was derived from the globular cluster self-enrichment model.

Table 2. Abundances () in the H-He intershell of the AGB star after the 400th pulse

In Paper II our estimate of the fraction of material which first takes part in the nucleosynthesis processes in intermediate mass AGB stars and is later captured by low mass stars q (the dilution coefficient) was . This estimate assumes homogeneous distribution of the processed material among low mass stars. While this assumption appears to be good one for the nucleosynthesis yields from SNe because the post-shock turbulence is thought to mix the protocluster material well (Brown et al. 1995), yields from AGB stars are most likely to be distributed inhomogeneously and primarily captured by low mass stars nearest to them during ejection of their envelopes. In this case the coefficient q may be even larger.

The discussion given above supports the idea that intermediate mass AGB stars could be a source of the increased initial ²⁵ Mg (and ²⁶ Mg) abundance in GCRGs. Indeed, it follows from Fig. 7 that a value of would be quite enough to increase the ²⁵ Mg abundance from [²⁵ Mg/Fe] = -0.59 (Table 1) up to [²⁵ Mg/Fe] as required by our deep mixing calculations (Sect. 3.4). At the same time this would bring the ²² Ne/Na ratio close to the value [²² Ne/Na] = 0 which makes possible the synthesis of Na in GCRGs inferred to occur at the expense of ²² Ne.

Our calculations of the nucleosynthesis yields from the AGB star confirm the conclusion of TWWA that AGB stars can contribute to the enrichment of the interstellar medium (and in our case of low mass stars in globular clusters) in C and N. We also repeat our result from Paper II that the intermediate mass AGB stars can be responsible for some primordial enrichment of low mass stars in Na and Al (Fig. 7). Contrary, however, to the situation for Na, which is produced during pulses, Al is produced from ²⁴ Mg only during HBB, the details of which are not fully constrained by theory. At temperatures higher than about K the ²⁴ Mg(p, Al reaction goes faster than proton captures by ²⁵ Mg and ²⁶ Mg (CF88), the latter two isotopes being also produced copiously during pulses. As a result of very hot bottom burning ( K) which is predicted by recent evolutionary calculations (Lattanzio et al. 1997), the ²⁵ Mg enhancement can be accompanied by a deficit of ²⁴ Mg and by an increase of Al. In order, however, to produce low mass stars with even a twofold decrease of the initial ²⁴ Mg abundance we need a dilution coefficient as large as and of course in addition we get some primordial Al enhancement. It should be noted that the abundance of O is not reduced as the result of HBB in intermediate mass AGB stars (Fig. 7) since O is synthesized from C during pulses. Deep mixing in red giants is therefore still required.

To summarize, the advantages of the proposed primordial scenario are the following: (i) it supplies low mass stars with a large initial abundance of ²⁵ Mg; (ii) it explains why in GCRGs with especially large Al enhancements some ²⁴ Mg depletion is also observed (because low mass stars with a low initial ²⁴ Mg abundance are expected to possess a large initial ²⁵ Mg); (iii) it accounts for some C (and N) primordial enrichment of low mass stars as is observed in globular clusters (Fig. 2, open symbols). Its apparent deficiencies are: (i) it assumes rather large dilution coefficients () to comply with the observed low abundance [²⁴ Mg/Fe] in M 13 giants; (ii) it seems to disagree with the approximate constancy of the sum C+N+O reported in several globular clusters (and noted in Sect. 1) because it assumes the initial abundance of C (and N) in low mass stars to be a function of the dilution coefficient q, which may change from star to star; (iii) and, unfortunately, there are still many uncertainties in this scenario which do not allow us to draw more definite conclusions.

We conclude this section by noting that our calculations of the s-process nucleosynthesis in the AGB star with (which are in excellent agreement with the earlier results of Busso et al. (1988)) show that there is no substantial production of neutron-addition nuclides. Hence, we do not expect that the increased initial ²⁵ Mg abundance in GCRGs has to correlate with any enhancement of the s-process elements. At present s-process nucleosynthesis is believed to occur in low mass () AGB stars where the neutron source reaction is ¹³ C(,n)¹⁶ O rather than ²² Ne(,n)²⁵ Mg as in our case (Gallino et al. 1988). Therefore, the observational data of ND95 showing that in  Cen giants abundances of some typical s-process elements (Y, Ba, La and Nd) rise as [Fe/H] increases was interpreted by them as evidence of primordial enrichment by AGB stars. Or to reverse the argument, if one accepts that the s-process elements are enhanced in  Cen by the ejecta of AGB stars, it follows that this should be accompanied by overabundances of the heavy nuclides of Mg resulting from the ejecta of their counterparts.

4.3. A "black box" solution

If the observed Al enhancements in red giants with depleted [Mg/Fe] in the clusters M 13 and  Cen are in fact produced at the expense of ²⁴ Mg and not ²⁵ Mg and if nuclear physicists confirm the currently-accepted rate of the reaction ²⁴ Mg(p, Al, the only remaining explanation of the MgAl anticorrelation is hydrogen burning at much higher temperatures than those () found in the HBS in the standard evolutionary models.

To test this idea we have considered hydrogen burning at constant temperature and density. The density was chosen as g cm^-3 as in the deep mixing study of Langer et al. (1993) and the initial chemical composition was that specified in Sect. 3.1. Nucleosynthesis calculations were interrupted when 5% of hydrogen was consumed. After that the calculated abundances were mixed with unprocessed material whose fraction was varied from 0% to 100%. Temperature was treated as a free parameter. The results are shown in Fig. 8 where the lines are the computed correlations between the final abundances of O, Na, Mg and Al. Crosses on the solid lines correspond (from right to left) to mixtures in which the fraction of unprocessed material is ... (the last crosses seen on the left on the solid lines have ). The range of temperatures fitting the anticorrelations of [O/Fe] versus [Na/Fe] and [Al/Fe] and the correlation of [O/Fe] versus [Mg/Fe] has turned out to be strikingly narrow: (short-dashed line), (solid line) and (dot-short-dashed line). Hence, were this idea right we could very precisely estimate the temperature of the hydrogen burning whose products are seen in GCRGs: ! The choice of density does not affect this estimate and if we take the amount of H to be consumed considerably different from 5% then it becomes more difficult to fit all three observed abundance correlations with the same value of temperature. It is interesting that a very similar result (with a slightly higher temperature ) is obtained when one considers hydrogen burning in a massive convective core (we have modelled the core structure with a polytrope and this time the free parameter to adjust was the central temperature).

Fig. 8. Relations between the abundances of O, Na, Mg and Al (lines) in mixtures with the fraction of unprocessed material varied from 0% to 100% (crosses correspond to 100%, 90%, 80%,... from right to left). In the processed material hydrogen burning at constant density g cm-3 and temperature has been followed until 5% of H was consumed. The temperature has been adjusted ( - short-dashed lines, - solid lines and - dot-short-dashed lines) to fit the correlations in M 13 giants (symbols). The initial chemical composition was that described in Sect. 3.1

The next question to answer is which stellar environment may be identified with the "black box" described above. We calculated a ZAMS model of a star with but found that it had a central temperature , which is too low. Any primordial origin of the hypothesized "black box" meets the difficulty of explaining why after consumption of only 5% of H the material was ejected into the intracluster medium. Another problem is understanding how some low mass stars succeeded in capturing as much as 90% of the material ejected by the "black box" (Fig. 8). These two problems are, however, easily solved if we place such a "black box" inside a star ascending the RGB, bearing in mind, of course, that we now have to think of a mechanism which can increase the temperature in the HBS up to the value . Recently Langer et al. (1997) came to similar conclusions. They have proposed that it is the thermal instability of the HBS that causes episodical rises of the HBS temperature.

This having been said, the idea of a hot hydrogen burning origin of the MgAl anticorrelation in GCRGs also disagrees with the M 13 magnesium isotopic analysis of S96 because at not only ²⁴ Mg but also ²⁵ Mg and ²⁶ Mg are quickly destroyed. For example, if we begin with the summed abundance [²⁵ Mg+²⁶ Mg/Fe] = 0 and isotopic ratios ²⁴ Mg/²⁵ Mg/²⁶ Mg = 90/4.5/5.0 (corresponding to the chemical composition described in Sect. 3.1, and which are also very close to the ratios observed in the "unmixed" M 13 giant L598 of S96), then after consumption of 5% of H we find [²⁵ Mg+²⁶ Mg/Fe] = -0.50 (whereas Shetrone reported values as large as +0.21) and ²⁴ Mg/²⁵ Mg/²⁶ Mg = 92.3/4.7/3.0 (in comparison with S96's average ratios 56/22/22). Is this an insuperable problem? A possible solution might be to postulate even higher initial abundances of the heavier Mg isotopes. What would certainly be most worthwhile is confirmation of the S96 result, and accurate data for a larger group of objects to more strongly constrain the situation.

© European Southern Observatory (ESO) 1998

Online publication: April 28, 1998

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