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

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1. Introduction

Recently Shetrone (1996b, hereafter S96) has determined magnesium isotopic compositions for a small sample of bright red giants in the globular cluster M 13. His finding that many giants in this system have [(25 Mg+26 Mg)/24 Mg] [FORMULA] +0.4, in stark contrast to values [FORMULA] -0.4 found in field halo stars (see also McWilliam & Lambert 1988 and references therein), is of fundamental importance, and highlights yet again the differences in abundance patterns found in cluster and field stars. Shetrone's work followed the earlier discovery that large Al enhancements were usually accompanied by moderate Mg depletions in this cluster (Shetrone 1996a), as well the demonstration that anticorrelations of Na and Al with O exist not only in "normal" monometallic clusters such as M 13 (see Kraft et al. 1997) but also in the massive globular cluster [FORMULA]  Cen whose stars show intrinsic spreads in both metallicity and the abundances of the s-process elements (Norris & Da Costa (1995, hereafter ND95)). These new data challenge stellar evolution theory to provide an appropriate explanation of the abundance anomalies, on the one hand, and present a number of new observational constraints on possible primordial processes responsible for abundance variations in globular clusters, on the other. In this paper we use the latest spectroscopic results to address the question of whether the modern theory of nucleosynthesis in stars can self-consistently reproduce the whole spectrum of abundance variations seen in globular-cluster red giants (GCRGs) and, if not, to seek constraints on additional ad hoc assumptions which make such reproduction possible.

Stars leaving the main sequence (MS) in present-day globular clusters have small masses [FORMULA] and very low metallicities, covering the range -2.4 [FORMULA] [Fe/H] [FORMULA] -0.2, corresponding to [FORMULA] [FORMULA] Z [FORMULA] 0.01, (where we adopt [Fe/H] = [FORMULA]), and [FORMULA] (Anders & Grevesse 1989)) 1. Standard stellar evolution theory has no doubts about subsequent structural and chemical histories of such stars, at least until the beginning of the core helium flash. MS central hydrogen burning, which was dominated by pp-chains, is now replaced by shell hydrogen burning with the main energy output provided by the CNO-cycle. The shell advancing outwards in mass causes a gradual growth of the underlying helium core until the core mass becomes large enough to trigger the helium flash. These internal structural changes are accompanied by the star ascending the red giant branch (RGB). Its surface chemical composition is not expected to change significantly during this evolutionary stage. The only important event between the MS turn-off and the core helium flash is the well-known first dredge-up episode which takes place on the subgiant branch. The displacement of the star from the MS to a cooler region of the HR diagram favours the convective envelope extending its base into deep layers which were in radiative equilibrium on the MS and where some mild transformations among CN isotopes in the then energetically unimportant CN-cycle occurred. As a result the surface abundances of 12 C, 13 C and 14 N (as well as those of 7 Li, 3 He and a few other light nuclides which are not discussed in this work; for recent theoretical results on their standard dredge-up and non-standard deep mixing evolutionary changes see Sackmann & Boothroyd (1997), Weiss et al. (1996) and Charbonnel (1995)) begin to decline from their initial values. This excursion of the base of the convective envelope (BCE) into the interior of the star continues until it arrives at its deepest penetration, which corresponds to the end of the first dredge-up; after that, convection begins to retreat and later follows approximately the outward advancement of the hydrogen burning shell (HBS). Our standard evolutionary calculations for a [FORMULA] star show that, depending on Z, the first dredge-up changes of the surface 12 C, 13 C and 14 N abundances are indeed very modest: [FORMULA]) = (10-4, 64, -0.0024, 0.0025), (5 10-4, 50, -0.0064, 0.012), (5 10-3, 45, -0.0092, 0.021) (on the MS 12 C/13 C [FORMULA] ; here and in what follows a nuclide's chemical symbol is used also to denote its number density).

When comparing these predictions of standard stellar evolution theory with available observational data on the atmospheric chemical composition of red giants in globular clusters one finds obvious and numerous disagreements. (i) The measured 12 C/13 C ratios have very low values often approaching the limit 3.5 which is a characteristic of the equilibrium CN-cycle (Smith & Suntzeff 1989; Brown & Wallerstein 1989; Suntzeff & Smith 1991; Brown et al. 1991a; Briley et al. 1994; S96). (ii) The differences in C and N among red giants in the same cluster reach an order of magnitude or even more. Moreover, carbon abundances [C/Fe] are found to anticorrelate with luminosity (to correlate with the absolute visual magnitude), consistent with a progressive C depletion as the star ascends the RGB at luminosities well above the end of the canonical first dredge-up (as seen, for example, in M 92 and NGC 6397 (Bell et al. 1979; Langer et al. 1986; Briley et al. 1990), M 4 and NGC 6752 (Suntzeff & Smith 1991)). (iii) The most intriguing result is that in many globular clusters there are large (up to 1 dex) variations of O and Na among red giants (Kraft 1994) and in some clusters Al and Mg abundances also vary from star to star (Kraft et al. 1997).

It is important to note that all nuclides mentioned above whose abundances show considerable scatter in GCRGs (12 C, 13 C, N, O, Na, Mg isotopes and Al) are potential participants in hydrostatic hydrogen burning. During transformation of H into He in the CNO-cycle, which plays the chief role in this process, the relative abundances of the CNO nuclides are changing whereas their net sum remains constant, i.e. the CNO nuclides actually work as catalysts. So do the NeNa and MgAl nuclides in the NeNa- and MgAl-cycles, respectively. Detailed flow-charts and the latest estimates of reaction rates for all three cycles can be found in the review of Arnould et al. (1995). Such approximate constancy of the sum C+N+O, despite the large spreads in the individual abundances of C, N and O, has been observed in M 13 and M 3 by Smith et al. (1996), in NGC 362 and NGC 288 by Dickens et al. (1991) and in [FORMULA]  Cen by ND95. There is also some evidence of constancy of the sum Mg+Al in M 13 (Kraft et al. 1997).

In contradistinction, the heavier [FORMULA] elements such as Si, Ca and Ti, which are believed to be produced by successive [FORMULA] -captures in massive stars and which do not participate in hydrostatic hydrogen burning, do not show any scatter in GCRGs. Instead their mean abundances agree well with the abundances of [FORMULA] -elements observed in field Population II dwarfs, i.e. [FORMULA] /Fe [FORMULA]. In addition, the iron peak elements Cr and Ni, synthesized during SNe explosions, do not exhibit abundance anomalies. As regards Fe itself, in most globular clusters its abundance is surprisingly constant within the same cluster. The only exception of the rule is [FORMULA]  Cen (M 22 may be another) where the abundance range [FORMULA] [Fe/H] [FORMULA] and the rise of abundances of s-process elements with that of Fe are certainly records of the cluster's more complicated chemical enrichment history (ND95).

To summarize, observations strongly support the idea that the star-to-star abundance variations (or, more precisely, at least a substantial part of them) in globular clusters were presumably produced during hydrogen burning. The fact that there are fairly good correlations between overabundances of N, Na and Al, on the one hand, and underabundances of C, O and Mg, on the other hand, is undoubtedly a sign of these abundance anomalies' simultaneous origin. The next question to answer is the place where these variations were produced. In our attempt to solve this puzzle we have chosen the latest spectroscopic data on the chemical composition of red giants in the globular clusters M 13 (Kraft et al. 1997; S96) and [FORMULA]  Cen (ND95). The former cluster is an extreme representative of "normal" (i.e. showing neither iron nor neutron-rich elements abundance variations) which contributes much to the "global anticorrelation" of [O/Fe] versus [Na/Fe] (see the review paper by Kraft 1994). [FORMULA]  Cen, on the other hand, provides evidence that the O vs. Na and O vs. Al anticorrelations are not a prerogative of "normal" clusters. Furthermore, [FORMULA]  Cen is the only globular cluster not obeying the "global anticorrelation" since it contains giants with extremely high [Na/Fe] (up to 1 dex) well above the general trend seen in "normal" clusters where [Na/Fe] saturates at [FORMULA] 0.5 dex. We shall see how theory can interpret this anomaly.

It should be noted that the standard stellar evolution theory fails to predict the low 12 C/13 C ratios seen in Population I giants of mass [FORMULA], too (Gilroy & Brown 1991; Charbonnel 1994). So, globular clusters are not unique in this regard. It is important to point out, however, that in GCRGs the number of nuclides whose abundances are known to vary from star to star is larger and the abundance variations themselves are more pronounced than in Population I giants.

The remainder of the paper is organized as follows. In Sect. 2 we briefly describe our theoretical tools - computer codes used to perform stellar evolution and nucleosynthesis calculations. Sect. 3 deals with the most promising candidate for the origin of the star-to-star abundance variations in globular clusters - deep mixing in evolving red giants. This, however, provides an incomplete solution to the problem. Sources of additional primordial pollution (SNe explosions, AGB stars and a "black box") which can contribute and modify the deep mixing scenario are discussed in Sect. 4. (We refer the reader also to Smith & Kraft (1996) who suggest that Ne novae may provide the additional pollution. In the present work we shall not address this possibility.) Our concluding remarks are given in Sect. 5.

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Online publication: April 28, 1998