...2002)

Star-to-star variations of the strengths of the lines of these elements (Na and Al in particular) were known to exist at the tip of the red giant branch (RGB) for a long time (Cohen 1978; Peterson 1980; Norris et al. 1981; see Kraft 1994, for an early review).

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...1981)

An alternative would be that the abundance anomalies were accreted onto the surface of low-mass stars from the mass loss by massive stars (D'Antona et al. 1983; Thoul et al. 2002). In this case, only the surface convective layers would have a polluted composition, and the anomalies would disappear on the RGB due to dilution during the first dredge-up event. However, turnoff and bright giant stars exhibit the same anti-correlations, which means that the entire star, or at least 80$\%$ of its mass (which corresponds approximately to the maximum depth of the convective envelope during the first dredge-up), has the composition of the photosphere.

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... [O/Fe]

In the usual notation of spectroscopists, [O/Fe $]=\log_{10}$(O/Fe) $_*-\log_{10}$(O/Fe)$_{\odot}$, where * and $\odot$ denote stellar and solar values, respectively.

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...1981)

In their pioneer paper, Cottrell & Da Costa (1981) suggest that Na and Al enrichment in CN-strong stars of the GCs 47Tuc and NGC 6752 might be produced within intermediate-mass stars ($\sim$5-10 $M_{\odot }$). However, the invoked process is neutron-captures on ²²Ne and ²⁵Mg within the thermal pulse (the neutrons being released by the ²²Ne($\alpha$, n)²⁵Mg reaction; see Iben 1976).

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...$\sigma=0.34\pm0.04$

This agrees well with various studies (Zinnecker 1984; Adams & Fatuzzo 1996; Elmegreen 1999) that show that one would expect a log-normal form for the IMF if the number of independent parameters governing the fragmentation of a proto-stellar cloud is large enough (>5).

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... generations

D'Antona et al. (2005) push the analysis of the CMD of NGC 2808 further. They propose that the main sequence width of this GC can be explained by the presence of three stellar generations born with different helium contents: $Y \sim 0.24$ (first generation born with proto-cluster abundance), $Y \sim 0.4$ (second generation, in chronological order, born from the winds of the most massive AGBs of the first generation), and $Y \sim 0.26{-}0.29$ (third generation born from the ejecta from less massive AGBs of the first generation). In their scenario, late binary type II supernova explosions are invoked to explain why there are no stars formed with Y between 0.29 and 0.4.

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... (b)

As mentioned in Sect. 3, the yields of massive AGB stars have been computed recently by several groups in the context of the self-enrichment hypothesis. Nevertheless, the predictions remain highly uncertain (mainly because they depend on the modelling of complex physical mechanisms such as HBB, third dredge-up, convection, mass loss, rotation etc) and none of the present models has properly accounted for the O-Na and Mg-Al anticorrelations yet. On the other hand, models of rotating massive stars with the appropriate initial composition will soon be available (Decressin et al. 2006).

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... requirements

Assuming that the second ("polluted'') generation of stars contained its own massive and fast-evolving "polluters'' (the ejecta of which would give rise to a third generation, and so on) would make the whole problem much more complex, and it would invalidate the analysis made here.

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