5 The O-Na and Mg-Al anticorrelation

In our analysis, oxygen abundances were derived from the permitted infrared triplet (7771-74 Å): the forbidden lines are too weak in the program stars to be reliably measured, and we did not observe the region of the OH band in the near UV because the required exposure times would be prohibitive even for an 8 meter telescope. Na abundances are based on the quite strong doublet at 8183-94 Å, clearly visible in all stars. We checked that telluric lines were not blended with the stellar features. For both O and Na, our abundances included non-LTE corrections, computed following the precepts of Gratton et al. (1999): however, these corrections are small and they do not affect any of the conclusion reached in this paper. Mg abundances are based on a few high excitation lines in the blue and yellow portion of the spectrum (typically three to four lines were measured for each star). Finally, whenever possible Al abundances were measured using the high excitation IR doublet at 8772.9/73.9 Å. However, this was possible only for subgiants in NGC 6752, since in the other cases this doublet is too weak, and the only chance to measure Al abundances is by using the resonance doublet at 3944/61 Å. These lines, while stronger, are not ideal abundance indicators due to saturation and the presence of large departures from LTE (see e.g. François 1986; Beyley & Cottrell 1987; and the discussion in Gratton & Sneden 1988). An extensive discussion of departures from LTE for Al has been presented by Baumüller & Gehren (1997): these authors found that rather large ($\sim$0.6 dex) non-LTE corrections are required for the resonance lines for model atmosphere parameters appropriate for the program stars, in the sense that an LTE analysis should grossly underestimate Al abundances. Application of such corrections greatly improve the agreement between abundances from the resonance lines and those derived from the 8772.9-73.9 Å doublet (for which non-LTE corrections are small). Such corrections were then included in the abundances listed in Tables 2 and 3. Although these large corrections might be somewhat uncertain, analysis of these lines may still be useful to discuss the Mg-Al anticorrelation insofar only stars with very similar atmospheric parameters are considered, because in this case we expect that departures from LTE should be essentially the same for all such stars.

For NGC 6397, the O abundance is ${\rm [O/Fe]}=+0.21\pm 0.05$ (internal error; systematic errors are $\sim$0.1 dex), and the average [Na/Fe] ratio is ${\rm [Na/Fe]}=+0.20\pm 0.05$. This O excess is quite small in comparison to the values usually found for metal-poor stars (see e.g. Gratton et al. 2000), but it agrees very well with the mean values determined by Minniti et al. (1997): ${\rm [O/Fe]}=+0.19$) and Norris & Da Costa (1995: [O/Fe]$\sim$0.1) from analysis of the forbidden lines in red giant spectra. Also the Mg abundance we get is quite low: this point will be discussed in a next paper. On the other side, the [Na/Fe] value we found agrees well with that determined for a single red giant by Carretta (1994: ${\rm [Na/Fe]}=+0.22$), and for two more by Norris & Da Costa (1995: [Na/Fe]$\sim$0.2), while it is somewhat larger than the value of ${\rm [Na/Fe]}=-0.01$ found by Minniti et al. (1997). We wish to remark that none of the program stars seem to be oxygen-poor and sodium-rich. The star-to-star scatter in our determinations (0.15 and 0.14 dex, rms, respectively) is larger than expected from errors in the EWs alone (we would expect rms values of $\sim$0.10 dex): however it may be justified by some star-to-star scatter in the atmospheric parameters (within the measuring errors), not accounted for in our analysis (we are assuming that all dwarfs and subgiants may be analyzed using the same model atmospheres), and by a small offset in the results for dwarfs and subgiants (again, likely due to small errors in the adopted set of atmospheric parameters, within our quoted uncertainties). Given the small spread in Fe abundances, and the absence of a clear O-Na anticorrelation, we conclude that NGC 6397 is indeed a very homogenous cluster. On the whole, our results indicate that stars in this cluster conforms to the paradigm set by field stars, confirming earlier findings by Bell & Dickens (1980).

Figure 6: Run of the abundances of Na and of O for stars in NGC 6752. Filled squares are TO-stars, open squares are subgiants, and lines represent upper limits (for O)

NGC 6752 presents a very different scenario (this is not too surprising, in view of the variations of the strength of CN and CH bands among stars on the MS already noticed by Suntzeff & Smith 1991). There is a clear anti-correlation between O and Na abundances even for stars at the TO. This is clearly illustrated by Figs. 4 and 5, where we plotted the spectral regions including the Na and O lines in these stars (stars are ordered according to decreasing Na abundances). Notice that all these stars have the same (or at least very similar) temperature, gravity, overall metal abundance and microturbulent velocity, so that observed variations in the line strengths may be directly interpreted as spread in the abundances: then, in spite of the fact that a few of the spectra are somewhat noisy, this result does not depend on details of the analysis, but rather is a solid purely observational evidence, largely independent of all the assumptions made. We found that Na abundances span a range of almost an order of magnitude. O abundances also change by a rather large factor; while not as extreme as in M 13, we found a rather extensive O-Na anticorrelation in NGC 6752 too. This anti-correlation is shown in Fig. 6. There is a small offset in the O-Na anticorrelation between TO-stars and subgiants, but we think this is an artefact of the analysis (slightly incorrect offsets in temperatures and gravities).

Figure 7: Run of the c1 index from Strömgren photometry with the Na abundance for stars in NGC 6752. Filled squares are TO-stars, and open squares are subgiants

There is some correlation between c₁ and the O-Na trends (see Fig. 7). Note however that the scatter in this relation is quite large and the correlation is significant only for subgiants; this is not surprising, since our spectra shows that molecular bands are very weak in the spectra of TO-stars of NGC 6752, and their variations are not likely to affect significantly intermediate band colours like c₁.

Figure 8: Run of the abundances of Mg against that of Al for stars in NGC 6752. The upper panel shows results for TO-stars; the lower panel those for subgiants. Note that Al abundances for TO-stars were obtained using the resonance doublet, which is affected by large departures from LTE

Figure 8 displays results for Mg and Al in NGC 6752. The star-to-star variations in the Al abundances are large: $\sim$1 dex among subgiants, and even more among TO-stars. These large variations cannot be explained by observational errors, and (for TO-stars) by any plausible differential non-LTE effect among stars with very similar atmospheric parameters. On the other side, star-to-star variations in the Mg abundances are much smaller ( $\;\lower.6ex\hbox{$\sim$ }\kern-7.75pt\raise.65ex\hbox{$<$ }\;$0.4 dex), and they may be seen clearly only among subgiants; for TO-stars, the used Mg lines are quite weak and a larger scatter in the abundances is due to errors in the EWs. Data for subgiants, for which reliable Al abundances could be obtained from the high excitation Al I doublet at 8772.9/73.9 Å, indicate that also for these elements there is a clear anticorrelation between Mg and Al. Stars 1460 and 1481 (the two most Na-rich subgiants) are clearly Mg-poor, Al-rich. We emphasize here that while the Mg-Al anticorrelation is not obvious in panel a of Fig. 8, we think that such an anticorrelation exists also for TO-stars because the Al abundances show a very large star-to-star variation, correlated with Na abundance variations; we think the anticorrelation is less obvious in this case because we had to measure the resonance doublet of Al at 3944/61 Å, not an ideal abundance indicator as we mentioned above, and moreover Mg abundances have larger errors, comparable to the star-to-star variations seen among subgiants.

We are now preparing line lists to study CH and CN abundances. However, it seems clear that the strength of these bands is correlated with Na and O abundances. Also, there is a correlation with the Stromgren c₁ index, albeit the scatter is quite large. Finally, in a forthcoming paper we will present a full discussion of the Li abundances in these stars. Here we anticipate that Li abundances in NGC 6752 stars seem also anticorrelated with the Na ones.