3 Analysis

Equivalent widths (EWs) for a large number of lines were measured using an authomatic procedure (similar to the one used in Bragaglia et al. 2001; full details will be given elsewhere). Typical errors in the EWs (obtained by comparing values measured on different, similar stars) are $\pm 3$ mÅ for NGC 6397 stars, and $\pm 5$ mÅ for NGC 6752 stars, but they are as low as $\pm 2.5$ mÅ in the best cases (e.g. the Li lines at 6707 Å). As an example, Fig. 3 compares EWs obtained for two TO-stars in NGC 6397 (stars 1543 and 1622) and two TO-stars in NGC 6752 (stars 4907 and 4428). From this comparison, we obtain rms of 3.4 mÅ and 4.8 mÅ respectively for typical EWs (assuming errors are the same for the two stars). These values are comparable with results obtained for much brighter stars at other telescopes.

As discussed in Gratton et al. (1998), the single major source of error in the derivation of distances to globular clusters is the possible existence of systematic differences (of 0.015 mag) in the reddening scales for nearby subdwarfs and the much farther globular clusters. One of the aims of the present analysis was to derive accurate reddening estimates for GCs by comparing the observed colours with (reddening free) effective temperatures $T_{\rm eff}$'s obtained from the spectra; for this reason our temperatures are based on fitting of the wings of the H$_\alpha$ profiles with synthesized lines and not on colours. We wish to emphasize that the major concern here is the derivation of temperatures using a uniform procedure for both field and cluster stars; this is also important to ensure that the derived abundances may be directly comparable (again, a basic issue in the derivation of accurate distances to clusters). This approach also allows a proper discussion of systematic differences between the chemical compostion of field and cluster stars. According to this approach, the systematic errors we will report are the possible offsets of groups of stars (e.g. those belonging to a cluster) with respect to the somewhat arbitrary scale defined by our field stars, used uniformly throughout our analysis.

The H$_\alpha$ model lines were computed according to the precepts given in Castelli et al. (1997); throughout this paper we used model atmospheres extracted by interpolation within the grid by Kurucz with the overshooting option switched off (Kurucz 1993). Within these models, convection is considered using a mixing length approach, with a pressure scale height value of $l/H_{\rm p}=1.25$. It must be noted that it is not easy to derive accurate H$_\alpha$ profiles from Echelle spectra, owing to the quite short free spectral range available for each order. We used the spectra extracted by the UVES pipeline; our procedure consisted in two steps:

1.

we eliminated the high frequency variations due to the presence of contaminating lines by dividing the spectra for a contaminating line spectrum; this last was obtained by dividing the spectra for a spline traced through local fiducial continuum points obtained after an iterative clipping average over the highest half of the spectral points in small spectral intervals within the wings of H$_\alpha$. To avoid possible errors due to the different S/N of field and cluster stars, in this last case the contaminating line spectrum was obtained from the sum of all spectra for similar stars. Note that the S/N (per pixel) of this summed spectra is $\geq$150 that is similar to that obtained for the field stars;

2.

we then compared the instrumental fluxes in regions at intermediate distances from the line center (typically 2 to 10 Å), with those obtained at large distances from the center (20 to 30 Å). These instrumental fluxes were then compared with those given by models for the same spectral regions. Note that the very central region of the line - the most critically affected by uncertainties in the model atmospheres - was not used in our comparisons. Also, our temperatures included appropriate corrections for the dependence of the profiles on gravity and metal abundance.

In the case of field stars, a comparison with temperatures obtained from colours (that have small internal errors) shows that errors of individual temperatures are $\sim$150-200 K for individual stars; nearly the same value is obtained by comparing values obtained for similar stars in globular clusters. These rather large errors are due to uncertainties in the flat fielding procedure, and are typical for such temperature derivations when only one Balmer line is used (see e.g. Fuhrmann et al. 1994).

Systematic errors in these temperatures might be not negligible, as shown by Barklem et al. (2000); however, as mentioned above, this is not our major concern, because, insofar temperatures are derived homogenously for cluster and field stars, such errors have very small impact on the present discussion, and on the derivation of distances and ages for globular clusters (discussed in a future paper). The adopted temperature scale is confirmed by analysis of line excitation: however, temperature from excitation have slightly larger error bars due to the limited range of excitation for lines measurable in warm, metal-poor dwarfs and subgiants.

For field stars, we compared these $T_{\rm eff}$'s (Col. 7 of Table 1) with those given by colours (B-V and b-y), using the calibration given by Kurucz (1993); here we assumed that all these nearby (field) stars are unreddened. Internal errors in $T_{\rm eff}$'s from colours are about 26 K. On average, temperatures derived from H$_\alpha$ are lower than those derived from colours by $97\pm 38$ K, with a large r.m.s scatter of 188 K. For field stars, we then corrected the temperatures from colours to those derived from H$_\alpha$, and averaged the two values, giving a weight 4 to temperatures from colours, and 1 to temperatures derived from ${\rm H}_\alpha$. These are our "best temperatures'' for the field stars (Col. 8 of Table 1).

We may compare these "best temperatures'' with those obtained by Alonso et al. (1996) using the IR flux method (Col. 9 of Table 1). Excluding the discrepant case of HD 132475, on average our best $T_{\rm eff}$'s are lower than those given by Alonso et al. by $5\pm 14$ K (rms ${\rm residuals}=45$ K, 10 stars). Hence our $T_{\rm eff}$'s can be assumed to be on the same scale of Alonso et al. Since temperatures from the IR flux method are rather robust with respect to possible errors in model atmospheres (although they are sensitive to uncertainties in the adopted reddening values), this comparison shows that systematic errors in our temperature scale from H$_\alpha$ profiles are likely not very large.

When plotted one on top of the other (separately: dwarfs and subgiants, and stars in different clusters), the H$_\alpha$ profiles for cluster stars look undistinguishable. Furthermore, we were unable to find any correlation between colours and temperatures either from line excitation or H$_\alpha$ profiles. We then concluded that the stars are intrinsically very similar, and that the slightly different values of colours and temperatures we derived for each star are due to random errors. In the following analysis, we have then adopted for all stars in these groups the same average temperatures (note however that this assumption is not critical in the present discussion).

Surface gravities $\log g$ were obtained from the location of the stars in the colour magnitude diagram, assuming masses consistent with an age of 14 Gyr (again, this assumption is not critical). As usual, microturbulent velocities were obtained by eliminating trends of abundances derived from individual Fe lines with expected line strength. Star-to-star scatter in Fe abundances within each group (same cluster, same evolutionary phase) were reduced by adopting for all stars the same microturbulent velocity; these average values were then adopted in the final analysis.

The finally adopted atmospheric parameters (effective temperatures in K/surface gravities/model metal abundances/microturbulent velocities in km s^-1) were as follows: NGC 6397 TO-stars (6476/4.10/-2.04/1.32); NGC 6397 subgiants (5478/3.42/-2.04/1.32); NGC 6752 TO-stars (6226/4.28/-1.43/0.70); NGC 6752 subgiants (5347/3.54/-1.43/1.10).

 

Table 4: Sensitivities of abundances to errors in the atmospheric parameters

Element	$\Delta T_{\rm eff}$	$\Delta \log g$	$\Delta v_{\rm t}$
	+100 K	+0.2 dex	+0.2 km s-1
TO-star
[Fe/H]	+0.096	-0.054	-0.050
[O/Fe]	-0.161	+0.123	+0.048
[Na/Fe]	-0.037	+0.007	+0.032
[Mg/Fe]	-0.034	+0.006	+0.041
[Al/Fe]	+0.001	-0.012	+0.007
Subgiants
[Fe/H]	+0.108	-0.023	-0.049
[O/Fe]	-0.200	+0.098	+0.044
[Na/Fe]	-0.044	-0.010	+0.026
[Mg/Fe]	-0.055	+0.020	+0.043
[Al/Fe]	-0.080	+0.021	+0.038

Sensitivities of abundances to errors in the atmospheric parameters are given in Table 4. Errors in final abundances are mostly due to possible errors in the adopted $T_{\rm eff}$'s. For our line list (dominated by low excitation lines), Fe I abundances rise by 0.10 dex, [O/Fe] values by -0.20 dex, and [Na/Fe] ones by -0.04 dex for a 100 K increase in the adopted $T_{\rm eff}$. Systematic errors in $T_{\rm eff}$'s are dominated by uncertainties in the fitting of the H$_\alpha$ profiles: they are about $\pm 90$ K for the dwarfs and $\pm 60$ K for the subgiants, leading to errors in the [Fe/H] values of $\pm 0.09$ dex and $\pm 0.06$ dex respectively for TO-stars and subgiants. This value, appropriate for cluster stars, is smaller than that given for field stars simply because our $T_{\rm eff}$'s for cluster stars are actually the average over the values obtained for several stars, and errors for individual stars are given by uncertainties in the flat fielding procedure, that are only weakly affected by S/N. Corresponding errors in [O/Fe]'s are $\pm 0.18$ and $\pm 0.12$ dex; those in [Na/Fe] are $\pm 0.04$ and $\pm 0.03$ dex. However, in the context of the O-Na anticorrelation, errors in temperatures adopted for individual stars are more important. In the case of NGC 6397, a quite realistic estimate can be obtained by the star-to-star scatter in Fe abundances, that is 0.032 dex, corresponding to an rms spread of 33 K in the $T_{\rm eff}$'s. The adoption of a uniform temperature would then yield errors of $\pm 0.07$ dex in [O/Fe]'s and $\pm 0.01$ dex in [Na/Fe]'s (to be compared with the observed star-to-star scatter). In the case of NGC 6752, the star-to-star scatter of 0.096 dex in [Fe/H]'s also includes an important contribution due to noise in the EWs: in fact the rms reduces to 0.074 dex if only spectra with S/N> 40 are considered. We conclude that errors in individual $T_{\rm eff}$'s are $\;\lower.6ex\hbox{$\sim$ }\kern-7.75pt\raise.65ex\hbox{$<$ }\;$73 K. Related errors in [O/Fe] and [Na/Fe] abundances are $\;\lower.6ex\hbox{$\sim$ }\kern-7.75pt\raise.65ex\hbox{$<$ }\;$0.15 and $\;\lower.6ex\hbox{$\sim$ }\kern-7.75pt\raise.65ex\hbox{$<$ }\;$0.03 dex. Again, these are the values to be compared with the observed scatter.