Issue 
A&A
Volume 540, April 2012



Article Number  A27  
Number of page(s)  20  
Section  Galactic structure, stellar clusters and populations  
DOI  https://doi.org/10.1051/00046361/201118138  
Published online  20 March 2012 
Online material
Metallicities for globular clusters from R97 on the Carretta et al. (2009) scale.
Appendix A: Transformation between the AD91 and G09 measurements
Fig. A.1
The sum of equivalent widths for the strongest two CaT lines measured with Gaussianonly fits are plotted here against the same quantity measured with Gaussian+Lorentzian fits. The latter are taken from the G09 paper, for stars in the clusters M 5 (+ signs), NGC 4372 (filled triangles), NGC 6752 (filled 5point stars), NGC 6397 (open 5point stars), NGC 6171 (open squares) and NGC 4590 (6point stars). The interpolating line has slope f = 1.147, and it was obtained by minimizing residuals and imposing the passage through the origin. 

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Fig. A.2
Same as Fig. A.1, for the stars observed for this work. The symbols identify NGC 3201 (open circles), M 10 (open triangles), M 4 (open diamonds), M 15 ( × signs) and M 71 (open squares). The fitting line has slope f = 1.090 and passes through the origin. 

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We define the reduced equivalent width for a single star as W′ = S − a (V − V_{HB}) where S = W_{8542} + W_{8662}^{10}. So we can write for the (G)09 and (A)D91 systems: and the averaged reduced equivalent widths are: By comparing measurements of individual S made with the G09 or the AD91 method, we found that S_{G} = f S_{A}, and by imposing a linear fit that is passing through (0,0) we found for clusters of the Leo I paper f = 1.147 (see Fig. A.1) and for clusters in this run f = 1.090 (see Fig. A.2). So then in the G09 system:
then we have and with a substitution where for simplicity we wrote Σ_{HB} = Σ(V − V_{HB}). Rearranging and simplifying a bit more: which gives as a function of f (with f = 1.090 or f = 1.147), the number of stars N measured for each cluster, the averaged reduced equivalent width in the AD91 system, the slopes a_{A} and a_{G} of the S vs. V − V_{HB} relations in the two systems, and the sum of the magnitude differences with respect to the HB, Σ_{HB}. The difference in slopes f is probably due to the fact that older spectra had a better resolution (slit of instead of 1″), so it might be that the Gaussonly fit does a worse job with line wings in that case.
© ESO, 2012
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