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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 Gaussian-only 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 5-point stars), NGC 6397 (open 5-point stars), NGC 6171 (open squares) and NGC 4590 (6-point 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 = W₈₅₄₂ + W₈₆₆₂¹⁰. 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 Gauss-only fit does a worse job with line wings in that case.

© ESO, 2012