ner_tags: O O O O O O O O O O O O O O B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: to depend on any model assumptions, so we will use the calibration based on V − V HB for these 19 clusters. For the remaining clusters, the absolute magnitude calibration would be the best choice, but we only have F606W photometry available for two additional clusters. So instead of presenting results from three different calibrations, the metallicities for all the remaining six clusters are derived from the luminosity approach. When necessary, these six clusters are marked in plots and tables with an asterisk. Using the set of average reduced equivalent widths as given in Table 3 , we now calibrate them with mean cluster metallicities from the literature (from Dias et al. 2016 ). The upper plot in Fig. 14 shows the metallicities from the literature as a function of reduced equivalent width. The three lines show a linear, quadratic, and cubic fit to the data, taking into account the errors on both axes (which are small), together with their corresponding root mean squares (rms). The coefficients for all relations are given in Table 4 for the following equation: Fig. 14. Upper panel : the metallicity from the literature ( Dias et al. 2016 ) is plotted over the mean reduced equivalent width of each cluster, derived from the quadratic relation on all RGB stars based on V − V HB . Three polynomials of different degree are fitted to the data and the rms for each is given in the legend. Lower panel : quadratic fits to three more calibrations using the same metallicity scale (only brighter than HB, and based on M and L ) are provided for comparison, together with all four on a different metallicity scale (C09, from Carretta et al. 2009a ). Table 4. Coefficients for CaT-metallicity calibration as given by Eq. ( 7 ) for three different polynomial degrees. Since both the Bayesian (BIC) and the Akaike (AIC) information criteria give the best results for the quadratic relation, we chose this for further analyses. Therefore, the relation between reduced equivalent width and metallicity is given by: The metallicities derived from this relation show two systematic errors: the mean metallicity of a cluster will be the value of the relation given above at the mean reduced EW of the cluster and, therefore, will have a small offset to the literature value for most clusters. Furthermore, the slope of the relation at any given point defines the metallicity spread. Following previous studies (see, e.g., Vásquez et al. 2018 ), the uncertainties are calculated as the quadratic sum of the uncertainty σ W ′ and the rms for the used relation as given in Fig. 14 . For the quadratic relation this yields: where rms is the root mean square for the used relation and σ r is the propagated uncertainty for σ W ′ : The derived metallicities and their uncertainties for all previously discussed calibrations are listed in Table 8. We already demonstrated that all previously discussed approaches yield a similar W ′. The lower panel in Fig. 14 shows that the metallicity calibrations