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Appendix A: Error estimates

Table A.1:   Sensitivities of abundance ratios to variations in the atmospheric parameters and to errors in the equivalent widths, and errors in abundances for stars in M 54 observed with UVES.

Table A.2:  Sensitivities of abundance ratios to variations in the atmospheric parameters and to errors in the equivalent widths, and errors in abundances for stars in M 54 observed with GIRAFFE.

Table A.3:   Sensitivities of abundance ratios to variations in the atmospheric parameters and to errors in the equivalent widths, and errors in abundances for stars in SgrN observed with GIRAFFE.

We refer the reader to the analogous Appendices in Carretta et al. (2009a,b) for a detailed discussion of the procedure adopted for error estimates. In the following, we provide only the main tables of sensitivities of abundance ratios to the adopted errors in the atmospheric parameters and EWs and the final estimates of internal and systematic errors for all species analysed using UVES and GIRAFFE spectra of stars in M 54 and in SgrN.

Sensitivities of abundance ratios to atmospheric parameters.

The amount of the variations in the atmospheric parameters is shown in the first line of the headers in Tables A.1-A.3, whereas the resulting response in abundance changes of all elements (the sensitivities) are shown in Cols. 3 to 6 of these tables, for abundances in M 54 from UVES and GIRAFFE spectra and for stars in the Sgr nucleus from GIRAFFE, respectively.

Errors in atmospheric parameters.

The other difference is that for the Sgr field (nucleus) stars, errors in temperature were derived directly from the calibration by Alonso et al. (1999), since we used the relation between and the K magnitudes only for the cluster M 54.

Adopted errors in atmospheric parameters are listed in the second (internal errors) and third line (systematic errors) of the headers in Tables A.1-A.3. These errors, multiplied by the sensitivities of abundances to variations in the individual parameters, and summed in quadrature, provide the total internal and systematic errors listed in the last two columns of these tables.