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Errors

The external errors on the mean abundances are obtained by propagating the uncertainties due to the measured , the atomic parameters, and stellar (which affects the ionization balance), assuming they are independent of one other. Following the SD93 convention, we have adopted estimates of the errors on each parameter as follows: 0.25dex in , 250K in , 50 percent in the Stark damping (), 0.5kms in the microturbulence (), and 5 percent in . Propagating these errors through the curve-of-growth analysis for the Mn II 4478 line, using a model atmosphere based around = 13000K, = 4.0, =1, with a +2dex Mn abundance enhancement over the solar value, leads to the following representative errors in the derived Mn abundances: 0.01dex (); 0.02dex ( ); 0.05dex ( ); 0.06dex (); 0.06dex ().

To obtain the internal error on the mean value of abundance for each star we calculate the standard deviation of the set of measured lines (Table 2). The mean standard deviation over the entire sample is 0.09 dex. Remarkably, there is no significant overall difference between the mean abundances derived from the Mn I and Mn II lines, despite the fact that the -sensitivity of MnI is 0.15dex for variations of 250K. There is no evidence for systematic differences between abundances derived from the different lines in Table 2; the average deviations, , are only a few hundredths of a dex.

Finally, we can estimate a purely `experimental' error on the abundance determinations for individual lines by varying the abundance values used in our synthetic fits (see Section 3.4) and seeing how rapidly the synthetic profiles depart from the observed profiles. For visual fitting of synthetic profiles to the observed data, changes of approximately 0.02-0.05dex produce a significantly degraded quality of fit, depending upon the S/N of the spectrum.

These comparisons give us confidence that the abundances we have derived are internally consistent with expected errors of observation. It is remarkable that there appears to be little significant extra scatter due to errors in . Throughout this analysis we assume that Mn is homogeneously distributed with depth. Stratification of elements by diffusion and gravitational settling, and non-LTE, are both possible complications which must be considered in such analyses. However, we do not maintain that the full agreement of Mn I and Mn II `proves' that there are no stratification or non-LTE effects on the Mn I abundances compared to Mn II, only that if any such effects are present, either they are small or the factors involved apparently cancel out over a wide range of . Detailed considerations of such possibilities are beyond the scope of this paper.



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