## 4. Re-calibration of the SMR method in the V,V-I planeThe SMR method was originally devised by Sarajedini (1994) in the plane. His calibration was based on the ZW scale and high precision CCD photometry obtained by Da Costa & Armandroff (1990). For the present analysis we used values for 6 clusters as in Table 1 of Sarajedini (1994), integrated by values for NGC 5053 (Sarajedini & Milone 1995) and M 68 (from photometry of Walker 1994, as quoted in Sarajedini & Milone 1995) in order to extend the method to very low metallicity clusters. Data are shown in Table 1. The parameter definition is analogous to that in the plane: we want [Fe/H] as a function both of and of .
Due to the small sample, all clusters were used to obtain the new calibrations. Original values from direct analysis by CG97 were used whenever possible; for the 3 remaining GCs, we transformed ZW values to the CG97 scale. Fig. 3 shows the resulting calibrations (and also a potential problem for the index). The relation obtained using the 8 clusters for is well fitted with a quadratic polynomial (Fig. 3, lower panel), like for the plane, and is given by:
(, ). The quadratic term is found to be highly significant, with a confidence level of 99.5 %. In the case of instead, both a linear and a
quadratic interpolation seem to fit equally well the data (see
Fig. 3, upper panel). The statistical significance of the
quadratic term is lower than in all previous cases, being only between
90 and 95 %. Circumstantial evidence in favour of a quadratic relation
comes, in our view, from the fact that the relation between
and seems to be a
straight line (see Fig. 4), the only discrepant point being
NGC1851, and the fact that
We have derived again the calibration for the index in the supposition something is wrong with the value for NGC1851. We have "corrected" it to the value it should have if it followed the fit in Fig. 4 (a correction of 0.024 mag, rather large given the errors quoted by Da Costa & Armandoff 1990). The statistical significance of the quadratic term remains virtually unchanged even if, of course, the dispersion of the quadratic interpolation decreases (from 0.12 to 0.08 dex). As a further test, we used the value = 0.951 (Ferraro et al. 1997) for M3, and obtained [Fe/H] and -1.34 using the quadratic and linear interpolations with the original value for NGC1851, respectively; and -1.32 and -1.37 using the equivalent relations where the has been corrected as described. These values, while nicely bracketing the spectroscopic value [Fe/H] (CG97), do not tell anything definitive about the true form of the calibration at the high metallicity end. In view of this, we give both the linear and quadratic expressions for the - [Fe/H] relation (with the modified value for NGC1851): We however think it safer to apply the SMR method in the plane, at least until more homogeneous values for are supplied. Moreover, note that while the values in the
and planes are linearly
correlated, the run of against
is not so clear, especially at the high
metallicity end. Uncertainties in the transformation between the
absorption coefficients in different bands, random errors in the
adopted reddenings, the adoption of different standard system for the
© European Southern Observatory (ESO) 1998 Online publication: December 16, 1997 |