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Astron. Astrophys. 329, 937-942 (1998)

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4. Re-calibration of the SMR method in the V,V-I plane

The SMR method was originally devised by Sarajedini (1994) in the [FORMULA] 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 [FORMULA] plane: we want [Fe/H] as a function both of [FORMULA] and of [FORMULA].


Table 1. GCs used as calibrators. Data are taken from GC97, ZW, SL (Table 5), Sarajedini (1994, Table 1), and Sarajedini & Milone (1995, for NGC5053 and NGC4590). Y or N indicate in columns 3 and 9 whether the GC is a primary calibrator for GC97 and SL respectively.

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 [FORMULA] index). The relation obtained using the 8 clusters for [FORMULA] is well fitted with a quadratic polynomial (Fig. 3, lower panel), like for the [FORMULA] plane, and is given by:

[FIGURE] Fig. 3. Calibration of the [FORMULA] (upper panel) and [FORMULA] (lower panel) parameters in the [FORMULA] plane using the new CG97 metallicities. The solid lines in the both panels represent a quadratic interpolation through the data; the dashed line is the linear best fit. In the upper panel the open symbol represents NGC1851 once "corrected" as explained in the text.


([FORMULA], [FORMULA]). The quadratic term is found to be highly significant, with a confidence level of 99.5 %.

In the case of [FORMULA] 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 [FORMULA] and [FORMULA] seems to be a straight line (see Fig. 4), the only discrepant point being NGC1851, and the fact that [FORMULA] is quadratically related to [Fe/H].

[FIGURE] Fig. 4. Comparison of the [FORMULA] and [FORMULA] values used by Sarajedini (1994) and Sarajedini and Milone (1995) to calibrate the SMR method in the [FORMULA] plane. The open symbol represents the value of [FORMULA] for NGC1851, "corrected" as explained in the text.

We have derived again the calibration for the [FORMULA] index in the supposition something is wrong with the [FORMULA] 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 [FORMULA] dispersion of the quadratic interpolation decreases (from 0.12 to 0.08 dex).

As a further test, we used the value [FORMULA] = 0.951 (Ferraro et al. 1997) for M3, and obtained [Fe/H] [FORMULA] and -1.34 using the quadratic and linear interpolations with the original [FORMULA] value for NGC1851, respectively; and -1.32 and -1.37 using the equivalent relations where the [FORMULA] has been corrected as described. These values, while nicely bracketing the spectroscopic value [Fe/H] [FORMULA] (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 [FORMULA] - [Fe/H] relation (with the modified [FORMULA] value for NGC1851):



We however think it safer to apply the SMR method in the [FORMULA] plane, at least until more homogeneous values for [FORMULA] are supplied.

Moreover, note that while the [FORMULA] values in the [FORMULA] and [FORMULA] planes are linearly correlated, the run of [FORMULA] against [FORMULA] 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 I magnitudes could all be possible sources for the observed disagreement, that seems to affect the [FORMULA], but much less a differential measure as the [FORMULA].

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© European Southern Observatory (ESO) 1998

Online publication: December 16, 1997