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

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3. Photometric metallicity indicators in the V,B-V plane

The position and morphology of the RGB in the [FORMULA] plane are theoretically well tied to the metal content of the stars in a cluster: the higher the metal content, the cooler the effective temperature Teff and the redder the RGB stars.

In principle, for every GC with a good CMD of the brightest evolutionary phases, metallicity indicators may be derived from its RGB. However, to obtain a reliable calibration, homogeneous measurements are needed. We will then select data sets homogeneous enough to match the quality of the calibrating metallicity scale.

3.1. The [FORMULA] index

The index [FORMULA] (Sandage & Smith 1966) is the de-reddened colour of the RGB at the luminosity level of the HB in the [FORMULA] CMD.

As one of the most homogeneous available samples, we adopted the one published by Sarajedini and Layden (1997, SL). Their study extended to the [FORMULA] plane the Simultaneous Metallicity Reddening method by Sarajedini (1994). They selected high quality CCD photometric studies of 17 globular clusters (15 galactic and 2 Magellanic Clouds clusters), 6 of which were used as primary calibrators. De-reddened colours are adopted from their Table 5.

Whenever possible, we try to rest our calibration on the GCs directly analyzed in CG97. Among the 17 SL clusters, only 9 have [Fe/H] values from direct high-resolution spectroscopy; for all other cases, we translated the older ZW value to the new scale with eq. 7 in CG97. The range in metallicity covered by CG97 is [FORMULA] [Fe/H] [FORMULA], so all relations here derived are strictly valid only in this interval. We did not try to extend their validity to higher metallicities, e.g. by applying a constant offset given by the difference between ZW and CG97 values at [Fe/H] = -0.54 (the most metal-rich clusters in common): there is in fact the possibility that the strong Ca lines, upon which ZW determinations are based, saturate at very high metallicities.

SL used the old ZW scale (ZW; Da Costa & Armandroff 1990; Armandroff et al. 1992). To derive the two expressions for [Fe/H], as a function i) of [FORMULA] and ii) of [FORMULA] needed to simultaneously solve for metallicity and reddening, they fitted the data using linear regressions. Note however that in previous studies (like Costar & Smith 1988) the linearity of the [FORMULA] calibration at the low and high metallicity ends was questioned. We have repeated the calibration, but in terms of [Fe/H] [FORMULA], and results are shown in Fig. 1. Adopting the CG97 scale, this non-linear effect is obviously enhanced, and it is possible to see also by eye that a linear fit is a poor approximation.

[FIGURE] Fig. 1. Calibration of the [FORMULA] parameter using the CG97 metallicity scale and the cluster sample by SL. The upper panel shows the calibrations obtained using only the 6 SL primary calibrators (solid line) and all the 17 clusters (dotted line). In the lower panel the calibration is based only upon the 9 clusters that have metallicities derived by CG97 from direct analysis (CG97 reference clusters). In both panels filled symbols represent clusters with [Fe/H]'s derived in CG97, while open symbols represent clusters with ZW metallicities corrected to the CG97 scale. Triangles, filled or open, indicate the 6 SL primary calibrators.

The resulting best-fit quadratic relations connecting [FORMULA] and [Fe/H] [FORMULA] shown in Fig. 1, upper panel, are:

[EQUATION]

when using only the 6 SL primary calibrating clusters (with [FORMULA] deviation [FORMULA], and correlation coefficient [FORMULA]) and

[EQUATION]

when using all the 17 SL clusters ([FORMULA], [FORMULA]). Error bars in [Fe/H] can be derived from the CG97 paper: they range from 0.01 to 0.11 dex, with an average value of 0.06 dex. SL apparently did not quote any error associated to their [FORMULA] values.

To corroborate the visual impression of non linearity, we tested the statistical significance of the terms of higher order in Eqs. 1 and 2 by a t -test.

The lower panel of Fig. 1 displays instead the calibration based only upon the 9 CG97 reference clusters; the corresponding relation is:

[EQUATION]

([FORMULA] and [FORMULA]). In our view, Eq. 3 is the best interpolating fit, since it has the lower formal statistical [FORMULA] and higher correlation coefficient. Note however that differences in the derived [Fe/H] values from the one obtained from Eqs. 1 and 2 look negligible (0.01 to 0.02 dex on average, on a range of 0.35 mag in colour).

As a check for the validity of the relations found, we used [FORMULA] values from two recent high quality photometric studies, namely M3 ([FORMULA] = 0.80; Ferraro et al. 1997) and M5 ([FORMULA] = 0.83; Sandquist et al. 1996), which are not among the clusters used to derive the calibrations. Using Eq. 3 we obtain [Fe/H] [FORMULA] for M3, and [Fe/H] [FORMULA] for M5. These values have to be compared with [FORMULA] (M3) and [FORMULA] (M5) obtained from direct analysis by CG97.

This test suggests that with the present calibration we are able to establish a very good ranking in cluster metallicities, quite comparable with that given by the CG97 scale. Eq. 3 comes out as best calibration of the [FORMULA] parameter as metallicity indicator, and can be adopted as one of the basic equations of the Simultaneous Metallicity Reddening method (SMR, Sarajedini 1994).

3.2. The [FORMULA] and [FORMULA] parameters

The second index we recalibrated is a variation of the classical [FORMULA] parameter, that measures the difference in V magnitude between the HB and the level of the RGB at the de-reddened colour [FORMULA] (Sandage & Wallerstein 1960). For consistency, we used again the data set from SL, that measured instead the indices [FORMULA] and [FORMULA], referred to the de-reddened colours [FORMULA] and [FORMULA], respectively. As stated by SL, choosing bluer reference colours could be useful in the case of RGBs poorly populated in their upper parts.

These parameters, taken as before from SL Table 5, have been calibrated (see Eqs. 4 and 5), and the case of [FORMULA] is presented in Fig. 2 ([FORMULA] has a very similar behaviour and is not shown).

[FIGURE] Fig. 2. Calibration of the [FORMULA] parameter of SL using the CG97 metallicities. The meaning of symbols is as in Fig. 1.

At odds with the case of [FORMULA], there seems to be a clear difference between the calibrations based on the 6 SL primary calibrating clusters and on the whole SL sample. In particular, for a given [FORMULA] the first relation gives a lower value of [Fe/H], and the effect seems to be stronger at low/intermediate metallicity, while at higher metallicities the two lines intersect. In fact, using the relation derived from the 6 SL calibrators [Fe/H] values are underestimated on average by 0.08 dex in the interval [FORMULA] [Fe/H] [FORMULA], with respect to the other calibration.

We have no explanation for this feature; here we only want to note that SL stated that "These secondary calibrators have not been used in the determination of the (omissis) fitted relations. They only serve to corroborate these relations". It is difficult to see from their Fig. 8 if also with ZW metallicities their primary calibrating clusters provide an underestimation of [Fe/H]. It is however interesting to note that the application of the SMR method in the V, [FORMULA] plane resulted in lower derived abundances with respect to spectroscopic determinations (based e.g. on the CaII triplet).

Finally, we re-calibrated the [FORMULA] - metallicity relation using the 9 CG97 primary calibrating clusters. The relation is shown in the lower panel of Fig. 2 and is given by:

[EQUATION]

([FORMULA], [FORMULA]). This calibration provides [Fe/H] values agreeing very well with those obtained from all the 17 clusters of SL, and clearly represent a good fit to all the data.

The case for the [FORMULA] index closely reproduces that of [FORMULA] ; the resulting calibration based on the 9 CG97 clusters is:

[EQUATION]

([FORMULA], [FORMULA]).

In conclusion, these new calibrations are able to provide metal abundance with a [FORMULA] dispersion of about [FORMULA] dex, comparable to the errors usually obtained from direct, high resolution spectroscopy of stars in GCs.

Eqs. 3 and 4 (or 3 and 5) can be used in the application of the SMR method in the [FORMULA] plane.

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© European Southern Observatory (ESO) 1998

Online publication: December 16, 1997
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