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*Astron. Astrophys. 355, 966-978 (2000)*
## 6. Calibration of the indices. Discussion
### 6.1. *S*
On the CG scale, the second-order fit has a residual rms of
0.12 dex in [Fe/H]. On the CG scale, the linear fit is obtained
with a rms of 0.12 dex. This index can therefore be calibrated on
both scales, with a comparable level of accuracy. A parabolic fit does
not improve the relation on the CG scale, since the coefficient of the
quadratic term is very small (-0.004) and the rms is the same. These
relations are shown in Fig. 8 as solid lines, where the upper
panel is for the CG scale, and the lower panel for the CG scale (this
layout is reproduced in all the following figures).
The cluster NGC 6656 (M22) was excluded from the fits, and is
plotted as an open circle in Fig. 8. It is well-known that M22 is
a cluster that shows a metallicity spread, and indeed it falls outside
the general trend in most of the present calibrations.
### 6.2.
The first definition of the index
was given in Da Costa & Armandroff (1990), where a calibration in
terms of the CG scale was also given:
. The same index (measured on the
absolute RGBs corrected with the LDZ HB luminosity-metallicity
relation) is plotted, in Fig. 9, as a function of the metallicity
on both scales, and the solid lines represent our calibrations. The
top panel shows the quadratic relation on the CG scale, whose rms is
0.14 dex. The bottom panel of Fig. 9 shows the relation on
the CG scale. In this case, a quadratic fit is not able to reproduce
the trend of the observational data. A better result can be obtained
by making a variable change, i.e. using the variable
; in this case, a linear relation is
found, and its rms is 0.15 dex. This measure of the residual
scatter has been computed after transforming back to metallicity, so
the reliability of the index can be compared to that of the other
ones. Again, the index can be calibrated on both scales with a
comparable accuracy. The dashed curve in the upper panel of
Fig. 9 shows the original relation obtained by DA90: there is a
small discrepancy at the high-metallicity end, which can be explained
by the different 47 Tuc fiducial line that was adopted by DA90
(cf. below the discussion on ).
As already recalled, we checked the effect of adopting another
distance scale, by repeating our measurements and fits, and adopting
the C99 distance scale. For the CG metallicity scale, we obtain the
quadratic relation whose coefficients are listed in Table 6, and
whose rms is 0.15 dex. The bottom panel of Fig. 9 shows the
relation on the CG scale. Again, a quadratic fit is not able to
reproduce the trend of the observational data. Making the already
discussed variable substitution, the linear relation in *z* has
an rms of 0.16 dex, so the two metallicity scales yield almost
comparable results.
### 6.3.
Using the same "standard" GC branches of DA90, Lee et al. (1993)
defined a new index, , to be used for
the farthest population II objects. It was also
calibrated in terms of the CG scale:
. A new calibration was also given
recently in Caldwell et al. (1998):
[Fe/H], where
. The index and our calibrations
(solid lines) are plotted, in Fig. 10, on both metallicity
scales. Again, the measurements were made in the absolute CMD,
assuming the LDZ distance scale. Our quadratic calibration vs. the CG
scale has a residual rms scatter of 0.13 dex, which is the same
of the linear relation on the CG metallicity vs. *z*.
The Lee et al. relation (dashed line) predicts slightly too larger
metallicities on the CG scale, for .
This can also be interpreted as if the DA90 47 Tuc branch were
mag bluer than ours. Indeed, if one
looks at Fig. 5 of DA90, one can easily see that some weight is
given to the brightest RGB star, which is brighter than the trend
defined by the previous ones. The result is a steeper branch, which
also justifies the DA90 slightly bluer RGB fiducial. Since our metal
richest point is defined by two clusters, and since the two measured
parameters agree very well, we are confident that our calibration is
reliable. In any case, the discrepancy between the two scales is no
larger than dex. It is also
reassuring that the Caldwell et al. (1998) relation (pluses) is closer
to the present calibration, since the former is based on a larger set
of clusters. This might be an indication that the Lee et al. relation
is actually inaccurate at the metal rich end, due to the small set of
calibrating clusters.
As before, we obtained a further calibration also using the C99
vs. [Fe/H] relation; the quadratic
fit on the CG scale has a residual rms scatter of 0.13 dex, while
the *z* variable can be fitted with a straight line, with an rms
of 0.14 dex.
### 6.4. The family and
For any index, the quadratic
relations vs. the CG metallicity do not improve the rms and they are
not plotted in the figures. The coefficients are listed in
Table 6.
The best metallicity estimates of the
" family" are obtained with the
index. The errors on
are just slightly larger than the
standard uncertainties of the spectroscopic determinations. The solid
lines of Fig. 11 show the calibrations that we obtain. The
quadratic equation on the CG scale, and the linear one on the CG
scale, are obtained with residual scatters of 0.16 dex.
The rest of the indices in this family, and
, lack the precision of the other
abundance indicators. This is due to the fact that the error on any
index is proportional to the
uncertainty on the color of the RGB (which depends on the reddening),
times its local slope where the reference point is measured. Since the
RGB slope increases going away from the tip (i.e. towards bluer
colors), we expect that the scatter on the
indices will also increase as the
color of the reference point gets bluer. Indeed, Table 6 shows
that in most cases the *rms* uncertainties are
dex for these indices. The
residual scatter is largest for the
index, which is the most affected by the uncertainties on the
reddening.
The and
parameters have been earlier
calibrated, on the CG scale, by Carretta & Bragaglia (1998). Using
their quadratic relation for , and
both their linear and quadratic relations for
, the corresponding rms of the
residuals in metallicity are 0.21 dex and
dex, respectively. Our new and
the old calibrations are therefore compatible, within the (albeit
large) uncertainties.
© European Southern Observatory (ESO) 2000
Online publication: April 3, 2000
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