## 5. Calibration of the indices. IntroductionIn order to obtain analytic relations between the indices and the
actual metallicity, our photometric parameters were compared both with
the ZW and the CG values. A summary of the resulting equations is
given in Table 6. For each index (first column) both linear and
quadratic fits were tried, of the form:
and
. The coefficients of the calibrating
relation are given in the columns labelled
, ,
and ; in Column 7, the rms of
the residuals is also given. In the case of the
and
indices, neither the linear nor the quadratic fits give satisfactory
results, when the CG scale is considered. Instead, a good fit is
obtained if a change of variables is performed, setting
, and linearly interpolating in the
index (i.e. setting ). The
Column 8 of Table 6 identifies the kind of fitting function
that is used for each parameter/metallicity combination: the symbols
"1", "2" and "
In order to measure the and indices (cf. Sect. 3) a distance scale must be adopted. The most straightforward way is to use the observed (cf. Table 1) coupled with a suitable law for the HB absolute magnitude. It has become customary to parameterize this magnitude as
, although there is no consensus on
the value of the two parameters As discussed in Sect. 4, since many current determinations of Population II distances within the Local Group are based on the Lee et al. (1990) distance scale, and for the purpose of comparison with previous studies, we provide a calibration using the latter HB luminosity-metallicity relation. However, in the last ten years revisions of this relation have been discussed by many authors, so we also calibrated the two indices using (Carretta et al. 1999), which is one of the most recent HB-based distance scales. We must stress that metallicities on the ZW scale must be used in the vs. [Fe/H] relation. Indeed, CG showed that their scale is not linearly correlated to that of ZW, so not even the vs. [Fe/H] relation will be linear: if one wishes to use the new scale, then the absolute magnitude of the HB must be re-calibrated in a more complicated way. The best calibrating relations are shown in Figs. 8 to 11. In the following sections, for each index a few remarks on the accuracy of the calibrations and comparisons with past studies are given.
© European Southern Observatory (ESO) 2000 Online publication: April 3, 2000 |