5 Index-metallicity relations

We use the mean [Fe/H] values from the 1999 update of the McMaster catalog (Harris 1996) to create parabolic relations between line indices and the globular cluster metallicity as expressed by [Fe/H], based on the Zinn-West scale (Zinn & West 1984). Together with the globular cluster data of Trager et al. (1998) the sample comprises 21 Galactic globular cluster with metallicities $-2.29\leq$  [Fe/H]  $\leq-0.17$. Figure 7 shows six indices as a function of [Fe/H] most of which show tight correlations. Least-square fitting of second-order polynomials

  

$${\rm [Fe/H]} a + b\cdot (EW) + c\cdot(EW)^2$$ = (4)

$$d + e\cdot {\rm [Fe/H]} + f\cdot{\rm [Fe/H]}^2$$ EW = (5)

where EW is the index equivalent width in Lick units, allows a simple parameterization of these sequences as index vs. [Fe/H] and vice versa. The obtained coefficients are summarized in Table 6. Higher-order terms improve the fits only marginally and are therefore unnecessary.

These empirical relations represent metallicity calibrations of Lick indices with the widest range in [Fe/H] ever obtained. Note that the best metallicity indicators in Table 6 are the [MgFe] and Mg₂ indices both with a rms of 0.15 dex. Leaving out globular clusters with poor luminosity sampling and relatively uncertain background subtraction (i.e. NGC 6218, NGC 6553, NGC 6626, and NGC 6637) changes the coefficients only little within their error limits. In particular, the high-metallicity part of all relations is not driven by the metal-rich globular cluster NGC 6553.

We point out that all relations could be equally well fit by first-order polynomials if the metal-rich clusters are excluded. Consequently, such linear relations would overestimate the metallicity for a given index value at high metallicities (except for H$\beta$ which would underestimate [Fe/H]; however, H$\beta$ is anyway not a good metallicity indicator). This clearly emphasizes the caution one has to exercise when deriving mean metallicities from SSP models which have been extrapolated to higher metallicities. The current sample enables a natural extension of the metallicity range for which Lick indices can now be calibrated. In the second paper of the series (Maraston et al. 2002) we compare the data with the predictions of SSP models.

We also point out that the fitting of the CN index improves when $\rm CN>0$ and $\rm CN<0$ data are fit separately by first-order polynomials. The lines are indicated in Fig. 7. Their functional forms are

$$\begin{eqnarray*}{\rm CN} =& (0.14\pm0.03)+(0.17\pm0.06)\cdot {\rm [Fe/H]}{:} ~{... ...=& (-0.04\pm0.02)+(0.03\pm0.01)\cdot {\rm [Fe/H]}{:} ~{\rm CN}<0 \end{eqnarray*}$$

with reduced $\chi^2$ of 0.025 and 0.023. The inverse relations are

$$\begin{eqnarray*}{\rm [Fe/H]} =& (-0.69\pm0.09)+(3.54\pm1.18)\cdot EW{:} ~{\rm C... ... [Fe/H]} =& (-0.86\pm0.32)+(8.10\pm3.86)\cdot EW{:} ~{\rm CN}<0 \end{eqnarray*}$$

with a rms of 0.115 and 0.380. The change in the slope occurs at $\rm [Fe/H]\sim-1.0$ dex and is significant in both parameterizations. The metallicity sensitivity in the metal-poor part is around six times smaller than in the metal-rich part. Only the inclusion of metal-rich bulge globular clusters allows the sampling of the transition region between the shallow and the steep sequence of the CN vs. [Fe/H] relation.