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6 Galactocentric index variations


  \begin{figure}
\includegraphics[width=13.1cm,clip]{2781f8.eps} \end{figure} Figure 8: Various line indices as a function of galactocentric radius $R_{\rm GC}$. Filled dots show our sample globular clusters. Their error bars are split into the Poisson error (solid error bars which are very small) and slit-to-slit variations (dashed error bars) Open circles mark the globular clusters from Trager et al. (1998).

In Fig. 8 we plot some Lick indices as a function of galactocentric radius $R_{\rm GC}$. To increase the range in radius, we again merge our sample with the data for metal-poor halo globular cluster of Trager et al. (1998). The galactocentric radius was taken from the 1999 update of the McMaster catalog of Milky Way globular clusters (Harris 1996). Our compilation includes now both bulge and halo globular clusters and spans a range $\sim $1-40 kpc in galactocentric distance.

All metal indices show a gradually declining index strength as a function of $R_{\rm GC}$. The inner globular clusters show a strong decrease in each index out to $\sim $10 kpc. The sequence continues at apparently constant low values out to large radii. Furthermore, some indices (CN, Mgb, and $\langle$Fe$\rangle$) show a dichotomy between the bulge and the halo globular cluster system. While the Mgb and $\langle$Fe$\rangle$ indices clearly reflect the bimodality in the metallicity distribution of Milky Way globular clusters, the striking bimodality in the CN index is more difficult to understand. In the context of Sect. 4.2 this may well be explained by evolutionary differences between metal-rich bulge and metal-poor halo globular clusters.

The behavior of H$\beta $ differs from that of the other indices. There is no clear sequence of a decreasing index as a function of $R_{\rm GC}$, as for the metal-sensitive indices. Instead we measure a mean H$\beta $ index with $2.1\pm0.5$ Å. The strength of the Balmer series is a function of $T_{\rm eff}$. In old stellar populations, relatively hot stars, which contribute significantly to the Balmer-line strength of the integrated light, are found at the main sequence turn-off and on the horizontal branch. The temperature of the turn-off is a function of age and metallicity while the temperature of the horizontal branch is primarily a function of metallicity and, with exceptions, of the so-called "second parameter''.

In the following we focus on the correlation of the horizontal branch morphology on the H$\beta $ index. We use the horizontal branch ratio HBR from the McMaster catalog ( ${\rm HBR} = (B-R)/(B+V+R)$: B and R are the number of stars bluewards and redwards of the instability strip; V is the number of variable stars inside the instability strip) to parameterize the horizontal branch morphology. Figure 9 shows that the HBR parameter vs. $R_{\rm GC}$follows a similar trend as H$\beta $ vs. $R_{\rm GC}$ in Fig. 8. This supports the idea that the change in H$\beta $(as a function of $R_{\rm GC}$) is mainly driven by the change of the horizontal branch morphology as one goes to more distant halo globular clusters with lower metallicities. Indeed, the lower panel in Fig. 9 shows that HBR is correlated with the H$\beta $index (Spearman rank coefficient 0.77). The functional form of this correlation is

 
$\displaystyle {\rm HBR} = (-3.71\pm0.41) + (1.75\pm0.19)\cdot{\rm H}\beta$     (6)

with an rms of 0.39 which is marginally larger than the mean measurement error (0.36). That is, the scatter found can be fully explained by observational uncertainties. Note that according to this relation the H$\beta $ index can vary by $\sim $1 Å when changing the horizontal branch morphology from an entirely red to an entirely blue horizontal branch (see also de Freitas Pacheco & Barbuy 1995). This behaviour is also predicted by previous stellar population models (e.g. Lee et al. 2000; Maraston & Thomas 2000).

Figure 9 implies that the change of H$\beta $ is mainly driven by the horizontal branch morphology which itself is influenced by the mean globular cluster metallicity. However, we know of globular cluster pairs - so-called "second parameter'' pairs -, such as the metal-poor halo globular clusters NGC 288 and NGC 362 ( $\rm [Fe/H]\approx-1.2$, Catelan et al. 2001) and the metal-rich bulge clusters NGC 6388 and NGC 6624 ( $\rm [Fe/H]\approx-0.5$, Rich et al. 1997; Zoccali et al. 2000), with very similar metallicities and different horizontal branch morphologies. In fact, NGC 6388 (and NGC 6441, another metal-rich cluster in our sample also featuring a blue horizontal branch) shows a stronger H$\beta $ index than other sample globular clusters at similar metallicities (see Sect. 4.3). Clearly, metallicity cannot be the only parameter which governs the horizontal branch morphology. In the context of the "second-parameter effect'' other global and non-global cluster properties (Freeman & Norris 1981) impinging on the horizontal branch morphology have been discussed of which the cluster age and/or several other structural and dynamical cluster properties are suspected to be the best candidates (e.g. Fusi Pecci et al. 1993; Rich et al. 1997). Our sample does not contain enough "second parameter'' pairs to study the systematic effects these "second parameters'' might have on H$\beta $, such as the correlation of the residuals of the HBR-H$\beta $ relation as a function of globular cluster age or internal kinematics. A larger data set would help to solve this issue.


  \begin{figure}
\includegraphics[width=8.8cm,clip]{2781f9a.eps}
\includegraphics[width=8.8cm,clip]{2781f9b.eps} \end{figure} Figure 9: Horizontal branch morphology in terms of the HBR parameter as a function of galactocentric radius $R_{\rm GC}$ (upper panel) and H$\beta $ (lower panel). Filled and open circles show our globular cluster data and the data of Trager et al. (1998), respectively.


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