4 Index ratios in globular clusters and bulge fields

Figure 5 shows two representative spectra of a metal-poor (NGC 6626) and a metal-rich (NGC 6528) globular cluster, together with the co-added spectrum from the 15 bulge pointings.

Figure 5: Representative spectra of two globular clusters, i.e. NGC 6626 and NGC 6528, and the Galactic bulge. The two clusters represent the limits of the metallicity range which is covered by our sample. NGC 6626 has a mean metallicity $\rm [Fe/H]=-1.45$ dex. NGC 6528, on the other hand, has a mean metallicity $\rm [Fe/H]=-0.17$ dex (Harris 1996). Note the similarity between the bulge and the NGC 6528 spectrum. Important Lick-index passbands are indicated at the bottom of the panel.

In the following we focus on the comparison of index ratios between globular clusters and the field stellar population in the Galactic bulge. We include the data of Trager et al. (1998) who measured Lick indices for metal-poor globular clusters and use our index measurements (due to higher S/N) whenever a globular cluster is a member of both data sets.

All Lick indices are measured on the cleaned and co-added globular-cluster and bulge spectra. Statistical uncertainties are determined in bootstrap tests (see Appendix A.2 for details). We additionally determine the statistical slit-to-slit variations between the different pointings for each globular cluster and estimate the maximum systematic error due to the uncertainty in radial velocity. All line indices and their statistical and systematic uncertainties are documented in Table C.1.

It is worth to mention that the slit-to-slit fluctuations of index values, which are calculated from different pointings (3 and 5 for globular clusters and 15 for the bulge), are generally larger than the Poisson noise of the co-added spectra. Such variations are expected from Poisson fluctuations in the number of bright stars inside the slit and the sampled luminosities of the single spectra correlate well with the slit-to-slit index variations for each globular cluster. More pointings are required to solidify this correlation and to search for other effects such as radial index changes.

4.1 The $\alpha$-element sensitive indices vs. $\mathsfsl{\langle}$Fe $\mathsfsl{\rangle}$

Figure 6: Lick-index ratios for Mg2, Mgb, NaD, H$\beta$ versus the mean iron index $\langle$Fe $\rangle=({\rm Fe~5270} + {\rm Fe~5335})/2$. Filled dots show the index measurements of our sample globular clusters, whilst open circles show the data of Trager et al. (1998). A solid star indicates the index values derived from the co-added spectrum of the Galactic bulge. Solid error bars show bootstrap errors which represent the total uncertainty due to the intrinsic noise of the co-added spectra. Statistical slit-to-slit fluctuations between different pointings are shown as dotted error bars. Systematic radial velocity errors are not plotted, but given in Table C.1. For clarity reasons no error bars are plotted for the Trager et al. sample which are generally an order of magnitude larger than the intrinsic noise of our spectra. The mean errors of the Trager et al. data are 0.3 Å for the $\langle$Fe$\rangle$ index, 0.01 mag for Mg2, and 0.3 Å for Mgb, NaD, and H$\beta$.

Figure 6: continued. G4300, CN1, TiO2, and Ca 4227 versus $\langle$Fe$\rangle$. The mean errors of the Trager et al. data are 0.3 Å for the $\langle$Fe$\rangle$ index, and 0.4 Å, 0.03 mag, 0.01 mag, and 0.4 Å for the G4300, CN1, TiO2, and Ca 4227 index, respectively.

$\alpha$-particle capture elements with even atomic numbers (C, O, Mg, Si, Ca, etc.) are predominantly produced in type II supernovae (Tsujimoto et al. 1995; Woosley & Weaver 1995; Thomas et al. 1998). The progenitors of SNe II are massive stars, which explode and pollute the interstellar medium after their short lifetime of some 10⁷ years. The ejecta of SNe II have a mean [$\alpha$/Fe] $~~\sim 0.4$ dex. On the other hand, type Ia supernovae eject mainly iron-peak elements ([$\alpha$/Fe] $~~\sim -0.3$ dex) $\sim$1 Gyr after the formation of their progenitor stars. Stellar populations which have been created on short timescales are likely to show [$\alpha$/Fe] enhancement. The [$\alpha$/Fe] ratio is therefore potentially a strong discriminator of star-formation histories. Alternative explanations, however, include a changing IMF slope and/or a changing binary fraction.

Such enhancements have already been suspected and observed in the stellar populations in giant elliptical galaxies (Worthey et al. 1992), the Galactic bulge (McWilliam & Rich 1994), and for disk and halo stars in the Milky Way (Edvardsson et al. 1993; Fuhrmann 1998). A detailed discussion of the [$\alpha$/Fe] ratio in our sample globular clusters and their assistance to parameterize simple stellar population models for varying [$\alpha$/Fe] ratios will be presented in the second paper of this series (Maraston et al. 2002).

To search for any trends in the index($\alpha$)/index(Fe) ratio in the globular cluster population and the bulge we plot supposedly $\alpha$-element sensitive indices against the mean iron index $\langle$Fe$\rangle$. Figure 6 shows some representative index measurements for globular clusters and bulge fields. Generally, all the correlations between $\alpha$-sensitive indices and the mean iron index are relatively tight. For our sample globular clusters a Spearman rank test yields values between 0.87 and 0.97 (1 indicates perfect correlation, -1 anti-correlation) for the indices CN₁, TiO₂, Ca 4227, Mgb, Mg₂. The CN₁ and TiO₂indices show the tightest correlation with $\langle$Fe$\rangle$, followed by Mg₂ and Ca 4227. All correlations are linear (no higher-order terms are necessary) and hold to very high metallicities of the order of the mean bulge metallicity (filled star in Fig. 6). The three most metal-rich globular clusters in our sample, i.e. NGC 5927, NGC 6528, and NGC 6553, have roughly the same mean iron index as the stellar populations in the Galactic bulge indicating similar [Fe/H]. This was also found in recent photometric CMD studies of the two latter globular clusters and the bulge (Ortolani et al. 1995b; Zoccali et al. 2002). Ranking by the $\langle$Fe$\rangle$ and Mg indices, which are among the best metallicity indicators in the Lick sample of indices (see Sect. 5), the most metal-rich globular cluster in our sample is NGC 6553, followed by NGC 6528 and NGC 5927.

The comparison of some $\alpha$-sensitive indices of globular clusters and the bulge requires some further words. The Ca 4227, Mgb, and Mg₂index of the bulge light is in good agreement with the sequence formed by globular clusters. All deviations from this sequence are of the order of ${\la}1\sigma$ according to the slit-to-slit variations. One exception is the CN index which is significantly higher in metal-rich globular clusters than in the bulge. We discuss this important point in Sect. 4.2. In general, our data show that the ratio of $\alpha$-sensitive to iron-sensitive indices is comparable in metal-rich globular clusters and in the stellar population of the Galactic bulge.

Likely super-solar [$\alpha$/Fe] ratios in globular clusters and the bulge were shown in numerous high-resolution spectroscopy studies. From a study of 11 giants in Baade's window McWilliam & Rich (1994) report an average [Mg/Fe] $~~\approx 0.3$ dex, while Barbuy et al. (1999) and Carretta et al. (2001) find similar [Mg/Fe] ratios in two red giants in NGC 6553 and in four red horizontal branch stars in NGC 6528. Similarly, McWilliam & Rich find [Ca/Fe] $~~\approx0.2$dex, which is reflected by the former observations in globular clusters. Although the studied number of stars is still very low, the first high-resolution spectroscopy results point to a similar super-solar $\alpha$-element abundance in both Milky Way globular clusters and the bulge which is supported by our data.

   
4.2 CN vs. $\mathsfsl{\langle}$Fe $\mathsfsl{\rangle}$

The CN index measures the strength of the CN absorption band at 4150 Å. The Lick system defines two CN indices, CN₁ and CN₂ which differ slightly in their continuum passband definitions. The measurements for both indices give very similar results, but we prefer the CN₁ index due to its smaller calibration biases (see Fig. 2) and refer in the following to CN₁ as the CN index.

Like for most other indices, the CN index of globular clusters correlates very tightly with the $\langle$Fe$\rangle$ index, following a linear relation (see Fig. 6). A Spearman rank test yields 0.97 as a correlation coefficient. The apparent gap at $\rm CN\sim0$ mag is a result of the bimodal distribution of metallicity in our cluster sample, and similar gaps are recognizable in all other index vs. $\langle$Fe$\rangle$ diagrams.

Quite striking is the comparison of the bulge value of the CN index with that of globular clusters at the same value of the $\langle$Fe$\rangle$ index: the CN index of the bulge is significantly offset to a lower value by $\sim$0.05 mag, corresponding to at least a 2$\sigma$ effect. This is also evident from Fig. 5, showing that the CN feature is indeed much stronger in the cluster NGC 6528 than in the bulge spectrum. We also note that the CN index of NGC 6528 and NGC 6553 is as strong as in the most metal-rich clusters in M 31 studied by Burstein et al. (1984).

It is well known that globular cluster stars often exhibit so-called CN anomalies, with stars in a cluster belonging either to a CN-strong or a CN-weak group (see Kraft 1994 for an extended review). Among the various possibilities to account for these anomalies, accretion of AGB ejecta during the early phases of the cluster evolution appears now the most likely explanation (Kraft 1994; Ventura et al. 2001), as originally proposed by D'Antona et al. (1983) and Renzini (1983). In this scenario, some ${\sim} 30\times 10^6$years after cluster formation (corresponding to the lifetime of ${\sim} 8~ M_\odot$ stars) the last type II supernovae explode and AGB stars begin to appear in the cluster. Then the low-velocity AGB wind and super-wind materials may accumulate inside the potential well of the cluster, and are highly enriched in carbon and/or nitrogen from the combined effect of the third dredge-up and envelope-burning processes (Renzini & Voli 1981). Conditions are then established for the low-mass stars (now still surviving in globular clusters) having a chance to accrete carbon and/or nitrogen-enriched material, thus preparing the conditions for the CN anomalies we observe in today clusters. One of the arguments in favor of the accretion scenario is that field stars do not share the CN anomalies of their cluster counterparts (Kraft et al. 1982). Indeed, contrary to the case of clusters, in the field no localized, high-density accumulation of AGB ejecta could take place, and low-mass stars would have not much chance to accrete AGB processed materials. In the case of the bulge, its much higher velocity dispersion ($\sim$100 km s^-1) compared to that of clusters (few km s^-1) would make accretion even less likely. In conclusion, we regard the lower CN index of the bulge relative to metal-rich globular clusters as consistent with - and actually supporting - the accretion scenario already widely entertained for the origin of CN anomalies in globular-cluster stars.

4.3 H$\beta$ vs. $\mathsfsl{\langle}$Fe $\mathsfsl{\rangle}$

Figure  6 shows a plot of H$\beta$ vs. $\langle$Fe$\rangle$. The Spearman rank coefficient for the globular cluster sequence is -0.52 indicating a mild anti-correlation. At high $\langle$Fe$\rangle$, the H$\beta$ index of globular clusters is slightly stronger than that of the bulge field. However, the values are consistent with each other within ${\sim}1\sigma$, with the large slit-to-slit variations exhibited by the bulge spectra being a result of the lower luminosity sampling due to the lower surface brightness in Baade's Window compared to globular clusters.

The two clusters NGC 6441 and NGC 6388 show somewhat stronger H$\beta$compared to clusters with similar $\langle$Fe$\rangle$ index. This offset is probably caused by the conspicuous blue extension of the HB of these two clusters, a so far unique manifestation of the "second parameter'' effect among the metal-rich population of bulge globular clusters (Rich et al. 1997). Contrary to NGC 6441 and NGC 6388, the other globular clusters with comparable $\langle$Fe$\rangle$ indices (i.e. NGC 5927, NGC 6356, NGC 6624, and NGC 6637) have without exception purely red horizontal branches ( $\rm HBR=-1.0$).

Also the two most metal-rich clusters in our sample, NGC 6553 and NGC 6528, appear to have a somewhat stronger H$\beta$ compared to a linear extrapolation of the trend from lower values of the $\langle$Fe$\rangle$ index. In this case, however, the relatively strong H$\beta$ cannot be ascribed to the HB morphology, since the HB of these two clusters is purely red (Ortolani et al. 1995a; Zoccali et al. 2001). In principle, a younger age would produce a higher H$\beta$ index, but optical and near-infrared HST color-magnitude diagrams of these two clusters indicate they are virtually coeval with halo clusters (Ortolani et al. 1995a,2001; Zoccali et al. 2001; Feltzing et al. 2002). So, we are left without an obvious interpretation of the relatively strong H$\beta$ feature in the spectra of these clusters. Perhaps the effect is just due to insecure sampling, i.e., to statistical fluctuations in the stars sampled by the slit in either the cluster or in the adjacent bulge field used in the background subtraction. Another reason for the offset might be the increasing dominance of metallic lines inside the H$\beta$ feature passband which could artificially increase the index value.

Figure 7: Line indices as a function of mean globular cluster metallicity. Our sample globular clusters are shown as filled circles while the open circles denote the globular cluster data of Trager et al. (1998).

   
4.4 Other Indices vs. $\mathsfsl{\langle}$Fe $\mathsfsl{\rangle}$

NaD - The correlation coefficient for this index pair is 0.94. Globular clusters and bulge compare well within the errors. Both stellar populations follow, within their uncertainties, the same trend. A clear exception from this correlation is NGC 6553, which shows a significantly lower NaD index for its relatively high $\langle$Fe$\rangle$ than the sequence of all other globular clusters. The reason for this offset is unclear.

G4300 - The G4300 index predominantly traces the carbon abundance in the G band. For giants, its sensitivity to oxygen is about 1/3 of that to carbon (Tripicco & Bell 1995). The metal-rich globular clusters fall in the same region as the bulge data. In combination with the CN index which mainly traces the CN molecule abundance, this implies that the offset between bulge and globular clusters in the CN vs. $\langle$Fe$\rangle$ plot is most likely due to an offset in the nitrogen abundance between bulge and clusters.

TiO - The TiO abundance is measured by the TiO₁ and TiO₂indices. Both indices do not differ in their correlation with the mean iron index (Spearman rank coefficient 0.96), but we use TiO₂because of its better calibration. In Fig. 6 we plot TiO₂ vs. $\langle$Fe$\rangle$ which shows the strongest indices for NGC 6553 and NGC 6528, followed by NGC 5927 and the bulge.

The absorption in the TiO band sensitively depends on $T_{\rm eff}$which is very low for very metal-rich RGB stars. While the strongest TiO bands are observed in metal-rich M-type giants almost no absorption is seen in metal-rich K-type RGB stars. As $T_{\rm eff}$decreases towards the RGB tip, a large increase in the TiO-band absorption occurs which drives the observed bending of the upper RGB in color-magnitude diagrams, in particular those which use V-band magnitudes (Carretta & Bragaglia 1998; Saviane et al. 2000). In fact, the most metal-rich globular clusters in the Milky Way, e.g. NGC 6553 and NGC 6528, show the strongest bending of the RGBs (e.g. Ortolani et al. 1991; Cohen & Sleeper 1995). Figure 6 shows that the slit-to-slit scatter is extremely large for the metal-rich data. This is likely reflecting the sparsely populated upper RGB. In other words, for metal-rich stellar populations the TiO index is prone to be dominated by single bright stars which increase the slit-to-slit scatter due to statistically less significant sampling (see also the high slit-to-slit scatter of NGC 6218 due to its small luminosity sampling). Another Ti-sensitive index in the Lick system is Fe 4531 (Gorgas et al. 1993). It shows similar behaviour as a function of $\langle$Fe$\rangle$.

 

 

Table 6: Coefficients of the index vs. [Fe/H] relations. The rms ( $\sqrt {\chi ^2 /n}$) is given in the units of the parameterization (in dex in equation 4 and in Å or mag in Eq. (5)).

index	a	b	c	rms	d	e	f	rms
Mg2	$-2.46\pm0.10$	$16.24\pm1.81$	$-29.88\pm6.52$	0.151	$0.29\pm0.01$	$0.22\pm0.02$	$0.05\pm0.01$	0.016
Mgb	$-2.53\pm0.14$	$1.11\pm0.16$	$-0.14\pm0.04$	0.182	$4.46\pm0.19$	$3.51\pm0.35$	$0.79\pm0.14$	0.254
$\langle$Fe$\rangle$	$-2.83\pm0.21$	$1.91\pm0.36$	$-0.35\pm0.13$	0.199	$2.68\pm0.12$	$1.85\pm0.23$	$0.39\pm0.09$	0.167
[MgFe]	$-2.76\pm0.14$	$1.59\pm0.20$	$-0.26\pm0.06$	0.150	$3.45\pm0.13$	$2.55\pm0.24$	$0.55\pm0.10$	0.173
H$\beta$	$-1.99\pm2.26$	$2.09\pm2.24$	$-0.78\pm0.54$	0.384	$1.55\pm0.20$	$-0.33\pm0.37$	$0.08\pm0.15$	0.271
CN1	$-0.83\pm0.11$	$6.84\pm0.86$	$-17.12\pm13.47$	0.314	$0.16\pm0.02$	$0.26\pm0.04$	$0.06\pm0.02$	0.032