4 The metallicity distribution of the bulge

 

 

Table 2: Globular cluster used as RGB templates.

Cluster	[M/H]	(m-M)0	E(B-V)
NGC 6528	-0.10	14.37	0.62
NGC 6553	-0.10	13.46	0.84
NGC 104	-0.57	13.32	0.05
NGC 6171	-0.88	13.95	0.31
NGC 6121	-1.06	11.68	0.35
NGC 6809	-1.59	13.82	0.10
NGC 7099	-1.84	14.71	0.01
NGC 4590	-1.90	15.14	0.04
NGC 7078	-1.92	15.15	0.09

Figure 9: Bulge CMD resulting from the combination of the optical WFI and near-IR 2MASS data. The line represents the fiducial locus of the globular cluster NGC 6528. The distance and reddening of the bulge field adopted for this comparison are (m-M)0=14.47 and E(B-V) =0.45, respectively, while for NGC 6528 it is assumed (m-M)0=14.37 and E(B-V) =0.62 (Ferraro et al. 2000).

From the combination of the optical (WFI) and near-IR (2MASS) decontaminated data, a (M_K,V-K) CMD was obtained including $\sim$22 000 stars with M_K<0.5, and the result is shown in Fig. 9. A comparison with the fiducial line of the globular cluster NGC 6528 from Ferraro et al. (2000) immediately suggests that the mean metallicity of the bulge is virtually identical to that of this cluster, with a quite modest dispersion about this mean. This is demonstrated by the slope of the giant branch of the cluster and of that of the bulge field being the same. (Note that the metallicity affects the slope, while the reddening causes a solid shift of the RGB.) Therefore, the metallicity of NGC 6528 (and that of the twin cluster NGC 6553) has a special importance in connection with our attempt at determining the bulge metallicity distribution. In Fig. 9, a distance modulus of (m-M)₀=14.47 $\pm$ 0.08 (7.8 kpc) was adopted for the bulge, according to the most recent determination by McNamara et al. (2000) using RR-Lyrae and $\delta$Scuti variables from the OGLE survey. The reddening of our bulge field relative to NGC 6528 can then be estimated from Fig. 9, and we obtain E(B-V) =0.45, needed to match the bulge and the cluster loci given the small difference in the two distance moduli. For NGC 6528 the corresponding quantities are given in Table 2. The large number of stars in the upper RGB of Fig. 9, coupled with the high sensitivity of the (V-K) color to metallicity, and its very small sensitivity to a possible age dispersion, allows a determination of the bulge MD via the method described in Saviane et al. (2000).

4.1 The method

The method is based on the construction of a family of hyperbolas in the plane (M_K,V-K) suitable to represent a grid of upper RGBs from empirical template globular clusters, with known metallicities. Each hyperbola is represented by the expression:

$$% M_K= a + b\times (V-K) + \frac{c}{(V\!-\!K)-d}$$ (1)

where the coefficients a,b,c and d are quadratic functions of the metallicity:

$$% a=k_1\mbox{[M/H]}^2 + k_2\mbox{[M/H]} + k_3$$ (2)

$$% b=k_4\mbox{[M/H]}^2 + k_5\mbox{[M/H]} + k_6$$ (3)

$$% c=k_7\mbox{[M/H]}^2 + k_8\mbox{[M/H]} + k_9$$ (4)

d=k₁₀. (5)

Finally, the inversion of Eq. (1) gives a value of the metallicity for each point in the (M_K,V-K) plane, hence for each bulge star.

Figure 10: The V, K RGBs of the template GCs published by Ferraro et al. (2000) (open squares), together with the analytical RGBs (dotted lines). The values of [M/H] for the analytical RGBs go from solar to [M/H] = -2.0 in steps of 0.2.

Although in principle spectroscopic determinations may be more accurate, the photometric approach has the advantage of relying on high S/N quantities (i.e., the magnitudes of the brightest stars) and on large statistics. However, it is entirely differential, i.e., it depends on the accuracy of the metallicity assigned to the templates, which ultimately relies on spectroscopic determinations. The most complete and homogeneous grid of near-IR GC RGB templates presently available in the literature (Ferraro et al. 2000; see Table 2) includes 10 low reddening, nearby GCs with metallicity [M/H] between -1.92 and -0.1. One cluster (NGC 6637) from the Ferraro et al. sample has been excluded from our calculations, for reasons explained below.

With the exception of the two most metal rich clusters (NGC 6528 and NGC 6553), for the GCs in Table 2 we adopted the iron abundance [Fe/H] from Harris (1996), and corrected it to [M/H] adopting an $\alpha$-element enhancement [$\alpha$/Fe] = 0.3 for clusters with [Fe/H] <-1.0, and [$\alpha$/Fe] = 0.20 for more metal-rich clusters (Carney 1996; Salaris & Cassisi 1996). As emphasized earlier, the case of NGC 6528 and NGC 6553 is particularly important. A few stars in each of the two clusters have been observed at intermediate and high spectral resolution, but different groups have obtained quite discrepant results. For NGC 6528, Carretta et al. (2001) and Coelho et al. (2001) report respectively [Fe/H] = +0.07 and -0.5 (the latter value coming from low-resolution spectra). For [M/H] the same authors derive +0.17 and -0.25, respectively. For NGC 6553 Barbuy et al. (1999) give [Fe/H] = -0.55 and [M/H] = -0.08, while Cohen et al. (1999) report [Fe/H] = -0.16, and Origlia et al. (2002) give [Fe/H] = -0.3, with [$\alpha$/Fe] = +0.3. These discrepancies are uncomfortably large, and may hopefully disappear as soon as more high-resolution data are gathered at 8-10 m class telescopes. For both clusters we finally adopt [M/H]=-0.1 (the value reported in Table 2) with the uncertainty of the resulting MD being dominated by the uncertainty of the metallicity of these two clusters.

Figure 10 shows the resulting grid of RGB loci: open squares represent the fiducial points extracted from the empirical templates, while the RGBs from the analytical interpolation are shown as dotted lines. The coefficients of the Eqs. (4)-(7) are listed inside the figure. The analytical RGBs are shown for metallicities ranging from [M/H] = 0 to [M/H] =-2.0, in steps of 0.2. All the empirical templates, with the exception of NGC 104 (third cluster from the right) follow very well the RGB shape trend of the analytical solution. We could find no obvious explanation for the apparent discrepancy of NGC 104: its CMD is quite populated in this region, and, being one of the best studied clusters, the adopted parameters (metallicity, reddening and distance) are rather robust. The near-IR observations of this cluster were done with the ESO/MPG 2.2 m telescope mounting IRAC-2, an early IR array detector (Ferraro et al. 2000); perhaps the use of a more modern instrument may clarify the issue.

As evident from Fig. 10, the sensitivity to metallicity is a strong function of the position in the CMD, hence of metallicity itself. The leverage increases with both luminosity and color, being favored at high metallicities by the increasing TiO blanketing in the V band causing redder and redder V-K colors.

Figure 11: Upper panel: the CMD of the globular cluster NGC 6553 with overplotted the analytical RGB templates. The dispersion in distance typical of the bulge field at $b=-6^\circ$ and a reddening dispersion of $\Delta E$(B-V) =0.3 have been added to the cluster CMD in order to simulate the observational biases affecting the derived bulge MD. Lower panel: MD obtained for NGC 6553. Shaded histogram is the MD obtained if only the stars brighter than MK=-4.5 are considered. This MD is well represented by a Gaussian centered in [M/H] = -0.1 and  $\sigma =0.1$.

In order to investigate the effect of distance and reddening dispersion on the MD derived using the adopted method we simulated such effects on the (M_K,V-K) CMD of the bulge cluster NGC 6553 (Guarnieri et al. 1998). To each star of NGC 6553 we associated a distance modulus randomly extracted according to a bulge space density distribution of the form $\rho={\rm const}\times r^{-3.7}$ (Sellwood & Sanders 1988; Terndrup 1988), where r is the spatial distance from the Galactic center. The line of sight integration at the field position ( (l,b)=(0,-6)) gives a 1-$\sigma$ dispersion of 0.13 mag in the distance modulus, the distribution being close to Gaussian in the core, but with somewhat broader wings. A top hat reddening distribution of $\pm$0.15 was also adopted. The latter is believed to be an upper limit to the observed bulge reddening variation across our field, but has been chosen as a conservative assumption, in order to have an upper limit on the possible biases in the derived MD. Random extractions of both distance modulus and reddening were repeated 6 times for each star in the original CMD by Guarnieri et al. (1998) in order to obtain a more populated CMD. Figure 11 shows the resulting simulated CMD including distance and reddening dispersion effects (upper panel). The lower panel shows the MD obtained in the same way as that to be applied to the bulge, and reveals two interesting effects. First, if all the stars brighter than M_K=-3 are considered, the resulting MD (dashed histogram) is extremely broad with a long metal-poor tail. This is entirely due to the fact mentioned above: the separation between the RGBs corresponding to different metallicities becomes very small towards faint magnitudes, much smaller than the magnitude/color dispersion due to distance and reddening dispersions. However, if the analysis is restricted to stars brighter than M_K=-4.5 then the derived MD shows a fairly sharp peak at [M/H] = -0.1 (i.e., centered on the adopted metallicity for this cluster), well fitted by a Gaussian distribution with $\sigma =0.1$(FWHM= 0.24). This exercise demonstrates that, as long as the analysis is confined to the stars brighter than M_K=-4.5: (i) one should not expect systematic biases; (ii) the spread introduced by the distance and reddening dispersions is of the order of $\sim$0.1 dex in [M/H]; and (iii) contamination by AGB stars (which would introduce a bias artificially skewing the distribution towards the metal-poor side) is negligible at these magnitudes due to the exclusion of the more populated (and bluer) AGB "clump'', located at $M_K\sim-3$. We therefore restrict to M_K<-4.5 the derivation of the bulge MD.

4.2 The resulting metallicity distribution

Figure 12: The bulge V,K CMD compared with the analytical RGB templates. The adopted bulge distance modulus is (m-M)0=14.47 while the mean reddening is E(B-V) =0.45. Only the stars inside the dashed box where used for the MD determination.

Figure 12 shows the analytical RGBs overplotted on the bulge upper RGB. The dotted part of each RGB is the extrapolation above the theoretical location of the RGB tip (cf. Sect. 7), hence only AGB stars are expected in this region. The metallicities of the analytical RGBs range from [M/H] = +0.2 to -1.8, in steps of 0.2. Note that the most metal-rich templates have metallicity of [M/H] =-0.1, therefore the shape of the analytical RGBs for higher metallicity is the result of a small extrapolation. Stars bluer than V-K=2.8 (vertical dashed line) were not considered, in order to exclude a few bluer objects that are most likely a disk residue due to imperfect statistical decontamination. Stars fainter than M_K=-4.5 (horizontal dashed line) were excluded as well, for the reasons explained above. After these cuts, a sample of 503 stars has been used to derive the bulge MD. It is already clear from this figure that most of the bulge stars are located between the [M/H]  $\simeq 0.1$ and [M/H] =-0.6 templates, with a peak at [M/H] =-0.1 and very few stars more metal-poor than $\sim$-1. Formally, super-solar metallicity stars ([M/H] >0) represent 29$\%$ of the sample. This should be regarded as an upper limit, due to the diffusion to higher [M/H] values caused by the dispersion in distance, reddening, etc. (see Fig. 11).

Figure 13: Upper panel: the ratio of the evolutionary flux at any Zto the same quantity at solar Z. Middle panel: the time spent on the RGB from MK=-4.5 to the tip, with respect to the value at $Z_\odot$. Lower panel: the product of the two factors above, i.e., the correction factor that one should apply to the MD found from the CMD, in order to take into account these effects.

Before proceeding to derive the bulge MD a few biases must be quantitatively evaluated and compensated for: 1) the rate at which stars leave the main sequence (called evolutionary flux in Renzini & Buzzoni 1986) has a slight metallicity dependence, 2) the rate of evolution along the RGB scales as Z^-0.04 (Rood 1972), and 3) by adopting the M_K=-4.5 cut one samples (bolometrically) deeper on the RGB the higher the metallicities.

Figure 14: Comparison between the bulge MD derived from Fig. 12 (shaded histogram) and those derived with spectroscopic surveys.

The amplitude of these factors is shown in Fig. 13. The upper panel shows how the evolutionary flux changes as a function on metallicity, relative to its value at $Z_\odot$. The middle panel shows the combination of effect 2) and 3) mentioned above: the time spent on the RGB, from M_K=-4.5 to the tip, normalized at solar value, slowly increases as a function of metallicity. Finally the lower panel shows the combination of the two factors above, which is the correction to apply to each metallicity bin of the MD to take into account the evolutionary effects. Since the evolutionary flux and the RGB lifetime have opposite behaviour with metallicity, the final correction factor is never larger than few percent, well within the intrinsic precision of our measurement.

The resulting bulge MD for the 503 stars in Fig. 12 is finally shown in the three panels of Fig. 14 as a shaded histogram. Also shown in Fig. 14, as thick "open'' histograms, are the bulge MDs determined from various spectroscopic studies, normalized to the total number of stars in our sample. Note that all these spectroscopic determinations of the bulge MD refer to [Fe/H] abundance. Since the template RGBs are on the [M/H] scale, we subtracted from the bulge [M/H] distribution the same $\alpha$-element enhancement (i.e., 0.2 for [Fe/H] >-1 and 0.3 for [Fe/H] <-1) that had been applied to the template GCs, in order to obtain a [Fe/H] distribution. Although the bulge high resolution studies do not permit to draw strong conclusions on the $\alpha$-element enhancement, the similarity of the bulge CMD with that of bulge GCs would favor a similar chemical enrichment history. Certainly the new generation multi-object spectrographs will allow us to improve our knowledge in this field.

The comparisons shown in Fig. 14 shows that the present, "photometric'' MD is broadly consistent with the spectroscopic ones by McWilliam & Rich (1994) and Ramirez et al. (2000), with just a somewhat less pronounced supersolar [Fe/H] tail in the photometric MD. (This characteristic is exacerbated in the comparison with the MD of Sadler et al. 1996, based on low resolution data.) We caution, however, that the position of the high [Fe/H] cutoff is entirely dependent on the metallicity assigned to the two template clusters NGC 6528 and NGC 6553. For instance, the apparent discrepancy with, e.g., McWilliam & Rich (1994) at high metallicity would disappear if we would have assigned to NGC 6528 and NGC 6553 a metallicity $\sim$0.2 dex higher. Indeed this would bring to coincidence with M&R the high metallicity cutoff, while stretching the distribution and reducing the excess at [Fe/H] $\sim -0.2$. We believe that the homogeneous high-resolution studies of cluster and bulge field stars that will soon become available, e.g., with the forthcoming FLAMES multifibre spectrograph on VLT (Pasquini et al. 2000), will clarify this problem.

On the other hand, we tend to consider as quite reliable the sharpness of the cutoff at high [M/H]. Due to the TiO blanketing in the V band, the V-K color of RGB stars has a strong, rapidly increasing sensitivity to [M/H], and any high metallicity tail would have resulted in a dramatic broadening of the upper RGB, which instead is clearly absent in the CMD of the bulge shown in Fig. 9. Moreover, the high [Fe/H] cutoff would be even sharper, had we underestimated the effect of the distance and reddening dispersions.

4.3 Inferences for the chemical evolution of the bulge

The most straightforward approach is now to compare this empirical MD with the Simple (or one-zone, closed-box) Model of chemical evolution (Searle & Sargent 1972). Rich (1990) first made this comparison for the bulge and found the Simple Model to be a good fit to the abundance distribution from Rich (1988). The Simple Model assumes that no infall or outflow of metals has occurred during the star-forming phase of the system. The distribution follows the relation $N(Z)=y^{-1}{\rm exp}^{-Z/y}$, where the single parameter y, the yield, is given by $y=\langle Z\rangle$. Hence, the yield is the average metallicity of the stars in a one-zone system following the exhaustion of the gas (Hartwick 1976; Mould 1984). If metals are lost from the system by outflow, the functional form of the distribution is unchanged, but the mean abundance $\langle Z\rangle$ is the yield (as would be calculated from supernova models) reduced by the appropriate outflow parameter.

Figure 15: Comparison between the metallicity distribution of bulge giants from the present study (histogram) and the prediction of the Simple Model ( closed-box model) with the indicated value of the yield ( $y\equiv \langle Z \rangle$). The model distribution has been scaled by the total area under the data histogram. There is a clear shortage of stars near zero metallicity, and an excess of stars near solar abundance, but the one-zone model appears to fit the abundance distribution reasonably well.

Figure 15 shows a plot of the Simple Model distribution (for $y=\langle Z\rangle = 0.015$) overlaying the data. Note that both panels show the same model and the same data, once using [M/H] and once using $Z/Z_\odot$ as abscissa. As the Simple Model satisfies the requirements of a probability distribution, the function is scaled by the area under the data histogram, so that the area covered by data and fit are identical.

From the plots, the general shape of the abundance distribution is in fairly good agreement with the Simple Model. However, there are noticeable deviations: in the subsolar regime ( $Z< 0.3~ Z_\odot$) less stars are observed than predicted, while with respect to the model there is an excess of near-solar metallicity objects. This excess can be traced back to the fairly sharp clustering of the bulge stars around the RGB template at such metallicity (see again Figs. 7 and 10). This feature is most likely real, as many factors conjure to broaden the derived distribution (dispersion along the line of sight, differential reddening, incomplete disk decontamination, etc.). For the same reasons, most likely real is the sharp cutoff at high metallicity, that may even be sharper given the mentioned effects that tend to smooth out any sharp feature in the MD. The moderate shortage of metal-poor stars compared to the Simple Model may flag the presence of a G-dwarf problem, a point on which we return in Sect. 8.

The sharp high-metallicity cutoff of the MD suggests that star formation did not proceed to complete gas consumption. If the bulge formed in a rapid and intense starburst, one can imagine that much of the metals would have been produced in situ in core-collapse supernovae, eventually driving strong, metal-rich galactic winds. There are at least two independent arguments favoring this scenario, one direct and one indirect: a) high redshift galaxies thought to be proto-bulges are observed to have strong metal enriched winds (Steidel et al. 1996), and b) in clusters of galaxies at least as much metal mass is out of galaxies in the intracluster medium, as there is locked into stars inside galaxies, which is taken as evidence for early metal-enriched galactic winds (Renzini 1997, 2002). Therefore, a relatively sharp cutoff at the metal rich end, such as we observe, would result if the star formation was sufficiently violent as to eventually evacuate the gas from the proto-bulge before it was exhausted by star formation.