8 Summary and conclusions

Optical and near-IR CMDs for the Galactic bulge have been presented based on data taken with WFI at the ESO/MPG 2.2 m telescope and with SOFI at the ESO NTT, respectively. This dataset has been supplemented by the NICMOS photometry from Paper II, and by public 2MASS data. The near-IR CMD has been statistically decontaminated from the disk stars in the foreground, producing a very clean CMD of the bulge. To ensure great statistical significance also for the upper RGB, the SOFI data have been combined with 2MASS data on a larger field including the SOFI field itself, and the 2MASS CMD has also been statistically decontaminated from the foreground stars.

By combining the best near-IR data in each corresponding luminosity range (2MASS, SOFI, and NICMOS) a luminosity function of the Galactic bulge has been constructed that extends over $\sim$15 mag, from a few bright AGB stars above the RGB tip, down to almost the bottom of the main sequence, corresponding to stars of $\sim$ $0.15~M_\odot$. This is the most extended and complete luminosity function so far obtained for the galactic bulge, hence for galactic spheroids in general.

Combining WFI optical data and 2MASS near-IR data, a disk decontaminated (K,V-K) CMD was constructed that includes 503 stars brighter than M_K=-4.5. Together with empirical RGBs of globular clusters of known metallicity used as templates, this fairly large sample of bulge stars is used to determine the bulge metallicity distribution. It is found to peak at [M/H] $\sim -0.1$, with a fairly sharp edge just above solar metallicity, and a low-metallicity tail that does not appreciably extend below [M/H] $\sim -1$, quite similar to the spectroscopic result of McWilliam & Rich (1994), but relative to a much larger sample. Such a distribution contains somewhat less metal poor stars than predicted by the closed box model of chemical evolution (e.g., Rich 1990), and indicates that the classical G-dwarf problem may affect also the Galactic bulge, as known since a long time for the disk (e.g., Tinsley 1980). Integrated light studies indicate that a G-dwarf problem is also present in early type galaxies, as a closed-box model metallicity distribution will result in too low values of the Mg₂ index (Greggio 1997). Yet, the reasons for both disks and spheroids sharing the same problem are likely to be at least in part quite different. For the Galactic disk (and perhaps disks in general) pre-enrichment by the older bulge is likely to set a floor metallicity at [Fe/H] $\sim -1.0$ (Renzini 2002). Clearly, this kind of pre-enrichment cannot be invoked for the bulge itself.

In the closed-box model one assumes the whole baryonic mass to be already assembled at t=0, while by adopting a gradual built up the G-dwarf problem can be eliminated. In the case of the Galactic disk this solution of the problem has taken the name of infall (e.g. Pagel 1997, and references therein). Since the star-forming ISM (either in a disk or in a proto-spheroid) is likely to be built up gradually, then the closed-box model would not apply. This situation is indeed established both in the case of continuous gas infall forming disks, as well as in the case of early, merging-driven starbursts building galactic spheroids. In turn, starbursts are likely to drive metal-rich galactic winds, thus discontinuing star formation before the gas is fully turned into stars. Therefore, the bulge likely departed from the closed-box approximation both for having being built gradually, albeit rapidly, and for having ejected gas and metals near the climax of its star formation activity.

The near-IR CMD of the Galactic bulge, carefully decontaminated from foreground stars, has been used to show that the bulge is virtually coeval with the Galactic halo. The region in the CMD above the main sequence turnoff of the bulge is so devoid of stars that no trace can be found of a population of bulge stars significantly younger than the main old component. This indicates that no appreciable new stars formed in the bulge, or were added to it, following the intense starburst activity that turned $\sim$ $10^{10}~M_\odot$ of gas into the bulge stars, some 10 Gyr ago.

Using both optical and near-IR data, the RGB tip of the bulge is clearly identified, and its systematics in the various bands is established. Contrary to the behavior at lower metallicities, in the metallicity range spanned by the bulge stars (-1 $\la$ ${\rm [Fe/H]}$ $\la$ 0) the I-band luminosity of the RGB tip is not constant, but decreases with increasing metallicity. Conversely, the RGB tip luminosity is found to be constant in the H band, while it increases with metallicity in the K band. This behavior is naturally accounted for by a combination of increasing blanketing which is stronger at short wavelengths (i.e. in the I and J band), with the bolometric luminosity of the RGB tip which increases with increasing metallicity. The metallicity distribution of galactic spheroids is therefore expected to affect the use of the surface brightness fluctuation method of distance determinations (Tonry & Schneider 1988). As a final remark, we would like to note that a group of stars is found at luminosities exceeding the RGB tip, and their number is roughly consistent with the expectation scaling from old, metal rich globular clusters. Their number is consistent with the purely old age for the bulge population as derived from the turnoff region.

Some limitations of the present study are worth mentioning. The location of the peak of the metallicity distribution coincides with the metallicity of the clusters NGC 6528 and NGC 6553, but in turn the metallicity itself of these clusters remain quite uncertain. Systematic, homogeneous, high spectral resolution studies of stars in these clusters and in the field are needed to properly match the cluster and field star metallicity scales. When such data will become available, it will be easy to re-derive the metallicity distribution of the bulge. Finally, we regret to have been unable to find the origin of the larger HB and RGB spread exhibited by the bulge CMD, compared to simulations that are meant to include all intrinsic spreads of the real bulge population (distance, metallicity, and reddening).

In closing, we would like to note that the Milky Way galaxy is a rather inconspicuous late-type spiral, member of a poor group of galaxies located quite away from major density peaks in the distribution of galaxies. Yet, virtually its whole spheroidal component, from the outer metal-poor halo all the way to the central metal-rich bulge, is $\sim$1 Hubble time old. There is now conclusive evidence that the stellar populations of galactic spheroids in general, elliptical and bulges, are also $\sim$1 Hubble time old (e.g. Renzini 1999, for an extensive review), while most such spheroids appear to be well in place and fully assembled already at $z\sim 1$, having passively evolved since at least $z\sim 2.5$(Cimatti et al. 2002). If the stellar mass in galactic spheroids amounts to 50-70$\%$ of the total stellar mass in the local universe (Fukugita et al. 1998), all this evidence indicates that a major fraction of all stars formed at high redshift, in deep potential wells bound to become the galactic spheroids of today. If such a build up of galaxies was promoted by the hierarchical merging of dark matter halos, it took place at a time and at a rate that no practical rendition of the hierarchical merging paradigm has yet succeded in reproducing (Cimatti et al. 2002 and references therein).

Acknowledgements

We thank the referee, Dr. E. Sadler, for careful reading of the manuscript and comments that lead to an improvement of the paper.

The present work has been partially supported by the Italian Ministero della Università e della Ricerca under the program "The Origin and Following Evolution of the Stellar Population in the Galactic Spheroid'' and by the Agenzia Spaziale Italiana.

S.C. acknowledges the financial support by (Cofin2001) under the scientific project: "Origin and evolution of stellar populations in the galactic spheroid''.

RMR acknowledges support from grant number AST-0098739, from the National Science Foundation and from grant GO-7891 from the Space Telescope Science Institute.