1 Introduction

Galactic spheroids, i.e., elliptical galaxies and the bulges of spiral galaxies, contain a large fraction, probably the majority, of all the stellar mass in the local universe (Persic & Salucci 1992; Fukugita et al. 1998). Understanding their formation and evolution is therefore crucial to understand galaxy formation in general, and to reconstruct the whole cosmic star formation history. However, it is only in the bulge of our own Galaxy that we can resolve the stellar population all the way to the bottom of the main sequence (MS), construct accurate color-magnitude diagrams (CMD) and luminosity functions (LF), and then address a series of issues of great importance for a better understanding of galactic spheroids in general. Such issues include the direct measure of some of the fundamental ingredients of galaxy models, like the initial mass function (IMF), the mass-to-light ratio and quantities such as the stellar age and metallicity distributions (MD).

Efforts in these directions have been quite numerous in recent years, and reviewing all of them is beyond the scope of this paper. However, here we briefly mention some of the most recent attempts at determining the age, IMF and MD of the bulge stellar population.

The only published study of the bulge MD based on high resolution (R= 17 000) spectra remains that by McWilliam & Rich (1994; hereafter M&R). They analyzed a sample of 11 red giants in Baade's Window, and used these data to re-calibrate a previous bulge MD based on low resolution spectra for 88 stars (Rich 1988). The resulting MD is centered around [Fe/H] =-0.2, with some 34$\%$ of the stars above solar metallicity, and no stars below [Fe/H]  $\simeq -1.3$.

The bulge MD has also been derived using lower resolution spectra. Sadler et al. (1996) measured line strength $<\!{\rm Fe}\!>$ indices in low resolution ($R\sim1000$) spectra of a sample of 322 bulge giants. These indices were calibrated vs. [Fe/H] following Faber et al. (1985). Although the derived [Fe/H] abundances for the few stars in common with M&R are in good agreement, the global MD by Sadler et al. (1996) is symmetric around [Fe/H] = 0, and shows a population of stars with metallicity above solar more prominent than in any other study, which may result from having applied the $<\!{\rm Fe}\!>$ vs. [Fe/H] calibration beyond its range of validity. More recently, Ramirez et al. (2000) derived the bulge MD by measuring the equivalent width of Ca, Na and CO lines in a sample of 110 M giants observed with resolutions from $R~\sim 1300$ to 4800. They converted equivalent widths into [Fe/H] by means of the Frogel et al. (2001) calibration, based on Galactic globular clusters (GCs) of independently known [Fe/H]. This assumes that the $\alpha$-element enhancement of the bulge is the same as that of the clusters. The MD obtained in this case is similar to that of M&R, but with a sharper peak at [Fe/H] = 0. The appreciable differences among the MDs derived in these studies are likely to arise from uncertainties in the calibration of the low resolution indices, that may introduce important systematics.

Dating bulge stars is complicated by several factors, such as crowding, depth effects, variable reddening, metallicity dispersion, and contamination by foreground disk stars. From WFPC1 observations of the bulge field known as Baade's Window, Holzman et al. (1993) inferred a dominant intermediate age component in the Galactic bulge. Shortly after the refurbishment of HST, two metal rich globular clusters of the bulge (NGC 6528 and NGC 6553) were observed with WFPC2 (Ortolani et al. 1995, hereafter Paper I). These clusters are respectively at $\sim$$4^\circ$ and $\sim$$6^\circ$ from the galactic center, and their overall metallicity [M/H] is about solar (Barbuy et al. 1999; Cohen et al. 1999), close to the average for stars in Baade's Window (M&R). Like most other clusters within $\sim$3 kpc from the Galactic center, they belong to the population of bulge globular clusters that have age, kinematical properties and metallicity distribution that are indistinguishable from those of bulge stars (e.g., Minniti 1995; Paper I; Coté 1999). Hence, we do not hesitate to refer to them as bulge globular clusters (see also Forbes et al. 2001; Harris 1976, 2001; Zinn 1996). In the case of NGC 6528 and NGC 6553 the bulge membership is also confirmed by the proper motion of the two clusters, in both cases well within the proper motion distribution of bulge stars (Zoccali et al. 2001a; Feltzing & Johnson 2002). In Paper I it was shown that (i) the two clusters have virtually identical CMDs, indicating that they have the same age and metallicity; (ii) their magnitude difference between the horizontal branch (HB) clump and the MS turnoff is virtually identical to that of the inner halo globular cluster NGC 104 ([Fe/H] =-0.7), and (iii) the LF of NGC 6528 (the least reddened of the two clusters) is virtually identical to the LF of bulge stars in Baade's Window, when allowance is made for the distribution of bulge star distance along the line of sight. From all these evidences Ortolani et al. concluded that  (i) the bulge underwent rapid chemical enrichment to solar abundance and beyond, very early in the evolution of the Milky Way (MW) Galaxy; (ii) the bulk of bulge stars formed nearly at the same time as the halo globular clusters, and (iii) no more than $\sim$$10\%$ by number of the bulge population can be represented by intermediate age stars. These conclusions have been further strengthened after a statistical decontamination of the bulge CMD from the foreground disk stars (Feltzing & Gilmore 2000).

Dating the bulge via the MS turnoff also allows one to check the usefulness of asymptotic giant branch (AGB) stars brighter than the red giant branch (RGB) tip as age indicators. Indeed, such AGB stars being much brighter than the MS turnoff, they have often been used in the attempt to date other galactic spheroids (such as M 32 and the bulge of M 31), sometimes inferring intermediate ages for some of these systems (e.g, Davidge & Nieto 1992; Freedman 1992; Elston & Silva 1992). However, the existence of AGB stars brighter than the RGB tip does not ensure a population to be of intermediate age: the old, metal rich ([Fe/H] $\ga-0.7$) globular clusters of the MW bulge and inner halo (such as, e.g., NGC 6553 and NGC 104) do indeed contain some AGB stars that are $\sim$1 mag brighter than the RGB tip (Frogel & Elias 1988; Guarnieri et al. 1997). The RGB+AGB luminosity function conveys important information concerning the stellar population of the bulge, and its better understanding is important for the interpretation of the observations of nearby spheroids.

At the opposite extreme of the luminosity range, the LF of the lower MS is the only part of the LF that depends on the IMF, and therefore it allows the determination of this important property of stellar populations. Recent near-infrared data obtained with HST+NICMOS, have provided the deepest ever J,H photometry in the bulge, and allowed the determination of the IMF from $\sim$$1~M_\odot$ down to $\sim$ $0.15~M_\odot$ (Zoccali et al. 2000, hereafter Paper II). The IMF resulted to be quite flat, with a slope $-1.33\pm0.07$ (compared to -2.35 for the Salpeter IMF), with a hint of a steepening toward the high mass end (see also Holzman et al. 1998).

The study of the NICMOS field extended to only 408 square arcsec, and therefore the number of stars on the upper MS is too small to allow any reliable location of the MS turnoff, while the evolutionary stages beyond the turnoff are not sampled at all. Thus, in Paper II an attempt was made to extend the main sequence LF to the evolved stars, using near-infrared data from the literature. A complete LF, extending from the bottom of the MS all the way to the AGB, was constructed by matching the NICMOS luminosity function of the lower MS, to the Tiede et al. (1995) LF extending from slightly above the turnoff to slightly above the HB, and finally to the Frogel & Whitford (1987) LF for the bulge M giants above the HB. While the resulting composite LF was constructed with the best data available in each luminosity range, several limitations were also obvious. Specifically, the MS turnoff region was not well sampled by neither the NICMOS data from Paper II (too few stars in the small field), nor by the Tiede et al. LF (not deep enough to reach the turnoff). Moreover, the upper RGB and AGB from Frogel & Whitford (1987) included only the M stars selected from an objective prism survey, hence omitting any luminous K giants that may be present in the explored bulge field. Finally, the NICMOS observations were conducted in a field $6^\circ$ from the Galactic center, while the two other datasets were relative to Baade's Window, at $4^\circ$ from the center.

In this paper we present a thorough attempt at overcoming the current limitations of the available CMDs and LFs of the bulge, thereby producing state of the art CMDs and LFs used for new determinations of the age and metallicity distribution of the bulge. This approach is based on new near-IR ( $J, H, K_{\rm s}$) data obtained with SOFI at the ESO New Technology Telescope (NTT), as well as on optical (V, I) data obtained with the Wide Field Imager (WFI) at the ESO/MPG 2.2 m telescope. These data are then coupled with the NICMOS data from Paper II for the lower MS, and with the 2MASS near-IR data for the upper RGB and AGB (van Dyk 2000; Carpenter 2001; and references therein).

The paper is organized as follows: Observations and data reduction procedures are presented in Sect. 2, the CMDs are displayed and discussed in Sect. 3, while Sect. 4 is devoted to the derivation of the metallicity distribution. The luminosity function of the bulge is constructed and discussed in Sect. 5, while Sect. 6 is devoted to determining the age of the bulge, and Sect. 7 to a discussion of the RGB tip in the different bands. Finally, the main results are again summarized in Sect. 8, along with some inferences on the formation of the Galactic bulge and spheroid, also in the context of the current evidence on the formation of galactic spheroids in general.