3 The color magnitude diagram

3.1 Near-IR CMD

Figure 4: J,H (left) and $J, K_{\rm s}$ (right) CMD of the bulge stars imaged with SOFI. In both panels, stars brighter than J=16 come from the $8\farcm3\times8\farcm3$ area mapped with short exposures and the SOFI-LARGE field, while fainter stars were measured in a $3.9\times 3.9$arcmin area observed with the SOFI-SMALL field.

Figure 4 shows the near-IR CMD of all the stars measured in the bulge field. The jump in the number of stars at J=16 is due to stars brighter than J=16 having been sampled from the $8\farcm3\times8\farcm3$ SOFI-LARGE field, while fainter stars have been measured with the larger angular resolution and deeper exposures of the SOFI-SMALL field, which mapped a $3\farcm9\times3\farcm9$ area.

The bulge HB red clump is visible at $J\sim14$ and J-H=0.6, partially merged into the RGB. The large magnitude spread of the HB is due to a combination of differential reddening, metallicity dispersion and depth effect. These factors also cause the HB clump to merge vertically with the RGB bump, expected to be located $\sim$0.7 mag fainter in J. The RGB bump (Iben 1968; Rood 1972; Salaris et al. 2002) is predicted to be very populated in a high metallicity system as the bulge, and would have itself a large magnitude spread due to the same depth and reddening effects mentioned for the HB clump.

The bulge turnoff is clearly visible at $J\sim17.5$ and J-$H\sim0.4$, while the almost vertical sequence departing from near the bulge turnoff and extending upwards and bluewards is due to foreground main sequence stars belonging to the disk, widely dispersed along the line of sight (Ng & Bertelli 1996).

Figure 5: a) The CMD of the bulge field. The solid line is the 1 Gyr isochrone for a solar metallicity population. b) CMD of the disk control field in the direction (l,b)=(30,0). The region inside the box has been used to normalize the number of disk stars seen through the bulge line of sight. c) CMD of the bulge field as statistically decontaminated from the disk population. The horizontal lines locate the main sequence turnoff at $J=17.65\pm 0.2$. The ridge line of the CMD is also shown. d) Stars that were subtracted from the bulge CMD in order to obtain the decontaminated CMD.

Figure 5a shows the CMD of the bulge field with superimposed a 1 Gyr isochrone, for a solar metallicity population, adopting a distance modulus of (m-M)₀=14.47 and a reddening of E(B-V) =0.45(see below). Clearly, a population of young stars physically located inside the bulge, would be definitely bluer than the vertical sequence of disk stars. The disk field, $30^\circ$ away from the Galactic center, was used to statistically decontaminate from the foreground disk stars the bulge CMD shown in Fig. 5a. Small differences in the disk stellar population may be expected between the two lines of sight. Yet, the results have shown that the procedure is indeed quite effective. The CMD of the disk control field for an area of 24 square arcmin is shown in Fig. 5b. The difference in reddening between the two fields was compensated by shifting the disk CMD shown in Fig. 5b by 0.17 mag in J-H so as to match the color location of the blue disk sequences, and in magnitude by the corresponding A_J=3.06E(J-H) extinction (Cardelli et al. 1989). A region of the CMD free of bulge stars was then selected in order to normalize the number of disk stars observed in the disk field to the number of disk stars contaminating the bulge field. This region is indicated by the box in the upper left region of the CMD in Fig 5a. This normalization is correct only if no bulge star is present in the box.

There are 91 stars in the box of the disk control field, which is 4.5 times less than in the corresponding box of the bulge SOFI-LARGE field. Therefore, 4.5 stars have been subtracted from the brighter region (J<16) of the bulge CMD for each star seen in the disk CMD. Since the fainter part of the CMD (J>16) was derived from the SOFI-SMALL field, the 4.5 scaling factor was divided by the ratio of the SOFI-LARGE to SMALL field area (4.6). Hence 0.98 stars have been subtracted from the fainter part of the CMD for each star in the disk control field.

For each disk star in the disk CMD (Fig. 5b) we picked up the closest star in the bulge CMD (see below), and subtracted it according to the normalization factors given above, and to the slightly different completeness of the two fields. The distance on the CMD from a disk star to each bulge star was defined as:

$$\begin{eqnarray*}d=\sqrt{[7\times\Delta(J\!-\!H)]^2 + \Delta J^2}. \end{eqnarray*}$$

The color difference has been enhanced by a factor of 7 because the color is much less sensitive than the magnitude to physical differences (in the distance, reddeninig or mass) between a given disk star in the control field, and another disk star along the bulge line of sight. The resulting, clean CMD of the bulge is shown in Fig. 5c, while the CMD of the stars statistically removed from the bulge CMD is shown in Fig. 5d. Also shown in this panel are the fiducial ridge line, helping the eye to identify the mean branches of the bulge CMD, and the brighter and fainter limits of our turnoff magnitude estimate ( $J=17.65\pm 0.2$).

The clumpy appearance of the RGB of Fig. 5d is due to the poor statistics in this region of the disk CMD since for each disk star we had to subtract 4.5 times more stars in the bulge field. Hence for each disk star a small "cluster'' of close stars was subtracted from the bulge CMD. In the attempt to minimize this effect we actually subtracted every other three closest stars in the region J<16. We expect a negligible effect on the 0.25 magnitude bins of the luminosity function discussed in the next section.

Figure 6: CMDs of the bulge (panel a) and disk b)) fields as constructed from the 2MASS photometry. c) The bulge CMD after statistical decontamination from disk stars; d) bona fide disk stars subtracted from a) in order to obtain c).

The 2MASS catalog was used to improve the statistics for the bright part of the CMD and of the luminosity function. Note however, that the $\sim$4'' resolution of 2MASS is significantly worse than either the SOFI or WFI data. This complicates somewhat the cross identifications with the SOFI and WFI databases, and crowding effects are much more severe since two objects closer than $\sim$4'' are counted as one in the catalog.

Figure 7: The optical CMD of the bulge from the WFI data. Each panel corresponds to each of the $2{\rm K}\times 4$K CCD chips of the WFI camera.

From the 2MASS point source catalog we extracted near-IR data for two large areas, $31\times31$ arcmin each, containing our bulge and disk field, respectively. A procedure identical to that described above for the SOFI data has been applied to the bulge CMD of Fig. 6a in order to statistically decontaminate bulge from disk stars, using the disk CMD shown in Fig. 6b. Note that since the disk and bulge field areas are now identical, the scaling factor for the decontamination (determined within a box similar to that shown in Fig. 5) is now very close to 1.

The result is again very satisfactory (Figs. 6c, d) for stars brighter than $J\sim13$. For fainter stars the decontamination is less effective because the magnitude and color spread of the disk and bulge CMD in Fig. 6 are quite different, due to the different drivers of the magnitude limits. Indeed, due to the low spatial resolution of the 2MASS data, the photometry is limited by the crowding in the bulge field, and by the background noise (including sky) in the disk. However, in the following only the brightest stars (J $\la$ 12) of the 2MASS decontaminated bulge CMD will be used.

3.2 The optical CMD

Figure 7 shows the (I,V-I) CMD of the 883 417 stars measured in the $34\times33$ arcmin field of WFI@2.2 m. The eight panels in this figure correspond to the eight CCD chips of the WFI mosaic, mantaining their relative spatial position. The huge number of points per panel saturates the plot in the most populated areas, like the bulge main sequence (I>18). The bulge turnoff is located around I=18, while the main sequence of the foreground disk hits the bulge locus approximately midway between the turnoff and the base of the RGB. The HB red clump (merged with the RGB bump) is visible at $I\sim14.5$ and V-$I\sim1.8$, while the upper RGB (brighter than the HB) is extremely wide due to the bulge metallicity dispersion. Note, however, that the narrow sequence departing from the bulge HB and extending upward, almost vertically is due to the red clump of the disk stars, dispersed in magnitude as a result of their large spread in distance (and reddening). The bulge main sequence extends almost vertically in this plot, becoming very broad towards faint magnitudes for the combination of photometric error and plot saturation, but its increasing skewness towards red colors is in fact due to the presence of the faint extension of the disk main sequence.

Although there is evidence for a bulge blue HB population in all the CMDs (with V- $I\simeq 0.5$ $\div$ 1 and $I\simeq 15$ $\div$ 18), note that chip#6 (panel f) contains the bulge globular cluster NGC 6558, already known to have a blue HB (Rich et al. 1998). The fact that the blue HB seen in this CMD belongs to the cluster becomes very clear when imposing a spatial selection around the cluster center. The other cluster features are not distinguishable from the bulge ones in this plot. A circular region of 2.4 arcmin radius, centered on NGC 6558, has been excluded from the following analysis. The radial trend of both cluster star counts and surface brightness flattens to the background level well inside this radius, ensuring a negligible cluster contamination outside 2.4 arcmin.

For a better visibility of the bright portion of the CMD, Fig. 8 displays only stars brighter than I=16, this time combining data from all the 8 chips of WFI. The disk main sequence is very prominent on the left side of the diagram, and is paralleled some $\sim$0.8 mag redder in V-I by the core helium burning clump sequence belonging to the same population. The bulge RGB and AGB occupy the right side of the diagram, and become very dispersed in their upper part due to the metallicity dispersion. The HB clump and the RGB bump are also indicated in the figure.

Figure 8: The optical CMD for the bright stars combining the data in the whole WFI field. The location of the HB clump and the RGB bump is indicated.