2 Observations and data reduction

The data presented here come from the combination of near-IR $J, H, K_{\rm s}$observations conducted with SOFI@NTT, implemented with public data from the 2MASS survey and with NICMOS data from Paper II, plus optical V, I images taken with the WFI@2.2 m as part of the EIS PRE-FLAMES survey (Momany et al. 2001; and references therein), and retrieved from the ESO archive. The relevant technical information about the observations are reported in Table 1, while details on the observational strategy and data reductions are described here below.

2.1 Near-IR data

A bulge mosaic field centered at ( l,b)=(0.277, -6.167) (RA = 18:11:13, Dec =-31:43:49; J2000) was observed with SOFI@NTT, through the filters $J, H, K_{\rm s}$, in the nights of 9-12 June 2001. This particular field was selected for the present study because it includes the field already covered by the NICMOS observations (Paper II), which in turn was chosen for having a reddening (E(B-V) =0.47) as low as that of the most widely studied Baade's Window while being less crowded. Indeed, being $\sim$$2^\circ$ further away from the Galactic center the density of stars is lower by a factor $\sim$2, which allows more accurate photometry especially at very faint magnitudes.

In order to optimize the photometry of both the turnoff region and the upper RGB, the observations were split in short and long exposures, each with a different field objective, and therefore mapping areas of different sizes. For a good sampling of RGB+AGB stars, short exposures were obtained for a  $8\farcm3\times8\farcm3$ region, with a mosaic of four fields of the low resolution camera, which has a pixel size of  $0\hbox{$.\!\!^{\prime\prime}$ }292$ and field of view of  $4\farcm9\times4\farcm9$ (hereafter SOFI-LARGE field). In order to better sample the PSF, a second mosaic of four deeper exposures mapping a smaller area ( $3\farcm9\times3\farcm9$) was secured with the same camera coupled with the focal elongator, therefore yielding a pixel size of  $0\hbox{$.\!\!^{\prime\prime}$ }144$ and a  $2\farcm5\times2\farcm5$ field of view (hereafter SOFI-SMALL field). An overlap of $\sim$$20\%$ was always present among the four fields of each mosaic.

 

 

Table 1: Log of the observations.

Date	Object	Camera	RA	Dec	Filter	Exptime
11 Jun. 2001	bulge	SOFI-LARGE	18:11:05.0	-31:45:49	J	36s
''	''	''	''	''	H	36 s
''	''	''	''	''	$K_{\rm s}$	36 s
''	''	''	18:11:22.0	-31:45:49	J	36 s
''	''	''	''	''	H	36 s
''	''	''	''	''	$K_{\rm s}$	36 s
''	''	''	18:11:22.0	-31:41:49	J	36 s
''	''	''	''	''	H	36 s
''	''	''	''	''	$K_{\rm s}$	36 s
''	''	''	18:11:05.0	-31:41:49	J	36 s
''	''	''	''	''	H	36 s
''	''	''	''	''	$K_{\rm s}$	36 s
11-12 Jun. 2001	bulge	SOFI-SMALL	18:11:05.0	-31:45:49	J	1180 s
''	''	''	''	''	H	1530 s
''	''	''	''	''	$K_{\rm s}$	2880 s
9-11 Jun. 2001	''	''	18:11:13.5	-31:45:49	J	1200 s
''	''	''	''	''	H	1020 s
''	''	''	''	''	$K_{\rm s}$	1920 s
9-11 Jun. 2001	''	''	18:11:13.5	-31:43:49	J	1200 s
''	''	''	''	''	H	1020 s
''	''	''	''	''	$K_{\rm s}$	1920 s
9-11 Jun. 2001	''	''	18:11:05.0	-31:43:49	J	1200 s
''	''	''	''	''	H	1020 s
''	''	''	''	''	$K_{\rm s}$	1920 s
11 Jun. 2001	disk	SOFI-LARGE	19:07:32.0	-05:19:57	J	600 s
''	''	''	''	''	H	510 s
''	''	''	''	''	$K_{\rm s}$	960 s
15 Apr. 1999	bulge	WFI	18:10:17.0	-31:45:16	V	20 s
''	''	WFI	''	''	V	$2\times300$ s
''	''	WFI	''	''	I	20 s
''	''	WFI	''	''	I	$3\times300$ s

Exposures of a disk control field located at (l,b) = (30,0) (RA = 19:07:32, Dec =-05:19:57) were also obtained for one pointing of the large field camera in order to estimate the disk contribution to the bulge CMD (Sect. 4).

Each of the deep exposures, both for the disk and the bulge field, was obtained with detector setup DIT = 6 NDIT = 5 (i.e., every frame was the average of 5 exposures of 6 s each), while for the shallow ones we used DIT = 1.2 and NDIT = 5. Both of them were repeated with a random dithering pattern until reaching the exposure time listed in Table 1. Both sky transparency and seeing were somewhat variable during the run, and for this reason the total exposure times on different fields were adjusted in order to compensate for these effects. The typical seeing during the observations was $0\hbox{$.\!\!^{\prime\prime}$ }80\pm0\hbox{$.\!\!^{\prime\prime}$ }15$.

Images were pre-reduced using standard IRAF routines. A sky image, obtained by median combination of the dithered frames of each filter, was subtracted from each frame. Flat fielding was then performed using the "SpecialDomeFlat'' template which applies the appropriate illumination corrections, as described in the SOFI User Manual. Finally, all the dithered frames obtained in a sequence were averaged in a single image for each filter. In what follows we will call "frame'' the combination of each of these sets.

Standard photometry, including PSF modeling, was carried out on each frame using the DAOPHOT II photometry package (Stetson 1987). We used all the stars identified in each frame to obtain the coordinate transformations among the frames. These transformations were used to register the frames and obtain a median image. The latter, having the highest S/N, was used to create the star list, by means of a complete run of DAOPHOT II and ALLSTAR. The final star list, together with the coordinate transformations, was finally used as input for ALLFRAME (Stetson 1994), for the simultaneous PSF-fitting photometry of all the frames of each field.

Only one of the four half-nights assigned to this programme was photometric. During that night we observed several standards from the Persson et al. (1998) catalog, three of which just before and after one of the bulge fields observed with SOFI-SMALL. This field was calibrated by means of the standard stars, whose frames were pre-processed in the same way as the science ones. Aperture photometry within a radius of 5.8 arcsec was obtained for the standard stars, and aperture corrections determined using some bulge isolated and unsaturated stars were applied to the PSF instrumental magnitudes of the bulge field. The calibration equations obtained from the standard stars were then applied to the magnitude of the bulge stars, neglecting the color term due to the very small color range of the near-IR standard stars. Having calibrated one bulge field, all the others were registered to the same photometric system by comparison of the common stars: a single large field included the whole mosaic of four small fields, and there was always $\sim$$20\%$ overlap among the four fields of each mosaic.

The whole bulge area mapped with SOFI is also included in the 2MASS near-IR survey (Carpenter 2001), whose second incremental release is publicly available on the WEB. Figure 1 shows the comparison between the $J, H, K_{\rm s}$ magnitudes from our calibrated photometry and the same quantities for the stars in common with the 2MASS point source catalog. The latter has a limit magnitude of  $K_{\rm s}\sim 15$, therefore only the stars measured in one of the four SOFI-LARGE fields (i.e., in the short exposures) are plotted in this figure. The solid line represents a least square fit to the data, while the dotted one is the relation between the 2MASS and the Persson et al. (1998) photometric system (Carpenter 2001). The latter is based on 2MASS observations of 82 standard stars from Persson's catalog.

Figure 1: Comparison between the SOFI photometry and that from the 2MASS survey, for the stars in common. The solid line is the least square fit to the data, while the dotted one is the relation found by Carpenter (2001).

A trend with magnitude is clearly visible in Fig. 1, with the difference between the two photometries being zero at the faintest limit but increasing up to $\sim$0.1 mag at the brightest end in Jand H, while remaining quite small ($\la$0.05 mag) in $K_{\rm s}$. Such a behavior points to a non-linearity effect in one of the two detectors. To our knowledge neither the 2MASS nor the SOFI measurements should be affected by non-linearity; in particular the SOFI detector has been tested to be linear within $2\%$ up to 10 000 ADU (cf. the SOFI User Manual), and only the three brightest stars in this plot have counts above this limit. We are then left with no explanation for the trend seen in Fig. 1, but none of our conclusions relies on an accuracy better than $\sim$0.1 in the magnitudes. Moreover, if the error is in our measurements and not in the 2MASS ones, the trend is identical in the J and H bands, therefore it would affect the magnitudes but not the J-H color we used to construct the CMD shown in Sect. 3.

The disk control field was not observed during the photometric night, therefore the only way we had to calibrate its CMD was to rely on the comparison with 2MASS. However, given that our main interest was to put the disk stars in the same photometric system as the bulge ones, we determined the calibration transformations between our disk instrumental magnitudes and 2MASS, but then also applied the small differences shown in Fig. 1, in order to try and keep consistency between the disk and bulge calibrated photometry.

Figure 2: Comparison between the SOFI photometry presented here and the deep NICMOS photometry from Paper II, for the stars in common. Open circles refer to stars that may be affected by blending in SOFI frames.

One of the goals of this project is to obtain a complete luminosity function for the galactic bulge, from the RGB tip down to the faintest stars ( $0.15~M_\odot$) measured with NICMOS. Therefore, it is crucial to make sure that the NICMOS photometry is consistent with that obtained here with SOFI, especially given the large uncertainties in the NICMOS calibration (Stephens et al. 2000). Figure 2 shows the differences in J and H for the stars in common between the two data sets. Given the large difference in spatial resolution between SOFI and NICMOS, this comparison may be affected by systematics due to the presence of close pairs of stars resolved by NICMOS but not by SOFI. For this reason, different symbols (filled) were adopted in Fig. 2 for the stars whose positions matched within 0.5 SOFI pixels. These stars are less likely to be blends, because the presence of a companion resolved by NICMOS would likely result in a displacement of the star centroid. The median differences, in J and H, between the common stars, if only the bona fide single stars are considered, are $\Delta J=-0.006$ and $\Delta H=-0.04$ as shown in the figure labels. If all the common stars were considered, the median differences would be anyway negligible for our purposes: $\Delta J= \Delta H=-0.09$.

Completeness estimates were determined via artificial-star experiments. A total of about 3500 stars were added to the original SOFI frames, both for the bulge and for the disk fields, with magnitudes and colors consistent with the RGB+MS instrumental fiducial lines. In order to avoid to artificially increase the crowding, at the same time optimizing the CPU time, in each independent experiment the artificial stars were added along the corners of an hexagonal grid, as explained in Paper II. As usual, photometry of the artificial frames was performed following the same procedures as for the original ones.

Figure 3 shows the results of these experiments, as the difference between the input and output magnitude of the artificial stars in each filter.

Note that the distribution is asymmetric about the zero, as occasional blendings result in brighter output magnitudes compared to the input ones. However, the ridge line (i.e., the peak of the distribution) remains close to zero up to $J\sim18$, and therefore the estimate of the turnoff magnitude, from the CMD ridge line is not affected by blending. We expect instead the luminosity function to be affected (see Sect. 5.1). The simulations have shown that the SOFI photometry is more than $50\%$ complete above $J\sim19$ and $H=K_{\rm s}\sim18$.

Figure 3: Difference between the input and the output magnitude of the artificial star experiments on the SOFI frames. The results obtained for the SOFI-LARGE and SOFI-SMALL frames were matched at J=16 as in the photometry of the real stars.

2.2 Optical data

A $34\times33$ arcmin bulge field including the whole area mapped with SOFI was observed with the wide field imager WFI@2.2 m telescope, as part of the EIS PRE-FLAMES programme (Momany et al. 2001). The V and I raw frames have been retrieved from the public ESO archive, while the pre-processed images were not released yet. The frames were taken under very good seeing conditions, with a PSF FWHM of $0\hbox{\rlap{\hbox{.}}\hbox{$''$ }}6$, as measured on the frames. Details about the observations are given in Table 1. Science images were de-biased and flatfielded by means of standard IRAF routines, using a set of sky flat-fields taken the same night.

The photometry for each of the 8 WFI chips was performed separately, in order to properly model the PSF variation across them. As usual, complete photometry and PSF modeling were carried out on each of the I and V frames, and then coordinate transformations were calculated among them in order to obtain a median frame to use for a more complete star finding. The star list obtained in this way was then used as input for ALLFRAME, which performed simultaneous PSF fitting photometry on the 3 V and 4 I frames. The whole procedure was repeated for each of the 8 chips.

Calibration to the Johnson photometric system was performed by means of a set of Landolt (1992) standard fields observed the same night through the 8 WFI chips. The number of standard stars present in each of these fields has been recently increased by Stetson (2000), allowing us to measure $\sim$40 standard stars per chip. A zero point and a color term were determined separately for each chip. The color terms were then averaged, and new zero points were calculated imposing the former to be fixed. Variations $\la$0.1 mag have been found among the photometric zero points of different chips.

Completeness estimates were determined for the WFI data in the same way described above for the SOFI ones. WFI data are more than $50\%$ complete above $I\sim22.5$, and $V\sim23$.