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Astron. Astrophys. 341, 641-652 (1999)

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3. Counts and colors

3.1. Differential galaxy counts

Before discussing the galaxy counts, we have to apply a correction for completeness at faint magnitudes. A standard way to estimate the fraction of lost sources, crowding, spurious objects, magnitude errors, etc..., is to generate simulations by assuming a typical profile for all kinds of galaxies and different cosmological models (Metcalfe et al, 1995). In the present case, we have to take into account that the detection of sources has been done by using the combined image of the four bands and that the noise in our drizzled frame is correlated due to the drizzling algorithm. To provide an estimation of the correction as close as possible to the characteristic of our raw data, we have adopted the following empirical approach:

  1. we extract objects in the magnitude ranges 23[FORMULA] 25.5 and 23[FORMULA]25.0 (by using the "check-images" tool of SExtractor software). At these magnitudes, the signal-to-noise is greater than 8.

  2. the object's fluxes are dimmed by factors 4, 6.5 and 10 and added randomly to the original frames (combined image and [FORMULA] images). The noise in the resulting combined and [FORMULA] images is identical to the original data.

  3. The algorithm of detection is applied to the combined image and the measure of the magnitudes is carried out on the [FORMULA] frames. The correction factor for each magnitude bin is derived from the fraction of the "simulated" sources that are detected.

The magnitude range of the original sources used in this simulation has been chosen in a way that a sufficient number of objects between 24.5-27.5 is generated, while avoiding a too large crowding at intermediate magnitudes. Besides, since the original galaxies have a mean expected redshift of 0.6-1.0 and we do not expect drastic differences of colors with respect to the fainter galaxy population (except for the ellipticals in the B band), this allows us to ignore any additional k-correction term. Note that this analysis doesn't include the Eddington bias and can overestimate the correction factor. The completeness factor ([FORMULA]) is reported in Table 2.


[TABLE]

Table 2. Number counts and errors


In Fig. 1, we plot the raw and corrected differential galaxy counts as a function of the magnitude ([FORMULA]) and we report the corrected number counts in Table 2. The error bars include the quadratic sum of the Poisson noise ([FORMULA]), the uncertainty in the completeness factor ([FORMULA]) and the clustering fluctuation due to the small size of the field as follows:

[EQUATION]

[EQUATION]

where IC is the integral constraint computed by a Monte-Carlo method for the appropriated size of the NTTDF field ([FORMULA]). The relationship between the amplitude [FORMULA] and the magnitude is assumed to evolve as [FORMULA], where [FORMULA] for the B, V, r and I bands respectively. The individual and total errors are reported in Table 2.

[FIGURE] Fig. 1. Differential galaxy number counts for the B, V, r and I bands. Open circles show the raw counts and filled circles show the corrected counts for incompleteness. The error bars include the correction factor, the density fluctuation and poisson errors. The large solid lines give the best fits for the slope. The previous works are drawn with different symbols. They include the data from Tyson (1988, open squares), Lilly et al. (1991, crosses), Metcalfe et al. (1995, triangles), Smail et al. (1995, filled squares), Williams et al. (1996, stars). Our r filter is significantly different to the R Cousins, thus we have applied to the previous works a shift of 0.2 ([FORMULA], by assuming [FORMULA]).

The slopes are estimated by linear regression. For the B and V bands, the counts show a significant flattening at magnitudes fainter than B[FORMULA] 25 and V[FORMULA] with slope values of [FORMULA] and [FORMULA]. The evidence of breaks in the B and V bands have been already produced by previous works (Metcalfe et al. (1995), Smail et al. (1995)). The low density of bright galaxies in the NTTDF produces an artificially steep slope at bright magnitudes, making more apparent the breaks in the counts at 25 and 24 in B and V.

The slopes at faint magnitudes in the B and V bands are similar to those observed in the whole range in r and I bands:

[EQUATION]

In Fig. 1, our results are compared with the previous works of Tyson (1988), Lilly et al. (1991), Steidel et al. (1993), Metcalfe et al. (1995), Smail et al. (1995) and Williams et al. (1996). At bright magnitudes, the discrepancy is large ([FORMULA] in the slope) due to the bias mentioned above. At faint magnitudes the slopes are consistent among the different works.

3.2. Colours of the galaxies in the sample

To measure colours, we have smoothed the I frame to the same effective seeing of the worst frame (B frame) and carried out photometry in 2 arcsec diameter apertures with the same center as defined in the summed frame. The colors versus magnitude plots are shown in Fig. 2, Fig. 3, Fig. 4. The 2[FORMULA] and 1[FORMULA] color limits within the 2 arcsec apertures are represented by open circles and triangles respectively. The median include the colour limits at 1 and 2 [FORMULA] and has been computed in bins with 60 objects except for bright magnitudes where bins extending from 20 to 22 and from 22 to 23 have been imposed. The error bars on the median colours have been computed by using a boot-strap resampling method. A comparison with previous works is shown with solid and dashed lines. This comparison has to be taken with caution because the colors are estimated with constant number of objects in each bin and not with a fixed bin. All the color distributions show up to r[FORMULA]24-24.5 a blueing trend at bright magnitudes. At deeper magnitudes, the median [FORMULA], [FORMULA] and [FORMULA] versus r (Fig. 2, 3) show stable values. The [FORMULA], [FORMULA] and [FORMULA] versus I (Fig. 3 and Fig. 4) show again a blueing trend but no color stabilization is observed at the fainter magnitudes. This flattening in the various colors is in good agreement with the observed convergence of the slopes ([FORMULA] 0.32) in the differential counts for all the four filters.

[FIGURE] Fig. 2. Color-magnitude diagram for [FORMULA] versus r and [FORMULA] versus r in our natural systems. The colors are computed in fixed aperture of 15 pixels. Open circles represent the colours at 2[FORMULA], open triangles the colours at 1[FORMULA] and stars show the stellar objects. The large filled points are the medians colors. The horizontal bars show the extent of magnitude bin. For magnitudes fainter than 23, the medians are computed for 60 objects per bin. The vertical error-bars give the 1[FORMULA] error calculated using boot-strap resampling of data. Comparison with Arnouts et al. (1997, short dashed line) and Metcalfe et al. (1995, long dashed line) are shown by applying the color correction given in Sect. 2.2.2.

[FIGURE] Fig. 3. Same as Fig. 2 for [FORMULA] versus r and [FORMULA] versus I. Comparison with Arnouts et al. (1997, dashed line) and Smail et al. (1995, solid line) are shown by applying the color correction given in Sect. 2.2.2.

[FIGURE] Fig. 4. Same as Fig. 2 for [FORMULA] versus I, and [FORMULA] versus I. Comparisons are shown for the data from Tyson (1988, solid line) and Lilly et al. (1991, dashed line) by applying the color correction given in Sect. 2.2.2.

3.3. Magnitudes and colours of the stellar objects

A by-product of this catalogue is a sample of stellar objects. As in the case of the HDF, the study of the stellar population present in the NTTDF can give useful insight in the galactic structure and/or give constraints on the baryonic dark matter. With the NTTDF it is possible to perform a direct comparison of its stellar content with the one of the HDF. The two fields have essentially the same galactic latitude (for NTTDF [FORMULA] and for HDF [FORMULA]), but different galactic longitude, with the NTTDF pointing toward the galactic center ([FORMULA]), while the HDF is pointing toward the galactic anti-center ([FORMULA]). Moreover, they cover essentially the same area in the sky ([FORMULA] square degrees), allowing us to make a direct comparison of the two stellar samples.

In the upper panels of Fig. 5 we show the V vs. (B-V) and I vs. (V-I) color-magnitude diagrams of the objects classified as stellar (star/galaxy class[FORMULA]) in our final catalog. The objects selected have colors in good agreement with the color expected for stellar objects. In the lower panels of Fig. 5 we have put the (B-V) vs. (V-I) and the (r-I) vs. (V-I) color-color diagrams. It can be clearly seen that, especially in the (r-I) vs. (V-I) (where the observational errors are lower), the objects follow very closely the colors expected for giants/dwarfs stars (the continuous lines are taken from Caldwell et al. 1993), assuring us that the classification parameter gave reliable results. In all the plots we have also included 4 objects with star/galaxy class[FORMULA] and [FORMULA] (shown as open dots). These blue objects have been included since they resemble the population of blue objects found by Mendez et al. (1996) in their analysis of the stellar content of the HDF: they could be interpreted as partially unresolved blue galaxies. In this sample the object in the (B-V) vs. V diagram at V[FORMULA] is the brightest and bluest member of this sample.

[FIGURE] Fig. 5. In these plots we present the color-magnitude and color-color diagrams of the objects classified as stellar in the NTTDF. Upper Left. V vs. (B-V) color-magnitude diagram. Upper Right. I vs. (V-I) color-magnitude diagram. Lower Left. (B-V) vs. (V-I) color-color diagram. Lower Right. (r-I) vs. (V-I) color-color diagram. Continuous lines are the colors expected for giants/dwarfs stars (from Caldwell et al. 1993).

Of some interest for a follow up spectroscopic observation is the object #606 of the catalogue, having a (V-I)[FORMULA]. The colors of this object, including an infrared (I-K)=3.2 (Fontana et al. 1998, to be submitted), are consistent with those expected for bright low mass stars (Delfosse et al 1998). This object has also colors very similar to KELU-1, a field brown dwarf with a mass below [FORMULA], and a distance from the Sun of [FORMULA]pc (Ruiz, Legget, & Allard 1997). Other likely faint brown dwarfs are the 5 objects with [FORMULA]; their catalogue number is: #93, 112, 249, 579, 600.

In our (V-I) vs. I diagram we do not have stars below I[FORMULA], even if our detection limit is I[FORMULA]. This difference could be explained by the fact that are needed at least 5 times more photons to classify objects rather than just detect them (Flynn et al. 1996). In the magnitude range [FORMULA]I[FORMULA] we found 26 objects, with 6 objects at (V-I)[FORMULA] ([FORMULA] of this sample). The number of objects are approximately 3 times the stars detected in the same magnitude range in the HDF (see Flynn et al. 1996, Mendez et al. 1996, Reid et al. 1996 for different results on the HDF). This difference in number may be explained by the fact that the NTTDF is pointing in the direction of the galactic center. It is compatible with the prediction obtained with the galactic model by Robin and Creze (1986), as available at www.ons-besancon.fr/www/modele_ang.html .

Finally, The object #570, classified as stellar-like on the basis of the SExtractor algorithm, is listed in the catalog by Giallongo et al 1998 (where it is #12) with colors typical of an high redshift candidate. Cowie and Hu (1998, private communication) obtained a spectrum at Keck. Although the S/N is low, an M star interpretation of the spectral features appears more likely. The colors of the object (including the [FORMULA]1.5 of Fontana et al. 1998) would be marginally consistent with a slightly earlier (K5-K7) classification. In Sect. 5 (see in particular Fig. 9) it will be shown that few red stars display colors similar to high-z galaxies.

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© European Southern Observatory (ESO) 1999

Online publication: December 16, 1998
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