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Astron. Astrophys. 345, 448-460 (1999)

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3. Data evaluation

Although this paper does not intend to interpret the data, some basic statistics are computed to evaluate the overall performance of the EIS pipeline in translating images into useful scientific products. For this purpose, the stellar and galaxy samples extracted in each passband and the preliminary color catalog for point-sources are compared below with other available data and model predictions.

3.1. Point-like sources

Fig. 13, shows the comparison of the star counts for patch B derived using the stellar sample extracted from the object catalogs produced in each passband (Sect. 2.5), with the predicted counts based on a galactic model composed of an old-disk, a thick disk and a halo. The star- and color-counts presented in this section have been computed using the model described by Méndez & van Altena (1996), using the standard parameters described in their Table 1. It is important to emphasize that no attempt has been made to fit any of the model parameters to the observed counts. The model is used solely as a guide to evaluate the data and, as can be seen from Fig. 13 one finds a remarkable agreement with the predicted counts down to the magnitude where the star-galaxy separation is expected to become unreliable. The excess in counts seen at the bright end is due to the saturation of brighter objects ([FORMULA]).

[FIGURE] Fig. 13. The EIS differential star counts versus magnitude compared to the galactic model predictions (solid line), as described in the text. The model includes an old disk population (dashed line), a thick disk component (long-dashed line) and a halo (dotted line).

Using the preliminary color catalog for point sources the observed color distribution of stars brighter than [FORMULA] is compared to model predictions in Fig. 14 over three ranges of magnitude as indicated in each panel. The model computes starcounts in [FORMULA] and I by adopting a series of color-magnitude diagrams appropriate for the disk, thick-disk and halo of our Galaxy. In order to output predicted counts in the natural passbands of the EIS survey, the transformation given by Eqs. (1)-(4) have been used to convert from the EIS magnitudes to the Johnson-Cousins system in such a way that the predicted counts are actually evaluated in the EIS passbands and are convolved using the error model given in Fig. 9. As can be seen from Fig. 5, the number of red ([FORMULA]) standard stars defining the color transformation is very small, so that one might expect possible discrepancies between the observed and predicted counts, particularly for redder colors. One way of overcoming this would be to use synthetic star colors using the system response functions given in paper I. However, for the purposes of describing the usefulness of the data, the current calibration is sufficient. Considering that none of the model parameters have been adjusted to fit the present data, the good agreement of the model to the observed counts in both [FORMULA] and [FORMULA] is remarkable, although some discrepancies can also be readily seen.

[FIGURE] Fig. 14. Color distribution for point-sources for different magnitude intervals as indicated in each panel. Also shown are predictions for the galactic model of Méndez & van Altena (1996).

At the brightest magnitude bin one sees a deficit of red objects relative to the model predictions in both ([FORMULA]) and [FORMULA], especially in the former, which is due to saturation effects. Note that objects with saturated pixels have been discarded from the color catalog.

In the range [FORMULA], the color-counts are known to split into two major peaks, each sampling a different stellar population (Bahcall 1986). The blue peak at [FORMULA] is due to halo stars near the turnoff ([FORMULA]), located at few kpc from the Galactic plane. The red peak at [FORMULA] is due to faint M-dwarf stars from the disk, located at less than 1 kpc from the Sun. Note the small relative offset ([FORMULA] mag) between the observed and predicted location of the red peak. As pointed out above this may be due to, and is consistent with, the departure of the color term from the linear correction adopted for objects with [FORMULA]. Note that the agreement is much better in [FORMULA] for which the contribution from color terms are expected to be negligible.

Traditionally, the observed splitting in the color peaks has been used to determine the local normalization of halo stars in the solar neighborhood. Note in this context the difference in the amplitude of the counts in the blue peak in the magnitude range [FORMULA], which is seen in both [FORMULA] and [FORMULA]. Most photometric surveys at faint magnitudes (e.g., Reid & Majewski 1993) have relied on pencil-beam surveys covering a small fraction of a degree. Therefore, the number of observed objects per bin has been very small, leading to large uncertainties in the derived model parameters. The EIS sample, covering [FORMULA] square degrees, represents a significant improvement and may allow for a better determination of these parameters.

Finally, it is interesting to point out the existence of a population of blue objects, in particular, the suggestion of a peak at [FORMULA] observed at faint magnitudes (20[FORMULA]). This peak does not match the location and the amplitude of the peak predicted by the white dwarf population assumed in the model. Instead the observed blue objects could consist of a mix of white dwarfs, blue horizontal branch stars or perhaps halo field blue stragglers. Further investigation on the nature of these objects seems worthwhile.

The results demonstrate that the stellar color catalog being produced is by and large consistent with model predictions and the observed differences may possibly point to deficiencies in the model which should be further investigated by interested groups. Although primarily driven by other goals, the above discussion shows that the EIS data is also useful for galatic studies.

3.2. Galaxies

In order to evaluate the quality and the depth of the galaxy samples, galaxy counts in the different passbands are shown in Fig. 15 and compared to those determined for patch A and by other authors as indicated in the figure caption. In these comparisons the I magnitudes of Lidman & Peterson (1996) have been shifted by +0.04 mag and those measured by Postman et al. (1996) by -0.43 mag to bring them into the Johnson-Cousins system. A small correction (-0.02 mag) has also been applied to the V counts of Postman et al. . No corrections were made to the Arnouts et al. (1997) data. As can be seen there is a remarkable agreement between the EIS counts and those obtained by other authors. They are also consistent with the counts determined from patch A, down to [FORMULA] and [FORMULA]. As emphasized in Paper I even for single exposures EIS reaches fainter magnitudes than previous data used for cluster searches.

[FIGURE] Fig. 15. EIS patch B galaxy counts (filled squares) in different passbands ([FORMULA], from top to bottom) compared to the counts obtained by: Lidman & Peterson (1996, triangles), Postman et al. (1996, diamonds) and Arnouts et al. (1997) (open squares), as provided by the authors. Also shown are the counts obtained in patch A (stars) for the V and I-band. The counts from other authors have been converted to the Johnson-Cousins system, as described in the text.

The overall uniformity of the EIS galaxy catalogs can be examined using the two-point angular correlation function, [FORMULA]. Indeed, [FORMULA] is a very efficient tool for detecting any kind of artificial patterns (such as a grid with scale comparable to an EMMI frame) or possible gradients in the density over the field (which could result from large-scale gradients of the photometric zero-point). Departures from uniformity should affect the correlation function especially at faint magnitudes.

Fig. 16 shows [FORMULA] obtained for each of the three passbands [FORMULA] and I, using the estimator proposed by Landy & Szalay (1993). The calculation has been done over the area defined above (see Fig. 7). The error bars are [FORMULA] errors calculated from ten bootstrap realizations. The angular correlation function is, in general, well described by a power law [FORMULA] for angular scales extending out to [FORMULA] degrees, with a value of [FORMULA] in the range 0.7-0.8. The absence of any strong feature at the scale of the individual survey frame should be noted. Furthermore, no significant variations of the slope are detected, except at the bright end in all the three passbands. In this case [FORMULA] is somewhat flatter than at fainter magnitudes. A possible explanation is the presence of the nearby cluster (ACO S84) at [FORMULA] located near the center of the patch. To test this hypothesis the correlation function was recomputed by discarding a square region of about 0.2 degrees on the side centered at the nominal position of the cluster. Using the pruned sample yields a steeper correlation function for the patch, consistent with the expected slope of 0.8. These results show the uniformity of the EIS catalogs, once obviously bad frames, selected on the basis of seeing and limiting isophote, are discarded.

[FIGURE] Fig. 16. The angular two-point correlation function calculated for patch B, in the [FORMULA] and I bands as indicated. In each panel the three curves correspond (from top to bottom) to the limiting magnitudes 21, 22, 24 (in B); 20, 22, 24 (in V); 19, 21, 23 (in I). The dotted line represents a power law with a slope of -0.8. The error bars are 1[FORMULA] errors obtained from 10 bootstrap realizations.

The angular correlation function can also be used to verify the consistency of the photometric zero-points determined for patches A and B. This can be done by studying the amplitude of the angular correlation function as a function of limiting magnitude and comparing the results obtained for the two patches. Fig. 17 shows the amplitude of the angular correlation function at a scale of 1 arcmin, [FORMULA], as a function of the limiting magnitude in the different passbands. This amplitude is calculated from the best linear-fits over the range [FORMULA] 10-200 arcsec of [FORMULA] shown in Fig. 16. For V and I one finds good agreement between the results for the two patches especially at the faint end. The differences seen in the bright end are fully accounted for by the presence of the nearby cluster described above. The plot shows the amplitude of the correlation with and without the cluster. As can be seen once the cluster is removed, the amplitude at the bright end decreases and shows a good agreement with the estimate from patch A. Similarly, one finds good agreement with the results obtained by other authors such as: in the B band, Roche et al. (1993) ([FORMULA]) and Jones et al. (1987) ([FORMULA]); in the V band, Woods & Fahlman (1997) (V=24); and in the I band, Postman et al. (1998) ([FORMULA]). The amplitude of the angular correlation function as determined from the EIS galaxy catalogs are consistent with those obtained by various authors over the entire range of magnitude. Note that for [FORMULA] the EIS points lie slightly below those recently computed by Postman et al. (1998).

[FIGURE] Fig. 17. Amplitude of the correlation function measured at 1 arcmin for patch A (open squares), and patch B (full circles) and after removing the nearby S84 cluster (full squares). These results are compared to those from Roche et al. (1993) (big open triangles) and Jones et al. (1987) (small open triangles) in the B band, from Woods & Fahlman (1997) in the V band (open pentagon), and from Postman et al. (1998) in the I band (open circles).

In summary, the above results are further evidence that the EIS galaxy catalogs are uniform within a patch, that the zero-points for the different patches are consistent and are in good agreement with external data.

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© European Southern Observatory (ESO) 1999

Online publication: April 19, 1999
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