Since EIS observations were carried out under varying conditions, it is important to evaluate the degree of homogeneity of the final object catalogs. This can be done by examining, for instance, the number counts as a function of magnitude and comparing with earlier work. To evaluate the variation in the number counts due to the varying observing conditions, the area of patch A covered by both even and odd tiles, comprising 3 square degrees, has been divided into six subregions, each having an area of 0.5 square degrees. Note that these areas cover most of patch A including highly incomplete regions (see Fig. 16). The number counts for each subregion are computed and the mean is shown in Fig. 23, where the error bars correspond to the standard deviation as measured from the observed scatter in the six sub-catalogs. From the figure it can be seen that the difference between the even and odd catalogs is negligible.

In Fig. 24 the galaxy counts derived from the EIS
catalogs are compared to those of Lidman & Peterson (1996) and
Postman et al. (1996). The error bars are computed as above.
There is a remarkable agreement between the EIS galaxy-counts and
those of the other authors. The slope of the EIS counts is found to be
. Also note that the EIS counts extend beyond those of
Postman et al. (1996) even for the counts derived from single
frames. The galaxies have been defined to be objects with a stellarity
index < 0.75 for *I* < 21 and all objects fainter than *I* =
21. At this limit galaxies already outnumber stars by a factor of 3.

Figure 24:
The EIS galaxy counts (filled squares) with error bars
compared to the galaxy counts derived by Lidman & Peterson (1996)
(triangles) and
Postman et al. (1996) (diamond). The data from the other authors have
been converted to the Johnson-Cousins system |

Figure 25:
The EIS star counts for stellarity index 0.75 (filled
squares) and for stellarity index 0.5 (open circles) compared
to the model by Mèndez& van Altena (1996) (solid line) |

As discussed before, the criteria adopted for classifying stars and
galaxies is somewhat arbitrary. While a large value for the stellarity
index is desirable to extract a galaxy catalog as complete as
possible, this may not be the most appropriate choice for extracting
stellar samples. This can be seen in Fig. 25 where
the EIS star-counts are shown for two different choices of the
stellarity index for objects brighter than *I* = 21. For comparison,
the star counts predicted by the galactic model of Méndez & van
Altena (1996) are shown. As can be seen the observed counts agree with
the model for low values of the stellarity index (0.5), while higher
values shows a deficiency of stars at the faint-end.

These preliminary results based on single-frame catalogs indicate that the depth of the survey is close to that originally expected and is sufficiently deep, especially after coaddition, to search for distant clusters of galaxies, one of the main science goals of EIS.

To compute the angular correlation function, a random catalog is created with the same geometry as the EIS catalog. The number of random points has been chosen in order to yield an error less than on the measured amplitude of at arcsec. The estimator used is that described by Landy & Szalay (1993):

(1) |

where *DD*, *DR*, and *RR* are the number of data-data, data-random,
and random-random pairs at a given angular separation .

In Fig. 26, for the even and odd catalogs are compared. The error bars are 1 errors calculated with 10 bootstrap realizations. The angular correlation function is well described by a power-law with (shown by the dotted line) over the entire range of angular scales, extending out to 0.5 degrees. In particular, there is no evidence for any feature related to the scale of the EMMI frame. Similar results are obtained when the angular correlation function is computed from counts-in-cells.

In Fig. 27, the amplitude, , of the correlation
function at a scale of 1 arcsec is shown as a function of the limiting
magnitude. The amplitude was computed from the best linear-fits over
the range 10-200 arcsec of the , shown in
Fig. 26, imposing a constant slope of . For
comparison, the power-law , originally
determined by Brainerd et al. (1996) in the *R*-band is also shown
corrected for the mean color difference (*R*-*I*) = 0.6
(Fukugita et al. 1995). The agreement with previous results
is excellent and demonstrates the good quality of the EIS catalogs,
even for a patch observed under less than ideal conditions.

Figure 27:
Amplitude of the correlation function at 1 arcsec
calculated from the best fits of Fig. 26 as a function of limiting
magnitude. The dotted line is from from Brainerd et al. (1996) |

In order to evaluate the contribution of large-scale clustering to the variance in the galaxy counts computed in the previous section, the correlation function has been computed for the sub-areas also used in estimating the number counts. This offers the opportunity to compare the amplitude of the cosmic variance to the bootstrap errors used above. The results are shown in Fig. 28 where the mean value over the sub-areas of for each magnitude limit is presented. The error bars, that correspond to the rms of the six sub-areas, are consistent with those found from the bootstrap technique.

The results show that for galaxies brighter than *I* = 20, all frames
fall within the 3 level, except four, and the varying
observing conditions do not seem to affect the completeness of these
bright object catalogs. Going to fainter magnitudes the fraction of frames
with low number counts increases. This can be used to estimate the
size of the homogeneous part of the patch at a given limiting magnitude
as shown in Fig. 30. From the figure, it can be seen that
for and the useful area for analysis
corresponds to 90% and 75%, respectively. Most of the
rejected tiles are located in the region and
(Sect. 6.2).

Figure 30:
Fraction of rejected tiles, corresponding to counts lower
than 3 from the mean in Fig. 29, as a
function of the limiting magnitudes |

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