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Astron. Astrophys. 345, 448-460 (1999)
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
( ).
![[FIGURE]](img90.gif) |
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).
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Using the preliminary color catalog for point sources the observed
color distribution of stars brighter than
is compared to model predictions in
Fig. 14 over three ranges of magnitude as indicated in each panel. The
model computes starcounts in 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 ( )
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 and
is remarkable, although some
discrepancies can also be readily seen.
![[FIGURE]](img94.gif) |
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).
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At the brightest magnitude bin one sees a deficit of red objects
relative to the model predictions in both
( ) and
, 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 , the color-counts
are known to split into two major peaks, each sampling a different
stellar population (Bahcall 1986). The blue peak at
is due to halo stars near the
turnoff ( ), located at few kpc from
the Galactic plane. The red peak at
is due to faint M-dwarf stars from the disk, located at less than
1 kpc from the Sun. Note the small relative offset
( 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
. Note that the agreement is much
better in 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
, which is seen in both
and
. 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 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
observed at faint magnitudes
(20 ). 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
and
. As emphasized in Paper I even
for single exposures EIS reaches fainter magnitudes than previous data
used for cluster searches.
![[FIGURE]](img110.gif) |
Fig. 15. EIS patch B galaxy counts (filled squares) in different passbands ( , 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.
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The overall uniformity of the EIS galaxy catalogs can be examined
using the two-point angular correlation function,
. Indeed,
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 obtained for each
of the three passbands 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 errors calculated
from ten bootstrap realizations. The angular correlation function is,
in general, well described by a power law
for angular scales extending out to
degrees, with a value of
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 is somewhat flatter than at
fainter magnitudes. A possible explanation is the presence of the
nearby cluster (ACO S84) at 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]](img122.gif) |
Fig. 16. The angular two-point correlation function calculated for patch B, in the 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 errors obtained from 10 bootstrap realizations.
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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,
, as a function of the limiting
magnitude in the different passbands. This amplitude is calculated
from the best linear-fits over the range
10-200 arcsec of
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)
( ) and Jones et al. (1987)
( ); in the V band, Woods &
Fahlman (1997) (V=24); and in the I band, Postman et al. (1998)
( ). 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
the EIS points lie slightly below those recently computed by Postman
et al. (1998).
![[FIGURE]](img129.gif) |
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).
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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.
© European Southern Observatory (ESO) 1999
Online publication: April 19, 1999
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