Byproducts of deep imaging surveys at different galactic latitudes are
stellar samples in different directions of our galaxy at very faint
magnitudes
(Shanks et al. 1980;
Kron 1980; Infante 1986;
Metcalfe et al. 1991).
In Figs. 10 (click here), 11 (click here),
we show for our stellar sample the
different colour histograms B-R, B-V,
for three magnitude ranges in V. Note that
the quasars are included in this
sample. Also, at bright magnitudes (V < 17),
a large fraction of stars are saturated,
thus raising the uncertainty in the
corresponding colours.
At faint magnitudes (
), two stellar populations can be seen.
Brightward of V < 18, one broad blue peak is present near 
.
Faintward of this magnitude a second peak appears in the red part near 
.
These results agree well with the other existing data (see Table 9.1 (click here) above).
The red peak is interpreted
as being nearby M stars belonging to the disk population.
The blue sequence
is interpreted as being stars belonging to the galactic halo
(Robin & Crézé 1986).
These observations are listed in Table 9.1 (click here) for 
.
The second column gives the
colours used by the author, the third and fourth columns show the colours of
the two peaks in this
initial colour and the subsequent columns show the transformed position of
the two peaks into the standard system Johnson-Cousins.
The transformation equations are given in the corresponding publications, and for
the Kron (1980) data we added the transformation equations given by
Majewski (1992) as (J-F)=0.738(B-R) -0.02.
Table 9.1 (click here) shows that our stellar color distributions are in good agreement with
those resulting from other faint CCD surveys.
Table 4: Stellar colour peak for 
Figure 10: B-R colour histogram for the stars selected in three different
ranges of V magnitude as specified within the graphs
Figure 11: same as Fig. 10 (click here) for B-V colour
a) Counts and slopes
We present the differential galaxy counts based on the total 0.4 square degree
of the survey in the R, V and B bands to limiting magnitudes of 23.5, 24.0 and
24.5 respectively. These limiting magnitudes are defined as the last magnitude
bin (
mag) before the turn-off in the number counts.
To these limits the galaxy catalogs contain about 13000, 12150 and 9500 objects
in the R, V and B bands respectively.
Note that there is no star-galaxy separation for 
and no correction for stellar contamination is done because the expected number
of stars at this galactic latitude (
) is lower than
4% (corresponding to an offset of 
of the logarithmic number
counts).
In Fig. 12 (click here), we show the differential galaxy
number counts per square degree in 0.5 magnitude bins.
The upper graphs show for each band the superimposed galaxy counts for all
individual CCD fields. The dots displaced to the right of the columns of galaxy
counts are the median counts offset by 0.2 mag for clarity.
The error bars measure the 1
rms field-to-field scatter.
The field-to-field scatter is 
in the R band between
21 < R < 23.5, 
in the V band between
21 < V < 24. and 
in the B band between 22 < B < 24.5.
These rms dispersions significantly exceed the expected Poisson variations in
because of galaxy-galaxy clustering
(Arnouts & de Lapparent 1997).
In the bright part, the large values of the scatter are essentially due to the
small number of bright galaxies per CCD frame.
The lower graphs give the median number counts.
In these graphs the error bars are given as:
The differential number counts (in deg
0.5 mag
) are fitted by a
power law in the same magnitude range as
Metcalfe et al. (1991) for the R and
B magnitudes.
The exponent of the fit in the three bands are measured by a least squares
fit in the 
plots.
These fits are shown by solid lines in the lower graphs of
Fig. 12 (click here) and are parameterized as follow:
for 20.5 
24.5
for 20.0 
24.0
for 
.
In Table 9.2.1 (click here), we summarize the results of previous CCD surveys on galaxy
counts in the visible bands.
Our slopes are in good agreement with the other works.
In Fig. 12, we detect two magnitude bins between 
where the density systematically decreases and this effect is seen in
the three bands (in the intervals 
and
). First of all, to see if this gap was
caused by inhomogeneities in the projected distributions, we examined
the angular distribution (RA, Dec) in different magnitude intervals, but
no particular feature in the clustering of the projected distributions was
visually detected.
This investigation will be pursued quantitatively in a forthcoming study of the
two-point angular
correlation function for these data
(Arnouts & de Lapparent 1997).
Figure 12: Galaxy number-magnitude counts by square degree per 0.5 mag
interval in the B (left), V (center) and R (right) bands.
The upper graph shows the counts for each observed CCD field and the median values
with error bars given as the 
field-to-field fluctuation.
The lower graph shows the median number count value in each bin.
The error bars are given by Eq. (13).
The solid line is the estimated slope by least squares fit.
a) Galaxy counts in B band;
b) Galaxy counts in V band;
c) Galaxy counts in R band.
Table 5: The galaxy number count exponents for several CCD photometric surveys
b) Counts comparison
In Figs. 13 (click here)-15 (click here) we compare the differential number
counts from our data with those from the other CCD surveys.
For the data given in other systems than the standard Johnson-Cousins system, we
apply the different transformations provided by the authors.
For the data from Metcalfe we apply a transformation only for the B band as
.
For the data from Tyson, the
transformation equations are not given. By default we use the transformations
into the photographic system (
) given in
Metcalfe et al. (1991) combined
with the transformations from photographic bands to the standard system given by
Shanks et al. (1984).
We obtain the approximate transformations defined as
and 
.
For the data from Driver no transformations are done because the color terms
are small.
Except for Metcalfe et al. (1991),
these other works are significantly deeper
than our data, and the number counts at very faint magnitudes
(
and 
) are corrected for confusion.
Figures 13 (click here), 14 (click here), 15 (click here) show that our counts in
B and R are in
good agreement with
the results from Metcalfe et al. (1991) in both the slope and the amplitude of the
logarithmic number counts in the red band but a small shift in the blue band
exists as we will see below in the discussion of the colour distributions
(Sect. 9.2.2).
The R number counts of our survey are significantly
higher (
) than those from Tyson in the common range of magnitudes.
This difference has been interpreted by Tyson (1988) as
being due to the a priori choice of fields devoid of bright galaxies, and
Metcalfe et al. (1991) suggest that this difference can originate from the use
of isophotal magnitudes by Tyson (1988) in contrast to the "total''
magnitudes used by the others authors.
The data of Driver et al. (1994) also show a small deficit in galaxy number
counts compared to ours at the 
level. Driver specifies that the
Hitchhiker data suffers from a calibration uncertainty, so a small shift
in zero-point could explain the deficit in the three visible bands but this
effect does not alter the slopes of the counts.
In the data from
Smail et al. (1995), the plotted points correspond to the
average of two single fields. Their V counts are in very good agreement with ours
but their R counts show a significant number excess by a factor of about 1.2
compared with all the others authors below R<24.
Finally we compare our deep counts with the recent bright galaxy counts in B
and R
bands performed by
Bertin & Dennefeld (1997). These counts are in good agreement with
ours and we use them to normalize the non-evolving model kindly provided by
M. Fioc.
Bertin & Dennefeld (1997) suggest:
in the B band (estimated at 
),
in R
band and
we adopt an intermediate value of 
in the V band (
is defined by 
). The other parameters of the luminosity function come from
Guiderdoni &
Rocca-Volmerange (1990): 
and 
.
Figure 13: Comparison with others published galaxy number
counts transformed into the B Johnson filter. The error bars for our data show
the 
estimated in Eq. (13). The dashed line shows the differential number
counts expected for a non evolving model using a 
normalized to the
bright galaxy number counts from
Bertin & Dennefeld (1997) as described in the
text. a) Comparison with others deep CCD galaxy number counts.
b) Comparison with bright photographic galaxy number counts from
Bertin & Dennefeld (1997)
Figure 14: Same as Fig. 13 (click here) in the V Johnson filter
Figure 15: Same as Fig. 13 (click here) in the R Cousins filter.
a) Comparison with others deep CCD galaxy number counts.
b) Comparison with bright photographic galaxy number counts from
Bertin
& Dennefeld (1997)
In this section, we present the first results of the colour distributions
for our galaxy catalogue in the B, V and R bands.
As shown in Fig. 7 (click here), there is a large
fraction of objects identified
in all 3 filters for B< 24 (
of objects).
In the following, we restrict the sample to these 7500 common objects.
In Figs. 16-18 we plot the mean
observed colours B-R, B-V, V-R as a function of magnitude for the
7500-object sample.
The solid lines draw the 1
envelope of the measured colours,
being the rms dispersion of the colour histogram within the
corresponding magnitude bin. This
envelope is larger in B-R than in B-V and V-R because the expected colour
in B-R varies in a large range for the different galaxy types.
The B-R and B-V colours clearly show a tendency to become bluer at fainter
magnitude as first observed by Kron
(1980) and subsequently confirmed by several
groups (Tyson 1988; Metcalfe et al. 1991, 1995).
At 
, the
typical mean colour is 
and a
blueing shift to 
is seen between 22 < V < 24.
The same tendency is visible in the B-V colour distribution.
It decreases from 
at V < 22 to 
at V = 24.
Note that in Fig. 16 (click here) , at B > 24 mag, the completeness level drops
to 
(see Fig. 7 (click here)) and the mean colours (B-R) and (B-V)
become redder due to the incompleteness in the R
and V bands where only the brighter objects are identified and contribute
to shift the colour toward redder colours.
In contrast, the (V-R) colours in
Figs. 16-18
show no evidence of colour evolution with magnitude up to 
.
The same stability is obtained by Driver et al. (1994).
In addition, we compare our observed mean colours B-R with those
from Metcalfe et al. (1991, 1995) and our mean V-R colours with those of
Smail et al. (1995).
Metcalfe et al's B-R colours are systematically 0.1 mag redder than
ours.
Half of this shift is expected due to reddening in the fields of
Metcalfe et al. (Metcalfe 1995).
Comparison with the V-R colours of Smail also show a small offset, but
the restricted overlap in the magnitude ranges covered does not allow us to
draw any firm conclusions about the agreement between the data sets.
Figure 16: Galaxy mean colours as a function of 0.5 bin of B magnitude.
The solid lines represent the 1
envelope of the measured colours.
The upper left graph shows the mean B-R from our data (filled circles) and
from the data of Metcalfe et al. (1991, 1995) (crosses). The error bars give
the quadratic errors in the magnitudes obtained from the simulations
Figure 17: same as Fig. 16 (click here) for V magnitude
Figure 18: same as Fig. 16 (click here) for R magnitude.
The upper left graph shows the mean B-R from our data (filled circles) and
from the data of Metcalfe et al. (1991, 1995)
(crosses). The lower graph compares
the mean V-R from our data (filled circles) with those from
Smail et al.
(1995) (crosses)