The ENACS galaxy samples were designed to constitute magnitude-limited subsets of the general galaxy population in the areas defined by the Optopus plates (see Table 5 for the centres of these circular, 31'-diameter, areas). In Sect. 3.1 (click here) we found that the ENACS samples contain a few galaxies (for which we measured an ENACS redshift, and therefore presumed real) which are not in the COSMOS catalogue. Apart from this fairly minor effect, the ENACS galaxy samples are indeed subsets of the COSMOS catalogue. A question which may be important for some types of analysis, is whether the ENACS galaxy samples, which were selected on magnitude, form unbiased subsets of the COSMOS catalogue as far as position is concerned. In other words: does the surface density of the ENACS galaxies more or less follow that of the COSMOS galaxies within the areas covered by the Optopus plates.
To investigate this question we have applied a 2-D Kolmogorov-Smirnov
test (Fasano & Franceschini 1987) to the ENACS and COSMOS
galaxy distributions in the solid angle of the ENACS survey (either a single
Optopus area, or the union of several Optopus areas). In order to make
the test meaningful we have applied it to subsamples of both the ENACS
and COSMOS catalogues complete to magnitude limits, and
that differ by the average value of < bj-R25
> for which we took 1.5. For each cluster, we applied the test for
five pairs of (
,
), with
=
16.5(0.5)18.5. Clearly, if
becomes fainter than the
actual magnitude limit of the ENACS data in a given cluster (see
Sect. 4.2 (click here)), the ENACS galaxies represent a progressively
smaller fraction of the COSMOS sample, and there will be a natural
tendency for the two projected distributions to become different, if
they were not so already at brighter limits.
We have analyzed for each cluster the KS-probabilities at the five different magnitude limits, and we conclude that for almost all clusters, the galaxy distributions in the ENACS and COSMOS catalogues are not different at a confidence level of more than 95%. There are only three clusters, viz. A3705, A3809 and A3825, for which it appears that the ENACS galaxy distribution differs from that of the COSMOS galaxies at more than 95% confidence level. In all three cases, inspection of contour maps of galaxy surface density visually supports this conclusion: the ENACS galaxies are relatively abundant at the edges of the concentrations present in the COSMOS surface density. In addition, there is one cluster, A3822, for which there is marginal evidence for a biased selection. However, in that case there is a secondary concentration in the COSMOS data which is not present in the distribution of the ENACS galaxies. For contour maps of projected galaxy density based on the COSMOS catalogue, we refer the reader to Adami et al. (1998).
In Fig. 1 (click here) we have given the overall magnitude distribution
of the galaxies for which the ENACS has yielded a redshift. This
distribution shows that on average the redshift catalogues start to
become incomplete below 17, but that the fraction of
ENACS galaxies with R25 between 17 and 19 is non-negligible. The
decrease in the number of galaxies beyond
17 is the
result of two factors. First, the galaxy catalogues that we prepared
have (fairly sharp) magnitude cut-offs at R25 between about 17.5
and 19.0. Second, our success in obtaining redshifts decreases quite
strongly for R25
17.
In Fig. 4 (click here) we show as a function of R25, for the ENACS
as a whole, the ratio of the number of galaxies for which the ENACS
observations have yielded a redshift and the total number of galaxies
that we observed in the ENACS. In other words: Fig. 4 (click here) shows
our success-rate of obtaining a redshift as a function of magnitude.
Figure 4 (click here) therefore quantifies our discussion in Sect. 5.5 of
Paper I, where we already mentioned that our maximum success-rate was
about 80%. The strong decrease for R25 17 is due to the
smaller S/N-ratio of the absorption lines in the spectra of the
fainter galaxies. The fact that we do not score 100% for the
brightest galaxies must be due to the less-than-ideal match between
the diameter of the Optopus fibres and the surface brightness
distribution of some of the brightest galaxies, which can have a
relatively low central surface brightness.
Figure 4: The ratio of the number of galaxies for which the Optopus
observations have yielded a redshift and the total number of
galaxies observed in the ENACS, as a function of R25
For some types of discussion it may be necessary to know, as a function of magnitude, the fraction of COSMOS galaxies (i.e. cluster and field galaxies) for which we obtained an ENACS redshift. This fraction is shown graphically in Fig. 5 (click here), as a function of R25, for all 73 clusters for which this fraction could be meaningfully determined. For 4 clusters no distributions are given because either the number of ENACS galaxies is very small (A2502 and A3144), or the overlap between ENACS and COSMOS data is too limited (A0543 and A2915). Rather than show the fraction itself, we give the magnitude distributions of ENACS and COSMOS galaxies, both normalized to the number of ENACS galaxies in the most populated 0.5-mag bin. The two magnitude distributions refer to the same solid angle, i.e. the overlap "area" between the two surveys.
Figure 5: The normalized magnitude distributions of COSMOS (line) and
ENACS (circles) galaxies in the overlap areas between the
COSMOS and ENACS catalogues, for 73 clusters (ACO number is
given below frame; number of ENACS galaxies - N - shown in
frame). Magnitudes are on the R25 scale (COSMOS bj
magnitudes have been corrected for the average
bj-R25 colour). Normalization is wrt the most
populated 0.5-mag bin in the distribution for the ENACS
galaxies
In general, the ENACS magnitude distribution coincides with, or falls below, that based on COSMOS, as expected. However, in some cases, the ENACS distribution exceeds that based on COSMOS, particularly at brighter magnitudes. One factor that may contribute to this is that some of the bright ENACS galaxies are not in the COSMOS catalogue (see Sect. 3.1 (click here)). Another reason for this small inconsistency which appears only occasionally, is that the two distributions are on different magnitude scales. The COSMOS distributions have been brought to the R25 scale by applying a correction for the average bj-R25 colour for the entire ENACS survey.
Figure 5 (click here) shows that, with one or two exceptions, the ENACS
galaxy samples are essentially complete, magnitude-limited, subsets of
the COSMOS samples up to an R25 of 16.5 0.5 (within the ENACS
apertures!). The fainter galaxies can, of course, be used in
discussions for which the completeness of the galaxy sample is not
important.
For several types of analysis it may be useful to have analytic expressions for the cut-offs towards faint magnitudes and higher redshifts for the ENACS as a whole. For the analysis of these cut-off functions we have restricted ourselves to the galaxies that are not in the main system, i.e. those in the field and in secondary systems. This avoids possible complications due to the rather uneven redshift distribution of galaxies in the rich systems. For reasons that are not important here, the analysis was done on a representative subset of 65 ENACS clusters, with a total of 681 "field" galaxies. The distribution of those 681 galaxies with respect to apparent (R25) magnitude and redshift is shown in the upper lefthand panel of Fig. 6 (click here).
We assume the following model when trying to reproduce this observed
distribution:
in which is the unbiased distribution for a
constant luminosity function. In other words: we assume that there are
two independent cut-off functions, S1(m) which describes the
magnitude cut-off in the galaxy sample for which we attempted
spectroscopy and S2(v) which describes the succes-rate of obtaining
a redshift as a function of velocity.
In the upper righthand panel of Fig. 6 (click here) we show a predicted
distribution, calculated without magnitude
or redshift cut-off, for a sample of 681 galaxies using a Schechter
luminosity function with M*R = -22.5 and
= -1.25, and
using
, to transform from absolute to
apparent magnitude. Clearly, this prediction is very different from
the observed distribution.
Figure 6: The distribution of the galaxies that are not in the main
system (i.e. in the "field") wrt to magnitude, R25,
and redshift. The upper lefthand panel shows the observed
distribution for 681 galaxies in 65 clusters. The upper
righthand panel gives the result of a simulation for the
same number of galaxies, without cut-offs in magnitude or
redshift. The lower lefthand panel also results from a
simulation, with the magnitude cut-off described in the
text, but without redshift cut-off. The lower righthand
panel shows the result of a simulation with the magnitude
and redshift cut-off functions described in the text
The introduction of a magnitude cut-off of the form
produces the distribution in the lower lefthand panel, which has more
or less the correct total magnitude distribution. However, the total
redshift distribution extends too much beyond 40 000 km/s.
Finally, the application of a redshift cut-off of the form
yields the distribution shown in the lower righthand panel. Note that
we do not pretend that this is the best description one may
give. However, we have chosen the functional forms of, and the
parameters in the cut-off functions not just by looking at
Fig. 6 (click here). Instead, we have tried to reproduce as closely as
possible the observed redshift distributions in several rather narrow
magnitude intervals. Short of introducing a possible dependence of
e.g. S2(v) on m etc., we think the selection functions given here
provide a sufficiently accurate description of the overall selection
functions in the ENACS as a whole (but these may not be
necessarily correct for individual clusters!).
That the selection functions given here, on the basis of the galaxies
in the "field" are at least reasonable is also supported by the
following evidence. For the galaxies in the clusters with v < 30000
km/s, only S1(m) is relevant. Using again a Schechter luminosity
function, with M*R = -22.5 and = -1.25, we predict
that the average number of observable galaxies in a cluster depends on
the redshift of the cluster as z-1. This is consistent with what
we find for the main systems in ENACS (see e.g. Paper I).