## 4. The reality of the galaxy setsIn this section we assign likelihoods to the 19 sets of galaxies which have been identified in the previous section. If is the incompleteness of our redshift sample in the magnitude interval (see Fig. 8), then the redshift distribution reads where is the volume element at
the redshift
In Fig. 9, we plot , computed
according to Eq. (1), along with the observed
We first convert the CFRS magnitudes to the system (see Lilly et al. 1995). We then extract 50000 galaxies from the CFRS, with a bootstrap sampling, adopting the magnitude distribution of our sample (see Fig. 7). A Kolmogorov-Smirnov test shows that the bootstrapped CFRS and our data-set have similar redshift distributions. This is expected since magnitude selection is the main process leading to the inclusion of galaxies in the sample. We extract random subsamples of 11 galaxies from the bootstrapped CFRS reference sample (11 is the mean number of galaxies with redshift in our EIS cluster fields). Using the same procedure described in Sect. 3, we identify sets of galaxies within these subsamples, and compute their probabilities relative to the uniform redshift distribution given by Eq. (1). In this way we construct a distribution of probabilities to detect a real system within a galaxy sample which includes large-scale clustering, but not galaxy clusters. We finally obtain the likelihoods of the 19 observed sets, by comparing their original -based probabilities to the distribution of probabilities for the random sets. These 19 likelihoods are listed in Table 3. We find that four of our 19 sets have a likelihood %; all of them have at least three galaxy members. The four sets are flagged in the last column of Table 3. We refer to these four sets as the `real systems' hereafter. As expected, many of the sets with a significant overdensity with respect to the uniform redshift distribution are no longer significant when compared to a redshift distribution which includes the large scale clustering. Our results are robust against modifications of the adopted LF (we
change by
, and
by
mag), and of the galaxy-type for which the evolutionary- and
K-corrections are computed. Furthermore, we verify that varying
cosmological parameters (h © European Southern Observatory (ESO) 2000 Online publication: August 23, 2000 |