11 Summary and conclusions

The main aim of the construction of this X-ray flux-limited galaxy cluster sample is its application to measure the large-scale structure of the Universe and to obtain constraints on cosmological models. To this end the sample has to be very homogenous in all its selection parameters in particular in its coverage of the sky. The unavoidable inhomogeneities have to be well quantified and modeled. Here, we described the construction of the cluster sample and the selection function (shown in Fig. 22) and have given the first demonstration that we have achieved our initial goal.

The primary candidate sample has been constructed from the refined second analysis of RASS II and we have used a starting list of detections that includes an overabundance of sources almost down to the $2\sigma$detection limit. To ensure that we do not introduce a bias against the flux measurement of extended sources we have reanalysed the sample with the GCA method which accounts for this difficulty (see Böhringer et al. 2000 for checks of this method with deeper X-ray observations). Independent checks for X-ray cluster sources which might have been missed by the source detection in the standard analysis of the RASS by means of the Abell catalogues have not shown a single case of a failed detection.

The second selection is based on a correlation with the galaxy distribution in the COSMOS data base. Alternatively we could have used a combined means of identification of the X-ray sources by correlating also with other galaxy or cluster catalogues to enhance the findings of clusters. The selection based on only one criterion was deliberately chosen because it is the best means to guarantee a fairly homogeneous sampling and to have some control on possible selection effects which can be tested (e.g. we did not find a signature in the correlation of the cluster density with the quality of the plate material to be shown in a following paper in this series). We have actually found an additional small fraction ($\sim$2%) of clusters which would fulfill the X-ray criteria of the sample as described in Sect. 8, but they are not part of the REFLEX sample to preserve the homogeneity of the present cluster catalogue. The second important point in the optical selection is the achievement of a high completeness. The smaller the missing fraction, the smaller is the imprint of the optical selection criteria on the overall sample. With an estimated completeness in excess of 90% the imprint should be negligible resulting in an effectively X-ray selected sample of galaxy clusters. This is another important feature of the catalogue since in the following application we will build on the close correlation between X-ray luminosity and cluster mass. The high estimated completeness of the catalogue is to a large part the result of a substantial oversampling of cluster candidates in the correlation process as described in Sects. 5 and 6. (At present we like to limit the statement about the high completeness of the sample to the luminosity range $L_{\rm X} \ge 10^{43}$ ergs^-1and redshifts $z \le 0.3$ until these regimes are explored with further studies.) The price to be paid for this was the large contamination fraction by non-cluster sources of about 30-40%, which required a comprehensive follow-up observation programme.

The following identification work, necessary to remove this substantial contamination has to be very rigorous not to introduce an uncontrolled bias at this step. Therefore the strategy was adopted that either a clear identification could be achieved or in the case of a classification by selection in parameter space at least two strong selection parameters (failure rate not larger than 10% for each) were required to rule out a cluster identification.

All these measures taken together are the base of the quality of the present sample and its high completeness. The improvement that has been achieved over previous samples can for example be illustrated by a comparison with the northern BCS and extended BCS samples (Ebeling et al. 1998, 2000a). At the flux-limit of BCS, the mean sky surface density of REFLEX clusters is 62.3 ster^-1 compared to 48.5 ster^-1 for BCS (78% of the REFLEX value). At the REFLEX flux-limit the two parameters are 101.3 ster^-1 (REFLEX) and 70.5 ster^-1 (extented BCS, 69.5% of the REFLEX value).

There is still the question of sample contamination. It is for example difficult to rule out in each case that the cluster contains an AGN which is producing the majority of the measured X-ray flux. For this case the standard optical identification, to secure several coincident galaxy redshifts to prove the presence of a cluster, does not help to resolve the situation. The high fraction of true source extents that could be established by our reanalysis and the further tests based on the statistics of the spectral parameter distribution (Sect. 10) show that this is not a serious problem compromising the statistical use of the sample.

We conclude that we have reached the aim of the project to establish a cluster catalogue which can be used for a variety of cosmological studies. Part of these are described in a series of papers already submitted or in preparation covering further tests and the construction of the correlation function (Collins et al. 2000), the power spectrum of the cluster density distribution (Schuecker et al. 2000) the clustering on very large scales (Guzzo et al. 2000), and the X-ray luminosity function (Böhringer et al. 2001a).

Acknowledgements

We thank Joachim Trümper and the ROSAT team providing the RASS data fields and the EXSAS software, Rudolf Dümmler, Harald Ebeling, Andrew Fabian, Herbert Gursky, Silvano Molendi, Marguerite Pierre, Thomas Reiprich, Giampaolo Vettolani, Waltraut Seitter, and Gianni Zamorani for their help in the optical follow-up observations at ESO and for their work in the early phase of the project, and Kathy Romer for providing some unpublished redshifts. We also thank Daryl Yentis and the team at NRL for providing some of the software used in connection with the analysis of the COSMOS data. We have in particular benefited from the use of the COSMOS digitized optical survey of the southern sky, operated by the Royal Observatory Edinburgh. This work has made use of the SIMBAD database operated at CDS, Strasbourg, and of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology under contract with NASA. P. S. acknowledges the support by the Verbundforschung under the grant No.50OR970835, H. B. the Verbundforschung under the grand No.50OR93065. L. G. acknowledges financial support by A.S.I. We thank the anonymous referee for helpful comments on the presentation.