1 Introduction

Clusters of galaxies as the largest well-defined building blocks of our Universe are ideal probes for the study of the cosmic large-scale structure. Statistical measures of the galaxy cluster population like the cluster mass function (e.g. Press & Schechter 1974; Kaiser 1986; Henry & Arnaud 1991; Böhringer & Wiedenmann 1992; White et al. 1993; Bahcall & Cen 1992; Oukbir & Blanchard 1992, 1997; Eke et al. 1996; Viana & Liddle 1996; Borgani et al. 1999), functions describing the spatial distribution as the two-point-correlation function (e.g. Bahcall & Soneira 1983; Klypin & Kopilev 1983; Bahcall 1988; Lahav et al. 1989; Nichol et al. 1992; Dalton et al. 1994; Romer et al. 1994; Abadi et al. 1998; Borgani et al. 1999; Moscardini et al. 2000; Collins et al. 2000, Paper II in this series) and the density fluctuation power spectrum (e.g. Peacock & West 1992; Einasto et al. 1997; Retzlaff et al. 1998; Tadros et al. 1998; Miller & Batuski 2000; Schuecker et al. 2000, Paper III in this series), can place very important constraints on the characteristic measures of the matter density distribution throughout the Universe and its evolution as a function of time. This is due to the fact that the formation of galaxy clusters is tightly linked to the formation of the large scale structure in our Universe as a whole. That clusters are indeed good tracers of the large-scale structure is discussed and demonstrated further in a following papers by Schuecker et al. (2000). The crucial step in any of these studies is the careful primary selection of the galaxy cluster sample to be used for the cosmological investigation. Ideally one would like to select the clusters by their mass, thus defining the sample by all clusters above a certain mass limit. This parameter is also the most direct parameters predicted by analytical cosmological models (e.g. Press-Schechter 1974 type models) or by N-body simulations (e.g. Frenk et al. 1990; Cen & Ostriker 1994; Kofman et al. 1996; Bryan & Norman 1998; Thomas et al. 1998; Frenk et al. 1999). The cluster mass is not easily and directly obtained from observations, however. Thus one has to resort to observable criteria, which should be as closely linked to the mass of the clusters as possible. Since galaxy clusters were first discovered by their galaxy density enhancements, a galaxy richness criterion was first used to define and select clusters of galaxies. The first large and very widely used compilation was that of Abell (1958) and Corwin & Olowin (Abell et al. 1989) whose selection criteria were fixed to a minimal galaxy number density within a metric radius of 3 h₅₀^-1 Mpc and a defined magnitude interval. This catalogue was compiled by eye inspection of the Palomar Sky Survey Plates and subsequently of UK Schmidt survey plates. Another comprehensive cluster catalogue was compiled visually by Zwicky and collaborators (Zwicky et al. 1961-68) with a significantly different cluster definition. Later, similar cluster catalogues were constructed based on machine work using digitized data from scans of the optical plates (by COSMOS, see Heydon-Dumbleton et al. 1989; Lumbsden et al. 1992 and APM; see Maddox et al. 1990; Dalton et al. 1997) using more objective criteria. Further improvement in the optical cluster searches was achieved by using multicolor CCD surveys and matched filter techniques (e.g. Postman et al. 1996; Olsen et al. 1999). But it is still very difficult and uncertain to assign a mass to a cluster with a given observed richness without comprehensive redshift data. One of the main problems in assigning a richness to a galaxy cluster in the optical is the fact that the cluster is seen against a background galaxy distribution which is far from being homogeneous but shows structure on all scales. The latter effect is clearly shown by the autocorrelation analysis of the two-dimensional projected galaxy distribution on the sky. It is therefore difficult to determine a background-subtracted galaxy number of a cluster in a unique fashion. Also, the so-called projection effects, in which several galaxy groups or a filamentary structure in the line of sight can mimic a compact rich cluster, are basically a result of this inhomogeneous matter distribution (e.g. van Haarlem 1997). The possibility of detecting galaxy clusters in X-rays has since been recognized as a way to improve the unambiguity of the detection. The X-ray emission observed in clusters originates from the thermal emission of hot intracluster gas (e.g. Sarazin 1986) which is distributed smoothly throughout the cluster. The plasma is bound by the gravitational potential well of the clusters and fills the potential approximately in a hydrostatic fashion. Therefore the plasma emission is a very good tracer of the cluster's gravitational potential. Even though the plasma is very tenuous, the large volume makes galaxy clusters the most luminous X-ray sources besides AGN. In addition the thermal emission for the typical intracluster plasma temperatures of several keV has the spectral maximum in the soft X-ray band where the available X-ray telescopes are most effective. This makes galaxy clusters readily detectable out to large distances with present X-ray telescopes. However, the main advantage of the X-ray detection is the fact that the X-ray luminosity is closely correlated to the cluster mass (Reiprich & Böhringer 1999), with a dispersion of about 50% in the determination of the mass for a given X-ray luminosity (Reiprich & Böhringer, in preparation). Thus, in summary X-ray selection provides the following positive features:

$\circ$ An effective selection by mass (with a known dispersion which can be taken into account in any corresponding modeling). $\circ$ The X-ray background originates mostly from distant point sources which are very homogeneously distributed (e.g. Soltan & Hasinger 1994). Therefore the X-ray background is very much easier to subtract from the cluster emission than the optical galaxy background distribution. $\circ$ The X-ray surface brightness is much more concentrated towards the cluster centre as compared to the galaxy distribution. Therefore the effect of overlaps along the line of sight is minimized. $\circ$ For an X-ray flux-limited survey the survey volume as a function of X-ray luminosity can exactly be calculated (e.g. for the construction of the X-ray luminosity or mass function).

The construction of statistically complete samples of X-ray clusters started with the completion of the first all-sky X-ray surveys by the HEAO-1 and ARIEL V satellites (Piccinotti et al. 1982; Kowalski et al. 1984). With additional observations from EINSTEIN and EXOSAT a cluster sample of the $\sim$50 X-ray brightest objects with more detailed X-ray data was compiled (Lahav et al. 1989; Edge et al. 1990) and with the analysis of deeper EINSTEIN observations the first deep X-ray cluster survey, within the EMSS, has been obtained (Gioia et al. 1990; Henry et al. 1992). The latter survey allowed in particular to address the question of the evolution of cluster abundance with redshift (e.g. Henry et al. 1992; Nichol et al. 1997). The ROSAT All-Sky Survey (RASS), the first X-ray all-sky survey conducted with an X-ray telescope (Trümper 1992, 1993) provides an ideal basis for the construction of a large X-ray cluster sample for cosmological studies. Previous cluster surveys based on the RASS include: Romer et al. (1994); Pierre et al. (1994); Burns et al. (1996); Ebeling et al. (1996, 1998, 2000a, 2000b); De Grandi (1999); Henry et al. (1997); Ledlow et al. (1999); Böhringer et al. (2000); and Cruddace et al. (2000). Two of these surveys are pilot projects to REFLEX concentrating on the South Galactic Pole and the Hydra regions with results reported in Romer et al. (1994, see also Cruddace 2001) and Pierre et al. (1994), respectively. The sample described by De Grandi et al. (1999) was compiled from an earlier version of the current cluster sample based on X-ray data from the first processing of the RASS and a significantly shallower correlation with the COSMOS data base as well as correlations with a variety of optical cluster catalogues. It constitutes a subsample of the present cluster sample comprising 130 clusters at a flux limit of 3-4 10^-12 ergs^-1 cm^-2 (as measured in the 0.5-2 keV energy band) in 2.5 sr of the southern sky. The work reported in Cruddace et al. (2001) uses the same starting material as the present work with a slightly different cluster search method applied to the COSMOS data and goes deeper in flux in an area limited to 1.013 ster around the South Galactic Pole. The cluster samples described in Ebeling et al. (1996); Burns et al. (1996), and Ledlow et al. (1999) are derived from correlations of the cluster catalogue by Abell et al. (1989) with the RASS data. The work described in Henry et al. (1997) concentrates on a small area around the North Ecliptic Pole with the special feature of this survey that all X-ray sources, not only the clusters, are identified up the flux-limit of the sample. The northern BCS survey (Allen et al. 1992; Crawford et al. 1995, 1999; Ebeling et al. 1998, 2000a) is optimising the search for clusters by combining the correlation with several optical catalogues, by relying on X-ray extent information, and by combining two different detection algorithms - the standard RASS processing for the complete region and the Voronoi Tesselation and Percolation method covering about one seventh of the survey area. The price payed for the application of several, partly inhomogeneous selection processes in parallel is an inhomogeneous selection function which is very hard to specify and no details have been published up to date.

The most important final goal of the present survey is the statistical and cosmographical characterisation of the large-scale structure of the present day Universe. This requires a large enough sample by number and volume and a nearly homogeneous and well controlled selection function in order to minimize and correct for any artificial fluctuations in the cluster density. The first condition is not provided by the above surveys concentrating on a small sky area while the latter point is not fulfiled by the surveys based on optical catalogues (e.g. the Abell catalogue) with known selection problems and inhomogeneous source detection as featured by the early RASS processing or reanalysis covering only part of the sky. Therefore, with the current survey (and its complement in the South Galactic Pole region by Cruddace et al.), we are following a completely new avenue using a highly homogeneous sampling of information from the X-ray RASS II data and the COSMOS optical data base. The importance and success of this new approach is demonstrated, for example, by preempting the results derived in this paper and comparing the sky surface density of the present cluster sample with the northern BCS sample: at the flux-limit of BCS, the BCS sample reaches 78% of the surface density of clusters in the present sample (see Sect. 11 for details). This reduction in incompleteness is expected to go along with an increase in homogeneity.

For the construction of the present cluster sample optical, follow-up observations, in addition to the X-ray analysis and X-ray/optical correlations, are necessary to clearly identify the nature of the X-ray sources and to determine the cluster redshifts. To this aim we have conducted an intensive follow-up optical survey project as an ESO key program from 1992 to 1999 (e.g. Böhringer 1994; Guzzo et al. 1995; Böhringer et al. 1998; Guzzo et al. 1999) which has been termed REFLEX (ROSAT-ESO-Flux-Limited-X-ray) Cluster Survey. Within this program the identification of all the cluster candidates at $\delta \le 2.5\deg$ and down to a flux limit of 3 10^-12 ergs^-1 cm^-2 in the ROSAT band (0.1 to 2.4 keV) has been completed. This sample includes 452 identified galaxy clusters, 449 of which have a measured redshift. An extension of the identification programme down to a lower flux limit has been started and a large number of redshifts for this extension has already been secured.

A complementary RASS cluster redshift survey programme is conducted for the northern celestial hemisphere in a collaboration by MPE, STScI, CfA, and ESO, the Northern ROSAT All-Sky Cluster Survey (NORAS; e.g. Böhringer 1994; Burg et al. 1994) and a first catalogue containing 483 identified X-ray galaxy clusters has recently been published (Böhringer et al. 2000). It is the future aim to combine the northern and southern surveys which in our ongoing program are based on slightly different identification strategies, mostly due to the different optical data available. Work on homogenization of this is in progress. We have also successfully extended the cluster search into the region close to the galactic plane covering about 2/3 of the region with galactic latitude $\vert b_{\rm II}\vert < 20\deg$ (Böhringer et al. 2001b). In this paper, we describe the selection of the cluster candidate sample for the REFLEX Survey. The layout of the paper is as follows. In Sect. 2 we characterize the depth and the sky area of the study and in Sect. 3 the basic RASS data used as input. It was found that a reanalysis of the X-ray properties of the clusters in the RASS was necessary for the project. This new reanalysis technique and its results are presented in Sect. 4. The selection of the galaxy cluster candidates by means of a correlation of the X-ray source positions with the optical data base from COSMOS is described in Sects. 5 and 6. The further X-ray source classification is discussed in Sect. 7. Section 8 provides tests of the sample completeness. The resulting REFLEX cluster sample for a flux limit of 3 10^-12 ergs^-1 cm^-2 (0.1-2.4 keV) and some of its characteristics is described in Sect. 9. Further statistics of the X-ray properties of the REFLEX clusters and the contamination of the sample by non-cluster sources is discussed in Sect. 10, and Sect. 11 provides a summary and conclusions.