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In the construction of an X-ray-selected sample of galaxy clusters for cosmological studies, we have assembled a sample of 495 X-ray sources found to show extended X-ray emission in the first processing of the ROSAT All-Sky Survey. The sample covers the celestial region with declination delta greater than or equal to 0 degrees and Galactic latitude \b(II)\ greater than or equal to 20 degrees and comprises sources with a count rate greater than or equal to 0.06 counts s(-1) and a source extent likelihood of L greater than or equal to 7. In an optical follow-up identification program we find 378 (76%) of these sources to be clusters of galaxies. It was necessary to reanalyze the sources in this sample with a new X-ray source characterization technique to provide more precise values for the X-ray flux and source extent than obtained from the standard processing. This new method, termed growth curve analysis (GCA), has the advantage over previous methods in its ability to be robust, to be easy to model and to integrate into simulations, to provide diagnostic plots for visual inspection, and to make extensive use of the X-ray data. The source parameters obtained assist the source identification and provide more precise X-ray fluxes. This reanalysis is based on data from the more recent second processing of the ROSAT Survey. We present a catalog of the cluster sources with the X-ray properties obtained as well as a list of the previously flagged extended sources that are found to have a noncluster counterpart. We discuss the process of source identification from the combination of optical and X-ray data. To investigate the overall completeness of the cluster sample as a function of the X-ray flux limit, we extend the search for X-ray cluster sources to the data of the second processing of the ROSAT Survey for the northern sky region between 9(h) and 14(h) in right ascension. We include the search for X-ray emission of known clusters as well as a new investigation of extended X-ray sources. In the course of this search we find X-ray emission from 85 additional Abell clusters and 56 very probable cluster candidates among the newly found extended sources. A comparison of the X-ray cluster number counts of the NORAS sample with the ROSAT-ESO Flux-limited X-Ray (REFLEX) Cluster Survey results leads to an estimate of the completeness of the NORAS sample of ROSAT All-Sky Survey (RASS) I extended clusters of about 50% at an X-ray flux of F(X)(0.1-2.4 keV) = 3 x 10(-12) ergs s(-1) cm(-2). The estimated completeness achieved by adding the supplementary sample in the study area amounts to about 82% in comparison to REFLEX. The low completeness introduces an uncertainty in the use of the sample for cosmological statistical studies that will be cured with the completion of the continuing Northern ROSAT All-Sky (NORAS) Cluster Survey project

The Northern ROSAT All‐Sky (NORAS) Galaxy Cluster Survey. I. X‐Ray Properties of Clusters Detected as Extended X‐Ray Sources