Correction for the Flux Measurement Bias in X‐Ray Source Detection

With a high spatial resolution imaging instrument such as the Chandra/ACIS, one can confidently identify an X-ray source with only a fewdetected counts. The detection threshold of such sources, however, variesstrongly across the field-of-view of the instrument. Furthermore, the lowdetection counting statistics, together with a typical steep source number-fluxrelation, causes more intrinsically faint sources to be detected at apparentlyhigher fluxes than the other way around. We quantify this ``X-ray Eddingtonbias'' as well as the detection threshold variation and devise simpleprocedures for their corrections. To illustrate our technique, we presentresults from our analysis of X-ray sources detected in the fields of thelarge-scale hierarchical complex Abell 2125 at $z = 0.247$ and the nearbygalaxy NGC 4594 (Sombrero). We show that the sources detected in the Abell 2125field, excluding 10 known complex members, have a number-flux relationconsistent with the expected from foreground or background objects. Incontrast, the number-flux relation of the NGC 4594 field is dominated by X-raysources associated with the galaxy. This galactic component of the relation iswell characterized by a broken power law.Comment: 19 pages. Accepted for publication in Ap