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 few detected counts. The detection threshold of such sources, however, varies strongly across the field-of-view of the instrument. Furthermore, the low detection counting statistics, together with a typical steep source number-flux relation, causes more intrinsically faint sources to be detected at apparently higher fluxes than the other way around. We quantify this ``X-ray Eddington bias'' as well as the detection threshold variation and devise simple procedures for their corrections. To illustrate our technique, we present results from our analysis of X-ray sources detected in the fields of the large-scale hierarchical complex Abell 2125 at $z = 0.247$ and the nearby galaxy NGC 4594 (Sombrero). We show that the sources detected in the Abell 2125 field, excluding 10 known complex members, have a number-flux relation consistent with the expected from foreground or background objects. In contrast, the number-flux relation of the NGC 4594 field is dominated by X-ray sources associated with the galaxy. This galactic component of the relation is well characterized by a broken power law.